Ass1 (linear regression)

 import pandas as pd

import numpy as np

import matplotlib.pyplot as plt

from sklearn.model_selection import train_test_split

from sklearn.metrics import mean_squared_error, r2_score

df = pd.read_csv('FuelConsumption.csv')

print(df.head())

# ========== STEP 2: LINEAR REGRESSION FUNCTIONS ==========

# Hypothesis: h(x) = X @ theta

def gradient_descent(X, y, theta, alpha, iterations):

m = len(y)

cost_history = []

for _ in range(iterations):

predictions = X.dot(theta)

error = predictions - y

gradient = (1/m) * X.T.dot(error)

theta -= alpha * gradient

cost = (1/(2*m)) * np.sum(error ** 2)

cost_history.append(cost)

if len(cost_history) > 1 and abs(cost_history[-1] - cost_history[-2]) < 1e-6:

break

return theta, cost_history

def evaluate(X, y, theta):

predictions = X.dot(theta)

mse = mean_squared_error(y, predictions)

r2 = r2_score(y, predictions)

return mse, r2

# ========== STEP 3: UNIVARIATE LINEAR REGRESSION ==========

print("\n--- Univariate Linear Regression ---")

X_uni = df[['ENGINESIZE']].values

y_uni = df[['CO2EMISSIONS']].values

X_uni = np.c_[np.ones(X_uni.shape[0]), X_uni]

X_train_uni, X_test_uni, y_train_uni, y_test_uni = train_test_split(X_uni, y_uni, test_size=0.2,

random_state=4)

theta_uni = np.zeros((X_uni.shape[1], 1))

alpha = 0.01

iterations = 1000

theta_uni_final, cost_history_uni = gradient_descent(X_train_uni, y_train_uni, theta_uni, alpha,

iterations)

# Print hypothesis

print(f"Hypothesis: h(x) = {theta_uni_final[0][0]:.2f} + {theta_uni_final[1][0]:.2f} *

EngineSize")

# Accuracy

mse_uni, r2_uni = evaluate(X_test_uni, y_test_uni, theta_uni_final)

print(f"MSE: {mse_uni:.2f}, R²: {r2_uni:.2f}")

# Plot cost

plt.plot(cost_history_uni)

plt.title("Univariate Cost Convergence")

plt.xlabel("Iterations")

plt.ylabel("Cost")

plt.grid(True)

plt.show()

# ========== STEP 4: MULTIVARIATE LINEAR REGRESSION ========== 

print("\n--- Multivariate Linear Regression ---") 

X_multi = df[['ENGINESIZE', 'CYLINDERS', 'FUELCONSUMPTION_COMB']].values 

y_multi = df[['CO2EMISSIONS']].values 

X_multi = np.c_[np.ones(X_multi.shape[0]), X_multi] 

X_train_multi, X_test_multi, y_train_multi, y_test_multi = train_test_split(X_multi, y_multi, 

test_size=0.2, random_state=42) 

theta_multi = np.zeros((X_multi.shape[1], 1)) 

theta_multi_final, cost_history_multi = gradient_descent(X_train_multi, y_train_multi, 

theta_multi, alpha, iterations) 

# Print hypothesis 

print("Hypothesis: h(x) = {:.2f} + {:.2f}*ENGINESIZE + {:.2f}*CYLINDERS + 

{:.2f}*FUELCONSUMPTION_COMB" 

.format(*theta_multi_final.flatten())) 

# Accuracy 

mse_multi, r2_multi = evaluate(X_test_multi, y_test_multi, theta_multi_final) 

print(f"MSE: {mse_multi:.2f}, R²: {r2_multi:.2f}") 

# Plot cost 

plt.plot(cost_history_multi) 

plt.title("Multivariate Cost Convergence") 

plt.xlabel("Iterations") 

plt.ylabel("Cost") 

plt.grid(True) 

plt.show()