Update pages/5Linear_Regression.py

pages/5Linear_Regression.py

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+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.")