pages/5Linear_Regression.py

import streamlit as st

# Page configuration
st.set_page_config(page_title="Linear Regression", page_icon="🤖", layout="wide")

# Custom CSS for styling
st.markdown("""
    <style>
        .stApp {
            background-color: #ECECEC;
        }
        h1, h2, h3 {
            color: #002244;
        }
        .custom-font, p {
            font-family: 'Arial', sans-serif;
            font-size: 18px;
            color: black;
            line-height: 1.6;
        }
    </style>
""", unsafe_allow_html=True)

# Title
st.markdown("<h1 style='color: #002244;'>Complete Overview of Linear Regression</h1>", unsafe_allow_html=True)

st.write("""
Linear Regression is a key **Supervised Learning** method mainly used for **regression problems**.
It predicts continuous outputs by identifying the best-fit line (or hyperplane) that minimizes the gap between actual and predicted values.
""")

# Understanding the Best Fit Line
st.markdown("<h2 style='color: #002244;'>What Defines the Best Fit Line?</h2>", unsafe_allow_html=True)
st.write("""
The ideal regression line is one that:
- Gets as close as possible to all data points.
- **Minimizes the error** between actual and predicted values.
- Is calculated using optimization techniques like **Ordinary Least Squares (OLS)** or **Gradient Descent**.
""")
st.image("linearregression.png", width=900)

# Training in Simple Linear Regression
st.markdown("<h2 style='color: #002244;'>Training Process: Simple Linear Regression</h2>", unsafe_allow_html=True)
st.write("""
Simple Linear Regression is typically used when there's only one or two features.
It models the relationship between \( x \) (independent variable) and \( y \) (dependent variable) as:
\[ y = w_1x + w_0 \]
Where:
- \( w_1 \) is the slope (weight)
- \( w_0 \) is the intercept (bias)

**Steps:**
- Initialize weights \( w_1 \), \( w_0 \) randomly.
- Predict output \( \hat{y} \) for each input \( x \).
- Compute **Mean Squared Error (MSE)** to assess prediction error.
- Update weights using **Gradient Descent**.
- Repeat until the error is minimized.
""")

# Testing Phase
st.markdown("<h2 style='color: #002244;'>Testing Phase</h2>", unsafe_allow_html=True)
st.write("""
Once trained:
1. Feed a new input \( x \).
2. Use the model to predict \( \hat{y} \).
3. Compare predicted value with actual to evaluate model accuracy.
""")

# Multiple Linear Regression
st.markdown("<h2 style='color: #002244;'>Multiple Linear Regression</h2>", unsafe_allow_html=True)
st.write("""
Multiple Linear Regression (MLR) extends simple linear regression by using multiple features to predict the output.
- Initialize all weights \( w_1, w_2, ..., w_n \) and \( w_0 \).
- Predict \( y \) for each data point.
- Calculate loss using **MSE**.
- Update weights via **Gradient Descent** to improve model accuracy.
""")

# Gradient Descent Optimization
st.markdown("<h2 style='color: #002244;'>Gradient Descent: Optimization Technique</h2>", unsafe_allow_html=True)
st.write("""
Gradient Descent is used to minimize the loss function:
- Begin with random weights and bias.
- Compute gradient (derivative) of the loss function.
- Update weights using the gradient:
  \[ w = w - \alpha \frac{dL}{dw} \]
- Repeat until convergence (minimum loss is achieved).
- Suggested learning rates: **0.1, 0.01** — avoid very large values.
""")

# Assumptions of Linear Regression
st.markdown("<h2 style='color: #002244;'>Core Assumptions in Linear Regression</h2>", unsafe_allow_html=True)
st.write("""
1. **Linearity**: Relationship between input and output is linear.
2. **No Multicollinearity**: Features should not be highly correlated.
3. **Homoscedasticity**: Errors should have constant variance.
4. **Normality of Errors**: Residuals are normally distributed.
5. **No Autocorrelation**: Residuals are independent of each other.
""")

# Evaluation Metrics
st.markdown("<h2 style='color: #002244;'>Model Evaluation Metrics</h2>", unsafe_allow_html=True)
st.write("""
- **Mean Squared Error (MSE)**: Average squared error between predicted and actual values.
- **Mean Absolute Error (MAE)**: Average absolute difference.
- **R-squared (R²)**: Proportion of variance explained by the model.
""")

# Jupyter Notebook Link
st.markdown("<h2 style='color: #002244;'>Practice Notebook: Linear Regression Implementation</h2>", unsafe_allow_html=True)
st.markdown("<a href='https://colab.research.google.com/drive/11-Rv7BC2PhOqk5hnpdXo6QjqLLYLDvTD?usp=sharing' target='_blank' style='font-size: 16px; color: #002244;'>Click here to open the Jupyter Notebook</a>", unsafe_allow_html=True)

# Closing Message
st.write("Linear Regression remains a simple yet powerful tool. Understanding how it works under the hood—optimization, assumptions, and evaluation—helps in building better models.")