diff --git "a/Fraud_Detection.ipynb" "b/Fraud_Detection.ipynb"
new file mode 100644--- /dev/null
+++ "b/Fraud_Detection.ipynb"
@@ -0,0 +1,2434 @@
+{
+  "cells": [
+    {
+      "cell_type": "markdown",
+      "metadata": {
+        "id": "nh8RwuXJMg6p"
+      },
+      "source": [
+        "Dependencies Import\n"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": 1,
+      "metadata": {
+        "id": "9u2Mg5v9MxcD"
+      },
+      "outputs": [],
+      "source": [
+        "# this code will import all the libraries that we need for this model.\n",
+        "import numpy as np\n",
+        "import pandas as pd\n",
+        "from matplotlib import pyplot as plt\n",
+        "from sklearn.model_selection import train_test_split\n",
+        "from sklearn.linear_model import LogisticRegression\n",
+        "from sklearn.metrics import accuracy_score"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": 8,
+      "metadata": {
+        "id": "O_fDIYrVmjcO"
+      },
+      "outputs": [],
+      "source": [
+        "# read the dataset that is holding the information for the credit card\n",
+        "# transactions.\n",
+        "credit_card_data = pd.read_csv('creditcard.csv')"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": 9,
+      "metadata": {
+        "colab": {
+          "base_uri": "https://localhost:8080/",
+          "height": 256
+        },
+        "id": "4Rytoup0m7Gd",
+        "outputId": "a7b44d70-6afa-4048-f14f-998ad8417b1c"
+      },
+      "outputs": [
+        {
+          "data": {
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+              "<table border=\"1\" class=\"dataframe\">\n",
+              "  <thead>\n",
+              "    <tr style=\"text-align: right;\">\n",
+              "      <th></th>\n",
+              "      <th>Time</th>\n",
+              "      <th>V1</th>\n",
+              "      <th>V2</th>\n",
+              "      <th>V3</th>\n",
+              "      <th>V4</th>\n",
+              "      <th>V5</th>\n",
+              "      <th>V6</th>\n",
+              "      <th>V7</th>\n",
+              "      <th>V8</th>\n",
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+              "      <th>...</th>\n",
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+              "      <th>V27</th>\n",
+              "      <th>V28</th>\n",
+              "      <th>Amount</th>\n",
+              "      <th>Class</th>\n",
+              "    </tr>\n",
+              "  </thead>\n",
+              "  <tbody>\n",
+              "    <tr>\n",
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+              "      <td>0.462388</td>\n",
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+              "      <td>0</td>\n",
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+              "      <td>0.266151</td>\n",
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+              "      <td>2.69</td>\n",
+              "      <td>0</td>\n",
+              "    </tr>\n",
+              "    <tr>\n",
+              "      <th>2</th>\n",
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+              "      <td>-1.358354</td>\n",
+              "      <td>-1.340163</td>\n",
+              "      <td>1.773209</td>\n",
+              "      <td>0.379780</td>\n",
+              "      <td>-0.503198</td>\n",
+              "      <td>1.800499</td>\n",
+              "      <td>0.791461</td>\n",
+              "      <td>0.247676</td>\n",
+              "      <td>-1.514654</td>\n",
+              "      <td>...</td>\n",
+              "      <td>0.247998</td>\n",
+              "      <td>0.771679</td>\n",
+              "      <td>0.909412</td>\n",
+              "      <td>-0.689281</td>\n",
+              "      <td>-0.327642</td>\n",
+              "      <td>-0.139097</td>\n",
+              "      <td>-0.055353</td>\n",
+              "      <td>-0.059752</td>\n",
+              "      <td>378.66</td>\n",
+              "      <td>0</td>\n",
+              "    </tr>\n",
+              "    <tr>\n",
+              "      <th>3</th>\n",
+              "      <td>1.0</td>\n",
+              "      <td>-0.966272</td>\n",
+              "      <td>-0.185226</td>\n",
+              "      <td>1.792993</td>\n",
+              "      <td>-0.863291</td>\n",
+              "      <td>-0.010309</td>\n",
+              "      <td>1.247203</td>\n",
+              "      <td>0.237609</td>\n",
+              "      <td>0.377436</td>\n",
+              "      <td>-1.387024</td>\n",
+              "      <td>...</td>\n",
+              "      <td>-0.108300</td>\n",
+              "      <td>0.005274</td>\n",
+              "      <td>-0.190321</td>\n",
+              "      <td>-1.175575</td>\n",
+              "      <td>0.647376</td>\n",
+              "      <td>-0.221929</td>\n",
+              "      <td>0.062723</td>\n",
+              "      <td>0.061458</td>\n",
+              "      <td>123.50</td>\n",
+              "      <td>0</td>\n",
+              "    </tr>\n",
+              "    <tr>\n",
+              "      <th>4</th>\n",
+              "      <td>2.0</td>\n",
+              "      <td>-1.158233</td>\n",
+              "      <td>0.877737</td>\n",
+              "      <td>1.548718</td>\n",
+              "      <td>0.403034</td>\n",
+              "      <td>-0.407193</td>\n",
+              "      <td>0.095921</td>\n",
+              "      <td>0.592941</td>\n",
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+              "      <td>0.817739</td>\n",
+              "      <td>...</td>\n",
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+              "      <td>0.798278</td>\n",
+              "      <td>-0.137458</td>\n",
+              "      <td>0.141267</td>\n",
+              "      <td>-0.206010</td>\n",
+              "      <td>0.502292</td>\n",
+              "      <td>0.219422</td>\n",
+              "      <td>0.215153</td>\n",
+              "      <td>69.99</td>\n",
+              "      <td>0</td>\n",
+              "    </tr>\n",
+              "  </tbody>\n",
+              "</table>\n",
+              "<p>5 rows × 31 columns</p>\n",
+              "</div>"
+            ],
+            "text/plain": [
+              "   Time        V1        V2        V3        V4        V5        V6        V7  \\\n",
+              "0   0.0 -1.359807 -0.072781  2.536347  1.378155 -0.338321  0.462388  0.239599   \n",
+              "1   0.0  1.191857  0.266151  0.166480  0.448154  0.060018 -0.082361 -0.078803   \n",
+              "2   1.0 -1.358354 -1.340163  1.773209  0.379780 -0.503198  1.800499  0.791461   \n",
+              "3   1.0 -0.966272 -0.185226  1.792993 -0.863291 -0.010309  1.247203  0.237609   \n",
+              "4   2.0 -1.158233  0.877737  1.548718  0.403034 -0.407193  0.095921  0.592941   \n",
+              "\n",
+              "         V8        V9  ...       V21       V22       V23       V24       V25  \\\n",
+              "0  0.098698  0.363787  ... -0.018307  0.277838 -0.110474  0.066928  0.128539   \n",
+              "1  0.085102 -0.255425  ... -0.225775 -0.638672  0.101288 -0.339846  0.167170   \n",
+              "2  0.247676 -1.514654  ...  0.247998  0.771679  0.909412 -0.689281 -0.327642   \n",
+              "3  0.377436 -1.387024  ... -0.108300  0.005274 -0.190321 -1.175575  0.647376   \n",
+              "4 -0.270533  0.817739  ... -0.009431  0.798278 -0.137458  0.141267 -0.206010   \n",
+              "\n",
+              "        V26       V27       V28  Amount  Class  \n",
+              "0 -0.189115  0.133558 -0.021053  149.62      0  \n",
+              "1  0.125895 -0.008983  0.014724    2.69      0  \n",
+              "2 -0.139097 -0.055353 -0.059752  378.66      0  \n",
+              "3 -0.221929  0.062723  0.061458  123.50      0  \n",
+              "4  0.502292  0.219422  0.215153   69.99      0  \n",
+              "\n",
+              "[5 rows x 31 columns]"
+            ]
+          },
+          "execution_count": 9,
+          "metadata": {},
+          "output_type": "execute_result"
+        }
+      ],
+      "source": [
