Update pages/13_Linear_Regression.py

pages/13_Linear_Regression.py

@@ -1,141 +1,100 @@
 import streamlit as st
+import pandas as pd
+import numpy as np
+import plotly.express as px
+from sklearn.linear_model import LinearRegression
+from sklearn.metrics import mean_squared_error, r2_score
 
 st.set_page_config(page_title="Linear Regression", page_icon="📊", layout="wide")
 
-st.markdown("<h1 style='text-align: center;'>📈 Linear Regression: A Visual and Theoretical Guide</h1>", unsafe_allow_html=True)
-
-section = st.sidebar.radio(
-    "🔍 Explore Topics",
-    [
-        "📘 What is Linear Regression?",
-        "📐 Best Fit Line",
-        "🔧 Training (Simple Linear Regression)",
-        "🔍 Testing Phase",
-        "📊 Multiple Linear Regression",
-        "⚙️ Gradient Descent",
-        "📏 Assumptions",
-        "📊 Evaluation Metrics",
-        "📓 Colab Notebook",
-    ]
-)
+st.title("📈 Linear Regression Explorer")
 
-if section == "📘 What is Linear Regression?":
-    st.subheader("📘 What is Linear Regression?")
-    st.write("""
-    Linear Regression is a **Supervised Learning Algorithm** used to predict **continuous values**.
-    - It models the relationship between the **dependent variable (target)** and one or more **independent variables (features)**.
-    - The goal is to fit the **best straight line** that minimizes the error.
-    """)
+section = st.radio(
+    "Navigate the Theory and Visuals",
+    ["Introduction", "Best Fit Line", "Simple vs Multiple", "Gradient Descent", "Assumptions", "Evaluation Metrics", "Interactive Example", "Colab Notebook"],
+    horizontal=True
+)
 
-elif section == "📐 Best Fit Line":
-    st.subheader("📐 What is the Best Fit Line?")
-    st.write("""
-    A **best fit line**:
-    - Minimizes the **Mean Squared Error (MSE)**
-    - Can be found using **Ordinary Least Squares (OLS)** or **Gradient Descent**
-    
-    #### Simple Linear Equation:
-    $$
-    \hat{y} = w_1 x + w_0
-    $$
-    - \( w_1 \): slope (coefficient)
-    - \( w_0 \): intercept (bias)
+if section == "Introduction":
+    st.header("📘 What is Linear Regression?")
+    st.markdown("""
+    Linear Regression is a **Supervised Learning** algorithm used for predicting **continuous outcomes**.
+    The idea is to fit a line that best captures the relationship between input variables and the output variable.
     """)
 
-elif section == "🔧 Training (Simple Linear Regression)":
-    st.subheader("🔧 Training: Simple Linear Regression")
-    st.write("""
-    Used when there’s only **one feature**.
-
-    **Steps to Train:**
-    1. Initialize weights: \( w_1, w_0 \)
-    2. Predict: \( \hat{y} = w_1 x + w_0 \)
-    3. Calculate **Mean Squared Error (MSE)**:
-       $$
-       \text{MSE} = \frac{1}{n} \sum (\hat{y}_i - y_i)^2
-       $$
-    4. Optimize weights using **Gradient Descent**
+elif section == "Best Fit Line":
+    st.header("📐 Best Fit Line")
+    st.latex(r"\hat{y} = w_1 x + w_0")
+    st.markdown("""
+    - \( w_1 \): Slope (how much \( y \) changes with \( x \))
+    - \( w_0 \): Intercept
+    - Found using **Ordinary Least Squares** or **Gradient Descent**
     """)
 
-elif section == "🔍 Testing Phase":
-    st.subheader("🔍 Prediction (Testing Phase)")
-    st.write("""
-    Once trained, the model can predict new outcomes:
+elif section == "Simple vs Multiple":
+    st.header("🔧 Simple vs Multiple Linear Regression")
+    st.subheader("Simple Linear Regression")
+    st.latex(r"\hat{y} = w_1 x + w_0")
+    st.subheader("Multiple Linear Regression")
+    st.latex(r"\hat{y} = w_1 x_1 + w_2 x_2 + \dots + w_n x_n + w_0")
 
-    **Given new input \( x \):**
-    $$
-    \hat{y} = w_1 x + w_0
-    $$
+elif section == "Gradient Descent":
+    st.header("⚙️ Gradient Descent")
+    st.latex(r"w := w - \alpha \cdot \frac{\partial \text{Loss}}{\partial w}")
+    st.markdown("""
+    - \( \alpha \): Learning Rate
+    - Goal: Minimize **Mean Squared Error**
+    """)
 
-    - Compare predicted \( \hat{y} \) with actual \( y \) (if known)
+elif section == "Assumptions":
+    st.header("📏 Assumptions of Linear Regression")
+    st.markdown("""
+    1. Linearity  
+    2. No Multicollinearity  
+    3. Homoscedasticity  
+    4. Normality of residuals  
+    5. No autocorrelation
     """)
 
