Linear Regression (Simple & Multiple)

Simple Linear Regression

Simple linear regression involves modeling the relationship between one independent variable (X) and one dependent variable (Y) using a straight line:

Y = β₀ + β₁X + ε

• β₀: Intercept (value of Y when X=0)
• β₁: Slope (change in Y for a one-unit change in X)
• ε: Error term (difference between predicted and actual Y)

Multiple Linear Regression

Multiple linear regression extends simple linear regression by using multiple independent variables to predict the dependent variable:

Y = β₀ + β₁X₁ + β₂X₂ + ... + βₙXₙ + ε

• Allows modeling more complex relationships involving multiple features.
• Each coefficient represents the effect of the corresponding feature on the target variable.

Simple Linear Regression Example in Python

import numpy as np
import matplotlib.pyplot as plt
from sklearn.linear_model import LinearRegression

# Sample data
X = np.array([1, 2, 3, 4, 5]).reshape(-1, 1)
y = np.array([3, 4, 2, 5, 6])

# Create and train model
model = LinearRegression()
model.fit(X, y)

# Predictions
y_pred = model.predict(X)

# Plot
plt.scatter(X, y, color='blue')
plt.plot(X, y_pred, color='red')
plt.title('Simple Linear Regression')
plt.xlabel('X')
plt.ylabel('Y')
plt.show()

Multiple Linear Regression Example in Python

import numpy as np
from sklearn.linear_model import LinearRegression

# Sample data (3 features)
X = np.array([
    [1, 2, 3],
    [2, 0, 1],
    [3, 5, 2],
    [4, 3, 3],
    [5, 4, 5]
])
y = np.array([14, 8, 19, 18, 25])

# Create and train model
model = LinearRegression()
model.fit(X, y)

# Coefficients
print("Intercept:", model.intercept_)
print("Coefficients:", model.coef_)

# Predict for new data
new_data = np.array([[6, 3, 4]])
prediction = model.predict(new_data)
print("Prediction for", new_data, "is", prediction)