+        "# this will display the first 5 rows of the dataset.\n",
+        "credit_card_data.head()"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": 10,
+      "metadata": {
+        "colab": {
+          "base_uri": "https://localhost:8080/",
+          "height": 256
+        },
+        "id": "IJ_IsflInDQc",
+        "outputId": "8990db4d-0d1f-48d3-d3ea-918951f8160d"
+      },
+      "outputs": [
+        {
+          "data": {
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+              "      <th></th>\n",
+              "      <th>Time</th>\n",
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+              "      <td>-4.918215</td>\n",
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+              "      <td>1.914428</td>\n",
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+              "      <td>0.250034</td>\n",
+              "      <td>0.943651</td>\n",
+              "      <td>0.823731</td>\n",
+              "      <td>0.77</td>\n",
+              "      <td>0</td>\n",
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+              "      <td>172787.0</td>\n",
+              "      <td>-0.732789</td>\n",
+              "      <td>-0.055080</td>\n",
+              "      <td>2.035030</td>\n",
+              "      <td>-0.738589</td>\n",
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+              "      <td>1.058415</td>\n",
+              "      <td>0.024330</td>\n",
+              "      <td>0.294869</td>\n",
+              "      <td>0.584800</td>\n",
+              "      <td>...</td>\n",
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+              "      <td>0.924384</td>\n",
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+              "      <td>-0.395255</td>\n",
+              "      <td>0.068472</td>\n",
+              "      <td>-0.053527</td>\n",
+              "      <td>24.79</td>\n",
+              "      <td>0</td>\n",
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+              "    <tr>\n",
+              "      <th>284804</th>\n",
+              "      <td>172788.0</td>\n",
+              "      <td>1.919565</td>\n",
+              "      <td>-0.301254</td>\n",
+              "      <td>-3.249640</td>\n",
+              "      <td>-0.557828</td>\n",
+              "      <td>2.630515</td>\n",
+              "      <td>3.031260</td>\n",
+              "      <td>-0.296827</td>\n",
+              "      <td>0.708417</td>\n",
+              "      <td>0.432454</td>\n",
+              "      <td>...</td>\n",
+              "      <td>0.232045</td>\n",
+              "      <td>0.578229</td>\n",
+              "      <td>-0.037501</td>\n",
+              "      <td>0.640134</td>\n",
+              "      <td>0.265745</td>\n",
+              "      <td>-0.087371</td>\n",
+              "      <td>0.004455</td>\n",
+              "      <td>-0.026561</td>\n",
+              "      <td>67.88</td>\n",
+              "      <td>0</td>\n",
+              "    </tr>\n",
+              "    <tr>\n",
+              "      <th>284805</th>\n",
+              "      <td>172788.0</td>\n",
+              "      <td>-0.240440</td>\n",
+              "      <td>0.530483</td>\n",
+              "      <td>0.702510</td>\n",
+              "      <td>0.689799</td>\n",
+              "      <td>-0.377961</td>\n",
+              "      <td>0.623708</td>\n",
+              "      <td>-0.686180</td>\n",
+              "      <td>0.679145</td>\n",
+              "      <td>0.392087</td>\n",
+              "      <td>...</td>\n",
+              "      <td>0.265245</td>\n",
+              "      <td>0.800049</td>\n",
+              "      <td>-0.163298</td>\n",
+              "      <td>0.123205</td>\n",
+              "      <td>-0.569159</td>\n",
+              "      <td>0.546668</td>\n",
+              "      <td>0.108821</td>\n",
+              "      <td>0.104533</td>\n",
+              "      <td>10.00</td>\n",
+              "      <td>0</td>\n",
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+              "    <tr>\n",
+              "      <th>284806</th>\n",
+              "      <td>172792.0</td>\n",
+              "      <td>-0.533413</td>\n",
+              "      <td>-0.189733</td>\n",
+              "      <td>0.703337</td>\n",
+              "      <td>-0.506271</td>\n",
+              "      <td>-0.012546</td>\n",
+              "      <td>-0.649617</td>\n",
+              "      <td>1.577006</td>\n",
+              "      <td>-0.414650</td>\n",
+              "      <td>0.486180</td>\n",
+              "      <td>...</td>\n",
+              "      <td>0.261057</td>\n",
+              "      <td>0.643078</td>\n",
+              "      <td>0.376777</td>\n",
+              "      <td>0.008797</td>\n",
+              "      <td>-0.473649</td>\n",
+              "      <td>-0.818267</td>\n",
+              "      <td>-0.002415</td>\n",
+              "      <td>0.013649</td>\n",
+              "      <td>217.00</td>\n",
+              "      <td>0</td>\n",
+              "    </tr>\n",
+              "  </tbody>\n",
+              "</table>\n",
+              "<p>5 rows × 31 columns</p>\n",
+              "</div>"
+            ],
+            "text/plain": [
+              "            Time         V1         V2        V3        V4        V5  \\\n",
+              "284802  172786.0 -11.881118  10.071785 -9.834783 -2.066656 -5.364473   \n",
+              "284803  172787.0  -0.732789  -0.055080  2.035030 -0.738589  0.868229   \n",
+              "284804  172788.0   1.919565  -0.301254 -3.249640 -0.557828  2.630515   \n",
+              "284805  172788.0  -0.240440   0.530483  0.702510  0.689799 -0.377961   \n",
+              "284806  172792.0  -0.533413  -0.189733  0.703337 -0.506271 -0.012546   \n",
+              "\n",
+              "              V6        V7        V8        V9  ...       V21       V22  \\\n",
+              "284802 -2.606837 -4.918215  7.305334  1.914428  ...  0.213454  0.111864   \n",
+              "284803  1.058415  0.024330  0.294869  0.584800  ...  0.214205  0.924384   \n",
+              "284804  3.031260 -0.296827  0.708417  0.432454  ...  0.232045  0.578229   \n",
+              "284805  0.623708 -0.686180  0.679145  0.392087  ...  0.265245  0.800049   \n",
+              "284806 -0.649617  1.577006 -0.414650  0.486180  ...  0.261057  0.643078   \n",
+              "\n",
+              "             V23       V24       V25       V26       V27       V28  Amount  \\\n",
+              "284802  1.014480 -0.509348  1.436807  0.250034  0.943651  0.823731    0.77   \n",
+              "284803  0.012463 -1.016226 -0.606624 -0.395255  0.068472 -0.053527   24.79   \n",
+              "284804 -0.037501  0.640134  0.265745 -0.087371  0.004455 -0.026561   67.88   \n",
+              "284805 -0.163298  0.123205 -0.569159  0.546668  0.108821  0.104533   10.00   \n",
+              "284806  0.376777  0.008797 -0.473649 -0.818267 -0.002415  0.013649  217.00   \n",
+              "\n",
+              "        Class  \n",
+              "284802      0  \n",
+              "284803      0  \n",
+              "284804      0  \n",
+              "284805      0  \n",
+              "284806      0  \n",
+              "\n",
+              "[5 rows x 31 columns]"
+            ]
+          },
+          "execution_count": 10,
+          "metadata": {},
+          "output_type": "execute_result"
+        }
+      ],
+      "source": [
+        "# this will display the last 5 rows of the dataset.\n",
+        "credit_card_data.tail()"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": 11,
+      "metadata": {
+        "colab": {
+          "base_uri": "https://localhost:8080/"
+        },
+        "id": "m0SvHGpcpjs1",
+        "outputId": "064c8080-e564-4c88-8514-04fd41deb663"
+      },
+      "outputs": [
+        {
+          "name": "stdout",
+          "output_type": "stream",
+          "text": [
+            "<class 'pandas.core.frame.DataFrame'>\n",
+            "RangeIndex: 284807 entries, 0 to 284806\n",
+            "Data columns (total 31 columns):\n",
