13. Multiple Regression

This chapter extends simple regression to models with several predictors. You will interpret coefficients, assess model assumptions, and evaluate prediction quality with training and testing data.

Chapter Video

Video credit: StatQuest with Josh Starmer. What Is Multiple Regression and How Is It Used?. YouTube. Watch on YouTube.

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Learning Objectives

By the end of this chapter, you will be able to:

1. Explain how multiple regression extends simple linear regression.

2. Interpret regression coefficients while holding other predictors fixed.

3. Recognize multicollinearity and other modeling assumptions.

4. Evaluate model quality with errors and train/test comparisons.

5. Use multiple regression for applied prediction and explanation questions.

Chapter Flow

Linear Regression

Multiple Regression

Glossary

#	Term	Explanation
1	Multiple regression	Regression with more than one predictor.
2	Predictor	An input variable used in a model.
3	Target	The outcome variable being modeled.
4	Coefficient	A model parameter attached to a predictor.
5	Intercept	The predicted target when all predictors equal zero.
6	Holding constant	Interpreting one predictor while other predictors stay fixed.
7	Feature matrix	A table of predictor values used for modeling.
8	Response vector	The target values used for modeling.
9	Multicollinearity	Strong association among predictors.
10	Additivity	A model assumption that predictor effects combine by addition.
11	Linearity	A model assumption that relationships are represented by straight-line effects.
12	Residual	Observed value minus predicted value.
13	Residual diagnostic	A check based on residual patterns.
14	Training data	Data used to fit a model.
15	Test data	Data reserved to evaluate model performance.
16	Mean squared error	Average squared prediction error.
17	Root mean squared error	Square root of mean squared prediction error.
18	R-squared	The proportion of outcome variation explained by a model.
19	Overfitting	When a model fits training data too closely and generalizes poorly.
20	Interpretability	How easily a model can be explained.
21	Prediction pipeline	The steps used to prepare data, fit a model, and evaluate predictions.

Chapter Overview Slides