diff --git "a/Week 2/week_2.ipynb" "b/Week 2/week_2.ipynb"
new file mode 100644--- /dev/null
+++ "b/Week 2/week_2.ipynb"
@@ -0,0 +1,4288 @@
+{
+  "nbformat": 4,
+  "nbformat_minor": 0,
+  "metadata": {
+    "colab": {
+      "provenance": []
+    },
+    "kernelspec": {
+      "name": "python3",
+      "display_name": "Python 3"
+    },
+    "language_info": {
+      "name": "python"
+    }
+  },
+  "cells": [
+    {
+      "cell_type": "code",
+      "execution_count": 36,
+      "metadata": {
+        "id": "GilDNZtwwrDP"
+      },
+      "outputs": [],
+      "source": [
+        "import numpy as np\n",
+        "import pandas as pd\n",
+        "import matplotlib.pyplot as plt\n",
+        "import seaborn as sns\n",
+        "from sklearn.model_selection import train_test_split\n",
+        "\n",
+        "%matplotlib inline"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "!wget https://raw.githubusercontent.com/alexeygrigorev/datasets/master/car_fuel_efficiency.csv"
+      ],
+      "metadata": {
+        "colab": {
+          "base_uri": "https://localhost:8080/"
+        },
+        "id": "uH4-4LA8wyfP",
+        "outputId": "e31d3897-222c-4903-ba3f-9c2c0ca51a27"
+      },
+      "execution_count": 4,
+      "outputs": [
+        {
+          "output_type": "stream",
+          "name": "stdout",
+          "text": [
+            "--2025-10-06 18:27:03--  https://raw.githubusercontent.com/alexeygrigorev/datasets/master/car_fuel_efficiency.csv\n",
+            "Resolving raw.githubusercontent.com (raw.githubusercontent.com)... 185.199.111.133, 185.199.110.133, 185.199.109.133, ...\n",
+            "Connecting to raw.githubusercontent.com (raw.githubusercontent.com)|185.199.111.133|:443... connected.\n",
+            "HTTP request sent, awaiting response... 200 OK\n",
+            "Length: 874188 (854K) [text/plain]\n",
+            "Saving to: ‘car_fuel_efficiency.csv’\n",
+            "\n",
+            "car_fuel_efficiency 100%[===================>] 853.70K  --.-KB/s    in 0.1s    \n",
+            "\n",
+            "2025-10-06 18:27:03 (5.84 MB/s) - ‘car_fuel_efficiency.csv’ saved [874188/874188]\n",
+            "\n"
+          ]
+        }
+      ]
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "df = pd.read_csv(\"car_fuel_efficiency.csv\")\n",
+        "df.head()"
+      ],
+      "metadata": {
+        "colab": {
+          "base_uri": "https://localhost:8080/",
+          "height": 206
+        },
+        "id": "CU_t600wxryA",
+        "outputId": "dff96ae5-7012-484d-e310-154f67766136"
+      },
+      "execution_count": 5,
+      "outputs": [
+        {
+          "output_type": "execute_result",
+          "data": {
+            "text/plain": [
+              "   engine_displacement  num_cylinders  horsepower  vehicle_weight  \\\n",
+              "0                  170            3.0       159.0     3413.433759   \n",
+              "1                  130            5.0        97.0     3149.664934   \n",
+              "2                  170            NaN        78.0     3079.038997   \n",
+              "3                  220            4.0         NaN     2542.392402   \n",
+              "4                  210            1.0       140.0     3460.870990   \n",
+              "\n",
+              "   acceleration  model_year  origin fuel_type         drivetrain  num_doors  \\\n",
+              "0          17.7        2003  Europe  Gasoline    All-wheel drive        0.0   \n",
+              "1          17.8        2007     USA  Gasoline  Front-wheel drive        0.0   \n",
+              "2          15.1        2018  Europe  Gasoline  Front-wheel drive        0.0   \n",
+              "3          20.2        2009     USA    Diesel    All-wheel drive        2.0   \n",
+              "4          14.4        2009  Europe  Gasoline    All-wheel drive        2.0   \n",
+              "\n",
+              "   fuel_efficiency_mpg  \n",
+              "0            13.231729  \n",
+              "1            13.688217  \n",
+              "2            14.246341  \n",
+              "3            16.912736  \n",
+              "4            12.488369  "
+            ],
+            "text/html": [
+              "\n",
+              "  <div id=\"df-e82ce16f-82ab-4af5-9e0c-0962789a1712\" class=\"colab-df-container\">\n",
+              "    <div>\n",
+              "<style scoped>\n",
+              "    .dataframe tbody tr th:only-of-type {\n",
+              "        vertical-align: middle;\n",
+              "    }\n",
+              "\n",
+              "    .dataframe tbody tr th {\n",
+              "        vertical-align: top;\n",
+              "    }\n",
+              "\n",
+              "    .dataframe thead th {\n",
+              "        text-align: right;\n",
+              "    }\n",
+              "</style>\n",
+              "<table border=\"1\" class=\"dataframe\">\n",
+              "  <thead>\n",
+              "    <tr style=\"text-align: right;\">\n",
+              "      <th></th>\n",
+              "      <th>engine_displacement</th>\n",
+              "      <th>num_cylinders</th>\n",
+              "      <th>horsepower</th>\n",
+              "      <th>vehicle_weight</th>\n",
+              "      <th>acceleration</th>\n",
+              "      <th>model_year</th>\n",
+              "      <th>origin</th>\n",
+              "      <th>fuel_type</th>\n",
+              "      <th>drivetrain</th>\n",
+              "      <th>num_doors</th>\n",
+              "      <th>fuel_efficiency_mpg</th>\n",
+              "    </tr>\n",
+              "  </thead>\n",
+              "  <tbody>\n",
+              "    <tr>\n",
+              "      <th>0</th>\n",
+              "      <td>170</td>\n",
+              "      <td>3.0</td>\n",
+              "      <td>159.0</td>\n",
+              "      <td>3413.433759</td>\n",
+              "      <td>17.7</td>\n",
+              "      <td>2003</td>\n",
+              "      <td>Europe</td>\n",
+              "      <td>Gasoline</td>\n",
+              "      <td>All-wheel drive</td>\n",
+              "      <td>0.0</td>\n",
+              "      <td>13.231729</td>\n",
+              "    </tr>\n",
+              "    <tr>\n",
+              "      <th>1</th>\n",
+              "      <td>130</td>\n",
+              "      <td>5.0</td>\n",
+              "      <td>97.0</td>\n",
+              "      <td>3149.664934</td>\n",
+              "      <td>17.8</td>\n",
+              "      <td>2007</td>\n",
+              "      <td>USA</td>\n",
+              "      <td>Gasoline</td>\n",
+              "      <td>Front-wheel drive</td>\n",
+              "      <td>0.0</td>\n",
+              "      <td>13.688217</td>\n",
+              "    </tr>\n",
+              "    <tr>\n",
+              "      <th>2</th>\n",
+              "      <td>170</td>\n",
+              "      <td>NaN</td>\n",
+              "      <td>78.0</td>\n",
+              "      <td>3079.038997</td>\n",
+              "      <td>15.1</td>\n",
+              "      <td>2018</td>\n",
+              "      <td>Europe</td>\n",
+              "      <td>Gasoline</td>\n",
+              "      <td>Front-wheel drive</td>\n",
+              "      <td>0.0</td>\n",
+              "      <td>14.246341</td>\n",
+              "    </tr>\n",
+              "    <tr>\n",
+              "      <th>3</th>\n",
+              "      <td>220</td>\n",
+              "      <td>4.0</td>\n",
+              "      <td>NaN</td>\n",
+              "      <td>2542.392402</td>\n",
+              "      <td>20.2</td>\n",
+              "      <td>2009</td>\n",
+              "      <td>USA</td>\n",
+              "      <td>Diesel</td>\n",
+              "      <td>All-wheel drive</td>\n",
+              "      <td>2.0</td>\n",
+              "      <td>16.912736</td>\n",
+              "    </tr>\n",
+              "    <tr>\n",
+              "      <th>4</th>\n",
+              "      <td>210</td>\n",
+              "      <td>1.0</td>\n",
+              "      <td>140.0</td>\n",
+              "      <td>3460.870990</td>\n",
+              "      <td>14.4</td>\n",
+              "      <td>2009</td>\n",
+              "      <td>Europe</td>\n",
+              "      <td>Gasoline</td>\n",
+              "      <td>All-wheel drive</td>\n",
+              "      <td>2.0</td>\n",
+              "      <td>12.488369</td>\n",
+              "    </tr>\n",
+              "  </tbody>\n",
+              "</table>\n",
+              "</div>\n",
+              "    <div class=\"colab-df-buttons\">\n",
+              "\n",
+              "  <div class=\"colab-df-container\">\n",
+              "    <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-e82ce16f-82ab-4af5-9e0c-0962789a1712')\"\n",
+              "            title=\"Convert this dataframe to an interactive table.\"\n",
+              "            style=\"display:none;\">\n",
+              "\n",
+              "  <svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\" viewBox=\"0 -960 960 960\">\n",
+              "    <path d=\"M120-120v-720h720v720H120Zm60-500h600v-160H180v160Zm220 220h160v-160H400v160Zm0 220h160v-160H400v160ZM180-400h160v-160H180v160Zm440 0h160v-160H620v160ZM180-180h160v-160H180v160Zm440 0h160v-160H620v160Z\"/>\n",
+              "  </svg>\n",
+              "    </button>\n",
+              "\n",
+              "  <style>\n",
+              "    .colab-df-container {\n",
+              "      display:flex;\n",
+              "      gap: 12px;\n",
+              "    }\n",
+              "\n",
+              "    .colab-df-convert {\n",
+              "      background-color: #E8F0FE;\n",
+              "      border: none;\n",
+              "      border-radius: 50%;\n",
+              "      cursor: pointer;\n",
+              "      display: none;\n",
+              "      fill: #1967D2;\n",
+              "      height: 32px;\n",
+              "      padding: 0 0 0 0;\n",
+              "      width: 32px;\n",
+              "    }\n",
+              "\n",
+              "    .colab-df-convert:hover {\n",
+              "      background-color: #E2EBFA;\n",
+              "      box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
+              "      fill: #174EA6;\n",
+              "    }\n",
+              "\n",
+              "    .colab-df-buttons div {\n",
+              "      margin-bottom: 4px;\n",
+              "    }\n",
+              "\n",
+              "    [theme=dark] .colab-df-convert {\n",
+              "      background-color: #3B4455;\n",
+              "      fill: #D2E3FC;\n",
+              "    }\n",
+              "\n",
+              "    [theme=dark] .colab-df-convert:hover {\n",
+              "      background-color: #434B5C;\n",
+              "      box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
+              "      filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n",
+              "      fill: #FFFFFF;\n",
+              "    }\n",
+              "  </style>\n",
+              "\n",
+              "    <script>\n",
+              "      const buttonEl =\n",
+              "        document.querySelector('#df-e82ce16f-82ab-4af5-9e0c-0962789a1712 button.colab-df-convert');\n",
+              "      buttonEl.style.display =\n",
+              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
+              "\n",
+              "      async function convertToInteractive(key) {\n",
+              "        const element = document.querySelector('#df-e82ce16f-82ab-4af5-9e0c-0962789a1712');\n",
+              "        const dataTable =\n",
+              "          await google.colab.kernel.invokeFunction('convertToInteractive',\n",
+              "                                                    [key], {});\n",
+              "        if (!dataTable) return;\n",
+              "\n",
+              "        const docLinkHtml = 'Like what you see? Visit the ' +\n",
+              "          '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
+              "          + ' to learn more about interactive tables.';\n",
+              "        element.innerHTML = '';\n",
+              "        dataTable['output_type'] = 'display_data';\n",
+              "        await google.colab.output.renderOutput(dataTable, element);\n",
+              "        const docLink = document.createElement('div');\n",
+              "        docLink.innerHTML = docLinkHtml;\n",
+              "        element.appendChild(docLink);\n",
+              "      }\n",
+              "    </script>\n",
+              "  </div>\n",
+              "\n",
+              "\n",
+              "    <div id=\"df-e34fb97a-100b-4b14-9c9c-98d290bf81b7\">\n",
+              "      <button class=\"colab-df-quickchart\" onclick=\"quickchart('df-e34fb97a-100b-4b14-9c9c-98d290bf81b7')\"\n",
+              "                title=\"Suggest charts\"\n",
+              "                style=\"display:none;\">\n",
+              "\n",
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+              "    </g>\n",
+              "</svg>\n",
+              "      </button>\n",
+              "\n",
+              "<style>\n",
+              "  .colab-df-quickchart {\n",
+              "      --bg-color: #E8F0FE;\n",
+              "      --fill-color: #1967D2;\n",
+              "      --hover-bg-color: #E2EBFA;\n",
+              "      --hover-fill-color: #174EA6;\n",
+              "      --disabled-fill-color: #AAA;\n",
+              "      --disabled-bg-color: #DDD;\n",
+              "  }\n",
+              "\n",
+              "  [theme=dark] .colab-df-quickchart {\n",
+              "      --bg-color: #3B4455;\n",
+              "      --fill-color: #D2E3FC;\n",
+              "      --hover-bg-color: #434B5C;\n",
+              "      --hover-fill-color: #FFFFFF;\n",
+              "      --disabled-bg-color: #3B4455;\n",
+              "      --disabled-fill-color: #666;\n",
+              "  }\n",
+              "\n",
+              "  .colab-df-quickchart {\n",
+              "    background-color: var(--bg-color);\n",
+              "    border: none;\n",
+              "    border-radius: 50%;\n",
+              "    cursor: pointer;\n",
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+              "    height: 32px;\n",
+              "    padding: 0;\n",
+              "    width: 32px;\n",
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+              "    fill: var(--button-hover-fill-color);\n",
+              "  }\n",
+              "\n",
+              "  .colab-df-quickchart-complete:disabled,\n",
+              "  .colab-df-quickchart-complete:disabled:hover {\n",
+              "    background-color: var(--disabled-bg-color);\n",
+              "    fill: var(--disabled-fill-color);\n",
+              "    box-shadow: none;\n",
+              "  }\n",
+              "\n",
+              "  .colab-df-spinner {\n",
+              "    border: 2px solid var(--fill-color);\n",
+              "    border-color: transparent;\n",
+              "    border-bottom-color: var(--fill-color);\n",
+              "    animation:\n",
+              "      spin 1s steps(1) infinite;\n",
+              "  }\n",
+              "\n",
+              "  @keyframes spin {\n",
+              "    0% {\n",
+              "      border-color: transparent;\n",
+              "      border-bottom-color: var(--fill-color);\n",
+              "      border-left-color: var(--fill-color);\n",
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+              "      border-right-color: var(--fill-color);\n",
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+              "      border-color: transparent;\n",
+              "      border-right-color: var(--fill-color);\n",
+              "      border-bottom-color: var(--fill-color);\n",
+              "    }\n",
+              "    90% {\n",
+              "      border-color: transparent;\n",
+              "      border-bottom-color: var(--fill-color);\n",
+              "    }\n",
+              "  }\n",
+              "</style>\n",
+              "\n",
+              "      <script>\n",
+              "        async function quickchart(key) {\n",
+              "          const quickchartButtonEl =\n",
+              "            document.querySelector('#' + key + ' button');\n",
+              "          quickchartButtonEl.disabled = true;  // To prevent multiple clicks.\n",
+              "          quickchartButtonEl.classList.add('colab-df-spinner');\n",
+              "          try {\n",
+              "            const charts = await google.colab.kernel.invokeFunction(\n",
+              "                'suggestCharts', [key], {});\n",
+              "          } catch (error) {\n",
+              "            console.error('Error during call to suggestCharts:', error);\n",
+              "          }\n",
+              "          quickchartButtonEl.classList.remove('colab-df-spinner');\n",
+              "          quickchartButtonEl.classList.add('colab-df-quickchart-complete');\n",
+              "        }\n",
+              "        (() => {\n",
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+              "\n",
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+            ],
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+              "type": "dataframe",
+              "variable_name": "df",
+              "summary": "{\n  \"name\": \"df\",\n  \"rows\": 9704,\n  \"fields\": [\n    {\n      \"column\": \"engine_displacement\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 49,\n        \"min\": 10,\n        \"max\": 380,\n        \"num_unique_values\": 36,\n        \"samples\": [\n          30,\n          260,\n          90\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"num_cylinders\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 1.9993225843926064,\n        \"min\": 0.0,\n        \"max\": 13.0,\n        \"num_unique_values\": 14,\n        \"samples\": [\n          9.0,\n          10.0,\n          3.0\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"horsepower\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 29.879555200339446,\n        \"min\": 37.0,\n        \"max\": 271.0,\n        \"num_unique_values\": 192,\n        \"samples\": [\n          128.0,\n          82.0,\n          167.0\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"vehicle_weight\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 497.8948600311838,\n        \"min\": 952.6817606436496,\n        \"max\": 4739.077089392099,\n        \"num_unique_values\": 9704,\n        \"samples\": [\n          2535.8875912388694,\n          2741.1704843893167,\n          2471.8802372627765\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"acceleration\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 2.510339293937879,\n        \"min\": 6.0,\n        \"max\": 24.3,\n        \"num_unique_values\": 162,\n        \"samples\": [\n          7.3,\n          20.3,\n          19.8\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"model_year\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 6,\n        \"min\": 2000,\n        \"max\": 2023,\n        \"num_unique_values\": 24,\n        \"samples\": [\n          2005,\n          2002,\n          2003\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"origin\",\n      \"properties\": {\n        \"dtype\": \"category\",\n        \"num_unique_values\": 3,\n        \"samples\": [\n          \"Europe\",\n          \"USA\",\n          \"Asia\"\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"fuel_type\",\n      \"properties\": {\n        \"dtype\": \"category\",\n        \"num_unique_values\": 2,\n        \"samples\": [\n          \"Diesel\",\n          \"Gasoline\"\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"drivetrain\",\n      \"properties\": {\n        \"dtype\": \"category\",\n        \"num_unique_values\": 2,\n        \"samples\": [\n          \"Front-wheel drive\",\n          \"All-wheel drive\"\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"num_doors\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 1.048162111427726,\n        \"min\": -4.0,\n        \"max\": 4.0,\n        \"num_unique_values\": 9,\n        \"samples\": [\n          -4.0,\n          2.0\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"fuel_efficiency_mpg\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 2.5564677028974288,\n        \"min\": 6.200970533392815,\n        \"max\": 25.96722204888372,\n        \"num_unique_values\": 9704,\n        \"samples\": [\n          16.642943419221385,\n          16.298377150953442\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    }\n  ]\n}"
+            }
+          },
+          "metadata": {},
+          "execution_count": 5
+        }
+      ]
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "df.info()"
+      ],
+      "metadata": {
+        "colab": {
+          "base_uri": "https://localhost:8080/"
+        },
+        "id": "LkOyXBAEyIX_",
+        "outputId": "0d48c4d9-833e-4165-cce9-ad5a0b31d5a3"
+      },
+      "execution_count": 7,
+      "outputs": [
+        {
+          "output_type": "stream",
+          "name": "stdout",
+          "text": [
+            "<class 'pandas.core.frame.DataFrame'>\n",
+            "RangeIndex: 9704 entries, 0 to 9703\n",
+            "Data columns (total 11 columns):\n",
+            " #   Column               Non-Null Count  Dtype  \n",
+            "---  ------               --------------  -----  \n",
+            " 0   engine_displacement  9704 non-null   int64  \n",
+            " 1   num_cylinders        9222 non-null   float64\n",
+            " 2   horsepower           8996 non-null   float64\n",
+            " 3   vehicle_weight       9704 non-null   float64\n",
+            " 4   acceleration         8774 non-null   float64\n",
+            " 5   model_year           9704 non-null   int64  \n",
+            " 6   origin               9704 non-null   object \n",
+            " 7   fuel_type            9704 non-null   object \n",
+            " 8   drivetrain           9704 non-null   object \n",
+            " 9   num_doors            9202 non-null   float64\n",
+            " 10  fuel_efficiency_mpg  9704 non-null   float64\n",
+            "dtypes: float64(6), int64(2), object(3)\n",
+            "memory usage: 834.1+ KB\n"
+          ]
+        }
+      ]
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "sns.histplot(df[\"fuel_efficiency_mpg\"])\n",
+        "plt.xlabel(\"Fuel Efficiency\")\n",
+        "plt.ylabel(\"Frequency\")"
+      ],
+      "metadata": {
+        "colab": {
+          "base_uri": "https://localhost:8080/",
+          "height": 467
+        },
+        "id": "U-0cuSfpyVsN",
+        "outputId": "f9726efb-d17b-4771-c523-108ba391bf90"
+      },
+      "execution_count": 35,
+      "outputs": [
+        {
+          "output_type": "execute_result",
+          "data": {
+            "text/plain": [
+              "Text(0, 0.5, 'Frequency')"
+            ]
+          },
+          "metadata": {},
+          "execution_count": 35
+        },
+        {
+          "output_type": "display_data",
+          "data": {
+            "text/plain": [
+              "<Figure size 640x480 with 1 Axes>"
+            ],
+            "image/png": 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\n"
+          },
+          "metadata": {}
+        }
+      ]
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "# check for outliers\n",
+        "sns.boxplot(df[\"fuel_efficiency_mpg\"]);"
+      ],
+      "metadata": {
+        "colab": {
+          "base_uri": "https://localhost:8080/",
+          "height": 411
+        },
+        "id": "GwqW9iX0zBtO",