+            " #   Column  Non-Null Count   Dtype  \n",
+            "---  ------  --------------   -----  \n",
+            " 0   Time    284807 non-null  float64\n",
+            " 1   V1      284807 non-null  float64\n",
+            " 2   V2      284807 non-null  float64\n",
+            " 3   V3      284807 non-null  float64\n",
+            " 4   V4      284807 non-null  float64\n",
+            " 5   V5      284807 non-null  float64\n",
+            " 6   V6      284807 non-null  float64\n",
+            " 7   V7      284807 non-null  float64\n",
+            " 8   V8      284807 non-null  float64\n",
+            " 9   V9      284807 non-null  float64\n",
+            " 10  V10     284807 non-null  float64\n",
+            " 11  V11     284807 non-null  float64\n",
+            " 12  V12     284807 non-null  float64\n",
+            " 13  V13     284807 non-null  float64\n",
+            " 14  V14     284807 non-null  float64\n",
+            " 15  V15     284807 non-null  float64\n",
+            " 16  V16     284807 non-null  float64\n",
+            " 17  V17     284807 non-null  float64\n",
+            " 18  V18     284807 non-null  float64\n",
+            " 19  V19     284807 non-null  float64\n",
+            " 20  V20     284807 non-null  float64\n",
+            " 21  V21     284807 non-null  float64\n",
+            " 22  V22     284807 non-null  float64\n",
+            " 23  V23     284807 non-null  float64\n",
+            " 24  V24     284807 non-null  float64\n",
+            " 25  V25     284807 non-null  float64\n",
+            " 26  V26     284807 non-null  float64\n",
+            " 27  V27     284807 non-null  float64\n",
+            " 28  V28     284807 non-null  float64\n",
+            " 29  Amount  284807 non-null  float64\n",
+            " 30  Class   284807 non-null  int64  \n",
+            "dtypes: float64(30), int64(1)\n",
+            "memory usage: 67.4 MB\n"
+          ]
+        }
+      ],
+      "source": [
+        "# information about the dataset showcasing the datatypes used and whether the\n",
+        "#dataset contains null values or not.\n",
+        "credit_card_data.info()"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": 12,
+      "metadata": {
+        "colab": {
+          "base_uri": "https://localhost:8080/"
+        },
+        "id": "NU32ZenZqCH6",
+        "outputId": "e22998c6-591a-427d-8026-a7e6a5fedc2e"
+      },
+      "outputs": [
+        {
+          "data": {
+            "text/plain": [
+              "Time      0\n",
+              "V1        0\n",
+              "V2        0\n",
+              "V3        0\n",
+              "V4        0\n",
+              "V5        0\n",
+              "V6        0\n",
+              "V7        0\n",
+              "V8        0\n",
+              "V9        0\n",
+              "V10       0\n",
+              "V11       0\n",
+              "V12       0\n",
+              "V13       0\n",
+              "V14       0\n",
+              "V15       0\n",
+              "V16       0\n",
+              "V17       0\n",
+              "V18       0\n",
+              "V19       0\n",
+              "V20       0\n",
+              "V21       0\n",
+              "V22       0\n",
+              "V23       0\n",
+              "V24       0\n",
+              "V25       0\n",
+              "V26       0\n",
+              "V27       0\n",
+              "V28       0\n",
+              "Amount    0\n",
+              "Class     0\n",
+              "dtype: int64"
+            ]
+          },
+          "execution_count": 12,
+          "metadata": {},
+          "output_type": "execute_result"
+        }
+      ],
+      "source": [
+        "# check for the number of missing values on each column.\n",
+        "credit_card_data.isnull().sum()"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": 13,
+      "metadata": {
+        "colab": {
+          "base_uri": "https://localhost:8080/"
+        },
+        "id": "Ui6hiIkMqQNs",
+        "outputId": "143e95a6-2065-4bc1-cb04-98c79caac2ab"
+      },
+      "outputs": [
+        {
+          "data": {
+            "text/plain": [
+              "Class\n",
+              "0    284315\n",
+              "1       492\n",
+              "Name: count, dtype: int64"
+            ]
+          },
+          "execution_count": 13,
+          "metadata": {},
+          "output_type": "execute_result"
+        }
+      ],
+      "source": [
+        "# check the distribution between acceptable transaction and fraudulent transaction.\n",
+        "credit_card_data['Class'].value_counts()"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+        "id": "WJo6c7ESs1JV"
+      },
+      "source": [
+        "Looking at the above values it shows that the dataset is very unstable and inbalanced."
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+        "id": "-R19R7eeq202"
+      },
+      "source": [
+        "0---> would represent acceptable transaction\n",
+        "\n",
+        "1---> would the represent fradulent transaction."
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": 14,
+      "metadata": {
+        "id": "XqcM9-T8rs2b"
+      },
+      "outputs": [],
+      "source": [
+        "# data seperation for analysis.\n",
+        "acceptable = credit_card_data[credit_card_data.Class == 0]\n",
+        "fraudulent = credit_card_data[credit_card_data.Class == 1]"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": 15,
+      "metadata": {
+        "colab": {
+          "base_uri": "https://localhost:8080/"
+        },
+        "id": "hbW83hntr51b",
+        "outputId": "0b363260-b65b-449c-fc9f-bbdda054bb11"
+      },
+      "outputs": [
+        {
+          "name": "stdout",
+          "output_type": "stream",
+          "text": [
+            "(284315, 31)\n",
+            "(492, 31)\n"
+          ]
+        }
+      ],
+      "source": [
+        "print(acceptable.shape)\n",
+        "print(fraudulent.shape)"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": 16,
+      "metadata": {
+        "colab": {
+          "base_uri": "https://localhost:8080/"
+        },
+        "id": "0mZn4ZWstJKy",
+        "outputId": "aa58edd1-a752-4235-8b96-9902ad98b3b3"
+      },
+      "outputs": [
+        {
+          "data": {
+            "text/plain": [
+              "count    284315.000000\n",
+              "mean         88.291022\n",
+              "std         250.105092\n",
+              "min           0.000000\n",
+              "25%           5.650000\n",
+              "50%          22.000000\n",
+              "75%          77.050000\n",
+              "max       25691.160000\n",
+              "Name: Amount, dtype: float64"
+            ]
+          },
+          "execution_count": 16,
+          "metadata": {},
+          "output_type": "execute_result"
+        }
+      ],
+      "source": [
+        "# statistical measures.\n",
+        "acceptable.Amount.describe()"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": 17,
+      "metadata": {
+        "colab": {
+          "base_uri": "https://localhost:8080/"
+        },
+        "id": "3KsBbYA-tZ4k",
+        "outputId": "e9f7d531-5e55-4eb0-8c17-51b2288f75f4"
+      },
+      "outputs": [
+        {
+          "data": {
+            "text/plain": [
+              "count     492.000000\n",
+              "mean      122.211321\n",
+              "std       256.683288\n",
+              "min         0.000000\n",
+              "25%         1.000000\n",
+              "50%         9.250000\n",
+              "75%       105.890000\n",
+              "max      2125.870000\n",
+              "Name: Amount, dtype: float64"
+            ]
+          },
+          "execution_count": 17,
+          "metadata": {},
+          "output_type": "execute_result"
+        }
+      ],
+      "source": [
+        "fraudulent.Amount.describe()"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": 18,
+      "metadata": {
+        "colab": {
+          "base_uri": "https://localhost:8080/",
+          "height": 193
+        },
+        "id": "FQj8FwYXt4v5",
