Linear Regression using Ordinary Least Square method

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Ordinary Least Square Method

Download Dataset

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()







 

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