Linear Regression using Ordinary Least Square method

Ordinary Least Square 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: Add a Column of Ones to X for the Intercept

# Add a column of ones to X for the intercept

X_b = np.c_[np.ones((X.shape[0], 1)), X]

Step 4: Implement the OLS Method

# Calculate the OLS estimate of theta (the coefficients)

theta_best = np.linalg.inv(X_b.T.dot(X_b)).dot(X_b.T).dot(y)

Step 5: Make Predictions

# Make predictions

y_pred = X_b.dot(theta_best)

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()

Dr.Muttipati