+        "outputId": "1fb6f248-a0db-4cdf-80a8-0fe432ab2130"
+      },
+      "execution_count": 14,
+      "outputs": [
+        {
+          "output_type": "display_data",
+          "data": {
+            "text/plain": [
+              "<Figure size 640x480 with 1 Axes>"
+            ],
+            "image/png": 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\n"
+          },
+          "metadata": {}
+        }
+      ]
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "# check for missing values\n",
+        "df.isnull().sum()"
+      ],
+      "metadata": {
+        "colab": {
+          "base_uri": "https://localhost:8080/",
+          "height": 429
+        },
+        "id": "LK1-Dwe7zjlX",
+        "outputId": "6930ecd0-1f60-4f82-b29c-8c2f9cee89df"
+      },
+      "execution_count": 16,
+      "outputs": [
+        {
+          "output_type": "execute_result",
+          "data": {
+            "text/plain": [
+              "engine_displacement      0\n",
+              "num_cylinders          482\n",
+              "horsepower             708\n",
+              "vehicle_weight           0\n",
+              "acceleration           930\n",
+              "model_year               0\n",
+              "origin                   0\n",
+              "fuel_type                0\n",
+              "drivetrain               0\n",
+              "num_doors              502\n",
+              "fuel_efficiency_mpg      0\n",
+              "dtype: int64"
+            ],
+            "text/html": [
+              "<div>\n",
+              "<style scoped>\n",
+              "    .dataframe tbody tr th:only-of-type {\n",
+              "        vertical-align: middle;\n",
+              "    }\n",
+              "\n",
+              "    .dataframe tbody tr th {\n",
+              "        vertical-align: top;\n",
+              "    }\n",
+              "\n",
+              "    .dataframe thead th {\n",
+              "        text-align: right;\n",
+              "    }\n",
+              "</style>\n",
+              "<table border=\"1\" class=\"dataframe\">\n",
+              "  <thead>\n",
+              "    <tr style=\"text-align: right;\">\n",
+              "      <th></th>\n",
+              "      <th>0</th>\n",
+              "    </tr>\n",
+              "  </thead>\n",
+              "  <tbody>\n",
+              "    <tr>\n",
+              "      <th>engine_displacement</th>\n",
+              "      <td>0</td>\n",
+              "    </tr>\n",
+              "    <tr>\n",
+              "      <th>num_cylinders</th>\n",
+              "      <td>482</td>\n",
+              "    </tr>\n",
+              "    <tr>\n",
+              "      <th>horsepower</th>\n",
+              "      <td>708</td>\n",
+              "    </tr>\n",
+              "    <tr>\n",
+              "      <th>vehicle_weight</th>\n",
+              "      <td>0</td>\n",
+              "    </tr>\n",
+              "    <tr>\n",
+              "      <th>acceleration</th>\n",
+              "      <td>930</td>\n",
+              "    </tr>\n",
+              "    <tr>\n",
+              "      <th>model_year</th>\n",
+              "      <td>0</td>\n",
+              "    </tr>\n",
+              "    <tr>\n",
+              "      <th>origin</th>\n",
+              "      <td>0</td>\n",
+              "    </tr>\n",
+              "    <tr>\n",
+              "      <th>fuel_type</th>\n",
+              "      <td>0</td>\n",
+              "    </tr>\n",
+              "    <tr>\n",
+              "      <th>drivetrain</th>\n",
+              "      <td>0</td>\n",
+              "    </tr>\n",
+              "    <tr>\n",
+              "      <th>num_doors</th>\n",
+              "      <td>502</td>\n",
+              "    </tr>\n",
+              "    <tr>\n",
+              "      <th>fuel_efficiency_mpg</th>\n",
+              "      <td>0</td>\n",
+              "    </tr>\n",
+              "  </tbody>\n",
+              "</table>\n",
+              "</div><br><label><b>dtype:</b> int64</label>"
+            ]
+          },
+          "metadata": {},
+          "execution_count": 16
+        }
+      ]
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "df[\"horsepower\"].head()"
+      ],
+      "metadata": {
+        "colab": {
+          "base_uri": "https://localhost:8080/",
+          "height": 241
+        },
+        "id": "Stn5QpQcz1aF",
+        "outputId": "8b6c9ff2-9e2a-4e8d-f7c3-e672bdad7e51"
+      },
+      "execution_count": 17,
+      "outputs": [
+        {
+          "output_type": "execute_result",
+          "data": {
+            "text/plain": [
+              "0    159.0\n",
+              "1     97.0\n",
+              "2     78.0\n",
+              "3      NaN\n",
+              "4    140.0\n",
+              "Name: horsepower, dtype: float64"
+            ],
+            "text/html": [
+              "<div>\n",
+              "<style scoped>\n",
+              "    .dataframe tbody tr th:only-of-type {\n",
+              "        vertical-align: middle;\n",
+              "    }\n",
+              "\n",
+              "    .dataframe tbody tr th {\n",
+              "        vertical-align: top;\n",
+              "    }\n",
+              "\n",
+              "    .dataframe thead th {\n",
+              "        text-align: right;\n",
+              "    }\n",
+              "</style>\n",
+              "<table border=\"1\" class=\"dataframe\">\n",
+              "  <thead>\n",
+              "    <tr style=\"text-align: right;\">\n",
+              "      <th></th>\n",
+              "      <th>horsepower</th>\n",
+              "    </tr>\n",
+              "  </thead>\n",
+              "  <tbody>\n",
+              "    <tr>\n",
+              "      <th>0</th>\n",
+              "      <td>159.0</td>\n",
+              "    </tr>\n",
+              "    <tr>\n",
+              "      <th>1</th>\n",
+              "      <td>97.0</td>\n",
+              "    </tr>\n",
+              "    <tr>\n",
+              "      <th>2</th>\n",
+              "      <td>78.0</td>\n",
+              "    </tr>\n",
+              "    <tr>\n",
+              "      <th>3</th>\n",
+              "      <td>NaN</td>\n",
+              "    </tr>\n",
+              "    <tr>\n",
+              "      <th>4</th>\n",
+              "      <td>140.0</td>\n",
+              "    </tr>\n",
+              "  </tbody>\n",
+              "</table>\n",
+              "</div><br><label><b>dtype:</b> float64</label>"
+            ]
+          },
+          "metadata": {},
+          "execution_count": 17
+        }
+      ]
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "# median of horsepower column\n",
+        "df[\"horsepower\"].median()"
+      ],
+      "metadata": {
+        "colab": {
+          "base_uri": "https://localhost:8080/"
+        },
+        "id": "ROkSz3LS0IBI",
+        "outputId": "cca41f00-3731-44b9-caa4-c9f3e462e7b5"
+      },
+      "execution_count": 18,
+      "outputs": [
+        {
+          "output_type": "execute_result",
+          "data": {
+            "text/plain": [
+              "149.0"
+            ]
+          },
+          "metadata": {},
+          "execution_count": 18
+        }
+      ]
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "# filter for the cols we'll only be using\n",
+        "\"\"\"\n",
+        "'engine_displacement',\n",
+        "'horsepower',\n",
+        "'vehicle_weight',\n",
+        "'model_year',\n",
+        "'fuel_efficiency_mpg'\n",
+        "\"\"\"\n",
+        "df.columns"
+      ],
+      "metadata": {
+        "colab": {
+          "base_uri": "https://localhost:8080/"
+        },
+        "id": "eDVKFZEU0Zuh",
+        "outputId": "164921f1-655c-42f3-babd-d0626d5dbd7a"
+      },
+      "execution_count": 21,
+      "outputs": [
+        {
+          "output_type": "execute_result",
+          "data": {
+            "text/plain": [
+              "Index(['engine_displacement', 'num_cylinders', 'horsepower', 'vehicle_weight',\n",
+              "       'acceleration', 'model_year', 'origin', 'fuel_type', 'drivetrain',\n",
+              "       'num_doors', 'fuel_efficiency_mpg'],\n",
+              "      dtype='object')"
+            ]
+          },
+          "metadata": {},
+          "execution_count": 21
+        }
+      ]
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "cols_to_keep=['engine_displacement',\n",
+        "              'horsepower',\n",
+        "              'vehicle_weight',\n",
+        "              'model_year',\n",
+        "              'fuel_efficiency_mpg']\n",
+        "\n",
+        "df2 = df[cols_to_keep]\n",
+        "df2.head()"
+      ],
+      "metadata": {
+        "colab": {
+          "base_uri": "https://localhost:8080/",
+          "height": 206
+        },
+        "id": "NYdpYfMT0skt",
+        "outputId": "a74b8eac-c039-42d1-94aa-14b4cf421b7e"
+      },
+      "execution_count": 23,
+      "outputs": [
+        {
+          "output_type": "execute_result",
+          "data": {
+            "text/plain": [
+              "   engine_displacement  horsepower  vehicle_weight  model_year  \\\n",
+              "0                  170       159.0     3413.433759        2003   \n",
+              "1                  130        97.0     3149.664934        2007   \n",
+              "2                  170        78.0     3079.038997        2018   \n",
+              "3                  220         NaN     2542.392402        2009   \n",
+              "4                  210       140.0     3460.870990        2009   \n",
+              "\n",
+              "   fuel_efficiency_mpg  \n",
+              "0            13.231729  \n",
+              "1            13.688217  \n",
+              "2            14.246341  \n",
+              "3            16.912736  \n",
+              "4            12.488369  "
+            ],
+            "text/html": [
+              "\n",
+              "  <div id=\"df-c8f636e6-b5fd-46e3-890d-89c37198034a\" class=\"colab-df-container\">\n",
+              "    <div>\n",
+              "<style scoped>\n",
+              "    .dataframe tbody tr th:only-of-type {\n",
+              "        vertical-align: middle;\n",
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+              "\n",
+              "    .dataframe thead th {\n",
+              "        text-align: right;\n",
+              "    }\n",
+              "</style>\n",
+              "<table border=\"1\" class=\"dataframe\">\n",
+              "  <thead>\n",
+              "    <tr style=\"text-align: right;\">\n",
+              "      <th></th>\n",
+              "      <th>engine_displacement</th>\n",
+              "      <th>horsepower</th>\n",
+              "      <th>vehicle_weight</th>\n",
+              "      <th>model_year</th>\n",
+              "      <th>fuel_efficiency_mpg</th>\n",
+              "    </tr>\n",
+              "  </thead>\n",
+              "  <tbody>\n",
+              "    <tr>\n",
+              "      <th>0</th>\n",
+              "      <td>170</td>\n",
+              "      <td>159.0</td>\n",
+              "      <td>3413.433759</td>\n",
+              "      <td>2003</td>\n",
+              "      <td>13.231729</td>\n",
+              "    </tr>\n",
+              "    <tr>\n",
+              "      <th>1</th>\n",
+              "      <td>130</td>\n",
+              "      <td>97.0</td>\n",
+              "      <td>3149.664934</td>\n",
+              "      <td>2007</td>\n",
+              "      <td>13.688217</td>\n",
+              "    </tr>\n",
+              "    <tr>\n",
+              "      <th>2</th>\n",
+              "      <td>170</td>\n",
+              "      <td>78.0</td>\n",
+              "      <td>3079.038997</td>\n",
+              "      <td>2018</td>\n",
+              "      <td>14.246341</td>\n",
+              "    </tr>\n",
+              "    <tr>\n",
+              "      <th>3</th>\n",
+              "      <td>220</td>\n",
+              "      <td>NaN</td>\n",
+              "      <td>2542.392402</td>\n",
+              "      <td>2009</td>\n",
+              "      <td>16.912736</td>\n",
+              "    </tr>\n",
+              "    <tr>\n",
+              "      <th>4</th>\n",
+              "      <td>210</td>\n",
+              "      <td>140.0</td>\n",
+              "      <td>3460.870990</td>\n",
+              "      <td>2009</td>\n",
+              "      <td>12.488369</td>\n",
+              "    </tr>\n",
+              "  </tbody>\n",
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+              "</div>\n",
+              "    <div class=\"colab-df-buttons\">\n",
+              "\n",
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+              "    <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-c8f636e6-b5fd-46e3-890d-89c37198034a')\"\n",
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+              "            style=\"display:none;\">\n",
+              "\n",
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+              "  </svg>\n",
+              "    </button>\n",
+              "\n",
+              "  <style>\n",
+              "    .colab-df-container {\n",
+              "      display:flex;\n",
+              "      gap: 12px;\n",
+              "    }\n",
+              "\n",
+              "    .colab-df-convert {\n",
+              "      background-color: #E8F0FE;\n",
+              "      border: none;\n",
+              "      border-radius: 50%;\n",
+              "      cursor: pointer;\n",
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+              "      padding: 0 0 0 0;\n",
+              "      width: 32px;\n",
+              "    }\n",
+              "\n",
+              "    .colab-df-convert:hover {\n",
+              "      background-color: #E2EBFA;\n",
+              "      box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
+              "      fill: #174EA6;\n",
+              "    }\n",
+              "\n",
+              "    .colab-df-buttons div {\n",
+              "      margin-bottom: 4px;\n",
+              "    }\n",
+              "\n",
+              "    [theme=dark] .colab-df-convert {\n",
+              "      background-color: #3B4455;\n",
+              "      fill: #D2E3FC;\n",
+              "    }\n",
+              "\n",
+              "    [theme=dark] .colab-df-convert:hover {\n",
+              "      background-color: #434B5C;\n",
+              "      box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
+              "      filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n",
+              "      fill: #FFFFFF;\n",
+              "    }\n",
+              "  </style>\n",
+              "\n",
+              "    <script>\n",
+              "      const buttonEl =\n",
+              "        document.querySelector('#df-c8f636e6-b5fd-46e3-890d-89c37198034a button.colab-df-convert');\n",
+              "      buttonEl.style.display =\n",
+              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
+              "\n",
+              "      async function convertToInteractive(key) {\n",
+              "        const element = document.querySelector('#df-c8f636e6-b5fd-46e3-890d-89c37198034a');\n",
+              "        const dataTable =\n",
+              "          await google.colab.kernel.invokeFunction('convertToInteractive',\n",
+              "                                                    [key], {});\n",
+              "        if (!dataTable) return;\n",
+              "\n",
+              "        const docLinkHtml = 'Like what you see? Visit the ' +\n",
+              "          '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
+              "          + ' to learn more about interactive tables.';\n",
+              "        element.innerHTML = '';\n",
+              "        dataTable['output_type'] = 'display_data';\n",
+              "        await google.colab.output.renderOutput(dataTable, element);\n",
+              "        const docLink = document.createElement('div');\n",
+              "        docLink.innerHTML = docLinkHtml;\n",
+              "        element.appendChild(docLink);\n",
+              "      }\n",
+              "    </script>\n",
+              "  </div>\n",
+              "\n",
+              "\n",
+              "    <div id=\"df-4ccea25b-6fcf-4a68-b4f6-6bbade483914\">\n",
+              "      <button class=\"colab-df-quickchart\" onclick=\"quickchart('df-4ccea25b-6fcf-4a68-b4f6-6bbade483914')\"\n",
+              "                title=\"Suggest charts\"\n",
+              "                style=\"display:none;\">\n",
+              "\n",
+              "<svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\"viewBox=\"0 0 24 24\"\n",
+              "     width=\"24px\">\n",
+              "    <g>\n",
+              "        <path d=\"M19 3H5c-1.1 0-2 .9-2 2v14c0 1.1.9 2 2 2h14c1.1 0 2-.9 2-2V5c0-1.1-.9-2-2-2zM9 17H7v-7h2v7zm4 0h-2V7h2v10zm4 0h-2v-4h2v4z\"/>\n",
+              "    </g>\n",
+              "</svg>\n",
+              "      </button>\n",
+              "\n",
+              "<style>\n",
+              "  .colab-df-quickchart {\n",
+              "      --bg-color: #E8F0FE;\n",
+              "      --fill-color: #1967D2;\n",
+              "      --hover-bg-color: #E2EBFA;\n",
+              "      --hover-fill-color: #174EA6;\n",
+              "      --disabled-fill-color: #AAA;\n",
+              "      --disabled-bg-color: #DDD;\n",
+              "  }\n",
+              "\n",
+              "  [theme=dark] .colab-df-quickchart {\n",
+              "      --bg-color: #3B4455;\n",
+              "      --fill-color: #D2E3FC;\n",
+              "      --hover-bg-color: #434B5C;\n",
+              "      --hover-fill-color: #FFFFFF;\n",
+              "      --disabled-bg-color: #3B4455;\n",
+              "      --disabled-fill-color: #666;\n",
+              "  }\n",
+              "\n",
+              "  .colab-df-quickchart {\n",
+              "    background-color: var(--bg-color);\n",
+              "    border: none;\n",
+              "    border-radius: 50%;\n",
+              "    cursor: pointer;\n",
+              "    display: none;\n",
+              "    fill: var(--fill-color);\n",
+              "    height: 32px;\n",
+              "    padding: 0;\n",
+              "    width: 32px;\n",
+              "  }\n",
+              "\n",
+              "  .colab-df-quickchart:hover {\n",
+              "    background-color: var(--hover-bg-color);\n",
+              "    box-shadow: 0 1px 2px rgba(60, 64, 67, 0.3), 0 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
+              "    fill: var(--button-hover-fill-color);\n",
+              "  }\n",
+              "\n",
+              "  .colab-df-quickchart-complete:disabled,\n",
+              "  .colab-df-quickchart-complete:disabled:hover {\n",
+              "    background-color: var(--disabled-bg-color);\n",
+              "    fill: var(--disabled-fill-color);\n",
+              "    box-shadow: none;\n",
+              "  }\n",
+              "\n",
+              "  .colab-df-spinner {\n",
+              "    border: 2px solid var(--fill-color);\n",
+              "    border-color: transparent;\n",
+              "    border-bottom-color: var(--fill-color);\n",
+              "    animation:\n",
+              "      spin 1s steps(1) infinite;\n",
+              "  }\n",
+              "\n",
+              "  @keyframes spin {\n",
+              "    0% {\n",
+              "      border-color: transparent;\n",
+              "      border-bottom-color: var(--fill-color);\n",
+              "      border-left-color: var(--fill-color);\n",
+              "    }\n",
+              "    20% {\n",
+              "      border-color: transparent;\n",
+              "      border-left-color: var(--fill-color);\n",
+              "      border-top-color: var(--fill-color);\n",
+              "    }\n",
+              "    30% {\n",
+              "      border-color: transparent;\n",
+              "      border-left-color: var(--fill-color);\n",
+              "      border-top-color: var(--fill-color);\n",
+              "      border-right-color: var(--fill-color);\n",
+              "    }\n",
+              "    40% {\n",
+              "      border-color: transparent;\n",
+              "      border-right-color: var(--fill-color);\n",
+              "      border-top-color: var(--fill-color);\n",
+              "    }\n",
+              "    60% {\n",
+              "      border-color: transparent;\n",
+              "      border-right-color: var(--fill-color);\n",
+              "    }\n",
+              "    80% {\n",
+              "      border-color: transparent;\n",
+              "      border-right-color: var(--fill-color);\n",
+              "      border-bottom-color: var(--fill-color);\n",
+              "    }\n",
+              "    90% {\n",
+              "      border-color: transparent;\n",
+              "      border-bottom-color: var(--fill-color);\n",
+              "    }\n",
+              "  }\n",
+              "</style>\n",
+              "\n",
+              "      <script>\n",
+              "        async function quickchart(key) {\n",
+              "          const quickchartButtonEl =\n",
+              "            document.querySelector('#' + key + ' button');\n",
+              "          quickchartButtonEl.disabled = true;  // To prevent multiple clicks.\n",
+              "          quickchartButtonEl.classList.add('colab-df-spinner');\n",
+              "          try {\n",
+              "            const charts = await google.colab.kernel.invokeFunction(\n",
+              "                'suggestCharts', [key], {});\n",
+              "          } catch (error) {\n",
+              "            console.error('Error during call to suggestCharts:', error);\n",
+              "          }\n",
+              "          quickchartButtonEl.classList.remove('colab-df-spinner');\n",
+              "          quickchartButtonEl.classList.add('colab-df-quickchart-complete');\n",
+              "        }\n",
+              "        (() => {\n",
+              "          let quickchartButtonEl =\n",
+              "            document.querySelector('#df-4ccea25b-6fcf-4a68-b4f6-6bbade483914 button');\n",
+              "          quickchartButtonEl.style.display =\n",
+              "            google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
+              "        })();\n",
+              "      </script>\n",
+              "    </div>\n",
+              "\n",
+              "    </div>\n",
+              "  </div>\n"
+            ],
+            "application/vnd.google.colaboratory.intrinsic+json": {
+              "type": "dataframe",
+              "variable_name": "df2",
+              "summary": "{\n  \"name\": \"df2\",\n  \"rows\": 9704,\n  \"fields\": [\n    {\n      \"column\": \"engine_displacement\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 49,\n        \"min\": 10,\n        \"max\": 380,\n        \"num_unique_values\": 36,\n        \"samples\": [\n          30,\n          260,\n          90\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"horsepower\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 29.879555200339446,\n        \"min\": 37.0,\n        \"max\": 271.0,\n        \"num_unique_values\": 192,\n        \"samples\": [\n          128.0,\n          82.0,\n          167.0\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"vehicle_weight\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 497.8948600311838,\n        \"min\": 952.6817606436496,\n        \"max\": 4739.077089392099,\n        \"num_unique_values\": 9704,\n        \"samples\": [\n          2535.8875912388694,\n          2741.1704843893167,\n          2471.8802372627765\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"model_year\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 6,\n        \"min\": 2000,\n        \"max\": 2023,\n        \"num_unique_values\": 24,\n        \"samples\": [\n          2005,\n          2002,\n          2003\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"fuel_efficiency_mpg\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 2.5564677028974288,\n        \"min\": 6.200970533392815,\n        \"max\": 25.96722204888372,\n        \"num_unique_values\": 9704,\n        \"samples\": [\n          16.642943419221385,\n          16.298377150953442,\n          18.59182197290521\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    }\n  ]\n}"
