Page 168 - Applied Statistics with R

168 CHAPTER 9. MULTIPLE LINEAR REGRESSION

82
X
80
78

year 76 X

74
72

70

1500 2000 2500 3000 3500 4000 4500 5000

wt

However, we have to consider weight and year together now. And based on the
above plot, one of the new cars is within the “blob” of observed values, while
the other, the car from 1981 weighing 5000 pounds, is noticeably outside of the
observed values. This is a hidden extrapolation which you should be aware of
when using multiple regression.
Shifting gears back to the new data pair that can be reasonably estimated, we
do a quick verification of some of the mathematics in R.

x0 = c(1, 3500, 76)
x0 %*% beta_hat

## [,1]
## [1,] 20.00684

1
⎡
= 3500 ⎤
⎢
⎥
0
⎣ 76 ⎦
−14.6376419
̂
= ⎡ −0.0066349 ⎤
⎥
⎢
⎣ 0.761402 ⎦