+        "outputId": "8a887195-36c3-49a4-cf36-e1e65ec4190c"
+      },
+      "outputs": [
+        {
+          "data": {
+            "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>Time</th>\n",
+              "      <th>V1</th>\n",
+              "      <th>V2</th>\n",
+              "      <th>V3</th>\n",
+              "      <th>V4</th>\n",
+              "      <th>V5</th>\n",
+              "      <th>V6</th>\n",
+              "      <th>V7</th>\n",
+              "      <th>V8</th>\n",
+              "      <th>V9</th>\n",
+              "      <th>...</th>\n",
+              "      <th>V20</th>\n",
+              "      <th>V21</th>\n",
+              "      <th>V22</th>\n",
+              "      <th>V23</th>\n",
+              "      <th>V24</th>\n",
+              "      <th>V25</th>\n",
+              "      <th>V26</th>\n",
+              "      <th>V27</th>\n",
+              "      <th>V28</th>\n",
+              "      <th>Amount</th>\n",
+              "    </tr>\n",
+              "    <tr>\n",
+              "      <th>Class</th>\n",
+              "      <th></th>\n",
+              "      <th></th>\n",
+              "      <th></th>\n",
+              "      <th></th>\n",
+              "      <th></th>\n",
+              "      <th></th>\n",
+              "      <th></th>\n",
+              "      <th></th>\n",
+              "      <th></th>\n",
+              "      <th></th>\n",
+              "      <th></th>\n",
+              "      <th></th>\n",
+              "      <th></th>\n",
+              "      <th></th>\n",
+              "      <th></th>\n",
+              "      <th></th>\n",
+              "      <th></th>\n",
+              "      <th></th>\n",
+              "      <th></th>\n",
+              "      <th></th>\n",
+              "      <th></th>\n",
+              "    </tr>\n",
+              "  </thead>\n",
+              "  <tbody>\n",
+              "    <tr>\n",
+              "      <th>0</th>\n",
+              "      <td>94838.202258</td>\n",
+              "      <td>0.008258</td>\n",
+              "      <td>-0.006271</td>\n",
+              "      <td>0.012171</td>\n",
+              "      <td>-0.007860</td>\n",
+              "      <td>0.005453</td>\n",
+              "      <td>0.002419</td>\n",
+              "      <td>0.009637</td>\n",
+              "      <td>-0.000987</td>\n",
+              "      <td>0.004467</td>\n",
+              "      <td>...</td>\n",
+              "      <td>-0.000644</td>\n",
+              "      <td>-0.001235</td>\n",
+              "      <td>-0.000024</td>\n",
+              "      <td>0.000070</td>\n",
+              "      <td>0.000182</td>\n",
+              "      <td>-0.000072</td>\n",
+              "      <td>-0.000089</td>\n",
+              "      <td>-0.000295</td>\n",
+              "      <td>-0.000131</td>\n",
+              "      <td>88.291022</td>\n",
+              "    </tr>\n",
+              "    <tr>\n",
+              "      <th>1</th>\n",
+              "      <td>80746.806911</td>\n",
+              "      <td>-4.771948</td>\n",
+              "      <td>3.623778</td>\n",
+              "      <td>-7.033281</td>\n",
+              "      <td>4.542029</td>\n",
+              "      <td>-3.151225</td>\n",
+              "      <td>-1.397737</td>\n",
+              "      <td>-5.568731</td>\n",
+              "      <td>0.570636</td>\n",
+              "      <td>-2.581123</td>\n",
+              "      <td>...</td>\n",
+              "      <td>0.372319</td>\n",
+              "      <td>0.713588</td>\n",
+              "      <td>0.014049</td>\n",
+              "      <td>-0.040308</td>\n",
+              "      <td>-0.105130</td>\n",
+              "      <td>0.041449</td>\n",
+              "      <td>0.051648</td>\n",
+              "      <td>0.170575</td>\n",
+              "      <td>0.075667</td>\n",
+              "      <td>122.211321</td>\n",
+              "    </tr>\n",
+              "  </tbody>\n",
+              "</table>\n",
+              "<p>2 rows × 30 columns</p>\n",
+              "</div>"
+            ],
+            "text/plain": [
+              "               Time        V1        V2        V3        V4        V5  \\\n",
+              "Class                                                                   \n",
+              "0      94838.202258  0.008258 -0.006271  0.012171 -0.007860  0.005453   \n",
+              "1      80746.806911 -4.771948  3.623778 -7.033281  4.542029 -3.151225   \n",
+              "\n",
+              "             V6        V7        V8        V9  ...       V20       V21  \\\n",
+              "Class                                          ...                       \n",
+              "0      0.002419  0.009637 -0.000987  0.004467  ... -0.000644 -0.001235   \n",
+              "1     -1.397737 -5.568731  0.570636 -2.581123  ...  0.372319  0.713588   \n",
+              "\n",
+              "            V22       V23       V24       V25       V26       V27       V28  \\\n",
+              "Class                                                                         \n",
+              "0     -0.000024  0.000070  0.000182 -0.000072 -0.000089 -0.000295 -0.000131   \n",
+              "1      0.014049 -0.040308 -0.105130  0.041449  0.051648  0.170575  0.075667   \n",
+              "\n",
+              "           Amount  \n",
+              "Class              \n",
+              "0       88.291022  \n",
+              "1      122.211321  \n",
+              "\n",
+              "[2 rows x 30 columns]"
+            ]
+          },
+          "execution_count": 18,
+          "metadata": {},
+          "output_type": "execute_result"
+        }
+      ],
+      "source": [
+        "# value comparison of both transactions.\n",
+        "credit_card_data.groupby('Class').mean()"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+        "id": "jqC4ru07uV7e"
+      },
+      "source": [
+        "Data Sampling"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": 19,
+      "metadata": {
+        "colab": {
+          "base_uri": "https://localhost:8080/"
+        },
+        "id": "rwFSIIBUugNW",
+        "outputId": "7d1990bf-c955-4a08-e708-390d0ba5b394"
+      },
+      "outputs": [
+        {
+          "name": "stdout",
+          "output_type": "stream",
+          "text": [
+            "99.82725143693798\n",
+            "0.1727485630620034\n"
+          ]
+        }
+      ],
+      "source": [
+        "# before sampling the dataset...\n",
+        "# calculate the percentage of both the acceptable and fraudulent transactions of\n",
+        "# the dataset.\n",
+        "classes=credit_card_data['Class'].value_counts()\n",
+        "acceptable_percent=classes[0]/credit_card_data['Class'].count()*100\n",
+        "fraudulent_percent=classes[1]/credit_card_data['Class'].count()*100\n",
+        "print(acceptable_percent)\n",
+        "print(fraudulent_percent)"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": 20,
+      "metadata": {
+        "colab": {
+          "base_uri": "https://localhost:8080/",
+          "height": 472
+        },
+        "id": "-LtU3QNczM0H",
+        "outputId": "c5555535-2d60-4523-ac45-a0650f554cc7"
+      },
+      "outputs": [
+        {
+          "data": {
+            "image/png": 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",
+            "text/plain": [
+              "<Figure size 640x480 with 1 Axes>"
+            ]
+          },
+          "metadata": {},
+          "output_type": "display_data"
+        }
+      ],
+      "source": [
+        "labels = ['Acceptable','Fraudulent']\n",
+        "count = credit_card_data.value_counts(credit_card_data['Class'])\n",
+        "count.plot(kind = \"bar\",rot=0)\n",
+        "plt.title(\"Labels\")\n",
+        "plt.ylabel(\"Count\")\n",
+        "plt.xticks(range(2), labels)\n",
+        "plt.show()"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+        "id": "d-hJnOqkugu8"
+      },
+      "source": [
+        "create a sample dataset that contains a normal distribution of both transactions."
