Page 261 - Applied Statistics with R

Chapter 13

Model Diagnostics

“Your assumptions are your windows on the world. Scrub them off
every once in a while, or the light won’t come in.”
— Isaac Asimov

After reading this chapter you will be able to:

• Understand the assumptions of a regression model.
• Assess regression model assumptions using visualizations and tests.
• Understand leverage, outliers, and influential points.
• Be able to identify unusual observations in regression models.

13.1 Model Assumptions

Recall the multiple linear regression model that we have defined.

= + + + ⋯ + −1 ( −1) + , = 1, 2, … , .

0
1 1
2 2

Using matrix notation, this model can be written much more succinctly as
= + .
Given data, we found the estimates for the parameters using

̂
⊤
⊤
= ( ) −1 .
We then noted that these estimates had mean
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