Page 101 - Applied Statistics with R

7.2. LEAST SQUARES APPROACH 101

min(cars$speed) < 21 & 21 < max(cars$speed)

## [1] TRUE

̂ = −17.58 + 3.93 × 21

beta_0_hat + beta_1_hat * 21

## [1] 65.00149

Lastly, we can make a prediction for the stopping distance of a car traveling at
50 miles per hour. This is considered extrapolation as 50 is not an observed
value of and is outside data range. We should be less confident in predictions
of this type.

range(cars$speed)

## [1] 4 25

range(cars$speed)[1] < 50 & 50 < range(cars$speed)[2]

## [1] FALSE

̂ = −17.58 + 3.93 × 50

beta_0_hat + beta_1_hat * 50

## [1] 179.0413

Cars travel 50 miles per hour rather easily today, but not in the 1920s!
̂
This is also an issue we saw when interpreting = −17.58, which is equivalent
0
to making a prediction at = 0. We should not be confident in the estimated
linear relationship outside of the range of data we have observed.