+            }
+          },
+          "metadata": {},
+          "execution_count": 23
+        }
+      ]
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "shuffled_df = df2.sample(frac=1, random_state=42).reset_index(drop=True)\n",
+        "shuffled_df.head()"
+      ],
+      "metadata": {
+        "colab": {
+          "base_uri": "https://localhost:8080/",
+          "height": 206
+        },
+        "id": "4_T8CSxf1D4i",
+        "outputId": "d1b3e668-489c-487d-ee88-a9696b02aa68"
+      },
+      "execution_count": 25,
+      "outputs": [
+        {
+          "output_type": "execute_result",
+          "data": {
+            "text/plain": [
+              "   engine_displacement  horsepower  vehicle_weight  model_year  \\\n",
+              "0                  220       144.0     2535.887591        2009   \n",
+              "1                  160       141.0     2741.170484        2019   \n",
+              "2                  230       155.0     2471.880237        2017   \n",
+              "3                  150       206.0     3748.164469        2015   \n",
+              "4                  300       111.0     2135.716359        2006   \n",
+              "\n",
+              "   fuel_efficiency_mpg  \n",
+              "0            16.642943  \n",
+              "1            16.298377  \n",
+              "2            18.591822  \n",
+              "3            11.818843  \n",
+              "4            19.402209  "
+            ],
+            "text/html": [
+              "\n",
+              "  <div id=\"df-851042a2-86b9-451f-801f-777366220430\" class=\"colab-df-container\">\n",
+              "    <div>\n",
+              "<style scoped>\n",
+              "    .dataframe tbody tr th:only-of-type {\n",
+              "        vertical-align: middle;\n",
+              "    }\n",
+              "\n",
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+              "        vertical-align: top;\n",
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+              "\n",
+              "    .dataframe thead th {\n",
+              "        text-align: right;\n",
+              "    }\n",
+              "</style>\n",
+              "<table border=\"1\" class=\"dataframe\">\n",
+              "  <thead>\n",
+              "    <tr style=\"text-align: right;\">\n",
+              "      <th></th>\n",
+              "      <th>engine_displacement</th>\n",
+              "      <th>horsepower</th>\n",
+              "      <th>vehicle_weight</th>\n",
+              "      <th>model_year</th>\n",
+              "      <th>fuel_efficiency_mpg</th>\n",
+              "    </tr>\n",
+              "  </thead>\n",
+              "  <tbody>\n",
+              "    <tr>\n",
+              "      <th>0</th>\n",
+              "      <td>220</td>\n",
+              "      <td>144.0</td>\n",
+              "      <td>2535.887591</td>\n",
+              "      <td>2009</td>\n",
+              "      <td>16.642943</td>\n",
+              "    </tr>\n",
+              "    <tr>\n",
+              "      <th>1</th>\n",
+              "      <td>160</td>\n",
+              "      <td>141.0</td>\n",
+              "      <td>2741.170484</td>\n",
+              "      <td>2019</td>\n",
+              "      <td>16.298377</td>\n",
+              "    </tr>\n",
+              "    <tr>\n",
+              "      <th>2</th>\n",
+              "      <td>230</td>\n",
+              "      <td>155.0</td>\n",
+              "      <td>2471.880237</td>\n",
+              "      <td>2017</td>\n",
+              "      <td>18.591822</td>\n",
+              "    </tr>\n",
+              "    <tr>\n",
+              "      <th>3</th>\n",
+              "      <td>150</td>\n",
+              "      <td>206.0</td>\n",
+              "      <td>3748.164469</td>\n",
+              "      <td>2015</td>\n",
+              "      <td>11.818843</td>\n",
+              "    </tr>\n",
+              "    <tr>\n",
+              "      <th>4</th>\n",
+              "      <td>300</td>\n",
+              "      <td>111.0</td>\n",
+              "      <td>2135.716359</td>\n",
+              "      <td>2006</td>\n",
+              "      <td>19.402209</td>\n",
+              "    </tr>\n",
+              "  </tbody>\n",
+              "</table>\n",
+              "</div>\n",
+              "    <div class=\"colab-df-buttons\">\n",
+              "\n",
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+              "    <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-851042a2-86b9-451f-801f-777366220430')\"\n",
+              "            title=\"Convert this dataframe to an interactive table.\"\n",
+              "            style=\"display:none;\">\n",
+              "\n",
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+              "  </svg>\n",
+              "    </button>\n",
+              "\n",
+              "  <style>\n",
+              "    .colab-df-container {\n",
+              "      display:flex;\n",
+              "      gap: 12px;\n",
+              "    }\n",
+              "\n",
+              "    .colab-df-convert {\n",
+              "      background-color: #E8F0FE;\n",
+              "      border: none;\n",
+              "      border-radius: 50%;\n",
+              "      cursor: pointer;\n",
+              "      display: none;\n",
+              "      fill: #1967D2;\n",
+              "      height: 32px;\n",
+              "      padding: 0 0 0 0;\n",
+              "      width: 32px;\n",
+              "    }\n",
+              "\n",
+              "    .colab-df-convert:hover {\n",
+              "      background-color: #E2EBFA;\n",
+              "      box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
+              "      fill: #174EA6;\n",
+              "    }\n",
+              "\n",
+              "    .colab-df-buttons div {\n",
+              "      margin-bottom: 4px;\n",
+              "    }\n",
+              "\n",
+              "    [theme=dark] .colab-df-convert {\n",
+              "      background-color: #3B4455;\n",
+              "      fill: #D2E3FC;\n",
+              "    }\n",
+              "\n",
+              "    [theme=dark] .colab-df-convert:hover {\n",
+              "      background-color: #434B5C;\n",
+              "      box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
+              "      filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n",
+              "      fill: #FFFFFF;\n",
+              "    }\n",
+              "  </style>\n",
+              "\n",
+              "    <script>\n",
+              "      const buttonEl =\n",
+              "        document.querySelector('#df-851042a2-86b9-451f-801f-777366220430 button.colab-df-convert');\n",
+              "      buttonEl.style.display =\n",
+              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
+              "\n",
+              "      async function convertToInteractive(key) {\n",
+              "        const element = document.querySelector('#df-851042a2-86b9-451f-801f-777366220430');\n",
+              "        const dataTable =\n",
+              "          await google.colab.kernel.invokeFunction('convertToInteractive',\n",
+              "                                                    [key], {});\n",
+              "        if (!dataTable) return;\n",
+              "\n",
+              "        const docLinkHtml = 'Like what you see? Visit the ' +\n",
+              "          '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
+              "          + ' to learn more about interactive tables.';\n",
+              "        element.innerHTML = '';\n",
+              "        dataTable['output_type'] = 'display_data';\n",
+              "        await google.colab.output.renderOutput(dataTable, element);\n",
+              "        const docLink = document.createElement('div');\n",
+              "        docLink.innerHTML = docLinkHtml;\n",
+              "        element.appendChild(docLink);\n",
+              "      }\n",
+              "    </script>\n",
+              "  </div>\n",
+              "\n",
+              "\n",
+              "    <div id=\"df-5b11b001-908f-4fc4-82ed-f46920c5dc2e\">\n",
+              "      <button class=\"colab-df-quickchart\" onclick=\"quickchart('df-5b11b001-908f-4fc4-82ed-f46920c5dc2e')\"\n",
+              "                title=\"Suggest charts\"\n",
+              "                style=\"display:none;\">\n",
+              "\n",
+              "<svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\"viewBox=\"0 0 24 24\"\n",
+              "     width=\"24px\">\n",
+              "    <g>\n",
+              "        <path d=\"M19 3H5c-1.1 0-2 .9-2 2v14c0 1.1.9 2 2 2h14c1.1 0 2-.9 2-2V5c0-1.1-.9-2-2-2zM9 17H7v-7h2v7zm4 0h-2V7h2v10zm4 0h-2v-4h2v4z\"/>\n",
+              "    </g>\n",
+              "</svg>\n",
+              "      </button>\n",
+              "\n",
+              "<style>\n",
+              "  .colab-df-quickchart {\n",
+              "      --bg-color: #E8F0FE;\n",
+              "      --fill-color: #1967D2;\n",
+              "      --hover-bg-color: #E2EBFA;\n",
+              "      --hover-fill-color: #174EA6;\n",
+              "      --disabled-fill-color: #AAA;\n",
+              "      --disabled-bg-color: #DDD;\n",
+              "  }\n",
+              "\n",
+              "  [theme=dark] .colab-df-quickchart {\n",
+              "      --bg-color: #3B4455;\n",
+              "      --fill-color: #D2E3FC;\n",
+              "      --hover-bg-color: #434B5C;\n",
+              "      --hover-fill-color: #FFFFFF;\n",
+              "      --disabled-bg-color: #3B4455;\n",
+              "      --disabled-fill-color: #666;\n",
+              "  }\n",
+              "\n",
+              "  .colab-df-quickchart {\n",
+              "    background-color: var(--bg-color);\n",
+              "    border: none;\n",
+              "    border-radius: 50%;\n",
+              "    cursor: pointer;\n",
+              "    display: none;\n",
+              "    fill: var(--fill-color);\n",
+              "    height: 32px;\n",
+              "    padding: 0;\n",
+              "    width: 32px;\n",
+              "  }\n",
+              "\n",
+              "  .colab-df-quickchart:hover {\n",
+              "    background-color: var(--hover-bg-color);\n",
+              "    box-shadow: 0 1px 2px rgba(60, 64, 67, 0.3), 0 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
+              "    fill: var(--button-hover-fill-color);\n",
+              "  }\n",
+              "\n",
+              "  .colab-df-quickchart-complete:disabled,\n",
+              "  .colab-df-quickchart-complete:disabled:hover {\n",
+              "    background-color: var(--disabled-bg-color);\n",
+              "    fill: var(--disabled-fill-color);\n",
+              "    box-shadow: none;\n",
+              "  }\n",
+              "\n",
+              "  .colab-df-spinner {\n",
+              "    border: 2px solid var(--fill-color);\n",
+              "    border-color: transparent;\n",
+              "    border-bottom-color: var(--fill-color);\n",
+              "    animation:\n",
+              "      spin 1s steps(1) infinite;\n",
+              "  }\n",
+              "\n",
+              "  @keyframes spin {\n",
+              "    0% {\n",
+              "      border-color: transparent;\n",
+              "      border-bottom-color: var(--fill-color);\n",
+              "      border-left-color: var(--fill-color);\n",
+              "    }\n",
+              "    20% {\n",
+              "      border-color: transparent;\n",
+              "      border-left-color: var(--fill-color);\n",
+              "      border-top-color: var(--fill-color);\n",
+              "    }\n",
+              "    30% {\n",
+              "      border-color: transparent;\n",
+              "      border-left-color: var(--fill-color);\n",
+              "      border-top-color: var(--fill-color);\n",
+              "      border-right-color: var(--fill-color);\n",
+              "    }\n",
+              "    40% {\n",
+              "      border-color: transparent;\n",
+              "      border-right-color: var(--fill-color);\n",
+              "      border-top-color: var(--fill-color);\n",
+              "    }\n",
+              "    60% {\n",
+              "      border-color: transparent;\n",
+              "      border-right-color: var(--fill-color);\n",
+              "    }\n",
+              "    80% {\n",
+              "      border-color: transparent;\n",
+              "      border-right-color: var(--fill-color);\n",
+              "      border-bottom-color: var(--fill-color);\n",
+              "    }\n",
+              "    90% {\n",
+              "      border-color: transparent;\n",
+              "      border-bottom-color: var(--fill-color);\n",
+              "    }\n",
+              "  }\n",
+              "</style>\n",
+              "\n",
+              "      <script>\n",
+              "        async function quickchart(key) {\n",
+              "          const quickchartButtonEl =\n",
+              "            document.querySelector('#' + key + ' button');\n",
+              "          quickchartButtonEl.disabled = true;  // To prevent multiple clicks.\n",
+              "          quickchartButtonEl.classList.add('colab-df-spinner');\n",
+              "          try {\n",
+              "            const charts = await google.colab.kernel.invokeFunction(\n",
+              "                'suggestCharts', [key], {});\n",
+              "          } catch (error) {\n",
+              "            console.error('Error during call to suggestCharts:', error);\n",
+              "          }\n",
+              "          quickchartButtonEl.classList.remove('colab-df-spinner');\n",
+              "          quickchartButtonEl.classList.add('colab-df-quickchart-complete');\n",
+              "        }\n",
+              "        (() => {\n",
+              "          let quickchartButtonEl =\n",
+              "            document.querySelector('#df-5b11b001-908f-4fc4-82ed-f46920c5dc2e button');\n",
+              "          quickchartButtonEl.style.display =\n",
+              "            google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
+              "        })();\n",
+              "      </script>\n",
+              "    </div>\n",
+              "\n",
+              "    </div>\n",
+              "  </div>\n"
+            ],
+            "application/vnd.google.colaboratory.intrinsic+json": {
+              "type": "dataframe",
+              "variable_name": "shuffled_df",
+              "summary": "{\n  \"name\": \"shuffled_df\",\n  \"rows\": 9704,\n  \"fields\": [\n    {\n      \"column\": \"engine_displacement\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 49,\n        \"min\": 10,\n        \"max\": 380,\n        \"num_unique_values\": 36,\n        \"samples\": [\n          10,\n          200,\n          100\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"horsepower\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 29.879555200339414,\n        \"min\": 37.0,\n        \"max\": 271.0,\n        \"num_unique_values\": 192,\n        \"samples\": [\n          101.0,\n          232.0,\n          142.0\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"vehicle_weight\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 497.89486003118515,\n        \"min\": 952.6817606436496,\n        \"max\": 4739.077089392099,\n        \"num_unique_values\": 9704,\n        \"samples\": [\n          2952.280077222956,\n          3527.0988925098245,\n          2697.391829652872\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"model_year\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 6,\n        \"min\": 2000,\n        \"max\": 2023,\n        \"num_unique_values\": 24,\n        \"samples\": [\n          2020,\n          2022,\n          2009\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"fuel_efficiency_mpg\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 2.556467702897423,\n        \"min\": 6.200970533392815,\n        \"max\": 25.96722204888372,\n        \"num_unique_values\": 9704,\n        \"samples\": [\n          14.748942858764156,\n          11.437054433578467,\n          15.54922028907195\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    }\n  ]\n}"
+            }
+          },
+          "metadata": {},
+          "execution_count": 25
+        }
+      ]
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "shuffled_df.shape"
+      ],
+      "metadata": {
+        "colab": {
+          "base_uri": "https://localhost:8080/"
+        },
+        "id": "_Wj67MfT3UTt",
+        "outputId": "b8872cb9-b965-4626-fe3a-6444d376367a"
+      },
+      "execution_count": 44,
+      "outputs": [
+        {
+          "output_type": "execute_result",
+          "data": {
+            "text/plain": [
+              "(9704, 5)"
+            ]
+          },
+          "metadata": {},
+          "execution_count": 44
+        }
+      ]
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "# col with missing vals\n",
+        "shuffled_df.isnull().sum()"
+      ],
+      "metadata": {
+        "colab": {
+          "base_uri": "https://localhost:8080/",
+          "height": 241
+        },
+        "id": "KEc7ajG99Wk9",
+        "outputId": "b0509ed5-c100-4e4b-8150-eb2dbf8fb8f6"
+      },
+      "execution_count": 45,
+      "outputs": [
+        {
+          "output_type": "execute_result",
+          "data": {
+            "text/plain": [
+              "engine_displacement      0\n",
+              "horsepower             708\n",
+              "vehicle_weight           0\n",
+              "model_year               0\n",
+              "fuel_efficiency_mpg      0\n",
+              "dtype: int64"
+            ],
+            "text/html": [
+              "<div>\n",
+              "<style scoped>\n",
+              "    .dataframe tbody tr th:only-of-type {\n",
+              "        vertical-align: middle;\n",
+              "    }\n",
+              "\n",
+              "    .dataframe tbody tr th {\n",
+              "        vertical-align: top;\n",
+              "    }\n",
+              "\n",
+              "    .dataframe thead th {\n",
+              "        text-align: right;\n",
+              "    }\n",
+              "</style>\n",
+              "<table border=\"1\" class=\"dataframe\">\n",
+              "  <thead>\n",
+              "    <tr style=\"text-align: right;\">\n",
+              "      <th></th>\n",
+              "      <th>0</th>\n",
+              "    </tr>\n",
+              "  </thead>\n",
+              "  <tbody>\n",
+              "    <tr>\n",
+              "      <th>engine_displacement</th>\n",
+              "      <td>0</td>\n",
+              "    </tr>\n",
+              "    <tr>\n",
+              "      <th>horsepower</th>\n",
+              "      <td>708</td>\n",
+              "    </tr>\n",
+              "    <tr>\n",
+              "      <th>vehicle_weight</th>\n",
+              "      <td>0</td>\n",
+              "    </tr>\n",
+              "    <tr>\n",
+              "      <th>model_year</th>\n",
+              "      <td>0</td>\n",
+              "    </tr>\n",
+              "    <tr>\n",
+              "      <th>fuel_efficiency_mpg</th>\n",
+              "      <td>0</td>\n",
+              "    </tr>\n",
+              "  </tbody>\n",
+              "</table>\n",
+              "</div><br><label><b>dtype:</b> int64</label>"
+            ]
+          },
+          "metadata": {},
+          "execution_count": 45
+        }
+      ]
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "X = shuffled_df.drop(columns='fuel_efficiency_mpg')\n",
+        "y = shuffled_df[\"fuel_efficiency_mpg\"]\n",
+        "print(f\"Shape of X: {X.shape}\\nShape of y: {y.shape}\")"
+      ],
+      "metadata": {
+        "colab": {
+          "base_uri": "https://localhost:8080/"
+        },
+        "id": "gUmPB4ne3GFr",
+        "outputId": "0df65a32-87d8-45f7-f292-a4ad0a73d652"
+      },
+      "execution_count": 100,
+      "outputs": [
+        {
+          "output_type": "stream",
+          "name": "stdout",
+          "text": [
+            "Shape of X: (9704, 4)\n",
+            "Shape of y: (9704,)\n"
+          ]
+        }
+      ]
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "shuffled_df.dtypes"
+      ],
+      "metadata": {
+        "colab": {
+          "base_uri": "https://localhost:8080/",
+          "height": 241
+        },
+        "id": "_dOdZaxmCwDs",
+        "outputId": "a6ba7bfe-fdcf-41b6-e110-8253d4369de7"
+      },
+      "execution_count": 101,
+      "outputs": [
+        {
+          "output_type": "execute_result",
+          "data": {
+            "text/plain": [
+              "engine_displacement      int64\n",
+              "horsepower             float64\n",
+              "vehicle_weight         float64\n",
+              "model_year               int64\n",
+              "fuel_efficiency_mpg    float64\n",
+              "dtype: object"
+            ],
+            "text/html": [
+              "<div>\n",
+              "<style scoped>\n",
+              "    .dataframe tbody tr th:only-of-type {\n",
+              "        vertical-align: middle;\n",
+              "    }\n",
+              "\n",
+              "    .dataframe tbody tr th {\n",
+              "        vertical-align: top;\n",
+              "    }\n",
+              "\n",
+              "    .dataframe thead th {\n",
+              "        text-align: right;\n",
+              "    }\n",
+              "</style>\n",
+              "<table border=\"1\" class=\"dataframe\">\n",
+              "  <thead>\n",
+              "    <tr style=\"text-align: right;\">\n",
+              "      <th></th>\n",
+              "      <th>0</th>\n",
+              "    </tr>\n",
+              "  </thead>\n",
+              "  <tbody>\n",
+              "    <tr>\n",
+              "      <th>engine_displacement</th>\n",
+              "      <td>int64</td>\n",
+              "    </tr>\n",
+              "    <tr>\n",
+              "      <th>horsepower</th>\n",
+              "      <td>float64</td>\n",
+              "    </tr>\n",
+              "    <tr>\n",
+              "      <th>vehicle_weight</th>\n",
+              "      <td>float64</td>\n",
+              "    </tr>\n",
+              "    <tr>\n",
+              "      <th>model_year</th>\n",
+              "      <td>int64</td>\n",
+              "    </tr>\n",
+              "    <tr>\n",
+              "      <th>fuel_efficiency_mpg</th>\n",
+              "      <td>float64</td>\n",
+              "    </tr>\n",
+              "  </tbody>\n",
+              "</table>\n",
+              "</div><br><label><b>dtype:</b> object</label>"
