multi-linear-regression

A basic implementation of multi linear regression using gradient descent. Synthetic housing price data is generated based on area and number of rooms. Includes data visualization and model training from scratch using NumPy and Matplotlib #MachineLearning #LinearRegression #GradientDescent #Python #NumPy #Matplotlib
#DataScience #ArtificialData #Regression #DeepLearning #AI #HousingPrices
#DataVisualization #ML #SyntheticData #Coding #OpenSource
import numpy as np import matplotlib.pyplot as plt

Number of data points

n = 200

Generate house area (X1) from a normal distribution with mean=175 and std=30

X1 = np.random.normal(loc=175, scale=30, size=n)

Clip values to keep them within the range [50, 300]

X1 = np.clip(X1, 50, 300)

Generate the number of rooms (X2) as random integers between 1 and 6

X2 = np.random.randint(1, 7, size=n)

Generate house prices using a linear equation with some noise

price = X1 * 200 + X2 * 100 + 500 + np.random.normal(0, 3000, size=n)

Initialize parameters (weights and bias) randomly with small values

w1 = np.random.randn() * 0.1 # Weight for X1 (house area) w2 = np.random.randn() * 0.1 # Weight for X2 (number of rooms) b = np.random.randn() * 0.1 # Bias term

Set learning rate and number of iterations for gradient descent

learning_rate = 0.00001 iterations = 1000

Perform gradient descent to optimize weights and bias

for i in range(iterations): # Compute predictions using the current weights and bias predictions = w1 * X1 + w2 * X2 + b

# Compute gradients (partial derivatives of the loss function)
dw1 = (2/n) * np.sum((predictions - price) * X1)  # Gradient for w1
dw2 = (2/n) * np.sum((predictions - price) * X2)  # Gradient for w2
db = (2/n) * np.sum((predictions - price))        # Gradient for bias

# Update parameters using gradient descent
w1 -= learning_rate * dw1
w2 -= learning_rate * dw2
b -= learning_rate * db

# Compute Mean Squared Error (MSE) loss
Loss = (1/n) * np.sum((predictions - price) ** 2)

# Print loss every 50 iterations to monitor training progress
if i % 50 == 0:
    print(f"Iteration {i}: Loss {Loss}")

Compute final predicted values using trained weights and bias

y = w1 * X1 + w2 * X2 + b

Plot the data points (house area vs price)

plt.scatter(X1, price, alpha=0.5, label='Data')

Plot the fitted regression line

plt.plot(X1, y, label='Fitted Line', color='r')

Add legend to the plot

plt.legend()

Show the plot

plt.show()