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": 21,
+      "metadata": {
+        "id": "Tqwwev53w6VK"
+      },
+      "outputs": [],
+      "source": [
+        "acceptable_sample=acceptable.sample(n=492)"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+        "id": "kLZdgOrcxMWm"
+      },
+      "source": [
+        "Concatinate the sample dataset into the already existing fraudulent dataframe"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": 22,
+      "metadata": {
+        "id": "w2xOTMlcw_G2"
+      },
+      "outputs": [],
+      "source": [
+        "# axis = 0 (rows)\n",
+        "# axis = 1 (columns)\n",
+        "new_dataset=pd.concat([acceptable_sample,fraudulent],axis=0)"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": 23,
+      "metadata": {
+        "colab": {
+          "base_uri": "https://localhost:8080/",
+          "height": 256
+        },
+        "id": "23TLgKczx0gQ",
+        "outputId": "9443a2c0-db45-4f46-9811-68ebaaf8ab2b"
+      },
+      "outputs": [
+        {
+          "data": {
+            "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>Time</th>\n",
+              "      <th>V1</th>\n",
+              "      <th>V2</th>\n",
+              "      <th>V3</th>\n",
+              "      <th>V4</th>\n",
+              "      <th>V5</th>\n",
+              "      <th>V6</th>\n",
+              "      <th>V7</th>\n",
+              "      <th>V8</th>\n",
+              "      <th>V9</th>\n",
+              "      <th>...</th>\n",
+              "      <th>V21</th>\n",
+              "      <th>V22</th>\n",
+              "      <th>V23</th>\n",
+              "      <th>V24</th>\n",
+              "      <th>V25</th>\n",
+              "      <th>V26</th>\n",
+              "      <th>V27</th>\n",
+              "      <th>V28</th>\n",
+              "      <th>Amount</th>\n",
+              "      <th>Class</th>\n",
+              "    </tr>\n",
+              "  </thead>\n",
+              "  <tbody>\n",
+              "    <tr>\n",
+              "      <th>127383</th>\n",
+              "      <td>78312.0</td>\n",
+              "      <td>-1.033684</td>\n",
+              "      <td>1.317406</td>\n",
+              "      <td>1.240114</td>\n",
+              "      <td>0.697731</td>\n",
+              "      <td>-0.237730</td>\n",
+              "      <td>-0.626897</td>\n",
+              "      <td>0.088513</td>\n",
+              "      <td>0.433316</td>\n",
+              "      <td>-0.773460</td>\n",
+              "      <td>...</td>\n",
+              "      <td>-0.186250</td>\n",
+              "      <td>-0.581192</td>\n",
+              "      <td>-0.059505</td>\n",
+              "      <td>0.379718</td>\n",
+              "      <td>0.025610</td>\n",
+              "      <td>0.292520</td>\n",
+              "      <td>0.014281</td>\n",
+              "      <td>-0.057068</td>\n",
+              "      <td>2.69</td>\n",
+              "      <td>0</td>\n",
+              "    </tr>\n",
+              "    <tr>\n",
+              "      <th>102015</th>\n",
+              "      <td>68022.0</td>\n",
+              "      <td>1.230948</td>\n",
+              "      <td>0.069872</td>\n",
+              "      <td>0.484287</td>\n",
+              "      <td>1.382559</td>\n",
+              "      <td>-0.395183</td>\n",
+              "      <td>-0.196777</td>\n",
+              "      <td>-0.181241</td>\n",
+              "      <td>0.027517</td>\n",
+              "      <td>0.737572</td>\n",
+              "      <td>...</td>\n",
+              "      <td>-0.128193</td>\n",
+              "      <td>-0.160311</td>\n",
+              "      <td>-0.147329</td>\n",
+              "      <td>-0.127866</td>\n",
+              "      <td>0.734199</td>\n",
+              "      <td>-0.263437</td>\n",
+              "      <td>0.033276</td>\n",
+              "      <td>0.015172</td>\n",
+              "      <td>3.29</td>\n",
+              "      <td>0</td>\n",
+              "    </tr>\n",
+              "    <tr>\n",
+              "      <th>89239</th>\n",
+              "      <td>62487.0</td>\n",
+              "      <td>0.986023</td>\n",
+              "      <td>-0.541423</td>\n",
+              "      <td>1.553750</td>\n",
+              "      <td>0.737388</td>\n",
+              "      <td>-1.313536</td>\n",
+              "      <td>0.481834</td>\n",
+              "      <td>-1.099914</td>\n",
+              "      <td>0.451702</td>\n",
+              "      <td>0.890411</td>\n",
+              "      <td>...</td>\n",
+              "      <td>0.291272</td>\n",
+              "      <td>0.874943</td>\n",
+              "      <td>-0.043822</td>\n",
+              "      <td>0.265505</td>\n",
+              "      <td>0.091530</td>\n",
+              "      <td>0.504073</td>\n",
+              "      <td>0.032954</td>\n",
+              "      <td>0.026374</td>\n",
+              "      <td>51.20</td>\n",
+              "      <td>0</td>\n",
+              "    </tr>\n",
+              "    <tr>\n",
+              "      <th>131185</th>\n",
+              "      <td>79516.0</td>\n",
+              "      <td>-1.201172</td>\n",
+              "      <td>-0.548377</td>\n",
+              "      <td>2.631439</td>\n",
+              "      <td>2.854492</td>\n",
+              "      <td>0.579070</td>\n",
+              "      <td>0.961969</td>\n",
+              "      <td>-0.091708</td>\n",
+              "      <td>0.221970</td>\n",
+              "      <td>0.172547</td>\n",
+              "      <td>...</td>\n",
+              "      <td>-0.171671</td>\n",
+              "      <td>-0.375741</td>\n",
+              "      <td>0.168826</td>\n",
+              "      <td>-0.451343</td>\n",
+              "      <td>0.028046</td>\n",
+              "      <td>0.021925</td>\n",
+              "      <td>-0.066196</td>\n",
+              "      <td>-0.071260</td>\n",
+              "      <td>124.09</td>\n",
+              "      <td>0</td>\n",
+              "    </tr>\n",
+              "    <tr>\n",
+              "      <th>236961</th>\n",
+              "      <td>149039.0</td>\n",
+              "      <td>1.725336</td>\n",
+              "      <td>0.005862</td>\n",
+              "      <td>0.499981</td>\n",
+              "      <td>4.083052</td>\n",
+              "      <td>-0.498462</td>\n",
+              "      <td>0.598846</td>\n",
+              "      <td>-0.568135</td>\n",
+              "      <td>0.223276</td>\n",
+              "      <td>0.078894</td>\n",
+              "      <td>...</td>\n",
+              "      <td>-0.206461</td>\n",
+              "      <td>-0.499058</td>\n",
+              "      <td>0.354503</td>\n",
+              "      <td>-0.079029</td>\n",
+              "      <td>-0.510911</td>\n",
+              "      <td>-0.305583</td>\n",
+              "      <td>0.024437</td>\n",
+              "      <td>-0.016899</td>\n",
+              "      <td>56.78</td>\n",
+              "      <td>0</td>\n",
+              "    </tr>\n",
+              "  </tbody>\n",
+              "</table>\n",
+              "<p>5 rows × 31 columns</p>\n",
+              "</div>"
+            ],
+            "text/plain": [
+              "            Time        V1        V2        V3        V4        V5        V6  \\\n",
+              "127383   78312.0 -1.033684  1.317406  1.240114  0.697731 -0.237730 -0.626897   \n",
+              "102015   68022.0  1.230948  0.069872  0.484287  1.382559 -0.395183 -0.196777   \n",
+              "89239    62487.0  0.986023 -0.541423  1.553750  0.737388 -1.313536  0.481834   \n",
+              "131185   79516.0 -1.201172 -0.548377  2.631439  2.854492  0.579070  0.961969   \n",
+              "236961  149039.0  1.725336  0.005862  0.499981  4.083052 -0.498462  0.598846   \n",
+              "\n",
+              "              V7        V8        V9  ...       V21       V22       V23  \\\n",
+              "127383  0.088513  0.433316 -0.773460  ... -0.186250 -0.581192 -0.059505   \n",
+              "102015 -0.181241  0.027517  0.737572  ... -0.128193 -0.160311 -0.147329   \n",
+              "89239  -1.099914  0.451702  0.890411  ...  0.291272  0.874943 -0.043822   \n",
+              "131185 -0.091708  0.221970  0.172547  ... -0.171671 -0.375741  0.168826   \n",
+              "236961 -0.568135  0.223276  0.078894  ... -0.206461 -0.499058  0.354503   \n",
+              "\n",
+              "             V24       V25       V26       V27       V28  Amount  Class  \n",
+              "127383  0.379718  0.025610  0.292520  0.014281 -0.057068    2.69      0  \n",
+              "102015 -0.127866  0.734199 -0.263437  0.033276  0.015172    3.29      0  \n",
+              "89239   0.265505  0.091530  0.504073  0.032954  0.026374   51.20      0  \n",
