Update pages/13_Linear_Regression.py

pages/13_Linear_Regression.py

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+import streamlit as st
+
+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",
+    ]
+)
+
+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.
+    """)
+
+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)
+    """)
+
+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 == "🔍 Testing Phase":
+    st.subheader("🔍 Prediction (Testing Phase)")
+    st.write("""
+    Once trained, the model can predict new outcomes:
+
+    **Given new input \( x \):**
+    $$
+    \hat{y} = w_1 x + w_0
+    $$
+
+    - Compare predicted \( \hat{y} \) with actual \( y \) (if known)
+    """)
+
+elif section == "📊 Multiple Linear Regression":
+    st.subheader("📊 Multiple Linear Regression")
+    st.write("""
+    Predicts using **multiple features**.
+
+    #### Equation:
+    $$
+    \hat{y} = w_1 x_1 + w_2 x_2 + \dots + w_n x_n + w_0
+    $$
+
+    - Each input feature has its own weight
+    - Use same process: predict → calculate loss → optimize
+    """)
+
+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
+    """)
+
+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  
+    """)
+
+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.
+    """)
+
+elif section == "📓 Colab Notebook":
+    st.subheader("📓 Hands-On Implementation 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
+    </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!")