+            ]
+          },
+          "metadata": {},
+          "execution_count": 101
+        }
+      ]
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "X.isnull().sum()"
+      ],
+      "metadata": {
+        "colab": {
+          "base_uri": "https://localhost:8080/",
+          "height": 209
+        },
+        "id": "B4ek_9ZxCcAN",
+        "outputId": "67dfc425-3543-455a-8e4d-0b1484543d0e"
+      },
+      "execution_count": 102,
+      "outputs": [
+        {
+          "output_type": "execute_result",
+          "data": {
+            "text/plain": [
+              "engine_displacement      0\n",
+              "horsepower             708\n",
+              "vehicle_weight           0\n",
+              "model_year               0\n",
+              "dtype: int64"
+            ],
+            "text/html": [
+              "<div>\n",
+              "<style scoped>\n",
+              "    .dataframe tbody tr th:only-of-type {\n",
+              "        vertical-align: middle;\n",
+              "    }\n",
+              "\n",
+              "    .dataframe tbody tr th {\n",
+              "        vertical-align: top;\n",
+              "    }\n",
+              "\n",
+              "    .dataframe thead th {\n",
+              "        text-align: right;\n",
+              "    }\n",
+              "</style>\n",
+              "<table border=\"1\" class=\"dataframe\">\n",
+              "  <thead>\n",
+              "    <tr style=\"text-align: right;\">\n",
+              "      <th></th>\n",
+              "      <th>0</th>\n",
+              "    </tr>\n",
+              "  </thead>\n",
+              "  <tbody>\n",
+              "    <tr>\n",
+              "      <th>engine_displacement</th>\n",
+              "      <td>0</td>\n",
+              "    </tr>\n",
+              "    <tr>\n",
+              "      <th>horsepower</th>\n",
+              "      <td>708</td>\n",
+              "    </tr>\n",
+              "    <tr>\n",
+              "      <th>vehicle_weight</th>\n",
+              "      <td>0</td>\n",
+              "    </tr>\n",
+              "    <tr>\n",
+              "      <th>model_year</th>\n",
+              "      <td>0</td>\n",
+              "    </tr>\n",
+              "  </tbody>\n",
+              "</table>\n",
+              "</div><br><label><b>dtype:</b> int64</label>"
+            ]
+          },
+          "metadata": {},
+          "execution_count": 102
+        }
+      ]
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "# fill the missing vals in horsepower with 0 then mean of horsepower col from training data\n",
+        "\"\"\"\n",
+        "\n",
+        "X[\"horsepower\"] = X[\"horsepower\"].fillna()\n",
+        "X.isnull().sum()\n",
+        "\"\"\""
+      ],
+      "metadata": {
+        "colab": {
+          "base_uri": "https://localhost:8080/",
+          "height": 36
+        },
+        "id": "OYb8n8H_C6ta",
+        "outputId": "2f35abd7-8369-433a-fbd6-205811461e21"
+      },
+      "execution_count": 94,
+      "outputs": [
+        {
+          "output_type": "execute_result",
+          "data": {
+            "text/plain": [
+              "'\\n\\nX[\"horsepower\"] = X[\"horsepower\"].fillna()\\nX.isnull().sum()\\n'"
+            ],
+            "application/vnd.google.colaboratory.intrinsic+json": {
+              "type": "string"
+            }
+          },
+          "metadata": {},
+          "execution_count": 94
+        }
+      ]
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "# train, val, test split\n",
+        "np.random.seed(42)\n",
+        "X_train, X_temp, y_train, y_temp = train_test_split(X, y, test_size=0.4)\n",
+        "X_val, X_test, y_val, y_test = train_test_split(X_temp, y_temp, test_size=0.5)"
+      ],
+      "metadata": {
+        "id": "9HFd6E6Z3SxL"
+      },
+      "execution_count": 104,
+      "outputs": []
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "print(X_train.shape)\n",
+        "print(y_train.shape)"
+      ],
+      "metadata": {
+        "colab": {
+          "base_uri": "https://localhost:8080/"
+        },
+        "id": "K0EETjBu3G2X",
+        "outputId": "564bdffa-f523-476e-f375-68e11bcad3c4"
+      },
+      "execution_count": 105,
+      "outputs": [
+        {
+          "output_type": "stream",
+          "name": "stdout",
+          "text": [
+            "(5822, 4)\n",
+            "(5822,)\n"
+          ]
+        }
+      ]
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "print(X_test.shape)\n",
+        "print(y_test.shape)"
+      ],
+      "metadata": {
+        "colab": {
+          "base_uri": "https://localhost:8080/"
+        },
+        "id": "3h-4RONL2IkJ",
+        "outputId": "5d16a248-3f46-4d28-8bb4-c73c28324ddd"
+      },
+      "execution_count": 106,
+      "outputs": [
+        {
+          "output_type": "stream",
+          "name": "stdout",
+          "text": [
+            "(1941, 4)\n",
+            "(1941,)\n"
+          ]
+        }
+      ]
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "print(y_val.shape)"
+      ],
+      "metadata": {
+        "colab": {
+          "base_uri": "https://localhost:8080/"
+        },
+        "id": "QDbJgNKPEbGf",
+        "outputId": "d3fa356c-2580-4f11-917b-b3d270aa8259"
+      },
+      "execution_count": 107,
+      "outputs": [
+        {
+          "output_type": "stream",
+          "name": "stdout",
+          "text": [
+            "(1941,)\n"
+          ]
+        }
+      ]
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "X_train.isnull().sum()"
+      ],
+      "metadata": {
+        "colab": {
+          "base_uri": "https://localhost:8080/",
+          "height": 209
+        },
+        "id": "8EnMEuMSIVuM",
+        "outputId": "841faaba-1d7d-4265-f533-c4a2394c906e"
+      },
+      "execution_count": 108,
+      "outputs": [
+        {
+          "output_type": "execute_result",
+          "data": {
+            "text/plain": [
+              "engine_displacement      0\n",
+              "horsepower             420\n",
+              "vehicle_weight           0\n",
+              "model_year               0\n",
+              "dtype: int64"
+            ],
+            "text/html": [
+              "<div>\n",
+              "<style scoped>\n",
+              "    .dataframe tbody tr th:only-of-type {\n",
+              "        vertical-align: middle;\n",
+              "    }\n",
+              "\n",
+              "    .dataframe tbody tr th {\n",
+              "        vertical-align: top;\n",
+              "    }\n",
+              "\n",
+              "    .dataframe thead th {\n",
+              "        text-align: right;\n",
+              "    }\n",
+              "</style>\n",
+              "<table border=\"1\" class=\"dataframe\">\n",
+              "  <thead>\n",
+              "    <tr style=\"text-align: right;\">\n",
+              "      <th></th>\n",
+              "      <th>0</th>\n",
+              "    </tr>\n",
+              "  </thead>\n",
+              "  <tbody>\n",
+              "    <tr>\n",
+              "      <th>engine_displacement</th>\n",
+              "      <td>0</td>\n",
+              "    </tr>\n",
+              "    <tr>\n",
+              "      <th>horsepower</th>\n",
+              "      <td>420</td>\n",
+              "    </tr>\n",
+              "    <tr>\n",
+              "      <th>vehicle_weight</th>\n",
+              "      <td>0</td>\n",
+              "    </tr>\n",
+              "    <tr>\n",
+              "      <th>model_year</th>\n",
+              "      <td>0</td>\n",
+              "    </tr>\n",
+              "  </tbody>\n",
+              "</table>\n",
+              "</div><br><label><b>dtype:</b> int64</label>"
+            ]
+          },
+          "metadata": {},
+          "execution_count": 108
+        }
+      ]
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "# impute with the mean of X_train\n",
+        "mean_val = X_train[\"horsepower\"].mean()\n",
+        "X_train[\"horsepower\"] = X_train[\"horsepower\"].fillna(mean_val)\n",
+        "X_val[\"horsepower\"] = X_val[\"horsepower\"].fillna(mean_val)"
+      ],
+      "metadata": {
+        "id": "tlR_SQLSINUN"
+      },
+      "execution_count": 110,
+      "outputs": []
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "X_train.isnull().sum() == X_val.isnull().sum()"
+      ],
+      "metadata": {
+        "colab": {
+          "base_uri": "https://localhost:8080/",
+          "height": 209
+        },
+        "id": "UHHaj_TlIzwc",
+        "outputId": "078cddfb-2d9f-478a-c114-8a7097e2bcd9"
+      },
+      "execution_count": 113,
+      "outputs": [
+        {
+          "output_type": "execute_result",
+          "data": {
+            "text/plain": [
+              "engine_displacement    True\n",
+              "horsepower             True\n",
+              "vehicle_weight         True\n",
+              "model_year             True\n",
+              "dtype: bool"
+            ],
+            "text/html": [
+              "<div>\n",
+              "<style scoped>\n",
+              "    .dataframe tbody tr th:only-of-type {\n",
+              "        vertical-align: middle;\n",
+              "    }\n",
+              "\n",
+              "    .dataframe tbody tr th {\n",
+              "        vertical-align: top;\n",
+              "    }\n",
+              "\n",
+              "    .dataframe thead th {\n",
+              "        text-align: right;\n",
+              "    }\n",
+              "</style>\n",
+              "<table border=\"1\" class=\"dataframe\">\n",
+              "  <thead>\n",
+              "    <tr style=\"text-align: right;\">\n",
+              "      <th></th>\n",
+              "      <th>0</th>\n",
+              "    </tr>\n",
+              "  </thead>\n",
+              "  <tbody>\n",
+              "    <tr>\n",
+              "      <th>engine_displacement</th>\n",
+              "      <td>True</td>\n",
+              "    </tr>\n",
+              "    <tr>\n",
+              "      <th>horsepower</th>\n",
+              "      <td>True</td>\n",
+              "    </tr>\n",
+              "    <tr>\n",
+              "      <th>vehicle_weight</th>\n",
+              "      <td>True</td>\n",
+              "    </tr>\n",
+              "    <tr>\n",
+              "      <th>model_year</th>\n",
+              "      <td>True</td>\n",
+              "    </tr>\n",
+              "  </tbody>\n",
+              "</table>\n",
+              "</div><br><label><b>dtype:</b> bool</label>"
+            ]
+          },
+          "metadata": {},
+          "execution_count": 113
+        }
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "source": [
+        "### Linear model from scratch"
+      ],
+      "metadata": {
+        "id": "uz9lbiK7-QHg"
+      }
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "x1 = [1, 148, 200, 333]\n",
+        "x2 = [1, 132, 201, 333]\n",
+        "x10 = [1, 2, 222, 333]\n",
+        "\n",
+        "w = [0.01, 0.04, 0.002, 0.1]\n",
+        "\n",
+        "X = [x1, x2, x10]\n",
+        "X = np.array(X)\n",
+        "X"
+      ],
+      "metadata": {
+        "colab": {
+          "base_uri": "https://localhost:8080/"
+        },
+        "id": "2Zqj2AsU3Ega",
+        "outputId": "cb1085b6-a08c-4dfd-d185-61fb53b1fdc4"
+      },
+      "execution_count": 48,
+      "outputs": [
+        {
+          "output_type": "execute_result",
+          "data": {
+            "text/plain": [
+              "array([[  1, 148, 200, 333],\n",
+              "       [  1, 132, 201, 333],\n",
+              "       [  1,   2, 222, 333]])"
+            ]
+          },
+          "metadata": {},
+          "execution_count": 48
+        }
+      ]
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "def linear_reg(X):\n",
+        "  return X.dot(w)"
+      ],
+      "metadata": {
+        "id": "iKLe4Dvm-n1z"
+      },
+      "execution_count": 50,
+      "outputs": []
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "linear_reg(X)"
+      ],
+      "metadata": {
+        "colab": {
+          "base_uri": "https://localhost:8080/"
+        },
+        "id": "yfAo4hvT-6Cb",
+        "outputId": "2dc62913-26d5-4d23-d8ad-09667d8877bf"
+      },
+      "execution_count": 51,
+      "outputs": [
+        {
+          "output_type": "execute_result",
+          "data": {
+            "text/plain": [
+              "array([39.63 , 38.992, 33.834])"
+            ]
+          },
+          "metadata": {},
+          "execution_count": 51
+        }
+      ]
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "# Use the sklearn linear reg\n",
+        "from sklearn.linear_model import LinearRegression\n",
+        "\n",
+        "model = LinearRegression()\n",
+        "model.fit(X_train, y_train)\n",
+        "y_pred_val = model.predict(X_val)"
+      ],
+      "metadata": {
+        "id": "KQLg2EU4_IDb"
+      },
+      "execution_count": 114,
+      "outputs": []
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "# plot the predictions\n",
+        "sns.histplot(y_pred_val, color='red')\n",
+        "sns.histplot(y_val, color='blue');"
+      ],
+      "metadata": {
+        "colab": {
+          "base_uri": "https://localhost:8080/",
+          "height": 450
+        },
+        "id": "nDKY3cEREUl4",
+        "outputId": "0365a17b-f410-4d0d-9694-c759a94df4c1"
+      },
+      "execution_count": 115,
+      "outputs": [
+        {
+          "output_type": "display_data",
+          "data": {
+            "text/plain": [
+              "<Figure size 640x480 with 1 Axes>"
+            ],
+            "image/png": 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0I5WVlfJ4PK3KXS7X6T+93ojtopUDQHeI+7DTHHTef/99bdu2LeyqTiTFxcUKBAJyu90qKiqKWCclJSVqEALQNZWVlSoqcsrnix5cSj4OPdE0GkZ3dwsA4jvsNAed9957Ty+//LKysrLabbNv3z5ZrVYNGjSoF3oIoJnH45HP55XTuV52uzNsn9dbJ5frXTlTB8ie0Hqo4PHAa3L7HlcgSNgB0P1iGnZOnTqlgwcPhrYrKiq0b98+ZWZmKjc3V1/84hf11ltv6W9/+5uampp05MgRSVJmZqaSk5O1c+dO7d69W+PGjZPD4dDOnTu1YMEClZSUaODAgbH6WEC/Zrc75XCMalFaKykge4JDjsSEVm28TRW90jcA/VNMw86ePXs0bty40HbzOJpZs2ZpyZIleuGFFyRJI0eODGv38ssva+zYsUpJSdHGjRu1ZMkSNTQ0qLCwUAsWLAgbjwMAAPq3mIadsWPHymjjHn1b+yRp1KhR2rVrV3d3CwAAmEifmmcHAACgswg7AADA1Ag7AADA1Ag7AADA1Ag7AADA1Ag7AADA1Ag7AADA1Ag7AADA1OJ6bSwA8ae9lc293jqdXh7iE6fLACA2CDsAOqyyslLOoiJ5fb6odVyudyUFIu4zjKCk1mtjAUBPIuwA6DCPxyOvz6f1TqecdnvYPpfXqxKX6+OVzR1h+04E/Krw+dpdAgYAegJhB0CnOe12jXI4Iu6zJ1hbrWzuDTb1RrcAICIGKAMAAFMj7AAAAFPjNhbQT0V7qkqSqqqqVF1d3aq8oqJC0unxOS1FKgOAeEDYAfqh9p+qskoKRm1f8vFj5pE0MggZQJwh7AD9UEeeqipIWaZUa2HYvpNNAR1ubFCRzaZzEpPC9h0PvCa373EFgoQdAPGFsAP0Y209VZWVNEyORGd4YWOjDjd6Zbfa5UhMDtvlbaroqW4CwFlhgDIAADA1wg4AADA1wg4AADA1wg4AADA1wg4AADA1wg4AADA1wg4AADA1wg4AADA1wg4AADA1wg4AADA1losAgH7K661rd5+rxaKv2dnZys/P79F+Ad2NsAMA/UyjcXpF+5ZBJtz/SpJKSkrCSu02m1zl5QQe9CmEHQDoZwLG6ZXpI61e38zbNECuemm90ymn3S5Jcnm9KnG55PF4CDvoUwg7ANBP2a1WORITouw9PaTTabdrlMPRe50CegADlAEAgKkRdgAAgKkRdgAAgKkRdgAAgKkRdgAAgKkRdgAAgKkRdgAAgKnFNOy88sormjp1qvLy8mSxWPT888+H7TcMQ/fff79yc3OVmpqqiRMn6r333gurc+LECc2cOVNpaWnKyMjQHXfcoVOnTvXipwAAAPEspmGnrq5OI0aM0KpVqyLu/9nPfqZHH31Ua9as0e7duzVgwABNmjRJPp8vVGfmzJl655139NJLL+lvf/ubXnnlFc2ZM6e3PgIAAIhzXQo7559/vo4fP96qvLq6Wueff36HjzNlyhQ9+OCDuvnmm1vtMwxDjzzyiO677z7ddNNNGj58uH7/+9/r8OHDoStALpdLmzdv1u9+9zsVFxfrs5/9rB577DFt3LhRhw8f7spHAwAAJtOlsON2u9XU1NSqvKGhQf/5z3/OulOSVFFRoSNHjmjixImhsvT0dBUXF2vnzp2SpJ07dyojI0NXXnllqM7EiRNltVq1e/fuqMduaGhQTU1N2AsAAJhTp9bGeuGFF0J//8c//qH09PTQdlNTk7Zu3aqCgoJu6diRI0ckSYMHDw4rHzx4cGjfkSNHNGjQoLD9iYmJyszMDNWJZPny5Vq6dGm39BMAAMS3ToWdadOmSZIsFotmzZoVti8pKUkFBQX6xS9+0W2d6ymlpaVauHBhaLumpkZDhgyJYY8AAEBP6VTYCQaDkqTCwkK9+eabys7O7pFOSVJOTo4k6ejRo8rNzQ2VHz16VCNHjgzVOXbsWFi7QCCgEydOhNpHkpKSopSUlO7vNAAAiDtdGrNTUVHRo0FHOh2ocnJytHXr1lBZTU2Ndu/erTFjxkiSxowZo+rqau3duzdUZ9u2bQoGgyouLu7R/gEAgL6hU1d2zrR161Zt3bpVx44dC13xafbkk0926BinTp3SwYMHQ9sVFRXat2+fMjMzlZ+fr+9+97t68MEHdcEFF6iwsFBlZWXKy8sL3U5zOp2aPHmyZs+erTVr1sjv92vevHmaMWOG8vLyuvrRAACAiXQp7CxdulTLli3TlVdeqdzcXFksli69+Z49ezRu3LjQdvM4mlmzZmndunX6/ve/r7q6Os2ZM0fV1dX67Gc/q82bN8tms4XaPP3005o3b54mTJggq9Wq6dOn69FHH+1SfwAAgPl0KeysWbNG69at09e+9rWzevOxY8fKMIyo+y0Wi5YtW6Zly5ZFrZOZmakNGzacVT8AAIB5dSnsNDY26uqrr+7uvgDoRpWVlfJ4PBH3uVyu0396va33RSgDgL6sS2Hnzjvv1IYNG1RWVtbd/QHQDSorK1VU5JTP13ZwKfk49ETS2MZVVwDoS7oUdnw+n37zm99oy5YtGj58uJKSksL2r1y5sls6B6BrPB6PfD6vnM71studrfZ7vXVyud6VM3WA7AnhD2UeD7wmt+9xBYKEHQDm0KWws3///tBcNwcOHAjb19XBygC6n93ulMMxKsKeWkkB2RMcciQmhO3xNlX0St8AoLd0Key8/PLL3d0PAACAHtHleXYAAP2Tq42xXtFkZ2crPz+/B3oDtK9LYWfcuHFt3q7atm1blzsEAIhPVY2NskoqKSnpdFu7zSZXeTmBBzHRpbDTPF6nmd/v1759+3TgwIFWC4QCAMyhOhBQUNJvCwo0Kiurw+1cXq9KXC55PB7CDmKiS2Hn4Ycfjli+ZMkSnTp16qw6BACIb0WpqRrlcMS6G0CHdeuYnZKSEo0ePVo///nPu/OwAIAYOXOSyYr6eklSeX29BtTWttkuOylJ+Wcs7QPEUreGnZ07d4atWwUA6Jsagx5J1ogTT852uyW3u832NmuiykdfSeBBXOhS2LnlllvCtg3DUFVVlfbs2cOsygBgAgGjVlJQBSnLlJU0TJJ0POCX2+dTkc2mcxKTorb1Bivk8t4nj99P2EFc6FLYSU9PD9u2Wq0qKirSsmXLdP3113dLxwAAsZdqLZQj8fQs3N5goySv7Fa7HInJ0RsFeqdvQEd1KeysXbu2u/sBAADQI85qzM7evXtDk0tdcskluvzyy7ulUwAAAN2lS2Hn2LFjmjFjhrZv366MjAxJUnV1tcaNG6eNGzfq3HPP7c4+AgAAdJm1/SqtzZ8/X7W1tXrnnXd04sQJnThxQgcOHFBNTY3uvvvu7u4jAABAl3Xpys7mzZu1ZcsWOZ3OUNnFF1+sVatWMUAZAADElS5d2QkGg0pKav3YYVJSkoLB4Fl3CgAAoLt0KeyMHz9e3/nOd3T48OFQ2X/+8x8tWLBAEyZM6LbOAQAAnK0uhZ1f/epXqqmpUUFBgYYNG6Zhw4apsLBQNTU1euyxx7q7jwAAAF3WpTE7Q4YM0VtvvaUtW7bo3//+tyTJ6XRq4sSJ3do5AACAs9WpKzvbtm3TxRdfrJqaGlksFn3uc5/T/PnzNX/+fF111VW65JJL9Oqrr/ZUXwEAADqtU2HnkUce0ezZs5WWltZqX3p6uu666y6tXLmy2zoHAABwtjoVdv71r39p8uTJUfdff/312rt371l3CgAAoLt0KuwcPXo04iPnzRITE/Xf//73rDsFAADQXToVdj71qU/pwIEDUffv379fubm5Z90pAACA7tKpsHPDDTeorKxMPp+v1b76+notXrxYn//857utcwAAAGerU4+e33fffXr22Wd14YUXat68eSoqKpIk/fvf/9aqVavU1NSkH/3oRz3SUQAAgK7oVNgZPHiwXn/9dX3rW99SaWmpDMOQJFksFk2aNEmrVq3S4MGDe6SjAAAAXdHpSQWHDh2qTZs26aOPPtLBgwdlGIYuuOACDRw4sCf6BwAAcFa6NIOyJA0cOFBXXXVVd/YFAACg23VpbSwAAIC+grADAABMjbADAABMjbADAABMjbADAABMjbADAABMjbADAABMLe7DTkFBgSwWS6vX3LlzJUljx45tte+b3/xmjHsNAADiRZcnFewtb775ppqamkLbBw4c0Oc+9zl96UtfCpXNnj1by5YtC23b7fZe7SMAAIhfcR92zj333LDtFStWaNiwYbruuutCZXa7XTk5Ob3dNQAA0AfE/W2sMzU2Nmr9+vW6/fbbZbFYQuVPP/20srOzdemll6q0tFRerzeGvQQAAPEk7q/snOn5559XdXW1brvttlDZV7/6VQ0dOlR5eXnav3+/Fi1apPLycj377LNRj9PQ0KCGhobQdk1NTU92GwAAxFCfCjtPPPGEpkyZory8vFDZnDlzQn+/7LLLlJubqwkTJujQoUMaNmxYxOMsX75cS5cu7fH+AgCA2Oszt7Hef/99bdmyRXfeeWeb9YqLiyVJBw8ejFqntLRUJ0+eDL0++OCDbu0rAACIH33mys7atWs1aNAg3XjjjW3W27dvnyQpNzc3ap2UlBSlpKR0Z/cAAECc6hNhJxgMau3atZo1a5YSEz/p8qFDh7RhwwbdcMMNysrK0v79+7VgwQJde+21Gj58eAx7DAAA4kWfCDtbtmxRZWWlbr/99rDy5ORkbdmyRY888ojq6uo0ZMgQTZ8+Xffdd1+MegoAAOJNnwg7119/vQzDaFU+ZMgQ7dixIwY9AgAAfUWfGaAMAADQFYQdAABgaoQdAABgan1izA7Qn1VWVsrj8XSqjcvl6qHeAEDfQ9gB4lhlZaWKipzy+bq23ltjY0P7lQDA5Ag7QBzzeDzy+bxyOtfLbnd2uN3x45vkdpcpEAj0YO8AoG8g7AB9gN3ulMMxqsP1vV5uYwFAMwYoAwAAUyPsAAAAU+M2FtDH+Xw++f3+sLL6+vrQn7W1ta3aeL11vdI3AIgHhB2gD/P5fHrjjd0KBoMt9lRIktzuCrndSVHbG0ZQUkLPdRAA4gBhB+jD/H6/gsGgnHa77NZPQstxf6rcDVKBzaasREerdicCflX4fBHXnAMAsyHsACZgtybIkfhJ2PE2WSRJqZbw8tD+YFOv9Q0AYo0BygAAwNQIOwAAwNQIOwAAwNQIOwAAwNQYoAwA6BUuV/vLmFRVVam6ujq0nZGRodzc3A4dPzs7W/n5+V3tHkyMsAMA6FFVjY2ySiopKelAbauklvNGdYzNZld5uYvAg1YIOwCAHlUdCCgo6bcFBRqVlRW1nsvrVYnLpYKUZUq1FqreaJLb55PTebHs9gFtvofX65LLVSKPx0PYQSuEHQBAryhKTdUoR+tJLlvKShomR6JTtYEmuVUru32kHB1oB0RD2AEA9AiX1ytJqvh4rbby+noNiLBWW8v6QHcj7AAAulVj0CPJqpIWA5Jnu92S291+e5YxQTcj7AAAulXAqJUUVEHKMmUlDdPxgF9un09FNpvOSYy+MO3xwGty+x5XIEjYQfci7AAAekSqtVCORKe8wUZJXtmtdjkSk6PW9zZV9F7n0K8wqSAAADA1wg4AADA1wg4AADA1wg4AADA1wg4AADA1wg4AADA1wg4AADA1wg4AADA1wg4AADA1wg4AADA1losA4kBlZaU8Hk+rctfHCyl6vXWSWq8WfbocANAWwg4QY5WVlXIWFcnr80Wt43K9KykQdb9hBCUldH/nAMAECDtAjHk8Hnl9Pq13OuW028P2ubxelbhccqYOkD3B0artiYBfFT6fDINVomFeHbmC2Vyn+WqoJGVnZys/P7/H+oW+g7ADxAmn3a5RjtaBRpLsCVY5EltfufEGm3q6W0DMNBpBSeEBJrr/lSSVlJSESuw2m1zl5QQeEHYAAPEp8PEVyyKbTeckJrVZ19s0QK56ha6QNl8V9Xg8hB3E99NYS5YskcViCXtddNFFof0+n09z585VVlaWzjnnHE2fPl1Hjx6NYY8BAN3Nbj19ZbOtlz3h9P/Omq+QtrwljP4trsOOJF1yySWqqqoKvf75z3+G9i1YsEB//etf9cwzz2jHjh06fPiwbrnllhj2FgAAxJu4v42VmJionJycVuUnT57UE088oQ0bNmj8+PGSpLVr18rpdGrXrl369Kc/3dtdBQAAcSjur+y89957ysvL0/nnn6+ZM2eqsrJSkrR37175/X5NnDgxVPeiiy5Sfn6+du7c2eYxGxoaVFNTE/YCAADmFNdhp7i4WOvWrdPmzZu1evVqVVRU6JprrlFtba2OHDmi5ORkZWRkhLUZPHiwjhw50uZxly9frvT09NBryJAhPfgpAABALMX1bawpU6aE/j58+HAVFxdr6NCh+tOf/qTU1NQuH7e0tFQLFy4MbdfU1BB4AAAwqbi+stNSRkaGLrzwQh08eFA5OTlqbGxUdXV1WJ2jR49GHONzppSUFKWlpYW9AACAOcX1lZ2WTp06pUOHDulrX/uarrjiCiUlJWnr1q2aPn26JKm8vFyVlZUaM2ZMjHuK/iraGldt6diEaQCArorrsHPvvfdq6tSpGjp0qA4fPqzFixcrISFBt956q9LT03XHHXdo4cKFyszMVFpamubPn68xY8bwJBZioiNrXLWlobGxm3sEAJDiPOx8+OGHuvXWW3X8+HGde+65+uxnP6tdu3bp3HPPlSQ9/PDDslqtmj59uhoaGjRp0iQ9/vjjMe41+qu21rhqy6bjx1XmdisQiL7QJwCg6+I67GzcuLHN/TabTatWrdKqVat6qUdA+9pa4yoSl9fbg70BAPSpAcoAAACdRdgBAACmFte3sQCzqPT55PH7I+6rqK+XJJXX12tAbW3YPm5xAcDZI+wAPazS51PRG3vkC7Y9AHm22y253RH3NRpG93cMAPoJwg7Qwzx+v3zBgJz2B2W3Frbafzzgl9vnU5HNpnMSk1rse01u3+MKBAk7ANBVhB2gl9ithXIkOluVe4ONkryyW+1yJCaH72uq6KXeAYB5MUAZAACYGmEHAACYGmEHAACYGmEHAACYGmEHAACYGmEHAACYGo+eAwBMo3nW8dCfLle7bbKzs5Wfn9+j/UJsEXYAAH1eY9AjyaqSFuGmpKSk3bY2m13l5S4Cj4kRdgAAfV7AqJUUVEHKMmUlDZO3KShXfZ2czotltw+I2s7rdcnlKpHH4yHsmBhhBwBgGqmhmcqbJNXKbh8ph8MR624hxgg76JcqKyvl8Xg63Y57+wDQ9xB20O9UVlaqqMgpn8/b6bbc2weAvoewg37H4/HI5/PK6Vwvu731wpzRcG8fAPomwg76LbvdKYdjVKy7AQDoYUwqCAAATI2wAwAATI2wAwAATI2wAwAATI0BykAEPp9Pfr8/rMzrrZMkbdq0KeJ6OxUVFZI+WZOnWcttAEDvIuwALfh8Pr3xxm4Fg8EWe3ZJsqqsrKzN9i3X5mnWaBjd00EAQKcQdoAW/H6/gsGgnHa77NaEUPlxf5PcDUHlJS9ResKwVu1ONgV0uLFBRTabzklM+qRd4DW5fY8rECTsAEAsEHaAKOzWBDkSPwk73iaLJCk9YZgGp1zSukFjow43emW32uVITD6jXUWP9xUAEB0DlAEAgKkRdgAAgKkRdgAAgKkRdgAAgKkRdgAAgKkRdgAAgKkRdgAAgKkRdgAAgKkRdgAAgKkRdgAAgKkRdgAAgKnFddhZvny5rrrqKjkcDg0aNEjTpk1TeXl5WJ2xY8fKYrGEvb75zW/GqMcAACDexPVCoDt27NDcuXN11VVXKRAI6Ic//KGuv/56vfvuuxowYECo3uzZs7Vs2bLQtt1uj0V3AQBxxuut69B+l8sVKsvOzlZ+fn6P9gu9K67DzubNm8O2161bp0GDBmnv3r269tprQ+V2u105OTm93T0AQJxqNIKSwkNMZP8rSSopKQmV2G02ucrLCTwmEtdhp6WTJ09KkjIzM8PKn376aa1fv145OTmaOnWqysrK2ry609DQoIaGhtB2TU1Nz3QYABATAcOQJBXZbDonMSlqPW/TALnqpfVOp5x2u1xer0pcLnk8HsKOifSZsBMMBvXd735Xn/nMZ3TppZeGyr/61a9q6NChysvL0/79+7Vo0SKVl5fr2WefjXqs5cuXa+nSpb3RbQBADNmtVjkSE9qocXroqtNu1yiHo3c6hV7XZ8LO3LlzdeDAAf3zn/8MK58zZ07o75dddplyc3M1YcIEHTp0SMOGDYt4rNLSUi1cuDC0XVNToyFDhvRMxwEAQEz1ibAzb948/e1vf9Mrr7yi8847r826xcXFkqSDBw9GDTspKSlKSUnp9n4CAID4E9dhxzAMzZ8/X88995y2b9+uwsLCdtvs27dPkpSbm9vDvQMAAH1BXIeduXPnasOGDfrLX/4ih8OhI0eOSJLS09OVmpqqQ4cOacOGDbrhhhuUlZWl/fv3a8GCBbr22ms1fPjwGPceAADEg7gOO6tXr5Z0euLAM61du1a33XabkpOTtWXLFj3yyCOqq6vTkCFDNH36dN13330x6C0AAIhHcR12jI8fHYxmyJAh2rFjRy/1BgAA9EVxvVwEAADA2SLsAAAAUyPsAAAAUyPsAAAAUyPsAAAAUyPsAAAAU4vrR8+Bs1VZWSmPxxNW5nK5JEleb52k2lZtTpcDAMyCsAPTqqyslLOoSF6fL+J+l+tdSYGo7Q0jKKmt1ZIBAH0BYQd9QqQrNO1xuVzy+nxa73TKabd/Uu71qsTlkjN1gOwJjlbtTgT8qvD52p3UEoB5uLze8D8/vgLcluzsbOXn5/dov9A9CDuIe+1doWnP+YmJGuVoHWrsCVY5EltfufEGm7r0PgD6nsagR5JVJS3CTUlJSbttbTa7ystdBJ4+gLCDuOfxeCJeoWnPpuPHVeZ2KxCIfqsKQP8WMGolBVWQskxZScPkbQrKVV8np/Ni2e0Dorbzel1yuUrk8XgIO30AYQd9htNuj3iFJprmy9EA0J5Ua6EciU5JTZJqZbePlKMTv28Q3wg76LMqfT55/P6o+yvq6yVJ5fX1GlD7yVNXhCAA6F8IO+iTKn0+Fb2xR75g+7eoZrvdktvdqryRAcgA0C8QdtAnefx++YIBOe0Pym4tjFjneMAvt8+nIptN5yQmnVH+mty+xxUIEnYAnJ2OPLUVCU9y9S7CDvo0e+g+e2veYKMkr+xWuxyJyZ+UN1X0Uu8AmFVjY5Uka4ee2oqEJ7l6F2EHAIBOCgSqJQVVUPBbZWWN6lTb5ie5Xn31VTmdkf+xFg1XhLqGsAMAQBelphbJ4ehc2Dmbq0JcEeoawg4AAC20t0Ze/cdPe9bX16v246c9k5KSZLPZ2j12V68KMbdP1xF2AAD4WKMRlNSRgcenx/653RVyu08/AGG1WjV6dHGHAo/UtatC6BrCDmKuvXWvmn/pnDk/DnPlAOgJgY+npGj5FGdLx/2pcjdIBTabshId8gab5PJ65ff7Oxx20HsIO4ipyspKFRU55fO1H15arl0jMVcOgJ5ht0ZeO6+Zt8kiSUq1JJyux6o0cY2wg06LdCWmqqpK1dXVbbbLyMhQbm5uWJnL5ZLP55XTuV52e5RHyL11crne/XiVcqsk5soBEJ/aG+sjtR7v09GxPug6wg46JfoK5FZJwS4fNzHx/DbuXddKCsie4Aj9S4u5cgDEk46P9ZFajvfp7FgfdB5hB50SaQVyl9erEpdLBSnLlBplNuN6o0lun6/VSsLHj2+S213GyuQA+rSOjvWRwsf7pFrtjPXpBYQddEmkFcizkoZFnc24NtAkd4SVhL3erk21DgDxqL2xPlL4eB+7te266B6EHfSqlvezI81V0V4bADCbjvyea67TfKuM2ZQ7jrCDXhH9fnbruSqiMYygJP4VBMA8OjfW538lKTTzst1mk6u8nMDTAYQd9Ipo97NbzlURyYmAXxU+nwweMwdgMp0Z6+NtGiBXvbT+4/W0SlwuZlPuIMIOwvT0BH8t72e3mqsiAm+wqcPHB4C+qCNjfU4