+              "131185 -0.451343  0.028046  0.021925 -0.066196 -0.071260  124.09      0  \n",
+              "236961 -0.079029 -0.510911 -0.305583  0.024437 -0.016899   56.78      0  \n",
+              "\n",
+              "[5 rows x 31 columns]"
+            ]
+          },
+          "execution_count": 23,
+          "metadata": {},
+          "output_type": "execute_result"
+        }
+      ],
+      "source": [
+        "# view the first 5 rows of the new dataset picked at random.\n",
+        "new_dataset.head()"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": 24,
+      "metadata": {
+        "colab": {
+          "base_uri": "https://localhost:8080/",
+          "height": 256
+        },
+        "id": "L7NHGvkay8DH",
+        "outputId": "bf1a4a78-44d0-42d0-e790-971e37421787"
+      },
+      "outputs": [
+        {
+          "data": {
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+              "      <th></th>\n",
+              "      <th>Time</th>\n",
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+              "      <th>V3</th>\n",
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+              "      <th>V26</th>\n",
+              "      <th>V27</th>\n",
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+              "      <th>280143</th>\n",
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+              "      <th>280149</th>\n",
+              "      <td>169351.0</td>\n",
+              "      <td>-0.676143</td>\n",
+              "      <td>1.126366</td>\n",
+              "      <td>-2.213700</td>\n",
+              "      <td>0.468308</td>\n",
+              "      <td>-1.120541</td>\n",
+              "      <td>-0.003346</td>\n",
+              "      <td>-2.234739</td>\n",
+              "      <td>1.210158</td>\n",
+              "      <td>-0.652250</td>\n",
+              "      <td>...</td>\n",
+              "      <td>0.751826</td>\n",
+              "      <td>0.834108</td>\n",
+              "      <td>0.190944</td>\n",
+              "      <td>0.032070</td>\n",
+              "      <td>-0.739695</td>\n",
+              "      <td>0.471111</td>\n",
+              "      <td>0.385107</td>\n",
+              "      <td>0.194361</td>\n",
+              "      <td>77.89</td>\n",
+              "      <td>1</td>\n",
+              "    </tr>\n",
+              "    <tr>\n",
+              "      <th>281144</th>\n",
+              "      <td>169966.0</td>\n",
+              "      <td>-3.113832</td>\n",
+              "      <td>0.585864</td>\n",
+              "      <td>-5.399730</td>\n",
+              "      <td>1.817092</td>\n",
+              "      <td>-0.840618</td>\n",
+              "      <td>-2.943548</td>\n",
+              "      <td>-2.208002</td>\n",
+              "      <td>1.058733</td>\n",
+              "      <td>-1.632333</td>\n",
+              "      <td>...</td>\n",
+              "      <td>0.583276</td>\n",
+              "      <td>-0.269209</td>\n",
+              "      <td>-0.456108</td>\n",
+              "      <td>-0.183659</td>\n",
+              "      <td>-0.328168</td>\n",
+              "      <td>0.606116</td>\n",
+              "      <td>0.884876</td>\n",
+              "      <td>-0.253700</td>\n",
+              "      <td>245.00</td>\n",
+              "      <td>1</td>\n",
+              "    </tr>\n",
+              "    <tr>\n",
+              "      <th>281674</th>\n",
+              "      <td>170348.0</td>\n",
+              "      <td>1.991976</td>\n",
+              "      <td>0.158476</td>\n",
+              "      <td>-2.583441</td>\n",
+              "      <td>0.408670</td>\n",
+              "      <td>1.151147</td>\n",
+              "      <td>-0.096695</td>\n",
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+              "      <td>-0.295135</td>\n",
+              "      <td>-0.072173</td>\n",
+              "      <td>-0.450261</td>\n",
+              "      <td>0.313267</td>\n",
+              "      <td>-0.289617</td>\n",
+              "      <td>0.002988</td>\n",
+              "      <td>-0.015309</td>\n",
+              "      <td>42.53</td>\n",
+              "      <td>1</td>\n",
+              "    </tr>\n",
+              "  </tbody>\n",
+              "</table>\n",
+              "<p>5 rows × 31 columns</p>\n",
+              "</div>"
+            ],
+            "text/plain": [
+              "            Time        V1        V2        V3        V4        V5        V6  \\\n",
+              "279863  169142.0 -1.927883  1.125653 -4.518331  1.749293 -1.566487 -2.010494   \n",
+              "280143  169347.0  1.378559  1.289381 -5.004247  1.411850  0.442581 -1.326536   \n",
+              "280149  169351.0 -0.676143  1.126366 -2.213700  0.468308 -1.120541 -0.003346   \n",
+              "281144  169966.0 -3.113832  0.585864 -5.399730  1.817092 -0.840618 -2.943548   \n",
+              "281674  170348.0  1.991976  0.158476 -2.583441  0.408670  1.151147 -0.096695   \n",
+              "\n",
+              "              V7        V8        V9  ...       V21       V22       V23  \\\n",
+              "279863 -0.882850  0.697211 -2.064945  ...  0.778584 -0.319189  0.639419   \n",
+              "280143 -1.413170  0.248525 -1.127396  ...  0.370612  0.028234 -0.145640   \n",
+              "280149 -2.234739  1.210158 -0.652250  ...  0.751826  0.834108  0.190944   \n",
+              "281144 -2.208002  1.058733 -1.632333  ...  0.583276 -0.269209 -0.456108   \n",
+              "281674  0.223050 -0.068384  0.577829  ... -0.164350 -0.295135 -0.072173   \n",
+              "\n",
+              "             V24       V25       V26       V27       V28  Amount  Class  \n",
+              "279863 -0.294885  0.537503  0.788395  0.292680  0.147968  390.00      1  \n",
+              "280143 -0.081049  0.521875  0.739467  0.389152  0.186637    0.76      1  \n",
+              "280149  0.032070 -0.739695  0.471111  0.385107  0.194361   77.89      1  \n",
+              "281144 -0.183659 -0.328168  0.606116  0.884876 -0.253700  245.00      1  \n",
+              "281674 -0.450261  0.313267 -0.289617  0.002988 -0.015309   42.53      1  \n",
+              "\n",
+              "[5 rows x 31 columns]"
+            ]
+          },
+          "execution_count": 24,
+          "metadata": {},
+          "output_type": "execute_result"
+        }
+      ],
+      "source": [
+        "new_dataset.tail()"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": 25,
+      "metadata": {
+        "colab": {
+          "base_uri": "https://localhost:8080/"
+        },
+        "id": "sDt3k12o0pip",
+        "outputId": "693193e5-a80c-4b3a-d7a6-26aa8545fd32"
+      },
+      "outputs": [
+        {
+          "data": {
+            "text/plain": [
+              "Class\n",
+              "0    492\n",
+              "1    492\n",
+              "Name: count, dtype: int64"
+            ]
+          },
+          "execution_count": 25,
+          "metadata": {},
+          "output_type": "execute_result"
+        }
+      ],
+      "source": [
+        "new_dataset['Class'].value_counts()"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": 26,
+      "metadata": {
+        "colab": {
+          "base_uri": "https://localhost:8080/",
+          "height": 193
+        },
+        "id": "yPZxI9bv3VhQ",
+        "outputId": "7c050329-f69c-4444-908b-6989712559a0"
+      },
+      "outputs": [
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+              "      <td>0.033608</td>\n",
+              "      <td>-0.081862</td>\n",
+              "      <td>0.034549</td>\n",
+              "      <td>-0.020167</td>\n",
+              "      <td>-0.047859</td>\n",
+              "      <td>...</td>\n",
+              "      <td>0.010722</td>\n",
+              "      <td>0.000671</td>\n",
+              "      <td>-0.034084</td>\n",
+              "      <td>-0.001508</td>\n",
+              "      <td>0.025786</td>\n",
+              "      <td>0.041784</td>\n",
+              "      <td>0.023764</td>\n",
+              "      <td>0.019137</td>\n",
+              "      <td>0.001844</td>\n",
+              "      <td>80.302053</td>\n",
+              "    </tr>\n",
+              "    <tr>\n",
+              "      <th>1</th>\n",
+              "      <td>80746.806911</td>\n",
+              "      <td>-4.771948</td>\n",
+              "      <td>3.623778</td>\n",
+              "      <td>-7.033281</td>\n",
+              "      <td>4.542029</td>\n",
+              "      <td>-3.151225</td>\n",
+              "      <td>-1.397737</td>\n",
+              "      <td>-5.568731</td>\n",
+              "      <td>0.570636</td>\n",
+              "      <td>-2.581123</td>\n",
+              "      <td>...</td>\n",
+              "      <td>0.372319</td>\n",
+              "      <td>0.713588</td>\n",
