Understanding Regression Algorithms in Machine Learning

Introduction to Regression

Regression is a supervised learning technique that predicts continuous numerical values by understanding relationships between variables in a dataset. Unlike classification, which predicts categories, regression predicts quantities.

Types of Regression

1. Simple Linear Regression

• Definition: Predicts a dependent variable based on a single independent variable

• Mathematical Form: Y = mx + b

  • Y: Dependent variable (output)

  • x: Independent variable (input)

  • m: Coefficient (slope)

  • b: Intercept

• Example: Real Estate Price Prediction

  • Input: House square footage

  • Output: House price

2. Multiple Linear Regression

• Definition: Predicts dependent variable based on multiple independent variables

• Mathematical Form: Y = m₁x₁ + m₂x₂ + ... + mₙxₙ + b

• Real Estate Example Features:

  • Square footage

  • Number of bathrooms

  • Number of bedrooms

  • Year built

  • Location

3. Polynomial Regression

• Definition: Handles non-linear relationships between variables

• Mathematical Form: Y = m₁x₁² + m₂x₂ + b

• Use Case: When relationship is exponential or non-linear

  • Example: House price increasing exponentially with number of bedrooms

Regression vs. Classification

Aspect	Regression	Classification
Objective	Predicts continuous values	Predicts categories/classes
Output Type	Quantitative (numerical)	Categorical (discrete)
Evaluation Metrics	MSE, RMSE, R-squared	Accuracy, Precision, Recall

Practical Implementation: Linear Regression Example

Setup and Data Preparation

# Import required libraries
import pandas as pd
from sklearn.linear_model import LinearRegression
import matplotlib.pyplot as plt

# Read the dataset
df = pd.read_csv('employee.csv')

Data Exploration

# Select features for analysis
X = df[['age']]  # Independent variable
y = df['salary']  # Dependent variable

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

# Print model parameters
print(f"Intercept: {model.intercept_:.2f}")
print(f"Coefficient: {model.coef_[0]:.2f}")

Visualization

# Plot the regression line
plt.figure(figsize=(10, 6))
plt.scatter(X, y, color='blue', alpha=0.5)
plt.plot(X, model.predict(X), color='red', linewidth=2)
plt.xlabel('Age')
plt.ylabel('Salary')
plt.title('Age vs Salary Linear Regression')
plt.grid(True)
plt.show()

Making Predictions

# Example prediction
age_test = [[35]]
predicted_salary = model.predict(age_test)
print(f"Predicted salary for age 35: ${predicted_salary[0]:,.2f}")

Best Practices in Regression

1. Data Preparation

• Check for missing values

• Handle outliers

• Normalize/standardize features if needed

• Split data into training and testing sets

2. Model Selection

• Consider relationship type (linear vs non-linear)

• Evaluate complexity needs

• Account for number of features

3. Model Evaluation

• Use appropriate metrics:

  • Mean Squared Error (MSE)

  • Root Mean Squared Error (RMSE)

  • R-squared (R²)

• Validate assumptions:

  • Linearity

  • Independence

  • Homoscedasticity

  • Normality

4. Common Pitfalls to Avoid

• Overfitting

• Multicollinearity in multiple regression

• Extrapolation beyond data range

• Ignoring outliers

Advanced Considerations

1. Feature Engineering

2. Regularization Techniques

3. Cross-Validation

4. Hyperparameter Tuning