Linear Regression and Its Applications

Python Implementation: Simple Linear Regression

# Import required libraries
from sklearn.linear_model import LinearRegression
import numpy as np
import matplotlib.pyplot as plt

# Sample data: Study hours vs. exam score
X = np.array([[1], [2], [3], [4], [5], [6]])  # Hours studied
y = np.array([50, 55, 65, 70, 75, 85])        # Exam score

# Create a Linear Regression model
model = LinearRegression()
model.fit(X, y)

# Predict
y_pred = model.predict(X)

# Coefficients
print("Intercept (b0):", model.intercept_)
print("Slope (b1):", model.coef_[0])

# Plotting the regression line
plt.scatter(X, y, color='blue', label='Actual Scores')
plt.plot(X, y_pred, color='red', label='Regression Line')
plt.xlabel("Hours Studied")
plt.ylabel("Exam Score")
plt.title("Linear Regression Example")
plt.legend()
plt.show()

Output -

Intercept (b0): 42.66666666666667
Slope (b1): 6.857142857142858

Model Evaluation Metrics

To evaluate the model, use metrics such as:

• Mean Absolute Error (MAE)
• Mean Squared Error (MSE)
• Root Mean Squared Error (RMSE)
• R² Score (Coefficient of Determination)

from sklearn.metrics import mean_squared_error, r2_score

mse = mean_squared_error(y, y_pred)
r2 = r2_score(y, y_pred)

print("MSE:", mse)
print("R² Score:", r2)

Output-

MSE: 1.746031746031747
R² Score: 0.9874285714285714

Tips for Beginners

• Always visualize your data to check if a linear model makes sense.
• Standardize or normalize features for better results in multiple regression.
• Use evaluation metrics to determine how well your model fits the data.

Tips for Professionals

• Regularize linear regression using Ridge or Lasso if overfitting occurs.
• Use statsmodels for statistical insight and p-values.
• Check for multicollinearity using Variance Inflation Factor (VIF) when working with multiple features.

Summary

• Linear Regression predicts continuous values using a linear approach.
• It's simple, interpretable, and often used as a baseline model.
• Ideal for scenarios where relationships between variables are approximately linear.