+              "      <td>0.014049</td>\n",
+              "      <td>-0.040308</td>\n",
+              "      <td>-0.105130</td>\n",
+              "      <td>0.041449</td>\n",
+              "      <td>0.051648</td>\n",
+              "      <td>0.170575</td>\n",
+              "      <td>0.075667</td>\n",
+              "      <td>122.211321</td>\n",
+              "    </tr>\n",
+              "  </tbody>\n",
+              "</table>\n",
+              "<p>2 rows × 30 columns</p>\n",
+              "</div>"
+            ],
+            "text/plain": [
+              "               Time        V1        V2        V3        V4        V5  \\\n",
+              "Class                                                                   \n",
+              "0      94071.087398  0.052736  0.028729  0.034768 -0.073095  0.033608   \n",
+              "1      80746.806911 -4.771948  3.623778 -7.033281  4.542029 -3.151225   \n",
+              "\n",
+              "             V6        V7        V8        V9  ...       V20       V21  \\\n",
+              "Class                                          ...                       \n",
+              "0     -0.081862  0.034549 -0.020167 -0.047859  ...  0.010722  0.000671   \n",
+              "1     -1.397737 -5.568731  0.570636 -2.581123  ...  0.372319  0.713588   \n",
+              "\n",
+              "            V22       V23       V24       V25       V26       V27       V28  \\\n",
+              "Class                                                                         \n",
+              "0     -0.034084 -0.001508  0.025786  0.041784  0.023764  0.019137  0.001844   \n",
+              "1      0.014049 -0.040308 -0.105130  0.041449  0.051648  0.170575  0.075667   \n",
+              "\n",
+              "           Amount  \n",
+              "Class              \n",
+              "0       80.302053  \n",
+              "1      122.211321  \n",
+              "\n",
+              "[2 rows x 30 columns]"
+            ]
+          },
+          "execution_count": 26,
+          "metadata": {},
+          "output_type": "execute_result"
+        }
+      ],
+      "source": [
+        "new_dataset.groupby('Class').mean()"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+        "id": "4IleywPs2xHB"
+      },
+      "source": [
+        "Splitting dataset into training and testind sets. (80%, 10%)"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": 27,
+      "metadata": {
+        "id": "MX647MoK1l9q"
+      },
+      "outputs": [],
+      "source": [
+        "# x represent the features(content of the dataset) and y represent the class.\n",
+        "x = new_dataset.drop(columns = 'Class',axis = 1)\n",
+        "y = new_dataset['Class']"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": 28,
+      "metadata": {
+        "colab": {
+          "base_uri": "https://localhost:8080/"
+        },
+        "id": "3mEbVdXH1unU",
+        "outputId": "0daa8179-bc57-41ba-dcc7-a5272de72ae4"
+      },
+      "outputs": [
+        {
+          "name": "stdout",
+          "output_type": "stream",
+          "text": [
+            "            Time        V1        V2        V3        V4        V5        V6  \\\n",
+            "127383   78312.0 -1.033684  1.317406  1.240114  0.697731 -0.237730 -0.626897   \n",
+            "102015   68022.0  1.230948  0.069872  0.484287  1.382559 -0.395183 -0.196777   \n",
+            "89239    62487.0  0.986023 -0.541423  1.553750  0.737388 -1.313536  0.481834   \n",
+            "131185   79516.0 -1.201172 -0.548377  2.631439  2.854492  0.579070  0.961969   \n",
+            "236961  149039.0  1.725336  0.005862  0.499981  4.083052 -0.498462  0.598846   \n",
+            "...          ...       ...       ...       ...       ...       ...       ...   \n",
+            "279863  169142.0 -1.927883  1.125653 -4.518331  1.749293 -1.566487 -2.010494   \n",
+            "280143  169347.0  1.378559  1.289381 -5.004247  1.411850  0.442581 -1.326536   \n",
+            "280149  169351.0 -0.676143  1.126366 -2.213700  0.468308 -1.120541 -0.003346   \n",
+            "281144  169966.0 -3.113832  0.585864 -5.399730  1.817092 -0.840618 -2.943548   \n",
+            "281674  170348.0  1.991976  0.158476 -2.583441  0.408670  1.151147 -0.096695   \n",
+            "\n",
+            "              V7        V8        V9  ...       V20       V21       V22  \\\n",
+            "127383  0.088513  0.433316 -0.773460  ...  0.114241 -0.186250 -0.581192   \n",
+            "102015 -0.181241  0.027517  0.737572  ... -0.220772 -0.128193 -0.160311   \n",
+            "89239  -1.099914  0.451702  0.890411  ... -0.074475  0.291272  0.874943   \n",
+            "131185 -0.091708  0.221970  0.172547  ...  0.585115 -0.171671 -0.375741   \n",
+            "236961 -0.568135  0.223276  0.078894  ... -0.208526 -0.206461 -0.499058   \n",
+            "...          ...       ...       ...  ...       ...       ...       ...   \n",
+            "279863 -0.882850  0.697211 -2.064945  ...  1.252967  0.778584 -0.319189   \n",
+            "280143 -1.413170  0.248525 -1.127396  ...  0.226138  0.370612  0.028234   \n",
+            "280149 -2.234739  1.210158 -0.652250  ...  0.247968  0.751826  0.834108   \n",
+            "281144 -2.208002  1.058733 -1.632333  ...  0.306271  0.583276 -0.269209   \n",
+            "281674  0.223050 -0.068384  0.577829  ... -0.017652 -0.164350 -0.295135   \n",
+            "\n",
+            "             V23       V24       V25       V26       V27       V28  Amount  \n",
+            "127383 -0.059505  0.379718  0.025610  0.292520  0.014281 -0.057068    2.69  \n",
+            "102015 -0.147329 -0.127866  0.734199 -0.263437  0.033276  0.015172    3.29  \n",
+            "89239  -0.043822  0.265505  0.091530  0.504073  0.032954  0.026374   51.20  \n",
+            "131185  0.168826 -0.451343  0.028046  0.021925 -0.066196 -0.071260  124.09  \n",
+            "236961  0.354503 -0.079029 -0.510911 -0.305583  0.024437 -0.016899   56.78  \n",
+            "...          ...       ...       ...       ...       ...       ...     ...  \n",
+            "279863  0.639419 -0.294885  0.537503  0.788395  0.292680  0.147968  390.00  \n",
+            "280143 -0.145640 -0.081049  0.521875  0.739467  0.389152  0.186637    0.76  \n",
+            "280149  0.190944  0.032070 -0.739695  0.471111  0.385107  0.194361   77.89  \n",
+            "281144 -0.456108 -0.183659 -0.328168  0.606116  0.884876 -0.253700  245.00  \n",
+            "281674 -0.072173 -0.450261  0.313267 -0.289617  0.002988 -0.015309   42.53  \n",
+            "\n",
+            "[984 rows x 30 columns]\n"
+          ]
+        }
+      ],
+      "source": [
+        "# this prints the data except the class column.\n",
+        "print(x)"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": 29,
+      "metadata": {
+        "colab": {
+          "base_uri": "https://localhost:8080/"
+        },
+        "id": "1EqhO2lx2hhL",
+        "outputId": "7791c58a-b03c-470b-a970-d46f7c0cb219"
+      },
+      "outputs": [
+        {
+          "name": "stdout",
+          "output_type": "stream",
+          "text": [
+            "127383    0\n",
+            "102015    0\n",
+            "89239     0\n",
+            "131185    0\n",
+            "236961    0\n",
+            "         ..\n",
+            "279863    1\n",
+            "280143    1\n",
+            "280149    1\n",
+            "281144    1\n",
+            "281674    1\n",
+            "Name: Class, Length: 984, dtype: int64\n"
+          ]
+        }
+      ],
+      "source": [
+        "# prints the classes.\n",
+        "print(y)"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+        "id": "qSqUv3E43xBc"
+      },
+      "source": [
+        "Splitting dataset into training and testind sets. (80%, 20%)"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": 30,
+      "metadata": {
+        "id": "-H0kGxDV3wlW"
+      },
+      "outputs": [],
+      "source": [
+        "x_train,x_test,y_train,y_test=train_test_split(x,y,test_size=0.2,stratify=y,random_state=2)"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": 31,
+      "metadata": {
+        "colab": {
+          "base_uri": "https://localhost:8080/"
+        },
+        "id": "PZkFOLu74aMv",
+        "outputId": "2953cca8-2139-4958-c27f-95bd792626be"
+      },
+      "outputs": [
+        {
+          "name": "stdout",
+          "output_type": "stream",
+          "text": [
+            "(984, 30) (787, 30) (197, 30)\n"
+          ]
+        }
+      ],
+      "source": [
+        "# original data, the training data, test data split.\n",
+        "print(x.shape,x_train.shape,x_test.shape)"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+        "id": "i_NpWsJq5xbV"
+      },
+      "source": [
+        "Training the Model."