/9arQwyFSR68ItdbfboERdhDCBH8A0DdUNTbKKnVpMVGp/90CI+wgxOPxMMEfAPQB1YGAgpJ+W1CgUVlZnWrbPF1If7oFRthBK3a7kwn+AKAPKEpNbTUNCFqzxroDAAAAPYmwAwAATI3bWP1Yyyevmkf1n564ign+AADtP6Xblnh56ouw009FX9BTcrneldT2WlVM8AcA5teZp3QjsdnsKi93xTzwEHZMqCMp3OVyyevz6YGCAhWmpkqSKurrVeZ2f/ykFRP8AUA8cnm9qvh4qZ3y+noNiLLUTksNwaBSrNbQ3GibNm1qd56eiooK+XxeFRT8VqmpRTKMoCyWjo2Aqa8vl9s9W6+++qquueaamAYewo7JdDaFl7ndrcoSrRYm+AOAONMY9Eiyhs1zNtvtliL8Ho/MKikY2iorK+vwe7vdTfrkin+wrapnOP3/i5KSkpjP62OasLNq1So99NBDOnLkiEaMGKHHHntMo0ePjnW3esWZV3JcLldYCo+mvr5ebncF8+UAQB8RMGolBVWQskyy5Mvt83VomQnpk9/vZ7Ydmpwie0LbMaA68Jqq/GtUYLPJIpsqOvGezctbPFBQoDK3O6bz+pgi7Pzxj3/UwoULtWbNGhUXF+uRRx7RpEmTVF5erkGDBsW6ez0q2tib8BQeSZKkC5VqHSDHx19a5ssBgPiXai2ULBdI8sputcuRmNxum+bf72e2zUy0Kz25vbbvq8p/ekkffXz7qmNLW0jND3w3D5WIJVOEnZUrV2r27Nn6xje+IUlas2aNXnzxRT355JP6wQ9+ENO+dWYUe1VVlaqrq0PbjY2NSm7ni1hRURE29qYj424kxt4AAPqPPh92GhsbtXfvXpWWlobKrFarJk6cqJ07d8awZ2c/ir3l/dW2tBx709a4G4mxNwCA/qPPhx2Px6OmpiYNHjw4rHzw4MH697//HbFNQ0ODGhoaQtsnT56UJNXU1HRr39xut3w+r4YM+Z6Sk4e0Wbex0acPPqjUwIQkJVosagi+q5rgZqVZv6oUa07Udg3BoGqCAZ2bkCRbQoJONb2jj5r+rv82HlBDU/SQVdMUkNQgjz9FdcHTX4OTgf+TJH0UeEdNRn2Pt4vX94yXdvH4nj3RLt7es6faRWvb1XaxeM+OtIvUtqfbxeI9u6uvp+c069l2sXpPX9AtSXLVnZ6f7dSpU93+/9nm47V7l8Lo4/7zn/8YkozXX389rPx73/ueMXr06IhtFi9ebEjixYsXL168eJng9cEHH7SZFfr8lZ3s7GwlJCTo6NGjYeVHjx5VTk7kKyKlpaVauHBhaDsYDOrEiRPKysqSxWLp0f7GUk1NjYYMGaIPPvhAaWlpse5OzHE+wnE+wnE+WuOchON8hIvF+TAMQ7W1tcrLy2uzXp8PO8nJybriiiu0detWTZs2TdLp8LJ161bNmzcvYpuUlBSlpKSElWVkZPRwT+NHWloaP5hn4HyE43yE43y0xjkJx/kI19vnIz09vd06fT7sSNLChQs1a9YsXXnllRo9erQeeeQR1dXVhZ7OAgAA/Zcpws5XvvIV/fe//9X999+vI0eOaOTIkdq8eXOrQcsAAKD/MUXYkaR58+ZFvW2F01JSUrR48eJWt/D6K85HOM5HOM5Ha5yTcJyPcPF8PiyGwaxyAADAvDq2dCkAAEAfRdgBAACmRtgBAACmRtgxiYKCAlksllavuXPnRqy/bt26VnVtNlsv97r7vPLKK5o6dary8vJksVj0/PPPh+03DEP333+/cnNzlZqaqokTJ+q9995r97irVq1SQUGBbDabiouL9cYbb/TQJ+hebZ0Pv9+vRYsW6bLLLtOAAQOUl5enr3/96zp8+HCbx1yyZEmr78xFF13Uw5+k+7T3Hbnttttafb7Jkye3e1wzfkckRfx9YrFY9NBDD0U9Zl/+jixfvlxXXXWVHA6HBg0apGnTpqm8vDysjs/n09y5c5WVlaVzzjlH06dPbzWhbUtd/d0Ta+2djxMnTmj+/PkqKipSamqq8vPzdffdd4eWX4qmqz9nZ4uwYxJvvvmmqqqqQq+XXnpJkvSlL30papu0tLSwNu+//35vdbfb1dXVacSIEVq1alXE/T/72c/06KOPas2aNdq9e7cGDBigSZMmyefzRT3mH//4Ry1cuFCLFy/WW2+9pREjRmjSpEk6duxYT32MbtPW+fB6vXrrrbdUVlamt956S88++6zKy8v1hS98od3jXnLJJWHfmX/+85890f0e0d53RJImT54c9vn+8Ic/tHlMs35HJIWdh6qqKj355JOyWCyaPn16m8ftq9+RHTt2aO7cudq1a5deeukl+f1+XX/99ar7eF0nSVqwYIH++te/6plnntGOHTt0+PBh3XLLLW0etyu/e+JBe+fj8OHDOnz4sH7+85/rwIEDWrdunTZv3qw77rij3WN39uesW3TH+lSIP9/5zneMYcOGGcFgMOL+tWvXGunp6b3bqV4iyXjuuedC28Fg0MjJyTEeeuihUFl1dbWRkpJi/OEPf4h6nNGjRxtz584NbTc1NRl5eXnG8uXLe6TfPaXl+YjkjTfeMCQZ77//ftQ6ixcvNkaMGNG9nYuRSOdk1qxZxk033dSp4/Sn78hNN91kjB8/vs06ZvqOHDt2zJBk7NixwzCM078zkpKSjGeeeSZUx+VyGZKMnTt3RjxGV3/3xKOW5yOSP/3pT0ZycrLh9/uj1unKz1l34MqOCTU2Nmr9+vW6/fbb21zr69SpUxo6dKiGDBmim266Se+8804v9rL3VFRU6MiRI5o4cWKoLD09XcXFxdq5c2fENo2Njdq7d29YG6vVqokTJ0Zt05edPHlSFoul3WVT3nvvPeXl5en888/XzJkzVVlZ2Tsd7CXbt2/XoEGDVFRUpG9961s6fvx41Lr96Tty9OhRvfjiix36V7tZviPNt2MyMzMlSXv37pXf7w/7733RRRcpPz8/6n/vrvzuiVctz0e0OmlpaUpMbHsKv878nHUXwo4JPf/886qurtZtt90WtU5RUZGefPJJ/eUvf9H69esVDAZ19dVX68MPP+y9jvaSI0eOSFKrGbUHDx4c2teSx+NRU1NTp9r0VT6fT4sWLdKtt97a5no2xcXFoUvVq1evVkVFha655hrV1tb2Ym97zuTJk/X73/9eW7du1U9/+lPt2LFDU6ZMUVNTU8T6/ek78tRTT8nhcLR7y8Ys35FgMKjvfve7+sxnPqNLL71U0unfI8nJya3+QdDWf++u/O6JR5HOR0sej0cPPPCA5syZ0+axOvtz1l1MM4MyPvHEE09oypQpba4CO2bMGI0ZMya0ffXVV8vpdOrXv/61Hnjggd7oJuKA3+/Xl7/8ZRmGodWrV7dZd8qUKaG/Dx8+XMXFxRo6dKj+9Kc/dehf/PFuxowZob9fdtllGj58uIYNG6bt27drwoQJMexZ7D355JOaOXNmuw8xmOU7MnfuXB04cKDPjDfqae2dj5qaGt144426+OKLtWTJkjaPFaufM67smMz777+vLVu26M477+xUu6SkJF1++eU6ePBgD/UsdnJyciSp1VMTR48eDe1rKTs7WwkJCZ1q09c0B533339fL730UqdXKc7IyNCFF15oyu+MJJ1//vnKzs6O+vn6w3dEkl599VWVl5d3+neK1De/I/PmzdPf/vY3vfzyyzrvvPNC5Tk5OWpsbFR1dXVY/bb+e3fld0+8iXY+mtXW1mry5MlyOBx67rnnlJSU1Knjt/dz1l0IOyazdu1aDRo0SDfeeGOn2jU1Nen//b//p9zc3B7qWewUFhYqJydHW7duDZXV1NRo9+7dYVe3zpScnKwrrrgirE0wGNTWrVujtulLmoPOe++9py1btigrK6vTxzh16pQOHTpkyu+MJH344Yc6fvx41M9n9u9IsyeeeEJXXHGFRowY0em2fek7YhiG5s2bp+eee07btm1TYWFh2P4rrrhCSUlJYf+9y8vLVVlZGfW/d1d+98SL9s6HdPqzXH/99UpOTtYLL7zQpelL2vs56za9PiQaPaapqcnIz883Fi1a1Grf1772NeMHP/hBaHvp0qXGP/7xD+PQoUPG3r17jRkzZhg2m8145513erPL3aa2ttZ4++23jbffftuQZKxcudJ4++23Q08XrVixwsjIyDD+8pe/GPv37zduuukmo7Cw0Kivrw8dY/z48cZjjz0W2t64caORkpJirFu3znj33XeNOXPmGBkZGcaRI0d6/fN1Vlvno7Gx0fjCF75gnHfeeca+ffuMqqqq0KuhoSF0jJbn45577jG2b99uVFRUGK+99poxceJEIzs72zh27FgsPmKntXVOamtrjXvvvdfYuXOnUVFRYWzZssUYNWqUccEFFxg+ny90jP7yHWl28uRJw263G6tXr454DDN9R771rW8Z6enpxvbt28N+Jrxeb6jON7/5TSM/P9/Ytm2bsWfPHmPMmDHGmDFjwo5TVFRkPPvss6HtjvzuiUftnY+TJ08axcXFxmWXXWYcPHgwrE4gEAgd58zz0dGfs55A2DGRf/zjH4Yko7y8vNW+6667zpg1a1Zo+7vf/a6Rn59vJCcnG4MHDzZuuOEG46233urF3navl19+2ZDU6tX8mYPBoFFWVmYMHjzYSElJMSZMmNDqPA0dOtRYvHhxWNljjz0WOk+jR482du3a1Uuf6Oy0dT4qKioi7pNkvPzyy6FjtDwfX/nKV4zc3FwjOTnZ+NSnPmV85StfMQ4ePNj7H66L2jonXq/XuP76641zzz3XSEpKMoYOHWrMnj27VWjpL9+RZr/+9a+N1NRUo7q6OuIxzPQdifYzsXbt2lCd+vp649vf/rYxcOBAw263GzfffLNRVVXV6jhntunI75541N75iPb9kWRUVFSEHae5TUd/znoCq54DAABTY8wOAAAwNcIOAAAwNcIOAAAwNcIOAAAwNcIOAAAwNcIOAAAwNcIOAAAwNcIOAAAwNcIOYEKGYWjOnDnKzMyUxWLRvn37zvqYS5Ys0ciRI8/6OM3+/e9/69Of/rRsNlvouC3L3G53p/p/2223adq0ad3WRwDmkBjrDgDofps3b9a6deu0ffv20KrC8Wbx4sUaMGCAysvLdc4550Qsy8jIUFVVVYf7/8tf/lJMCg+gJcIOYELNK01fffXVse5KVIcOHdKNN96ooUOHtlmWk5PT4WOmp6d3ax8BmAO3sQCTue222zR//nxVVlbKYrGooKBABQUFeuSRR8LqjRw5UkuWLAltV1dX684779S5556rtLQ0jR8/Xv/617+63I/f/e53cjqdstlsuuiii/T444+H9lksFu3du1fLli2TxWLRkiVLIpZFuo31zjvv6POf/7zS0tLkcDh0zTXX6NChQ6HPfuZtrGAwqOXLl6uwsFCpqakaMWKE/vznP4f2b9++XRaLRVu3btWVV14pu92uq6++WuXl5WGf5a9//auuuuoq2Ww2ZWdn6+abb5YkLVu2TJdeemmrzz5y5EiVlZW1e46a+/uTn/xEgwcPVkZGhpYtW6ZAIKDvfe97yszM1Hnnnae1a9eG2jSfk40bN+rqq6+WzWbTpZdeqh07doQd+4UXXtAFF1wgm82mcePG6amnnpLFYlF1dXW7/QLMhrADmMwvf/lLLVu2TOedd56qqqr05ptvdqjdl770JR07dkx///vftXfvXo0aNUoTJkzQiRMnOt2Hp59+Wvfff79+/OMfy+Vy6Sc/+YnKysr01FNPSZKqqqp0ySWX6J577lFVVZXuvffeiGUt/ec//9G1116rlJQUbdu2TXv37tXtt9+uQCAQsR/Lly/X73//e61Zs0bvvPOOFixYoJKSklbB4Ec/+pF+8YtfaM+ePUpMTNTtt98e2vfiiy/q5ptv1g033KC3335bW7du1ejRoyVJt99+u1wuV9g5fvvtt7V//3594xvf6NC52rZtmw4fPqxXXnlFK1eu1OLFi/X5z39eAwcO1O7du/XNb35Td911lz788MOwdt/73vd0zz336O2339aYMWM0depUHT9+XJJUUVGhL37xi5o2bZr+9a9/6a677tKPfvSjDvUHMKUeX1cdQK97+OGHjaFDh4a2hw4dajz88MNhdUaMGGEsXrzYMAzDePXVV420tDTD5/OF1Rk2bJjx61//2jAMw1i8eLExYsSIDr3/sGHDjA0bNoSVPfDAA8aYMWMivn+0soqKCkOS8fbbbxuGYRilpaVGYWGh0djYGPF9Z82aZdx0002GYRiGz+cz7Ha78frrr4fVueOOO4xbb73VMAzDePnllw1JxpYtW0L7X3zxRUOSUV9fbxiGYYwZM8aYOXNm1M86ZcoU41vf+lZoe/78+cbYsWOj1m/Z36FDhxpNTU2hsqKiIuOaa64JbQcCAWPAgAHGH/7wB8MwPjknK1asCNXx+/3GeeedZ/z0pz81DMMwFi1aZFx66aVh7/WjH/3IkGR89NFHHeobYCaM2QGgf/3rXzp16pSysrLCyuvr60O3iDqqrq5Ohw4d0h133KHZs2eHygOBwFmPqdm3b5+uueYaJSUltVv34MGD8nq9+tznPhdW3tjYqMsvvzysbPjw4aG/5+bmSpKOHTum/Px87du3L+xztDR79mzdfvvtWrlypaxWqzZs2KCHH364w5/pkksukdX6yUX2wYMHh90aS0hIUFZWlo4dOxbWbsyYMaG/JyYm6sorr5TL5ZIklZeX66qrrgqr33w1CuiPCDtAP2C1Wls9peT3+0N/P3XqlHJzc7V9+/ZWbTMyMjr1XqdOnZIk/fa3v1VxcXHYvoSEhE4dq6XU1NRO9+PFF1/Upz71qbB9KSkpYdtnhieLxSLp9Hifjrzn1KlTlZKSoueee07Jycny+/364he/2OF+tgxuFoslYllzfwB0HmEH6AfOPfdcVVVVhbZrampUUVER2h41apSOHDmixMREFRQUnNV7DR48WHl5efq///s/zZw586yO1dLw4cP11FNPye/3t3t15+KLL1ZKSooqKyt13XXXndV7bt26NeoYnMTERM2aNUtr165VcnKyZsyY0alQ1lW7du3StddeK+n0VbO9e/dq3rx5kqSioiJt2rQprH5Hx24BZkTYAfqB8ePHa926dZo6daoyMjJ0//33h11lmThxosaMGaNp06bpZz/7mS688EIdPnw4NDj3yiuv7NT7LV26VHfffbfS09M1efJkNTQ0aM+ePfroo4+0cOHCLn+OefPm6bHHHtOMGTNUWlqq9PR07dq1S6NHj1ZRUVFYXYfDoXvvvVcLFixQMBjUZz/7WZ08eVKvvfaa0tLSNGvWrA695+LFizVhwgQNGzZMM2bMUCAQ0KZNm7Ro0aJQnTvvvFNOp1OS9Nprr3X583XGqlWrdMEFF8jpdOrhhx/WRx99FBpYfdddd2nlypVatGiR7rjjDu3bt0/r1q2T9MmVK6A/4WksoB8oLS3Vddddp89//vO68cYbNW3aNA0bNiy032KxaNOmTbr22mv1jW98QxdeeKFmzJih999/X4MHD+70+91555363e9+p7Vr1+qyyy7Tddddp3Xr1qmwsPCsPkdWVpa2bdumU6dO6brrrtMVV1yh3/72t1Gv8jzwwAMqKyvT8uXL5XQ6NXnyZL344oud6sfYsWP1zDPP6IUXXtDIkSM1fvx4vfHGG2F1LrjgAl199dW66KKLWt266ykrVqzQihUrNGLECP3zn//UCy+8EJp8sbCwUH/+85/17LPPavjw4Vq9enXoaayWt/CA/sBitLyRDwDoFMMwdMEFF+jb3/72WV256gi3263CwkK9/fbbnVq+48c//rHWrFmjDz74oOc6B8QpbmMBwFn473//q40bN+rIkSMdnlunNzz++OO66qqrlJWVpddee00PPfRQaEwP0N8QdgB0WvNaVpH8/e9/1zXXXNOLvYmtQYMGKTs7W7/5zW80cODAsH2xPE/vvfeeHnzwQZ04cUL5+fm65557VFpa2mPvB8QzbmMB6LSDBw9G3fepT32qV55G6gs4T0B8IOwAAABT42ksAABgaoQdAABgaoQdAABgaoQdAABgaoQdAABgaoQdAABgaoQdAABgaoQdAABgav8fDVhfpzPCgHcAAAAASUVORK5CYII=\n"
+          },
+          "metadata": {}
+        }
+      ]
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "y_val.shape == y_pred_val.shape"
+      ],
+      "metadata": {
+        "colab": {
+          "base_uri": "https://localhost:8080/"
+        },
+        "id": "ke9_p6WKGB-G",
+        "outputId": "72a80a64-77ff-4d78-8422-51c9ea9745e8"
+      },
+      "execution_count": 116,
+      "outputs": [
+        {
+          "output_type": "execute_result",
+          "data": {
+            "text/plain": [
+              "True"
+            ]
+          },
+          "metadata": {},
+          "execution_count": 116
+        }
+      ]
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "# Calculates the root mean of squared error\n",
+        "def rmse(y_true, y_pred):\n",
+        "  squared_error = (y_true - y_pred) ** 2\n",
+        "  mean_se = squared_error.mean()\n",
+        "  r_mse = np.sqrt(mean_se)\n",
+        "  return round(float(r_mse), 2)"
+      ],
+      "metadata": {
+        "id": "QsA_C38kFQue"
+      },
+      "execution_count": 155,
+      "outputs": []
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "# from imputing NaN values with 0 we get RMSE\n",
+        "rmse(y_val, y_pred_val)"
+      ],
+      "metadata": {
+        "colab": {
+          "base_uri": "https://localhost:8080/"
+        },
+        "id": "i6sQdjS-GAYZ",
+        "outputId": "7ebfdaca-1871-4fc9-df07-0e119b47563a"
+      },
+      "execution_count": 153,
+      "outputs": [
+        {
+          "output_type": "execute_result",
+          "data": {
+            "text/plain": [
+              "np.float64(0.4585064814908114)"
+            ]
+          },
+          "metadata": {},
+          "execution_count": 153
+        }
+      ]
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "# from imputing NaN values with the mean\n",
+        "rmse(y_val, y_pred_val)"
+      ],
+      "metadata": {
+        "colab": {
+          "base_uri": "https://localhost:8080/"
+        },
+        "id": "dDXWaMNcGieb",
+        "outputId": "139f83d4-add0-4817-b887-51410aa87e51"
+      },
+      "execution_count": 118,
+      "outputs": [
+        {
+          "output_type": "execute_result",
+          "data": {
+            "text/plain": [
+              "0.46"
+            ]
+          },
+          "metadata": {},
+          "execution_count": 118
+        }
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "source": [
+        "## Q4. Regularisation"
+      ],
+      "metadata": {
+        "id": "JwhfRLZ_LE5E"
+      }
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "shuffled_df.head()"
+      ],
+      "metadata": {
+        "colab": {
+          "base_uri": "https://localhost:8080/",
+          "height": 206
+        },
+        "id": "JQC5_7DUJL8z",
+        "outputId": "814aabda-ae7a-4873-f720-885da0b0ee65"
+      },
+      "execution_count": 119,
+      "outputs": [
+        {
+          "output_type": "execute_result",
+          "data": {
+            "text/plain": [
+              "   engine_displacement  horsepower  vehicle_weight  model_year  \\\n",
+              "0                  220       144.0     2535.887591        2009   \n",
+              "1                  160       141.0     2741.170484        2019   \n",
+              "2                  230       155.0     2471.880237        2017   \n",
+              "3                  150       206.0     3748.164469        2015   \n",
+              "4                  300       111.0     2135.716359        2006   \n",
+              "\n",
+              "   fuel_efficiency_mpg  \n",
+              "0            16.642943  \n",
+              "1            16.298377  \n",
+              "2            18.591822  \n",
+              "3            11.818843  \n",
+              "4            19.402209  "
+            ],
+            "text/html": [
+              "\n",
+              "  <div id=\"df-a8eecab6-c08d-451d-9bd4-27f4efe0a75b\" class=\"colab-df-container\">\n",
+              "    <div>\n",
+              "<style scoped>\n",
+              "    .dataframe tbody tr th:only-of-type {\n",
+              "        vertical-align: middle;\n",
+              "    }\n",
+              "\n",
+              "    .dataframe tbody tr th {\n",
+              "        vertical-align: top;\n",
+              "    }\n",
+              "\n",
+              "    .dataframe thead th {\n",
+              "        text-align: right;\n",
+              "    }\n",
+              "</style>\n",
+              "<table border=\"1\" class=\"dataframe\">\n",
+              "  <thead>\n",
+              "    <tr style=\"text-align: right;\">\n",
+              "      <th></th>\n",
+              "      <th>engine_displacement</th>\n",
+              "      <th>horsepower</th>\n",
+              "      <th>vehicle_weight</th>\n",
+              "      <th>model_year</th>\n",
+              "      <th>fuel_efficiency_mpg</th>\n",
+              "    </tr>\n",
+              "  </thead>\n",
+              "  <tbody>\n",
+              "    <tr>\n",
+              "      <th>0</th>\n",
+              "      <td>220</td>\n",
+              "      <td>144.0</td>\n",
+              "      <td>2535.887591</td>\n",
+              "      <td>2009</td>\n",
+              "      <td>16.642943</td>\n",
+              "    </tr>\n",
+              "    <tr>\n",
+              "      <th>1</th>\n",
+              "      <td>160</td>\n",
+              "      <td>141.0</td>\n",
+              "      <td>2741.170484</td>\n",
+              "      <td>2019</td>\n",
+              "      <td>16.298377</td>\n",
+              "    </tr>\n",
+              "    <tr>\n",
+              "      <th>2</th>\n",
+              "      <td>230</td>\n",
+              "      <td>155.0</td>\n",
+              "      <td>2471.880237</td>\n",
+              "      <td>2017</td>\n",
+              "      <td>18.591822</td>\n",
+              "    </tr>\n",
+              "    <tr>\n",
+              "      <th>3</th>\n",
+              "      <td>150</td>\n",
+              "      <td>206.0</td>\n",
+              "      <td>3748.164469</td>\n",
+              "      <td>2015</td>\n",
+              "      <td>11.818843</td>\n",
+              "    </tr>\n",
+              "    <tr>\n",
+              "      <th>4</th>\n",
+              "      <td>300</td>\n",
+              "      <td>111.0</td>\n",
+              "      <td>2135.716359</td>\n",
+              "      <td>2006</td>\n",
+              "      <td>19.402209</td>\n",
+              "    </tr>\n",
+              "  </tbody>\n",
+              "</table>\n",
+              "</div>\n",
+              "    <div class=\"colab-df-buttons\">\n",
+              "\n",
+              "  <div class=\"colab-df-container\">\n",
+              "    <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-a8eecab6-c08d-451d-9bd4-27f4efe0a75b')\"\n",
+              "            title=\"Convert this dataframe to an interactive table.\"\n",
+              "            style=\"display:none;\">\n",
+              "\n",
+              "  <svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\" viewBox=\"0 -960 960 960\">\n",
+              "    <path d=\"M120-120v-720h720v720H120Zm60-500h600v-160H180v160Zm220 220h160v-160H400v160Zm0 220h160v-160H400v160ZM180-400h160v-160H180v160Zm440 0h160v-160H620v160ZM180-180h160v-160H180v160Zm440 0h160v-160H620v160Z\"/>\n",
+              "  </svg>\n",
+              "    </button>\n",
+              "\n",
+              "  <style>\n",
+              "    .colab-df-container {\n",
+              "      display:flex;\n",
+              "      gap: 12px;\n",
+              "    }\n",
+              "\n",
+              "    .colab-df-convert {\n",
+              "      background-color: #E8F0FE;\n",
+              "      border: none;\n",
+              "      border-radius: 50%;\n",
+              "      cursor: pointer;\n",
+              "      display: none;\n",
+              "      fill: #1967D2;\n",
+              "      height: 32px;\n",
+              "      padding: 0 0 0 0;\n",
+              "      width: 32px;\n",
+              "    }\n",
+              "\n",
+              "    .colab-df-convert:hover {\n",
+              "      background-color: #E2EBFA;\n",
+              "      box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
+              "      fill: #174EA6;\n",
+              "    }\n",
+              "\n",
+              "    .colab-df-buttons div {\n",
+              "      margin-bottom: 4px;\n",
+              "    }\n",
+              "\n",
+              "    [theme=dark] .colab-df-convert {\n",
+              "      background-color: #3B4455;\n",
+              "      fill: #D2E3FC;\n",
+              "    }\n",
+              "\n",
+              "    [theme=dark] .colab-df-convert:hover {\n",
+              "      background-color: #434B5C;\n",
+              "      box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
+              "      filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n",
+              "      fill: #FFFFFF;\n",
+              "    }\n",
+              "  </style>\n",
+              "\n",
+              "    <script>\n",
+              "      const buttonEl =\n",
+              "        document.querySelector('#df-a8eecab6-c08d-451d-9bd4-27f4efe0a75b button.colab-df-convert');\n",
+              "      buttonEl.style.display =\n",
+              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
+              "\n",
+              "      async function convertToInteractive(key) {\n",
+              "        const element = document.querySelector('#df-a8eecab6-c08d-451d-9bd4-27f4efe0a75b');\n",
+              "        const dataTable =\n",
+              "          await google.colab.kernel.invokeFunction('convertToInteractive',\n",
+              "                                                    [key], {});\n",
+              "        if (!dataTable) return;\n",
+              "\n",
+              "        const docLinkHtml = 'Like what you see? Visit the ' +\n",
+              "          '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
+              "          + ' to learn more about interactive tables.';\n",
+              "        element.innerHTML = '';\n",
+              "        dataTable['output_type'] = 'display_data';\n",
+              "        await google.colab.output.renderOutput(dataTable, element);\n",
+              "        const docLink = document.createElement('div');\n",
+              "        docLink.innerHTML = docLinkHtml;\n",
+              "        element.appendChild(docLink);\n",
+              "      }\n",
+              "    </script>\n",
+              "  </div>\n",
+              "\n",
+              "\n",
+              "    <div id=\"df-fcd97d60-a70a-4e93-afa7-18bc0b1e4efd\">\n",
+              "      <button class=\"colab-df-quickchart\" onclick=\"quickchart('df-fcd97d60-a70a-4e93-afa7-18bc0b1e4efd')\"\n",
+              "                title=\"Suggest charts\"\n",
+              "                style=\"display:none;\">\n",
+              "\n",
+              "<svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\"viewBox=\"0 0 24 24\"\n",
+              "     width=\"24px\">\n",
+              "    <g>\n",
+              "        <path d=\"M19 3H5c-1.1 0-2 .9-2 2v14c0 1.1.9 2 2 2h14c1.1 0 2-.9 2-2V5c0-1.1-.9-2-2-2zM9 17H7v-7h2v7zm4 0h-2V7h2v10zm4 0h-2v-4h2v4z\"/>\n",
+              "    </g>\n",
+              "</svg>\n",
+              "      </button>\n",
+              "\n",
+              "<style>\n",
+              "  .colab-df-quickchart {\n",
+              "      --bg-color: #E8F0FE;\n",
+              "      --fill-color: #1967D2;\n",
+              "      --hover-bg-color: #E2EBFA;\n",
+              "      --hover-fill-color: #174EA6;\n",
+              "      --disabled-fill-color: #AAA;\n",
+              "      --disabled-bg-color: #DDD;\n",
+              "  }\n",
+              "\n",
+              "  [theme=dark] .colab-df-quickchart {\n",
+              "      --bg-color: #3B4455;\n",
+              "      --fill-color: #D2E3FC;\n",
+              "      --hover-bg-color: #434B5C;\n",
+              "      --hover-fill-color: #FFFFFF;\n",
+              "      --disabled-bg-color: #3B4455;\n",
+              "      --disabled-fill-color: #666;\n",
+              "  }\n",
+              "\n",
+              "  .colab-df-quickchart {\n",
+              "    background-color: var(--bg-color);\n",
+              "    border: none;\n",
+              "    border-radius: 50%;\n",
+              "    cursor: pointer;\n",
+              "    display: none;\n",
+              "    fill: var(--fill-color);\n",
+              "    height: 32px;\n",
+              "    padding: 0;\n",
+              "    width: 32px;\n",
+              "  }\n",
+              "\n",
+              "  .colab-df-quickchart:hover {\n",
+              "    background-color: var(--hover-bg-color);\n",
+              "    box-shadow: 0 1px 2px rgba(60, 64, 67, 0.3), 0 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
+              "    fill: var(--button-hover-fill-color);\n",
+              "  }\n",
+              "\n",
+              "  .colab-df-quickchart-complete:disabled,\n",
+              "  .colab-df-quickchart-complete:disabled:hover {\n",
+              "    background-color: var(--disabled-bg-color);\n",
+              "    fill: var(--disabled-fill-color);\n",
+              "    box-shadow: none;\n",
+              "  }\n",
+              "\n",
+              "  .colab-df-spinner {\n",
+              "    border: 2px solid var(--fill-color);\n",
+              "    border-color: transparent;\n",
+              "    border-bottom-color: var(--fill-color);\n",
+              "    animation:\n",
+              "      spin 1s steps(1) infinite;\n",
+              "  }\n",
+              "\n",
+              "  @keyframes spin {\n",
+              "    0% {\n",
+              "      border-color: transparent;\n",
+              "      border-bottom-color: var(--fill-color);\n",
+              "      border-left-color: var(--fill-color);\n",
+              "    }\n",
+              "    20% {\n",
+              "      border-color: transparent;\n",
+              "      border-left-color: var(--fill-color);\n",
+              "      border-top-color: var(--fill-color);\n",
+              "    }\n",
+              "    30% {\n",
+              "      border-color: transparent;\n",
+              "      border-left-color: var(--fill-color);\n",
+              "      border-top-color: var(--fill-color);\n",
+              "      border-right-color: var(--fill-color);\n",
+              "    }\n",
+              "    40% {\n",
+              "      border-color: transparent;\n",
+              "      border-right-color: var(--fill-color);\n",
+              "      border-top-color: var(--fill-color);\n",
+              "    }\n",
+              "    60% {\n",
+              "      border-color: transparent;\n",
+              "      border-right-color: var(--fill-color);\n",
+              "    }\n",
+              "    80% {\n",
+              "      border-color: transparent;\n",
+              "      border-right-color: var(--fill-color);\n",
+              "      border-bottom-color: var(--fill-color);\n",
+              "    }\n",
+              "    90% {\n",
+              "      border-color: transparent;\n",
+              "      border-bottom-color: var(--fill-color);\n",
+              "    }\n",
+              "  }\n",
+              "</style>\n",
+              "\n",
+              "      <script>\n",
