Regression

Regression

Regression is a type of supervised learning used to predict a continuous output variable based on one or more input features.

What is Regression?

In regression tasks, the goal is to model the relationship between input variables (features) and a continuous target variable. The model learns to estimate the output value for new inputs.

Types of Regression

• Simple Linear Regression: Models the relationship between a single input feature and output as a straight line.

 Example: Predicting house price based on size.  

• Multiple Linear Regression: Uses multiple features to predict the output.
• Polynomial Regression: Models nonlinear relationships by adding polynomial terms.
• Other Regression Types: Ridge regression, Lasso regression, Logistic regression (for classification), etc.

How Regression Works

The model learns parameters (coefficients) that minimize the difference between predicted and actual values using a loss function, typically Mean Squared Error (MSE):

$MSE=\frac{1}{n}\sum _{i=1}^n(y_i-{\hat{y}}_i{)}^2$

Where:

• $y_i$ = actual output
• ${\hat{y}}_i$ = predicted output
• $n$ = number of samples

Applications of Regression

• Predicting prices (houses, stocks)
• Estimating temperatures
• Forecasting sales or demand
• Modeling relationships between variables in science and engineering

Advantages of Regression

• Easy to interpret and implement.
• Provides quantitative predictions.
• Useful for understanding relationships between variables.

Challenges in Regression

• Sensitive to outliers.
• Assumes a specific functional form (linear or polynomial).
• Can underfit or overfit if not properly tuned.

Related Pages

• Supervised Learning
• Classification
• Regularization
• Overfitting
• Underfitting
• Evaluation Metrics

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