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+        "id": "emS5fKrq54_t"
+      },
+      "source": [
+        "Logistics Regression Model"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": 32,
+      "metadata": {
+        "id": "MSeO0e5N53x8"
+      },
+      "outputs": [],
+      "source": [
+        "model = LogisticRegression()"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": 33,
+      "metadata": {
+        "colab": {
+          "base_uri": "https://localhost:8080/",
+          "height": 75
+        },
+        "id": "X7OyTmKh6EFQ",
+        "outputId": "23e23b9b-ee32-4756-f0e9-f2ae0751ef7b"
+      },
+      "outputs": [
+        {
+          "name": "stderr",
+          "output_type": "stream",
+          "text": [
+            "c:\\Fraud_Detection\\Lib\\site-packages\\sklearn\\linear_model\\_logistic.py:469: ConvergenceWarning: lbfgs failed to converge (status=1):\n",
+            "STOP: TOTAL NO. of ITERATIONS REACHED LIMIT.\n",
+            "\n",
+            "Increase the number of iterations (max_iter) or scale the data as shown in:\n",
+            "    https://scikit-learn.org/stable/modules/preprocessing.html\n",
+            "Please also refer to the documentation for alternative solver options:\n",
+            "    https://scikit-learn.org/stable/modules/linear_model.html#logistic-regression\n",
+            "  n_iter_i = _check_optimize_result(\n"
+          ]
+        },
+        {
+          "data": {
+            "text/html": [
+              "<style>#sk-container-id-1 {\n",
+              "  /* Definition of color scheme common for light and dark mode */\n",
+              "  --sklearn-color-text: black;\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-1 {\n",
+              "  color: var(--sklearn-color-text);\n",
+              "}\n",
+              "\n",
+              "#sk-container-id-1 pre {\n",
+              "  padding: 0;\n",
+              "}\n",
+              "\n",
+              "#sk-container-id-1 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-1 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-1 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-1 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-1 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-1 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-1 div.sk-parallel-item {\n",
+              "  display: flex;\n",
+              "  flex-direction: column;\n",
+              "}\n",
+              "\n",
+              "#sk-container-id-1 div.sk-parallel-item:first-child::after {\n",
+              "  align-self: flex-end;\n",
+              "  width: 50%;\n",
+              "}\n",
+              "\n",
+              "#sk-container-id-1 div.sk-parallel-item:last-child::after {\n",
+              "  align-self: flex-start;\n",
+              "  width: 50%;\n",
+              "}\n",
+              "\n",
+              "#sk-container-id-1 div.sk-parallel-item:only-child::after {\n",
+              "  width: 0;\n",
+              "}\n",
+              "\n",
+              "/* Serial-specific style estimator block */\n",
+              "\n",
+              "#sk-container-id-1 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-1 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-1 label.sk-toggleable__label {\n",
+              "  cursor: pointer;\n",
+              "  display: block;\n",
+              "  width: 100%;\n",
+              "  margin-bottom: 0;\n",
+              "  padding: 0.5em;\n",
+              "  box-sizing: border-box;\n",
+              "  text-align: center;\n",
+              "}\n",
+              "\n",
+              "#sk-container-id-1 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-1 label.sk-toggleable__label-arrow:hover:before {\n",
+              "  color: var(--sklearn-color-text);\n",
+              "}\n",
+              "\n",
+              "/* Toggleable content - dropdown */\n",
+              "\n",
+              "#sk-container-id-1 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-1 div.sk-toggleable__content.fitted {\n",
+              "  /* fitted */\n",
+              "  background-color: var(--sklearn-color-fitted-level-0);\n",
+              "}\n",
+              "\n",
+              "#sk-container-id-1 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-1 div.sk-toggleable__content.fitted pre {\n",
+              "  /* unfitted */\n",
+              "  background-color: var(--sklearn-color-fitted-level-0);\n",
+              "}\n",
+              "\n",
+              "#sk-container-id-1 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-1 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-1 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-1 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-1 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-1 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-1 div.sk-label label.sk-toggleable__label,\n",
+              "#sk-container-id-1 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-1 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-1 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-1 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-1 div.sk-label-container {\n",
+              "  text-align: center;\n",
+              "}\n",
+              "\n",
+              "/* Estimator-specific */\n",
+              "#sk-container-id-1 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-1 div.sk-estimator.fitted {\n",
+              "  /* fitted */\n",
+              "  background-color: var(--sklearn-color-fitted-level-0);\n",
+              "}\n",
+              "\n",
+              "/* on hover */\n",
+              "#sk-container-id-1 div.sk-estimator:hover {\n",
+              "  /* unfitted */\n",
+              "  background-color: var(--sklearn-color-unfitted-level-2);\n",
+              "}\n",
+              "\n",
+              "#sk-container-id-1 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: 1ex;\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-1 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-1 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-1 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-1 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-1\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>LogisticRegression()</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-1\" type=\"checkbox\" checked><label for=\"sk-estimator-id-1\" class=\"sk-toggleable__label fitted sk-toggleable__label-arrow fitted\">&nbsp;&nbsp;LogisticRegression<a class=\"sk-estimator-doc-link fitted\" rel=\"noreferrer\" target=\"_blank\" href=\"https://scikit-learn.org/1.5/modules/generated/sklearn.linear_model.LogisticRegression.html\">?<span>Documentation for LogisticRegression</span></a><span class=\"sk-estimator-doc-link fitted\">i<span>Fitted</span></span></label><div class=\"sk-toggleable__content fitted\"><pre>LogisticRegression()</pre></div> </div></div></div></div>"
+            ],
+            "text/plain": [
+              "LogisticRegression()"
+            ]
+          },
+          "execution_count": 33,
+          "metadata": {},
+          "output_type": "execute_result"
+        }
+      ],
+      "source": [
+        "# train the logistics regression model using the training data.\n",
+        "model.fit(x_train, y_train)"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": 34,
+      "metadata": {
+        "id": "22xncDXh79gU"
+      },
+      "outputs": [],
+      "source": [
+        "# check the accuracy of the training data.\n",
+        "x_train_prediction = model.predict(x_train)\n",
+        "training_data_accuracy = accuracy_score(x_train_prediction, y_train)"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": 35,
+      "metadata": {
+        "colab": {
+          "base_uri": "https://localhost:8080/"
+        },
+        "id": "_Hcjw3J48aRC",
+        "outputId": "947658b6-562a-4c69-9715-c9c2e5dc06c7"
+      },
+      "outputs": [
+        {
+          "name": "stdout",
+          "output_type": "stream",
+          "text": [
+            "Accuracy on the Training data :  94.40914866581956\n"
+          ]
+        }
+      ],
+      "source": [
+        "# if the accuracy is above 80% then it means the model is good\n",
+        "print('Accuracy on the Training data : ', training_data_accuracy * 100)"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": 36,
+      "metadata": {
+        "id": "ANEy8pA-9LJC"
+      },
+      "outputs": [],
+      "source": [
+        "# accuracy on the test data\n",
+        "x_test_prediction = model.predict(x_test)\n",
+        "test_data_accuracy = accuracy_score(x_test_prediction, y_test)"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": 37,
+      "metadata": {
+        "colab": {
+          "base_uri": "https://localhost:8080/"
+        },
+        "id": "t1LQFPd19WWn",
+        "outputId": "f9c3a93e-c88e-4de1-ad56-659bc5853244"
+      },
+      "outputs": [
+        {
+          "name": "stdout",
+          "output_type": "stream",
+          "text": [
+            "Accuracy on the Test data :  91.87817258883248\n"
+          ]
+        }
+      ],
+      "source": [
+        "print('Accuracy on the Test data : ', test_data_accuracy * 100)"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "id": "Ct-52L3RADo0"
+      },
+      "outputs": [
+        {
+          "ename": "",
+          "evalue": "",
+          "output_type": "error",
+          "traceback": [
+            "\u001b[1;31mRunning cells with 'c:\\Users\\chris\\AppData\\Local\\Programs\\Python\\Python311\\python.exe' requires the ipykernel package.\n",
+            "\u001b[1;31mRun the following command to install 'ipykernel' into the Python environment. \n",
+            "\u001b[1;31mCommand: 'c:/Users/chris/AppData/Local/Programs/Python/Python311/python.exe -m pip install ipykernel -U --user --force-reinstall'"
+          ]
+        }
+      ],
+      "source": [
+        "import pickle\n",
+        "pickle.dump(model,open('model.pkl','wb'))"
+      ]
+    }
+  ],
+  "metadata": {
+    "colab": {
+      "provenance": []
+    },
+    "kernelspec": {
+      "display_name": "Python 3",
+      "name": "python3"
+    },
+    "language_info": {
+      "codemirror_mode": {
+        "name": "ipython",
+        "version": 3
+      },
+      "file_extension": ".py",
+      "mimetype": "text/x-python",
+      "name": "python",
+      "nbconvert_exporter": "python",
+      "pygments_lexer": "ipython3",
+      "version": "3.12.4"
+    }
+  },
+  "nbformat": 4,
+  "nbformat_minor": 0
+}