-elif section == "📊 Multiple Linear Regression":
-    st.subheader("📊 Multiple Linear Regression")
-    st.write("""
-    Predicts using **multiple features**.
+elif section == "Evaluation Metrics":
+    st.header("📊 Evaluation Metrics")
+    st.latex(r"MSE = \frac{1}{n} \sum (\hat{y}_i - y_i)^2")
+    st.latex(r"MAE = \frac{1}{n} \sum |\hat{y}_i - y_i|")
+    st.latex(r"R^2 = 1 - \frac{\text{SS}_{res}}{\text{SS}_{tot}}")
 
-    #### Equation:
-    $$
-    \hat{y} = w_1 x_1 + w_2 x_2 + \dots + w_n x_n + w_0
-    $$
+elif section == "Interactive Example":
+    st.header("🎯 Try Linear Regression on Real Data")
+    
+    df = px.data.tips()  # Load sample dataset
+    st.write("Dataset preview:", df.head())
 
-    - Each input feature has its own weight
-    - Use same process: predict → calculate loss → optimize
-    """)
+    x_feature = st.selectbox("Select Independent Variable (X)", df.select_dtypes(include=np.number).columns)
+    y_feature = st.selectbox("Select Dependent Variable (Y)", df.select_dtypes(include=np.number).columns, index=1)
 
-elif section == "⚙️ Gradient Descent":
-    st.subheader("⚙️ Gradient Descent Optimization")
-    st.write("""
-    **Goal:** Minimize the loss function (like MSE)
-
-    #### Update Rule:
-    $$
-    w := w - \alpha \cdot \frac{\partial \text{MSE}}{\partial w}
-    $$
-
-    - \( \alpha \): learning rate
-    - Choose carefully:
-        - Too high → overshoot
-        - Too low → slow convergence
-        - Common choices: 0.01, 0.1
-    """)
+    X = df[[x_feature]]
+    y = df[y_feature]
 
-elif section == "📏 Assumptions":
-    st.subheader("📏 Assumptions of Linear Regression")
-    st.write("""
-    1. **Linearity**: Relationship between variables is linear  
-    2. **No Multicollinearity**: Features shouldn't be highly correlated  
-    3. **Homoscedasticity**: Constant variance of residuals  
-    4. **Normality of Errors**: Errors are normally distributed  
-    5. **No Autocorrelation**: Errors should not be related across observations  
-    """)
+    model = LinearRegression()
+    model.fit(X, y)
+    y_pred = model.predict(X)
 
-elif section == "📊 Evaluation Metrics":
-    st.subheader("📊 Evaluation Metrics for Linear Regression")
-    st.write("""
-    - **Mean Squared Error (MSE)**:
-      $$
-      \text{MSE} = \frac{1}{n} \sum (\hat{y}_i - y_i)^2
-      $$
-    - **Mean Absolute Error (MAE)**:
-      $$
-      \text{MAE} = \frac{1}{n} \sum |\hat{y}_i - y_i|
-      $$
-    - **R-squared ( \( R^2 \) )**:
-      $$
-      R^2 = 1 - \frac{SS_{res}}{SS_{tot}}
-      $$
-    Measures how well the model explains the variance in data.
-    """)
+    fig = px.scatter(df, x=x_feature, y=y_feature, title="Scatter Plot with Regression Line")
+    fig.add_scatter(x=df[x_feature], y=y_pred, mode='lines', name='Best Fit Line')
+    st.plotly_chart(fig, use_container_width=True)
+
+    st.subheader("Model Performance")
+    st.write(f"**Slope (w₁)**: {model.coef_[0]:.4f}")
+    st.write(f"**Intercept (w₀)**: {model.intercept_:.4f}")
+    st.write(f"**R² Score**: {r2_score(y, y_pred):.4f}")
+    st.write(f"**MSE**: {mean_squared_error(y, y_pred):.4f}")
 
-elif section == "📓 Colab Notebook":
-    st.subheader("📓 Hands-On Implementation in Google Colab")
+elif section == "Colab Notebook":
+    st.header("📓 Open in Google Colab")
     st.markdown("""
     <a href='https://colab.research.google.com/drive/11-Rv7BC2PhOqk5hnpdXo6QjqLLYLDvTD?usp=sharing' target='_blank'>
-        🔗 Click here to open the Linear Regression Notebook in Colab
+    🔗 Open Linear Regression Colab Notebook
     </a>
     """, unsafe_allow_html=True)
 
 st.markdown("---")
-st.success("Mastering Linear Regression is essential — it's the foundation for many advanced models in machine learning!")
+st.success("This app blends theory with visuals and interaction to help you master Linear Regression!")