Linear Regression using Gradient Descent method

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Gradient Descent Method

Step 1: Import the necessary libraries

import numpy as np 
import pandas as pd 
import matplotlib.pyplot as plt

Step 2: Load the CSV Data

# Load the dataset  
data = pd.read_csv('house_data.csv') 

# Extract the features (X) and target variable (y) 
X = data['Size'].values
y = data['Price'].values

# Reshape X to be a 2D array
X = X.reshape(-1, 1)

# Add a column of ones to X for the intercept
 X_b = np.c_[np.ones((X.shape[0], 1)), X] 

Step 3: Initialize Parameters
# Initialize the parameters
theta = np.random.randn(2)  # Random initialization of theta (intercept and slope)
learning_rate = 0.01
n_iterations = 1000
m = len(y)  # Number of training examples

Step 4: Implement the Gradient Descent Algorithm
# Gradient Descent
for iteration in range(n_iterations):
    gradients = 2/m * X_b.T.dot(X_b.dot(theta) - y)
    theta = theta - learning_rate * gradients

Step 5: Make Predictions
# Make predictions
y_pred = X_b.dot(theta)

Step 6: Visualize the Results
# Plot the data and the regression line
plt.scatter(X, y, color='blue', label='Data')
plt.plot(X, y_pred, color='red', label='Regression Line')
plt.xlabel('Size (Square Feet)')
plt.ylabel('Price (Dollars)')
plt.legend()
plt.show()


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