pages/13_Linear_Regression.py

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.title("📈 Linear Regression Explorer")

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
)

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 == "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 == "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")

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**
    """)

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 == "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}}")

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())

    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)

    X = df[[x_feature]]
    y = df[y_feature]

    model = LinearRegression()
    model.fit(X, y)
    y_pred = model.predict(X)

    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.header("📓 Open in Google Colab")
    st.markdown("""
    <a href='https://colab.research.google.com/drive/11-Rv7BC2PhOqk5hnpdXo6QjqLLYLDvTD?usp=sharing' target='_blank'>
    🔗 Open Linear Regression Colab Notebook
    </a>
    """, unsafe_allow_html=True)

st.markdown("---")
st.success("This app blends theory with visuals and interaction to help you master Linear Regression!")