Update app/pages/week_1.py

app/pages/week_1.py

@@ -1,4 +1,7 @@
 import streamlit as st
+import numpy as np
+import plotly.graph_objects as go
+from sklearn.linear_model import LinearRegression
 
 def show_week_content():
     st.markdown("""
@@ -38,8 +41,78 @@ def show_week_content():
         if submitted:
             st.success("Topic submitted successfully! We'll review and provide feedback.")
     
+    # Linear Regression Visualization
+    st.header("2. Linear Regression Demo")
+    st.markdown("""
+    ### Understanding Linear Regression
+    
+    Linear regression is a fundamental machine learning algorithm that models the relationship between a dependent variable and one or more independent variables.
+    Below is an interactive demonstration of simple linear regression.
+    """)
+    
+    # Create interactive controls
+    col1, col2 = st.columns(2)
+    with col1:
+        n_points = st.slider("Number of data points", 10, 100, 50)
+        noise = st.slider("Noise level", 0.1, 2.0, 0.5)
+    with col2:
+        slope = st.slider("True slope", -2.0, 2.0, 1.0)
+        intercept = st.slider("True intercept", -5.0, 5.0, 0.0)
+    
+    # Generate synthetic data
+    np.random.seed(42)
+    X = np.random.rand(n_points) * 10
+    y = slope * X + intercept + np.random.normal(0, noise, n_points)
+    
+    # Fit linear regression
+    X_reshaped = X.reshape(-1, 1)
+    model = LinearRegression()
+    model.fit(X_reshaped, y)
+    y_pred = model.predict(X_reshaped)
+    
+    # Create the plot
+    fig = go.Figure()
+    
+    # Add scatter plot of actual data
+    fig.add_trace(go.Scatter(
+        x=X,
+        y=y,
+        mode='markers',
+        name='Actual Data',
+        marker=dict(color='blue')
+    ))
+    
+    # Add regression line
+    fig.add_trace(go.Scatter(
+        x=X,
+        y=y_pred,
+        mode='lines',
+        name='Regression Line',
+        line=dict(color='red')
+    ))
+    
+    # Update layout
+    fig.update_layout(
+        title='Linear Regression Visualization',
+        xaxis_title='X',
+        yaxis_title='Y',
+        showlegend=True,
+        height=500
+    )
+    
+    # Display the plot
+    st.plotly_chart(fig, use_container_width=True)
+    
+    # Display regression coefficients
+    st.markdown(f"""
+    ### Regression Results
+    - Estimated slope: {model.coef_[0]:.2f}
+    - Estimated intercept: {model.intercept_:.2f}
+    - R² score: {model.score(X_reshaped, y):.2f}
+    """)
+    
     # Literature Review Section
-    st.header("2. Literature Review")
+    st.header("3. Literature Review")
     st.markdown("""
     ### Steps for Conducting Literature Review:
     1. Search for relevant papers