+              "        async function quickchart(key) {\n",
+              "          const quickchartButtonEl =\n",
+              "            document.querySelector('#' + key + ' button');\n",
+              "          quickchartButtonEl.disabled = true;  // To prevent multiple clicks.\n",
+              "          quickchartButtonEl.classList.add('colab-df-spinner');\n",
+              "          try {\n",
+              "            const charts = await google.colab.kernel.invokeFunction(\n",
+              "                'suggestCharts', [key], {});\n",
+              "          } catch (error) {\n",
+              "            console.error('Error during call to suggestCharts:', error);\n",
+              "          }\n",
+              "          quickchartButtonEl.classList.remove('colab-df-spinner');\n",
+              "          quickchartButtonEl.classList.add('colab-df-quickchart-complete');\n",
+              "        }\n",
+              "        (() => {\n",
+              "          let quickchartButtonEl =\n",
+              "            document.querySelector('#df-fcd97d60-a70a-4e93-afa7-18bc0b1e4efd button');\n",
+              "          quickchartButtonEl.style.display =\n",
+              "            google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
+              "        })();\n",
+              "      </script>\n",
+              "    </div>\n",
+              "\n",
+              "    </div>\n",
+              "  </div>\n"
+            ],
+            "application/vnd.google.colaboratory.intrinsic+json": {
+              "type": "dataframe",
+              "variable_name": "shuffled_df",
+              "summary": "{\n  \"name\": \"shuffled_df\",\n  \"rows\": 9704,\n  \"fields\": [\n    {\n      \"column\": \"engine_displacement\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 49,\n        \"min\": 10,\n        \"max\": 380,\n        \"num_unique_values\": 36,\n        \"samples\": [\n          10,\n          200,\n          100\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"horsepower\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 29.879555200339414,\n        \"min\": 37.0,\n        \"max\": 271.0,\n        \"num_unique_values\": 192,\n        \"samples\": [\n          101.0,\n          232.0,\n          142.0\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"vehicle_weight\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 497.89486003118515,\n        \"min\": 952.6817606436496,\n        \"max\": 4739.077089392099,\n        \"num_unique_values\": 9704,\n        \"samples\": [\n          2952.280077222956,\n          3527.0988925098245,\n          2697.391829652872\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"model_year\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 6,\n        \"min\": 2000,\n        \"max\": 2023,\n        \"num_unique_values\": 24,\n        \"samples\": [\n          2020,\n          2022,\n          2009\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"fuel_efficiency_mpg\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 2.556467702897423,\n        \"min\": 6.200970533392815,\n        \"max\": 25.96722204888372,\n        \"num_unique_values\": 9704,\n        \"samples\": [\n          14.748942858764156,\n          11.437054433578467,\n          15.54922028907195\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    }\n  ]\n}"
+            }
+          },
+          "metadata": {},
+          "execution_count": 119
+        }
+      ]
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "X2 = shuffled_df.drop(columns='fuel_efficiency_mpg')\n",
+        "y2 = shuffled_df[\"fuel_efficiency_mpg\"]\n",
+        "print(f\"Shape of X: {X.shape}\\nShape of y: {y.shape}\")"
+      ],
+      "metadata": {
+        "colab": {
+          "base_uri": "https://localhost:8080/"
+        },
+        "id": "usu1f9e4LYyD",
+        "outputId": "d8ecceb2-05ac-4b0b-aa64-3613baabfc64"
+      },
+      "execution_count": 135,
+      "outputs": [
+        {
+          "output_type": "stream",
+          "name": "stdout",
+          "text": [
+            "Shape of X: (9704, 4)\n",
+            "Shape of y: (9704,)\n"
+          ]
+        }
+      ]
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "# fill with 0 as asked in the question\n",
+        "X2[\"horsepower\"].fillna(0, inplace=True);"
+      ],
+      "metadata": {
+        "colab": {
+          "base_uri": "https://localhost:8080/"
+        },
+        "id": "9zWvGRMrLe8q",
+        "outputId": "4f19e7a1-bcec-4565-bf65-40e59fc1bd66"
+      },
+      "execution_count": 136,
+      "outputs": [
+        {
+          "output_type": "stream",
+          "name": "stderr",
+          "text": [
+            "/tmp/ipython-input-3329028345.py:2: FutureWarning: A value is trying to be set on a copy of a DataFrame or Series through chained assignment using an inplace method.\n",
+            "The behavior will change in pandas 3.0. This inplace method will never work because the intermediate object on which we are setting values always behaves as a copy.\n",
+            "\n",
+            "For example, when doing 'df[col].method(value, inplace=True)', try using 'df.method({col: value}, inplace=True)' or df[col] = df[col].method(value) instead, to perform the operation inplace on the original object.\n",
+            "\n",
+            "\n",
+            "  X2[\"horsepower\"].fillna(0, inplace=True);\n"
+          ]
+        }
+      ]
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "X2.isnull().sum()"
+      ],
+      "metadata": {
+        "colab": {
+          "base_uri": "https://localhost:8080/",
+          "height": 209
+        },
+        "id": "SNyDGux8OkR6",
+        "outputId": "c9fb25ae-0386-4287-b3c0-acb46785c2a3"
+      },
+      "execution_count": 137,
+      "outputs": [
+        {
+          "output_type": "execute_result",
+          "data": {
+            "text/plain": [
+              "engine_displacement    0\n",
+              "horsepower             0\n",
+              "vehicle_weight         0\n",
+              "model_year             0\n",
+              "dtype: int64"
+            ],
+            "text/html": [
+              "<div>\n",
+              "<style scoped>\n",
+              "    .dataframe tbody tr th:only-of-type {\n",
+              "        vertical-align: middle;\n",
+              "    }\n",
+              "\n",
+              "    .dataframe tbody tr th {\n",
+              "        vertical-align: top;\n",
+              "    }\n",
+              "\n",
+              "    .dataframe thead th {\n",
+              "        text-align: right;\n",
+              "    }\n",
+              "</style>\n",
+              "<table border=\"1\" class=\"dataframe\">\n",
+              "  <thead>\n",
+              "    <tr style=\"text-align: right;\">\n",
+              "      <th></th>\n",
+              "      <th>0</th>\n",
+              "    </tr>\n",
+              "  </thead>\n",
+              "  <tbody>\n",
+              "    <tr>\n",
+              "      <th>engine_displacement</th>\n",
+              "      <td>0</td>\n",
+              "    </tr>\n",
+              "    <tr>\n",
+              "      <th>horsepower</th>\n",
+              "      <td>0</td>\n",
+              "    </tr>\n",
+              "    <tr>\n",
+              "      <th>vehicle_weight</th>\n",
+              "      <td>0</td>\n",
+              "    </tr>\n",
+              "    <tr>\n",
+              "      <th>model_year</th>\n",
+              "      <td>0</td>\n",
+              "    </tr>\n",
+              "  </tbody>\n",
+              "</table>\n",
+              "</div><br><label><b>dtype:</b> int64</label>"
+            ]
+          },
+          "metadata": {},
+          "execution_count": 137
+        }
+      ]
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "# train, val, test split\n",
+        "np.random.seed(42)\n",
+        "X_train, X_temp, y_train, y_temp = train_test_split(X2, y2, test_size=0.4)\n",
+        "X_val, X_test, y_val, y_test = train_test_split(X_temp, y_temp, test_size=0.5)"
+      ],
+      "metadata": {
+        "id": "sMrvPT24OVIf"
+      },
+      "execution_count": 139,
+      "outputs": []
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "# for regularisation importing Ridge\n",
+        "from sklearn.linear_model import Ridge\n",
+        "r_values = [0, 0.01, 0.1, 1, 5, 10, 100]\n",
+        "hist = []\n",
+        "\n",
+        "for r in r_values:\n",
+        "  model = Ridge(alpha=r)\n",
+        "  model.fit(X_train, y_train)\n",
+        "  y_preds = model.predict(X_val)\n",
+        "  error = rmse(y_val, y_preds)\n",
+        "  print(f\"With r = {r}: RMSE: {error}\")\n",
+        "  hist.append(error)\n",
+        "\n"
+      ],
+      "metadata": {
+        "colab": {
+          "base_uri": "https://localhost:8080/"
+        },
+        "id": "p_IlLV_GLw_A",
+        "outputId": "a3e760c4-f727-4cd5-bd2e-9af025cc4e96"
+      },
+      "execution_count": 149,
+      "outputs": [
+        {
+          "output_type": "stream",
+          "name": "stdout",
+          "text": [
+            "With r = 0: RMSE: 0.51\n",
+            "With r = 0.01: RMSE: 0.51\n",
+            "With r = 0.1: RMSE: 0.51\n",
+            "With r = 1: RMSE: 0.51\n",
+            "With r = 5: RMSE: 0.51\n",
+            "With r = 10: RMSE: 0.51\n",
+            "With r = 100: RMSE: 0.51\n"
+          ]
+        }
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "source": [
+        "Clearly, no effect of regularisation"
+      ],
+      "metadata": {
+        "id": "vcferr4UR1Si"
+      }
+    },
+    {
+      "cell_type": "markdown",
+      "source": [
+        "## Q5 Different seed values"
+      ],
+      "metadata": {
+        "id": "anq35JmwSLJr"
+      }
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "# --- Load dataset\n",
+        "df2 = pd.read_csv(\"car_fuel_efficiency.csv\").fillna(0)\n",
+        "\n",
+        "# --- Features and target\n",
+        "X = df2[['engine_displacement', 'num_cylinders', 'horsepower', 'vehicle_weight']]\n",
+        "y = df2['fuel_efficiency_mpg']\n",
+        "\n",
+        "\n",
+        "# Calculates the root mean of squared error\n",
+        "def rmse(y_true, y_pred):\n",
+        "  squared_error = (y_true - y_pred) ** 2\n",
+        "  mean_se = squared_error.mean()\n",
+        "  r_mse = np.sqrt(mean_se)\n",
+        "  return float(r_mse)\n",
+        "\n",
+        "# iterate with different random seeds\n",
+        "hist = []\n",
+        "\n",
+        "for i in [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]:\n",
+        "  X_tr, X_temp, y_tr, y_temp = train_test_split(X, y, test_size=0.4, random_state=i)\n",
+        "  X_val, X_t, y_val, y_t = train_test_split(X_temp, y_temp, test_size=0.5, random_state=i)\n",
+        "\n",
+        "  model = LinearRegression()\n",
+        "  model.fit(X_tr, y_tr)\n",
+        "  y_p = model.predict(X_val)\n",
+        "  r_mse = rmse(y_val, y_p)\n",
+        "\n",
+        "  print(f\"With seed {i}: RMSE: {r_mse}\")\n",
+        "\n",
+        "  hist.append(r_mse)\n"
+      ],
+      "metadata": {
+        "colab": {
+          "base_uri": "https://localhost:8080/"
+        },
+        "id": "NFRzMsuZN6mc",
+        "outputId": "52591494-6b76-4171-9496-189c4fbc2b9a"
+      },
+      "execution_count": 170,
+      "outputs": [
+        {
+          "output_type": "stream",
+          "name": "stdout",
+          "text": [
+            "With seed 0: RMSE: 0.5179381763288806\n",
+            "With seed 1: RMSE: 0.5171639086555457\n",
+            "With seed 2: RMSE: 0.5198562964522706\n",
+            "With seed 3: RMSE: 0.5215830764201178\n",
+            "With seed 4: RMSE: 0.5113660125711117\n",
+            "With seed 5: RMSE: 0.5150801979905301\n",
+            "With seed 6: RMSE: 0.5145383165566438\n",
+            "With seed 7: RMSE: 0.5357713657145978\n",
+            "With seed 8: RMSE: 0.5183959791528321\n",
+            "With seed 9: RMSE: 0.5197067240692991\n"
+          ]
+        }
+      ]
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "hist"
+      ],
+      "metadata": {
+        "colab": {
+          "base_uri": "https://localhost:8080/"
+        },
+        "id": "cfhC_SmmUwm7",
+        "outputId": "087d1839-eb49-4ac1-c8c2-d4a6fdc38f54"
+      },
+      "execution_count": 171,
+      "outputs": [
+        {
+          "output_type": "execute_result",
+          "data": {
+            "text/plain": [
+              "[0.5179381763288806,\n",
+              " 0.5171639086555457,\n",
+              " 0.5198562964522706,\n",
+              " 0.5215830764201178,\n",
+              " 0.5113660125711117,\n",
+              " 0.5150801979905301,\n",
+              " 0.5145383165566438,\n",
+              " 0.5357713657145978,\n",
+              " 0.5183959791528321,\n",
+              " 0.5197067240692991]"
+            ]
+          },
+          "metadata": {},
+          "execution_count": 171
+        }
+      ]
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "# get the stddev of the RMSEs\n",
+        "ans = float(np.std(hist))\n",
+        "print(f\"STD: {ans}\")"
+      ],
+      "metadata": {
+        "colab": {
+          "base_uri": "https://localhost:8080/"
+        },
+        "id": "ojRU_dQsU19q",
+        "outputId": "af81ae44-b3d1-4a22-cc18-4c671640f7ae"
+      },
+      "execution_count": 172,
+      "outputs": [
+        {
+          "output_type": "stream",
+          "name": "stdout",
+          "text": [
+            "STD: 0.006224150161088512\n"
+          ]
+        }
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "source": [
+        "# Final modular functions after going through all the processes above"
+      ],
+      "metadata": {
+        "id": "j5Z98DRNX9Im"
+      }
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "def load_data(file_path=\"car_fuel_efficiency.csv\"):\n",
+        "    df = pd.read_csv(file_path)[[\n",
+        "        'engine_displacement', 'horsepower', 'vehicle_weight', 'model_year', 'fuel_efficiency_mpg'\n",
+        "    ]]\n",
+        "    return df"
+      ],
+      "metadata": {
+        "id": "NyClaIiiVKTv"
+      },
+      "execution_count": 173,
+      "outputs": []
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "def preprocess(df, fill_method=\"zero\"):\n",
+        "    df = df.copy()\n",
+        "    if fill_method == \"zero\":\n",
+        "        df = df.fillna(0)\n",
+        "    elif fill_method == \"mean\":\n",
+        "        # Fill NA using training mean; done later in train function\n",
+        "        pass\n",
+        "    return df"
+      ],
+      "metadata": {
+        "id": "KpzAtCJvYLna"
+      },
+      "execution_count": 174,
+      "outputs": []
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "# split into train, val, test sets\n",
+        "def split_data(X, y, val, seed=42):\n",
+        "  if val:\n",
+        "    X_tr, X_temp, y_tr, y_temp = train_test_split(X, y, test_size=0.4, random_state=seed)\n",
+        "    X_val, X_t, y_val, y_t = train_test_split(X_temp, y_temp, test_size=0.5, random_state=seed)\n",
+        "    return X_tr, X_val, X_t, y_tr, y_val, y_t\n",
+        "\n",
+        "  else:\n",
+        "      X_tr, X_t, y_tr, y_t = train_test_split(X, y, test_size=0.4, random_state=seed)\n",
+        "      return X_tr, X_t, y_tr, y_t\n",
+        "\n"
+      ],
+      "metadata": {
+        "id": "97QpEYAIYSXK"
+      },
+      "execution_count": 185,
+      "outputs": []
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "def rmse(y_true, y_pred):\n",
+        "  squared_error = (y_true - y_pred) ** 2\n",
+        "  mean_se = squared_error.mean()\n",
+        "  r_mse = np.sqrt(mean_se)\n",
+        "  return float(r_mse)"
+      ],
+      "metadata": {
+        "id": "OXZCZ-nHYbMm"
+      },
+      "execution_count": 177,
+      "outputs": []
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "# Train Linear Regression\n",
+        "def train_linear(X_tr, y_tr):\n",
+        "    model = LinearRegression()\n",
+        "    model.fit(X_tr, y_tr)\n",
+        "    return model\n",
+        "\n",
+        "# Train Ridge Regression with regularization r (alpha)\n",
+        "def train_ridge(X_tr, y_tr, r):\n",
+        "    model = Ridge(alpha=r)\n",
+        "    model.fit(X_tr, y_tr)\n",
+        "    return model"
+      ],
+      "metadata": {
+        "id": "O91JeC82Ymqy"
+      },
+      "execution_count": 178,
+      "outputs": []
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "# Evaluate model on given dataset\n",
+        "def evaluate(model, X, y):\n",
+        "    y_pred = model.predict(X)\n",
+        "    return rmse(y, y_pred)"
+      ],
+      "metadata": {
+        "id": "7Avk62gmYzee"
+      },
+      "execution_count": 179,
+      "outputs": []
+    },
+    {
+      "cell_type": "markdown",
+      "source": [
+        "## Q6: Evaluating on test data"
+      ],
+      "metadata": {
+        "id": "9qGthqsJZA3x"
+      }
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "df_ = load_data(\"car_fuel_efficiency.csv\")\n",
+        "df_.head()"
+      ],
+      "metadata": {
+        "colab": {
+          "base_uri": "https://localhost:8080/",
+          "height": 206
+        },
+        "id": "oEtdur9pY50X",
+        "outputId": "69816a05-4a0f-4698-f895-e7096f256982"
+      },
+      "execution_count": 214,
+      "outputs": [
+        {
+          "output_type": "execute_result",
+          "data": {
+            "text/plain": [
+              "   engine_displacement  horsepower  vehicle_weight  model_year  \\\n",
+              "0                  170       159.0     3413.433759        2003   \n",
+              "1                  130        97.0     3149.664934        2007   \n",
+              "2                  170        78.0     3079.038997        2018   \n",
+              "3                  220         NaN     2542.392402        2009   \n",
+              "4                  210       140.0     3460.870990        2009   \n",
+              "\n",
+              "   fuel_efficiency_mpg  \n",
+              "0            13.231729  \n",
+              "1            13.688217  \n",
+              "2            14.246341  \n",
+              "3            16.912736  \n",
+              "4            12.488369  "
+            ],
+            "text/html": [
+              "\n",
+              "  <div id=\"df-ee118e0e-1eae-4804-961c-d6b8ad4c8e0f\" class=\"colab-df-container\">\n",
+              "    <div>\n",
+              "<style scoped>\n",
+              "    .dataframe tbody tr th:only-of-type {\n",
+              "        vertical-align: middle;\n",
+              "    }\n",
+              "\n",
+              "    .dataframe tbody tr th {\n",
+              "        vertical-align: top;\n",
+              "    }\n",
+              "\n",
+              "    .dataframe thead th {\n",
+              "        text-align: right;\n",
+              "    }\n",
+              "</style>\n",
+              "<table border=\"1\" class=\"dataframe\">\n",
+              "  <thead>\n",
+              "    <tr style=\"text-align: right;\">\n",
+              "      <th></th>\n",
+              "      <th>engine_displacement</th>\n",
+              "      <th>horsepower</th>\n",
+              "      <th>vehicle_weight</th>\n",
+              "      <th>model_year</th>\n",
+              "      <th>fuel_efficiency_mpg</th>\n",
+              "    </tr>\n",
+              "  </thead>\n",
+              "  <tbody>\n",
+              "    <tr>\n",
+              "      <th>0</th>\n",
+              "      <td>170</td>\n",
+              "      <td>159.0</td>\n",
+              "      <td>3413.433759</td>\n",
+              "      <td>2003</td>\n",
+              "      <td>13.231729</td>\n",
+              "    </tr>\n",
+              "    <tr>\n",
+              "      <th>1</th>\n",
+              "      <td>130</td>\n",
+              "      <td>97.0</td>\n",
+              "      <td>3149.664934</td>\n",
+              "      <td>2007</td>\n",
+              "      <td>13.688217</td>\n",
+              "    </tr>\n",
+              "    <tr>\n",
+              "      <th>2</th>\n",
+              "      <td>170</td>\n",
+              "      <td>78.0</td>\n",
+              "      <td>3079.038997</td>\n",
+              "      <td>2018</td>\n",
+              "      <td>14.246341</td>\n",
+              "    </tr>\n",
+              "    <tr>\n",
+              "      <th>3</th>\n",
+              "      <td>220</td>\n",
+              "      <td>NaN</td>\n",
+              "      <td>2542.392402</td>\n",
+              "      <td>2009</td>\n",
+              "      <td>16.912736</td>\n",
+              "    </tr>\n",
+              "    <tr>\n",
+              "      <th>4</th>\n",
+              "      <td>210</td>\n",
+              "      <td>140.0</td>\n",
+              "      <td>3460.870990</td>\n",
+              "      <td>2009</td>\n",
+              "      <td>12.488369</td>\n",
+              "    </tr>\n",
+              "  </tbody>\n",
+              "</table>\n",
+              "</div>\n",
+              "    <div class=\"colab-df-buttons\">\n",
+              "\n",
+              "  <div class=\"colab-df-container\">\n",
+              "    <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-ee118e0e-1eae-4804-961c-d6b8ad4c8e0f')\"\n",
+              "            title=\"Convert this dataframe to an interactive table.\"\n",
+              "            style=\"display:none;\">\n",
+              "\n",
+              "  <svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\" viewBox=\"0 -960 960 960\">\n",
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+              "  </svg>\n",
+              "    </button>\n",
+              "\n",
+              "  <style>\n",
+              "    .colab-df-container {\n",
+              "      display:flex;\n",
+              "      gap: 12px;\n",
+              "    }\n",
+              "\n",
+              "    .colab-df-convert {\n",
+              "      background-color: #E8F0FE;\n",
+              "      border: none;\n",
+              "      border-radius: 50%;\n",
+              "      cursor: pointer;\n",
+              "      display: none;\n",
+              "      fill: #1967D2;\n",
+              "      height: 32px;\n",
+              "      padding: 0 0 0 0;\n",
+              "      width: 32px;\n",
+              "    }\n",
+              "\n",
+              "    .colab-df-convert:hover {\n",
+              "      background-color: #E2EBFA;\n",
+              "      box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
+              "      fill: #174EA6;\n",
+              "    }\n",
+              "\n",
+              "    .colab-df-buttons div {\n",
+              "      margin-bottom: 4px;\n",
+              "    }\n",
+              "\n",
+              "    [theme=dark] .colab-df-convert {\n",
+              "      background-color: #3B4455;\n",
+              "      fill: #D2E3FC;\n",
+              "    }\n",
+              "\n",
+              "    [theme=dark] .colab-df-convert:hover {\n",
+              "      background-color: #434B5C;\n",
+              "      box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
+              "      filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n",
+              "      fill: #FFFFFF;\n",
+              "    }\n",
+              "  </style>\n",
+              "\n",
+              "    <script>\n",
+              "      const buttonEl =\n",
+              "        document.querySelector('#df-ee118e0e-1eae-4804-961c-d6b8ad4c8e0f button.colab-df-convert');\n",
