Page 214 - Applied Statistics with R

214 CHAPTER 11. CATEGORICAL PREDICTORS AND INTERACTIONS

So here we see that

̂
̂
+ = 46.0548423 + −12.5754714 = 33.4793709
0
2
is the estimated average mpg for a domestic car with 0 disp.
Now let’s try to do the same, but using our new factor variable.

(mod_factor = lm(mpg ~ disp * origin, data = autompg))

##
## Call:
## lm(formula = mpg ~ disp * origin, data = autompg)
##
## Coefficients:
## (Intercept) disp originforeign disp:originforeign
## 33.47937 -0.05441 12.57547 -0.10252

It seems that it doesn’t produce the same results. Right away we notice that
the intercept is different, as is the the coefficient in front of disp. We also notice
that the remaining two coefficients are of the same magnitude as their respective
counterparts using the domestic variable, but with a different sign. Why is this
happening?
It turns out, that by using a factor variable, R is automatically creating a dummy
variable for us. However, it is not the dummy variable that we had originally
used ourselves.
R is fitting the model

= + + + + ,
2 2
3 1 2
0
1 1
where
• is mpg, the fuel efficiency in miles per gallon,
• is disp, the displacement in cubic inches,
1
• is a dummy variable created by R. It uses 1 to represent a foreign
2
car.

So now,

̂
= 33.4793709
0
is the estimated average mpg for a domestic car with 0 disp, which is indeed
the same as before.