Page 209 - Applied Statistics with R

11.2. INTERACTIONS 209

Foreign
Domestic
40

mpg 30

20

10

100 200 300 400

disp

We see that these lines fit the data much better, which matches the result of
our tests.
So far we have only seen interaction between a categorical variable (domestic)
and a numerical variable (disp). While this is easy to visualize, since it allows
for different slopes for two lines, it is not the only type of interaction we can use
in a model. We can also consider interactions between two numerical variables.
Consider the model,

= + + + + ,
1 1
0
3 1 2
2 2
where
• is mpg, the fuel efficiency in miles per gallon,
• is disp, the displacement in cubic inches,
1
• is hp, the horsepower, in foot-pounds per second.
2
How does mpg change based on disp in this model? We can rearrange some
terms to see how.

= + ( + ) + +
2 2
1
0
1
3 2
So, for a one unit increase in (disp), the mean of (mpg) increases + ,
1
1
3 2
which is a different value depending on the value of (hp)!
2