+              "      buttonEl.style.display =\n",
+              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
+              "\n",
+              "      async function convertToInteractive(key) {\n",
+              "        const element = document.querySelector('#df-ee118e0e-1eae-4804-961c-d6b8ad4c8e0f');\n",
+              "        const dataTable =\n",
+              "          await google.colab.kernel.invokeFunction('convertToInteractive',\n",
+              "                                                    [key], {});\n",
+              "        if (!dataTable) return;\n",
+              "\n",
+              "        const docLinkHtml = 'Like what you see? Visit the ' +\n",
+              "          '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
+              "          + ' to learn more about interactive tables.';\n",
+              "        element.innerHTML = '';\n",
+              "        dataTable['output_type'] = 'display_data';\n",
+              "        await google.colab.output.renderOutput(dataTable, element);\n",
+              "        const docLink = document.createElement('div');\n",
+              "        docLink.innerHTML = docLinkHtml;\n",
+              "        element.appendChild(docLink);\n",
+              "      }\n",
+              "    </script>\n",
+              "  </div>\n",
+              "\n",
+              "\n",
+              "    <div id=\"df-f4cd4795-d278-477d-a824-8289e0fbf07e\">\n",
+              "      <button class=\"colab-df-quickchart\" onclick=\"quickchart('df-f4cd4795-d278-477d-a824-8289e0fbf07e')\"\n",
+              "                title=\"Suggest charts\"\n",
+              "                style=\"display:none;\">\n",
+              "\n",
+              "<svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\"viewBox=\"0 0 24 24\"\n",
+              "     width=\"24px\">\n",
+              "    <g>\n",
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+              "    </g>\n",
+              "</svg>\n",
+              "      </button>\n",
+              "\n",
+              "<style>\n",
+              "  .colab-df-quickchart {\n",
+              "      --bg-color: #E8F0FE;\n",
+              "      --fill-color: #1967D2;\n",
+              "      --hover-bg-color: #E2EBFA;\n",
+              "      --hover-fill-color: #174EA6;\n",
+              "      --disabled-fill-color: #AAA;\n",
+              "      --disabled-bg-color: #DDD;\n",
+              "  }\n",
+              "\n",
+              "  [theme=dark] .colab-df-quickchart {\n",
+              "      --bg-color: #3B4455;\n",
+              "      --fill-color: #D2E3FC;\n",
+              "      --hover-bg-color: #434B5C;\n",
+              "      --hover-fill-color: #FFFFFF;\n",
+              "      --disabled-bg-color: #3B4455;\n",
+              "      --disabled-fill-color: #666;\n",
+              "  }\n",
+              "\n",
+              "  .colab-df-quickchart {\n",
+              "    background-color: var(--bg-color);\n",
+              "    border: none;\n",
+              "    border-radius: 50%;\n",
+              "    cursor: pointer;\n",
+              "    display: none;\n",
+              "    fill: var(--fill-color);\n",
+              "    height: 32px;\n",
+              "    padding: 0;\n",
+              "    width: 32px;\n",
+              "  }\n",
+              "\n",
+              "  .colab-df-quickchart:hover {\n",
+              "    background-color: var(--hover-bg-color);\n",
+              "    box-shadow: 0 1px 2px rgba(60, 64, 67, 0.3), 0 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
+              "    fill: var(--button-hover-fill-color);\n",
+              "  }\n",
+              "\n",
+              "  .colab-df-quickchart-complete:disabled,\n",
+              "  .colab-df-quickchart-complete:disabled:hover {\n",
+              "    background-color: var(--disabled-bg-color);\n",
+              "    fill: var(--disabled-fill-color);\n",
+              "    box-shadow: none;\n",
+              "  }\n",
+              "\n",
+              "  .colab-df-spinner {\n",
+              "    border: 2px solid var(--fill-color);\n",
+              "    border-color: transparent;\n",
+              "    border-bottom-color: var(--fill-color);\n",
+              "    animation:\n",
+              "      spin 1s steps(1) infinite;\n",
+              "  }\n",
+              "\n",
+              "  @keyframes spin {\n",
+              "    0% {\n",
+              "      border-color: transparent;\n",
+              "      border-bottom-color: var(--fill-color);\n",
+              "      border-left-color: var(--fill-color);\n",
+              "    }\n",
+              "    20% {\n",
+              "      border-color: transparent;\n",
+              "      border-left-color: var(--fill-color);\n",
+              "      border-top-color: var(--fill-color);\n",
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+              "      border-left-color: var(--fill-color);\n",
+              "      border-top-color: var(--fill-color);\n",
+              "      border-right-color: var(--fill-color);\n",
+              "    }\n",
+              "    40% {\n",
+              "      border-color: transparent;\n",
+              "      border-right-color: var(--fill-color);\n",
+              "      border-top-color: var(--fill-color);\n",
+              "    }\n",
+              "    60% {\n",
+              "      border-color: transparent;\n",
+              "      border-right-color: var(--fill-color);\n",
+              "    }\n",
+              "    80% {\n",
+              "      border-color: transparent;\n",
+              "      border-right-color: var(--fill-color);\n",
+              "      border-bottom-color: var(--fill-color);\n",
+              "    }\n",
+              "    90% {\n",
+              "      border-color: transparent;\n",
+              "      border-bottom-color: var(--fill-color);\n",
+              "    }\n",
+              "  }\n",
+              "</style>\n",
+              "\n",
+              "      <script>\n",
+              "        async function quickchart(key) {\n",
+              "          const quickchartButtonEl =\n",
+              "            document.querySelector('#' + key + ' button');\n",
+              "          quickchartButtonEl.disabled = true;  // To prevent multiple clicks.\n",
+              "          quickchartButtonEl.classList.add('colab-df-spinner');\n",
+              "          try {\n",
+              "            const charts = await google.colab.kernel.invokeFunction(\n",
+              "                'suggestCharts', [key], {});\n",
+              "          } catch (error) {\n",
+              "            console.error('Error during call to suggestCharts:', error);\n",
+              "          }\n",
+              "          quickchartButtonEl.classList.remove('colab-df-spinner');\n",
+              "          quickchartButtonEl.classList.add('colab-df-quickchart-complete');\n",
+              "        }\n",
+              "        (() => {\n",
+              "          let quickchartButtonEl =\n",
+              "            document.querySelector('#df-f4cd4795-d278-477d-a824-8289e0fbf07e button');\n",
+              "          quickchartButtonEl.style.display =\n",
+              "            google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
+              "        })();\n",
+              "      </script>\n",
+              "    </div>\n",
+              "\n",
+              "    </div>\n",
+              "  </div>\n"
+            ],
+            "application/vnd.google.colaboratory.intrinsic+json": {
+              "type": "dataframe",
+              "variable_name": "df_",
+              "summary": "{\n  \"name\": \"df_\",\n  \"rows\": 9704,\n  \"fields\": [\n    {\n      \"column\": \"engine_displacement\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 49,\n        \"min\": 10,\n        \"max\": 380,\n        \"num_unique_values\": 36,\n        \"samples\": [\n          30,\n          260,\n          90\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"horsepower\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 29.879555200339446,\n        \"min\": 37.0,\n        \"max\": 271.0,\n        \"num_unique_values\": 192,\n        \"samples\": [\n          128.0,\n          82.0,\n          167.0\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"vehicle_weight\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 497.8948600311838,\n        \"min\": 952.6817606436496,\n        \"max\": 4739.077089392099,\n        \"num_unique_values\": 9704,\n        \"samples\": [\n          2535.8875912388694,\n          2741.1704843893167,\n          2471.8802372627765\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"model_year\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 6,\n        \"min\": 2000,\n        \"max\": 2023,\n        \"num_unique_values\": 24,\n        \"samples\": [\n          2005,\n          2002,\n          2003\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"fuel_efficiency_mpg\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 2.5564677028974288,\n        \"min\": 6.200970533392815,\n        \"max\": 25.96722204888372,\n        \"num_unique_values\": 9704,\n        \"samples\": [\n          16.642943419221385,\n          16.298377150953442,\n          18.59182197290521\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    }\n  ]\n}"
+            }
+          },
+          "metadata": {},
+          "execution_count": 214
+        }
+      ]
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "df_ = preprocess(df_)\n",
+        "df_.isnull().sum()"
+      ],
+      "metadata": {
+        "colab": {
+          "base_uri": "https://localhost:8080/",
+          "height": 241
+        },
+        "id": "24zaNiO9ZPSV",
+        "outputId": "0193dfd9-a06f-4a0b-d017-f3c3d0552dab"
+      },
+      "execution_count": 215,
+      "outputs": [
+        {
+          "output_type": "execute_result",
+          "data": {
+            "text/plain": [
+              "engine_displacement    0\n",
+              "horsepower             0\n",
+              "vehicle_weight         0\n",
+              "model_year             0\n",
+              "fuel_efficiency_mpg    0\n",
+              "dtype: int64"
+            ],
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+              "    <tr style=\"text-align: right;\">\n",
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+              "      <th>0</th>\n",
+              "    </tr>\n",
+              "  </thead>\n",
+              "  <tbody>\n",
+              "    <tr>\n",
+              "      <th>engine_displacement</th>\n",
+              "      <td>0</td>\n",
+              "    </tr>\n",
+              "    <tr>\n",
+              "      <th>horsepower</th>\n",
+              "      <td>0</td>\n",
+              "    </tr>\n",
+              "    <tr>\n",
+              "      <th>vehicle_weight</th>\n",
+              "      <td>0</td>\n",
+              "    </tr>\n",
+              "    <tr>\n",
+              "      <th>model_year</th>\n",
+              "      <td>0</td>\n",
+              "    </tr>\n",
+              "    <tr>\n",
+              "      <th>fuel_efficiency_mpg</th>\n",
+              "      <td>0</td>\n",
+              "    </tr>\n",
+              "  </tbody>\n",
+              "</table>\n",
+              "</div><br><label><b>dtype:</b> int64</label>"
+            ]
+          },
+          "metadata": {},
+          "execution_count": 215
+        }
+      ]
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "df_.head()\n"
+      ],
+      "metadata": {
+        "colab": {
+          "base_uri": "https://localhost:8080/",
+          "height": 206
+        },
+        "id": "oNAWrjSiapyT",
+        "outputId": "31ede318-f4cc-4469-a4eb-7d78c81fd6bf"
+      },
+      "execution_count": 216,
+      "outputs": [
+        {
+          "output_type": "execute_result",
+          "data": {
+            "text/plain": [
+              "   engine_displacement  horsepower  vehicle_weight  model_year  \\\n",
+              "0                  170       159.0     3413.433759        2003   \n",
+              "1                  130        97.0     3149.664934        2007   \n",
+              "2                  170        78.0     3079.038997        2018   \n",
+              "3                  220         0.0     2542.392402        2009   \n",
+              "4                  210       140.0     3460.870990        2009   \n",
+              "\n",
+              "   fuel_efficiency_mpg  \n",
+              "0            13.231729  \n",
+              "1            13.688217  \n",
+              "2            14.246341  \n",
+              "3            16.912736  \n",
+              "4            12.488369  "
+            ],
+            "text/html": [
+              "\n",
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+              "      <th></th>\n",
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+              "      <td>159.0</td>\n",
+              "      <td>3413.433759</td>\n",
+              "      <td>2003</td>\n",
+              "      <td>13.231729</td>\n",
+              "    </tr>\n",
+              "    <tr>\n",
+              "      <th>1</th>\n",
+              "      <td>130</td>\n",
+              "      <td>97.0</td>\n",
+              "      <td>3149.664934</td>\n",
+              "      <td>2007</td>\n",
+              "      <td>13.688217</td>\n",
+              "    </tr>\n",
+              "    <tr>\n",
+              "      <th>2</th>\n",
+              "      <td>170</td>\n",
+              "      <td>78.0</td>\n",
+              "      <td>3079.038997</td>\n",
+              "      <td>2018</td>\n",
+              "      <td>14.246341</td>\n",
+              "    </tr>\n",
+              "    <tr>\n",
+              "      <th>3</th>\n",
+              "      <td>220</td>\n",
+              "      <td>0.0</td>\n",
+              "      <td>2542.392402</td>\n",
+              "      <td>2009</td>\n",
+              "      <td>16.912736</td>\n",
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+              "      <td>3460.870990</td>\n",
+              "      <td>2009</td>\n",
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+              "\n",
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+              "  </svg>\n",
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+              "\n",
+              "  <style>\n",
+              "    .colab-df-container {\n",
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+              "      gap: 12px;\n",
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+              "\n",
+              "    .colab-df-convert {\n",
+              "      background-color: #E8F0FE;\n",
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+              "      padding: 0 0 0 0;\n",
+              "      width: 32px;\n",
+              "    }\n",
+              "\n",
+              "    .colab-df-convert:hover {\n",
+              "      background-color: #E2EBFA;\n",
+              "      box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
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+              "\n",
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+              "      background-color: #3B4455;\n",
+              "      fill: #D2E3FC;\n",
+              "    }\n",
+              "\n",
+              "    [theme=dark] .colab-df-convert:hover {\n",
+              "      background-color: #434B5C;\n",
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+              "      filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n",
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+              "        document.querySelector('#df-be70f02f-76ca-4600-b422-5befe6cb64de button.colab-df-convert');\n",
+              "      buttonEl.style.display =\n",
+              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
+              "\n",
+              "      async function convertToInteractive(key) {\n",
+              "        const element = document.querySelector('#df-be70f02f-76ca-4600-b422-5befe6cb64de');\n",
+              "        const dataTable =\n",
+              "          await google.colab.kernel.invokeFunction('convertToInteractive',\n",
+              "                                                    [key], {});\n",
+              "        if (!dataTable) return;\n",
+              "\n",
+              "        const docLinkHtml = 'Like what you see? Visit the ' +\n",
+              "          '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
+              "          + ' to learn more about interactive tables.';\n",
+              "        element.innerHTML = '';\n",
+              "        dataTable['output_type'] = 'display_data';\n",
+              "        await google.colab.output.renderOutput(dataTable, element);\n",
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+              "    </g>\n",
+              "</svg>\n",
+              "      </button>\n",
+              "\n",
+              "<style>\n",
+              "  .colab-df-quickchart {\n",
+              "      --bg-color: #E8F0FE;\n",
+              "      --fill-color: #1967D2;\n",
+              "      --hover-bg-color: #E2EBFA;\n",
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+              "      --disabled-fill-color: #AAA;\n",
+              "      --disabled-bg-color: #DDD;\n",
+              "  }\n",
+              "\n",
+              "  [theme=dark] .colab-df-quickchart {\n",
+              "      --bg-color: #3B4455;\n",
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+              "      --hover-bg-color: #434B5C;\n",
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+              "      --disabled-bg-color: #3B4455;\n",
+              "      --disabled-fill-color: #666;\n",
+              "  }\n",
+              "\n",
+              "  .colab-df-quickchart {\n",
+              "    background-color: var(--bg-color);\n",
+              "    border: none;\n",
+              "    border-radius: 50%;\n",
+              "    cursor: pointer;\n",
+              "    display: none;\n",
+              "    fill: var(--fill-color);\n",
+              "    height: 32px;\n",
+              "    padding: 0;\n",
+              "    width: 32px;\n",
+              "  }\n",
+              "\n",
+              "  .colab-df-quickchart:hover {\n",
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+              "    box-shadow: 0 1px 2px rgba(60, 64, 67, 0.3), 0 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
+              "    fill: var(--button-hover-fill-color);\n",
+              "  }\n",
+              "\n",
+              "  .colab-df-quickchart-complete:disabled,\n",
+              "  .colab-df-quickchart-complete:disabled:hover {\n",
+              "    background-color: var(--disabled-bg-color);\n",
+              "    fill: var(--disabled-fill-color);\n",
+              "    box-shadow: none;\n",
+              "  }\n",
+              "\n",
+              "  .colab-df-spinner {\n",
+              "    border: 2px solid var(--fill-color);\n",
+              "    border-color: transparent;\n",
+              "    border-bottom-color: var(--fill-color);\n",
+              "    animation:\n",
+              "      spin 1s steps(1) infinite;\n",
+              "  }\n",
+              "\n",
+              "  @keyframes spin {\n",
+              "    0% {\n",
+              "      border-color: transparent;\n",
+              "      border-bottom-color: var(--fill-color);\n",
+              "      border-left-color: var(--fill-color);\n",
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+              "      border-top-color: var(--fill-color);\n",
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+              "      border-right-color: var(--fill-color);\n",
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+              "    60% {\n",
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+              "      border-right-color: var(--fill-color);\n",
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+              "      border-color: transparent;\n",
+              "      border-right-color: var(--fill-color);\n",
+              "      border-bottom-color: var(--fill-color);\n",
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+              "      border-bottom-color: var(--fill-color);\n",
+              "    }\n",
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+              "</style>\n",
+              "\n",
+              "      <script>\n",
+              "        async function quickchart(key) {\n",
+              "          const quickchartButtonEl =\n",
+              "            document.querySelector('#' + key + ' button');\n",
+              "          quickchartButtonEl.disabled = true;  // To prevent multiple clicks.\n",
+              "          quickchartButtonEl.classList.add('colab-df-spinner');\n",
+              "          try {\n",
+              "            const charts = await google.colab.kernel.invokeFunction(\n",
+              "                'suggestCharts', [key], {});\n",
+              "          } catch (error) {\n",
+              "            console.error('Error during call to suggestCharts:', error);\n",
+              "          }\n",
+              "          quickchartButtonEl.classList.remove('colab-df-spinner');\n",
+              "          quickchartButtonEl.classList.add('colab-df-quickchart-complete');\n",
+              "        }\n",
+              "        (() => {\n",
+              "          let quickchartButtonEl =\n",
+              "            document.querySelector('#df-caa0b0f9-48b2-4f62-92dd-621174639240 button');\n",
+              "          quickchartButtonEl.style.display =\n",
+              "            google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
+              "        })();\n",
+              "      </script>\n",
+              "    </div>\n",
+              "\n",
+              "    </div>\n",
+              "  </div>\n"
+            ],
+            "application/vnd.google.colaboratory.intrinsic+json": {
+              "type": "dataframe",
+              "variable_name": "df_",
+              "summary": "{\n  \"name\": \"df_\",\n  \"rows\": 9704,\n  \"fields\": [\n    {\n      \"column\": \"engine_displacement\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 49,\n        \"min\": 10,\n        \"max\": 380,\n        \"num_unique_values\": 36,\n        \"samples\": [\n          30,\n          260,\n          90\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"horsepower\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 48.40118923604211,\n        \"min\": 0.0,\n        \"max\": 271.0,\n        \"num_unique_values\": 193,\n        \"samples\": [\n          199.0,\n          82.0,\n          189.0\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"vehicle_weight\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 497.8948600311838,\n        \"min\": 952.6817606436496,\n        \"max\": 4739.077089392099,\n        \"num_unique_values\": 9704,\n        \"samples\": [\n          2535.8875912388694,\n          2741.1704843893167,\n          2471.8802372627765\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"model_year\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 6,\n        \"min\": 2000,\n        \"max\": 2023,\n        \"num_unique_values\": 24,\n        \"samples\": [\n          2005,\n          2002,\n          2003\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"fuel_efficiency_mpg\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 2.5564677028974288,\n        \"min\": 6.200970533392815,\n        \"max\": 25.96722204888372,\n        \"num_unique_values\": 9704,\n        \"samples\": [\n          16.642943419221385,\n          16.298377150953442,\n          18.59182197290521\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    }\n  ]\n}"
