Chapter 12.4, Problem 51E

Refer to Example 12.12 in which x = test track speed and y = rolling test speed.

1. a. Minitab gave $s_{{\hat{\beta }}_0+{\hat{\beta }}_1(45)}=.120$ and $s_{{\hat{\beta }}_0+{\hat{\beta }}_1(47)}=.186$. Why is the former estimated standard deviation smaller than the latter one?
2. b. Use the Minitab output from the example to calculate a 95% CI for expected rolling speed when test speed = 45.
3. c. Use the Minitab output to calculate a 95% PI for a single value of rolling speed when test speed = 47.