Page 153 - Applied Statistics with R

Chapter 9

Multiple Linear Regression

“Life is really simple, but we insist on making it complicated.”
— Confucius

After reading this chapter you will be able to:

• Construct and interpret linear regression models with more than one pre-
dictor.
• Understand how regression models are derived using matrices.
• Create interval estimates and perform hypothesis tests for multiple regres-
sion parameters.
• Formulate and interpret interval estimates for the mean response under
various conditions.
• Compare nested models using an ANOVA F-Test.

The last two chapters we saw how to fit a model that assumed a linear relation-
ship between a response variable and a single predictor variable. Specifically,
we defined the simple linear regression model,

= + +
0

1
2
where ∼ (0, ).

However, it is rarely the case that a dataset will have a single predictor variable.
It is also rarely the case that a response variable will only depend on a single
variable. So in this chapter, we will extend our current linear model to allow a
response to depend on multiple predictors.

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