+            }
+          },
+          "metadata": {},
+          "execution_count": 216
+        }
+      ]
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "X = df_.drop(columns=\"fuel_efficiency_mpg\")\n",
+        "y = df_[\"fuel_efficiency_mpg\"]"
+      ],
+      "metadata": {
+        "id": "5kALcG5KadAs"
+      },
+      "execution_count": 217,
+      "outputs": []
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "X_train, X_test, y_train, y_test = split_data(X, y, False, seed=9)"
+      ],
+      "metadata": {
+        "id": "KL7451XJZiZJ"
+      },
+      "execution_count": 218,
+      "outputs": []
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "model = train_ridge(X_tr=X_train, y_tr=y_train, r=0.001)\n",
+        "model"
+      ],
+      "metadata": {
+        "colab": {
+          "base_uri": "https://localhost:8080/",
+          "height": 80
+        },
+        "id": "lmIFBhiDbiET",
+        "outputId": "3d30c613-2a4c-4955-ed47-1cc6f374db79"
+      },
+      "execution_count": 219,
+      "outputs": [
+        {
+          "output_type": "execute_result",
+          "data": {
+            "text/plain": [
+              "Ridge(alpha=0.001)"
+            ],
+            "text/html": [
+              "<style>#sk-container-id-4 {\n",
+              "  /* Definition of color scheme common for light and dark mode */\n",
+              "  --sklearn-color-text: #000;\n",
+              "  --sklearn-color-text-muted: #666;\n",
+              "  --sklearn-color-line: gray;\n",
+              "  /* Definition of color scheme for unfitted estimators */\n",
+              "  --sklearn-color-unfitted-level-0: #fff5e6;\n",
+              "  --sklearn-color-unfitted-level-1: #f6e4d2;\n",
+              "  --sklearn-color-unfitted-level-2: #ffe0b3;\n",
+              "  --sklearn-color-unfitted-level-3: chocolate;\n",
+              "  /* Definition of color scheme for fitted estimators */\n",
+              "  --sklearn-color-fitted-level-0: #f0f8ff;\n",
+              "  --sklearn-color-fitted-level-1: #d4ebff;\n",
+              "  --sklearn-color-fitted-level-2: #b3dbfd;\n",
+              "  --sklearn-color-fitted-level-3: cornflowerblue;\n",
+              "\n",
+              "  /* Specific color for light theme */\n",
+              "  --sklearn-color-text-on-default-background: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, black)));\n",
+              "  --sklearn-color-background: var(--sg-background-color, var(--theme-background, var(--jp-layout-color0, white)));\n",
+              "  --sklearn-color-border-box: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, black)));\n",
+              "  --sklearn-color-icon: #696969;\n",
+              "\n",
+              "  @media (prefers-color-scheme: dark) {\n",
+              "    /* Redefinition of color scheme for dark theme */\n",
+              "    --sklearn-color-text-on-default-background: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, white)));\n",
+              "    --sklearn-color-background: var(--sg-background-color, var(--theme-background, var(--jp-layout-color0, #111)));\n",
+              "    --sklearn-color-border-box: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, white)));\n",
+              "    --sklearn-color-icon: #878787;\n",
+              "  }\n",
+              "}\n",
+              "\n",
+              "#sk-container-id-4 {\n",
+              "  color: var(--sklearn-color-text);\n",
+              "}\n",
+              "\n",
+              "#sk-container-id-4 pre {\n",
+              "  padding: 0;\n",
+              "}\n",
+              "\n",
+              "#sk-container-id-4 input.sk-hidden--visually {\n",
+              "  border: 0;\n",
+              "  clip: rect(1px 1px 1px 1px);\n",
+              "  clip: rect(1px, 1px, 1px, 1px);\n",
+              "  height: 1px;\n",
+              "  margin: -1px;\n",
+              "  overflow: hidden;\n",
+              "  padding: 0;\n",
+              "  position: absolute;\n",
+              "  width: 1px;\n",
+              "}\n",
+              "\n",
+              "#sk-container-id-4 div.sk-dashed-wrapped {\n",
+              "  border: 1px dashed var(--sklearn-color-line);\n",
+              "  margin: 0 0.4em 0.5em 0.4em;\n",
+              "  box-sizing: border-box;\n",
+              "  padding-bottom: 0.4em;\n",
+              "  background-color: var(--sklearn-color-background);\n",
+              "}\n",
+              "\n",
+              "#sk-container-id-4 div.sk-container {\n",
+              "  /* jupyter's `normalize.less` sets `[hidden] { display: none; }`\n",
+              "     but bootstrap.min.css set `[hidden] { display: none !important; }`\n",
+              "     so we also need the `!important` here to be able to override the\n",
+              "     default hidden behavior on the sphinx rendered scikit-learn.org.\n",
+              "     See: https://github.com/scikit-learn/scikit-learn/issues/21755 */\n",
+              "  display: inline-block !important;\n",
+              "  position: relative;\n",
+              "}\n",
+              "\n",
+              "#sk-container-id-4 div.sk-text-repr-fallback {\n",
+              "  display: none;\n",
+              "}\n",
+              "\n",
+              "div.sk-parallel-item,\n",
+              "div.sk-serial,\n",
+              "div.sk-item {\n",
+              "  /* draw centered vertical line to link estimators */\n",
+              "  background-image: linear-gradient(var(--sklearn-color-text-on-default-background), var(--sklearn-color-text-on-default-background));\n",
+              "  background-size: 2px 100%;\n",
+              "  background-repeat: no-repeat;\n",
+              "  background-position: center center;\n",
+              "}\n",
+              "\n",
+              "/* Parallel-specific style estimator block */\n",
+              "\n",
+              "#sk-container-id-4 div.sk-parallel-item::after {\n",
+              "  content: \"\";\n",
+              "  width: 100%;\n",
+              "  border-bottom: 2px solid var(--sklearn-color-text-on-default-background);\n",
+              "  flex-grow: 1;\n",
+              "}\n",
+              "\n",
+              "#sk-container-id-4 div.sk-parallel {\n",
+              "  display: flex;\n",
+              "  align-items: stretch;\n",
+              "  justify-content: center;\n",
+              "  background-color: var(--sklearn-color-background);\n",
+              "  position: relative;\n",
+              "}\n",
+              "\n",
+              "#sk-container-id-4 div.sk-parallel-item {\n",
+              "  display: flex;\n",
+              "  flex-direction: column;\n",
+              "}\n",
+              "\n",
+              "#sk-container-id-4 div.sk-parallel-item:first-child::after {\n",
+              "  align-self: flex-end;\n",
+              "  width: 50%;\n",
+              "}\n",
+              "\n",
+              "#sk-container-id-4 div.sk-parallel-item:last-child::after {\n",
+              "  align-self: flex-start;\n",
+              "  width: 50%;\n",
+              "}\n",
+              "\n",
+              "#sk-container-id-4 div.sk-parallel-item:only-child::after {\n",
+              "  width: 0;\n",
+              "}\n",
+              "\n",
+              "/* Serial-specific style estimator block */\n",
+              "\n",
+              "#sk-container-id-4 div.sk-serial {\n",
+              "  display: flex;\n",
+              "  flex-direction: column;\n",
+              "  align-items: center;\n",
+              "  background-color: var(--sklearn-color-background);\n",
+              "  padding-right: 1em;\n",
+              "  padding-left: 1em;\n",
+              "}\n",
+              "\n",
+              "\n",
+              "/* Toggleable style: style used for estimator/Pipeline/ColumnTransformer box that is\n",
+              "clickable and can be expanded/collapsed.\n",
+              "- Pipeline and ColumnTransformer use this feature and define the default style\n",
+              "- Estimators will overwrite some part of the style using the `sk-estimator` class\n",
+              "*/\n",
+              "\n",
+              "/* Pipeline and ColumnTransformer style (default) */\n",
+              "\n",
+              "#sk-container-id-4 div.sk-toggleable {\n",
+              "  /* Default theme specific background. It is overwritten whether we have a\n",
+              "  specific estimator or a Pipeline/ColumnTransformer */\n",
+              "  background-color: var(--sklearn-color-background);\n",
+              "}\n",
+              "\n",
+              "/* Toggleable label */\n",
+              "#sk-container-id-4 label.sk-toggleable__label {\n",
+              "  cursor: pointer;\n",
+              "  display: flex;\n",
+              "  width: 100%;\n",
+              "  margin-bottom: 0;\n",
+              "  padding: 0.5em;\n",
+              "  box-sizing: border-box;\n",
+              "  text-align: center;\n",
+              "  align-items: start;\n",
+              "  justify-content: space-between;\n",
+              "  gap: 0.5em;\n",
+              "}\n",
+              "\n",
+              "#sk-container-id-4 label.sk-toggleable__label .caption {\n",
+              "  font-size: 0.6rem;\n",
+              "  font-weight: lighter;\n",
+              "  color: var(--sklearn-color-text-muted);\n",
+              "}\n",
+              "\n",
+              "#sk-container-id-4 label.sk-toggleable__label-arrow:before {\n",
+              "  /* Arrow on the left of the label */\n",
+              "  content: \"▸\";\n",
+              "  float: left;\n",
+              "  margin-right: 0.25em;\n",
+              "  color: var(--sklearn-color-icon);\n",
+              "}\n",
+              "\n",
+              "#sk-container-id-4 label.sk-toggleable__label-arrow:hover:before {\n",
+              "  color: var(--sklearn-color-text);\n",
+              "}\n",
+              "\n",
+              "/* Toggleable content - dropdown */\n",
+              "\n",
+              "#sk-container-id-4 div.sk-toggleable__content {\n",
+              "  max-height: 0;\n",
+              "  max-width: 0;\n",
+              "  overflow: hidden;\n",
+              "  text-align: left;\n",
+              "  /* unfitted */\n",
+              "  background-color: var(--sklearn-color-unfitted-level-0);\n",
+              "}\n",
+              "\n",
+              "#sk-container-id-4 div.sk-toggleable__content.fitted {\n",
+              "  /* fitted */\n",
+              "  background-color: var(--sklearn-color-fitted-level-0);\n",
+              "}\n",
+              "\n",
+              "#sk-container-id-4 div.sk-toggleable__content pre {\n",
+              "  margin: 0.2em;\n",
+              "  border-radius: 0.25em;\n",
+              "  color: var(--sklearn-color-text);\n",
+              "  /* unfitted */\n",
+              "  background-color: var(--sklearn-color-unfitted-level-0);\n",
+              "}\n",
+              "\n",
+              "#sk-container-id-4 div.sk-toggleable__content.fitted pre {\n",
+              "  /* unfitted */\n",
+              "  background-color: var(--sklearn-color-fitted-level-0);\n",
+              "}\n",
+              "\n",
+              "#sk-container-id-4 input.sk-toggleable__control:checked~div.sk-toggleable__content {\n",
+              "  /* Expand drop-down */\n",
+              "  max-height: 200px;\n",
+              "  max-width: 100%;\n",
+              "  overflow: auto;\n",
+              "}\n",
+              "\n",
+              "#sk-container-id-4 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {\n",
+              "  content: \"▾\";\n",
+              "}\n",
+              "\n",
+              "/* Pipeline/ColumnTransformer-specific style */\n",
+              "\n",
+              "#sk-container-id-4 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
+              "  color: var(--sklearn-color-text);\n",
+              "  background-color: var(--sklearn-color-unfitted-level-2);\n",
+              "}\n",
+              "\n",
+              "#sk-container-id-4 div.sk-label.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
+              "  background-color: var(--sklearn-color-fitted-level-2);\n",
+              "}\n",
+              "\n",
+              "/* Estimator-specific style */\n",
+              "\n",
+              "/* Colorize estimator box */\n",
+              "#sk-container-id-4 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
+              "  /* unfitted */\n",
+              "  background-color: var(--sklearn-color-unfitted-level-2);\n",
+              "}\n",
+              "\n",
+              "#sk-container-id-4 div.sk-estimator.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
+              "  /* fitted */\n",
+              "  background-color: var(--sklearn-color-fitted-level-2);\n",
+              "}\n",
+              "\n",
+              "#sk-container-id-4 div.sk-label label.sk-toggleable__label,\n",
+              "#sk-container-id-4 div.sk-label label {\n",
+              "  /* The background is the default theme color */\n",
+              "  color: var(--sklearn-color-text-on-default-background);\n",
+              "}\n",
+              "\n",
+              "/* On hover, darken the color of the background */\n",
+              "#sk-container-id-4 div.sk-label:hover label.sk-toggleable__label {\n",
+              "  color: var(--sklearn-color-text);\n",
+              "  background-color: var(--sklearn-color-unfitted-level-2);\n",
+              "}\n",
+              "\n",
+              "/* Label box, darken color on hover, fitted */\n",
+              "#sk-container-id-4 div.sk-label.fitted:hover label.sk-toggleable__label.fitted {\n",
+              "  color: var(--sklearn-color-text);\n",
+              "  background-color: var(--sklearn-color-fitted-level-2);\n",
+              "}\n",
+              "\n",
+              "/* Estimator label */\n",
+              "\n",
+              "#sk-container-id-4 div.sk-label label {\n",
+              "  font-family: monospace;\n",
+              "  font-weight: bold;\n",
+              "  display: inline-block;\n",
+              "  line-height: 1.2em;\n",
+              "}\n",
+              "\n",
+              "#sk-container-id-4 div.sk-label-container {\n",
+              "  text-align: center;\n",
+              "}\n",
+              "\n",
+              "/* Estimator-specific */\n",
+              "#sk-container-id-4 div.sk-estimator {\n",
+              "  font-family: monospace;\n",
+              "  border: 1px dotted var(--sklearn-color-border-box);\n",
+              "  border-radius: 0.25em;\n",
+              "  box-sizing: border-box;\n",
+              "  margin-bottom: 0.5em;\n",
+              "  /* unfitted */\n",
+              "  background-color: var(--sklearn-color-unfitted-level-0);\n",
+              "}\n",
+              "\n",
+              "#sk-container-id-4 div.sk-estimator.fitted {\n",
+              "  /* fitted */\n",
+              "  background-color: var(--sklearn-color-fitted-level-0);\n",
+              "}\n",
+              "\n",
+              "/* on hover */\n",
+              "#sk-container-id-4 div.sk-estimator:hover {\n",
+              "  /* unfitted */\n",
+              "  background-color: var(--sklearn-color-unfitted-level-2);\n",
+              "}\n",
+              "\n",
+              "#sk-container-id-4 div.sk-estimator.fitted:hover {\n",
+              "  /* fitted */\n",
+              "  background-color: var(--sklearn-color-fitted-level-2);\n",
+              "}\n",
+              "\n",
+              "/* Specification for estimator info (e.g. \"i\" and \"?\") */\n",
+              "\n",
+              "/* Common style for \"i\" and \"?\" */\n",
+              "\n",
+              ".sk-estimator-doc-link,\n",
+              "a:link.sk-estimator-doc-link,\n",
+              "a:visited.sk-estimator-doc-link {\n",
+              "  float: right;\n",
+              "  font-size: smaller;\n",
+              "  line-height: 1em;\n",
+              "  font-family: monospace;\n",
+              "  background-color: var(--sklearn-color-background);\n",
+              "  border-radius: 1em;\n",
+              "  height: 1em;\n",
+              "  width: 1em;\n",
+              "  text-decoration: none !important;\n",
+              "  margin-left: 0.5em;\n",
+              "  text-align: center;\n",
+              "  /* unfitted */\n",
+              "  border: var(--sklearn-color-unfitted-level-1) 1pt solid;\n",
+              "  color: var(--sklearn-color-unfitted-level-1);\n",
+              "}\n",
+              "\n",
+              ".sk-estimator-doc-link.fitted,\n",
+              "a:link.sk-estimator-doc-link.fitted,\n",
+              "a:visited.sk-estimator-doc-link.fitted {\n",
+              "  /* fitted */\n",
+              "  border: var(--sklearn-color-fitted-level-1) 1pt solid;\n",
+              "  color: var(--sklearn-color-fitted-level-1);\n",
+              "}\n",
+              "\n",
+              "/* On hover */\n",
+              "div.sk-estimator:hover .sk-estimator-doc-link:hover,\n",
+              ".sk-estimator-doc-link:hover,\n",
+              "div.sk-label-container:hover .sk-estimator-doc-link:hover,\n",
+              ".sk-estimator-doc-link:hover {\n",
+              "  /* unfitted */\n",
+              "  background-color: var(--sklearn-color-unfitted-level-3);\n",
+              "  color: var(--sklearn-color-background);\n",
+              "  text-decoration: none;\n",
+              "}\n",
+              "\n",
+              "div.sk-estimator.fitted:hover .sk-estimator-doc-link.fitted:hover,\n",
+              ".sk-estimator-doc-link.fitted:hover,\n",
+              "div.sk-label-container:hover .sk-estimator-doc-link.fitted:hover,\n",
+              ".sk-estimator-doc-link.fitted:hover {\n",
+              "  /* fitted */\n",
+              "  background-color: var(--sklearn-color-fitted-level-3);\n",
+              "  color: var(--sklearn-color-background);\n",
+              "  text-decoration: none;\n",
+              "}\n",
+              "\n",
+              "/* Span, style for the box shown on hovering the info icon */\n",
+              ".sk-estimator-doc-link span {\n",
+              "  display: none;\n",
+              "  z-index: 9999;\n",
+              "  position: relative;\n",
+              "  font-weight: normal;\n",
+              "  right: .2ex;\n",
+              "  padding: .5ex;\n",
+              "  margin: .5ex;\n",
+              "  width: min-content;\n",
+              "  min-width: 20ex;\n",
+              "  max-width: 50ex;\n",
+              "  color: var(--sklearn-color-text);\n",
+              "  box-shadow: 2pt 2pt 4pt #999;\n",
+              "  /* unfitted */\n",
+              "  background: var(--sklearn-color-unfitted-level-0);\n",
+              "  border: .5pt solid var(--sklearn-color-unfitted-level-3);\n",
+              "}\n",
+              "\n",
+              ".sk-estimator-doc-link.fitted span {\n",
+              "  /* fitted */\n",
+              "  background: var(--sklearn-color-fitted-level-0);\n",
+              "  border: var(--sklearn-color-fitted-level-3);\n",
+              "}\n",
+              "\n",
+              ".sk-estimator-doc-link:hover span {\n",
+              "  display: block;\n",
+              "}\n",
+              "\n",
+              "/* \"?\"-specific style due to the `<a>` HTML tag */\n",
+              "\n",
+              "#sk-container-id-4 a.estimator_doc_link {\n",
+              "  float: right;\n",
+              "  font-size: 1rem;\n",
+              "  line-height: 1em;\n",
+              "  font-family: monospace;\n",
+              "  background-color: var(--sklearn-color-background);\n",
+              "  border-radius: 1rem;\n",
+              "  height: 1rem;\n",
+              "  width: 1rem;\n",
+              "  text-decoration: none;\n",
+              "  /* unfitted */\n",
+              "  color: var(--sklearn-color-unfitted-level-1);\n",
+              "  border: var(--sklearn-color-unfitted-level-1) 1pt solid;\n",
+              "}\n",
+              "\n",
+              "#sk-container-id-4 a.estimator_doc_link.fitted {\n",
+              "  /* fitted */\n",
+              "  border: var(--sklearn-color-fitted-level-1) 1pt solid;\n",
+              "  color: var(--sklearn-color-fitted-level-1);\n",
+              "}\n",
+              "\n",
+              "/* On hover */\n",
+              "#sk-container-id-4 a.estimator_doc_link:hover {\n",
+              "  /* unfitted */\n",
+              "  background-color: var(--sklearn-color-unfitted-level-3);\n",
+              "  color: var(--sklearn-color-background);\n",
+              "  text-decoration: none;\n",
+              "}\n",
+              "\n",
+              "#sk-container-id-4 a.estimator_doc_link.fitted:hover {\n",
+              "  /* fitted */\n",
+              "  background-color: var(--sklearn-color-fitted-level-3);\n",
+              "}\n",
+              "</style><div id=\"sk-container-id-4\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>Ridge(alpha=0.001)</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item\"><div class=\"sk-estimator fitted sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-4\" type=\"checkbox\" checked><label for=\"sk-estimator-id-4\" class=\"sk-toggleable__label fitted sk-toggleable__label-arrow\"><div><div>Ridge</div></div><div><a class=\"sk-estimator-doc-link fitted\" rel=\"noreferrer\" target=\"_blank\" href=\"https://scikit-learn.org/1.6/modules/generated/sklearn.linear_model.Ridge.html\">?<span>Documentation for Ridge</span></a><span class=\"sk-estimator-doc-link fitted\">i<span>Fitted</span></span></div></label><div class=\"sk-toggleable__content fitted\"><pre>Ridge(alpha=0.001)</pre></div> </div></div></div></div>"
+            ]
+          },
+          "metadata": {},
+          "execution_count": 219
+        }
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "source": [
+        "## Let's see the error on the test data"
+      ],
+      "metadata": {
+        "id": "EQ7vhHswcqbm"
+      }
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "y_pred_test = model.predict(X_test)\n",
+        "rmse(y_test, y_pred_test)"
+      ],
+      "metadata": {
+        "colab": {
+          "base_uri": "https://localhost:8080/"
+        },
+        "id": "x3oRNJf8bxDw",
+        "outputId": "fa2a2fc5-4e55-462e-c89c-5b04961a304d"
+      },
+      "execution_count": 220,
+      "outputs": [
+        {
+          "output_type": "execute_result",
+          "data": {
+            "text/plain": [
+              "0.520226928799458"
+            ]
+          },
+          "metadata": {},
+          "execution_count": 220
+        }
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "source": [
+        "## The error on the test set is still pretty reasonable compared to the training and validation sets. For now, looks good!"
+      ],
+      "metadata": {
+        "id": "N5U4gLN7cvBC"
+      }
+    },
+    {
+      "cell_type": "code",
+      "source": [],
+      "metadata": {
+        "id": "ZHYeAUJ0cFjH"
+      },
+      "execution_count": 213,
+      "outputs": []
+    }
+  ]
+}
\ No newline at end of file