Mileage study. The effectiveness of a new experimental overdrive gear in reducing gasoline consumption was studied in 12 trials with a light truck equipped with this gear. In the data ) that follow, Xi denotes the constant speed (in miles per hour) on the test track in the ith trial and Yi denotes miles per gallon obtained.
Second-order regression model (8.2) with independent normal error terms is expected to be appropriate.
a. Fit regression model (8.2). Plot the fitted regression function and the data. Does the quadratic regression function appear to be a good fit here?
b. Automotive engineers would like to estimate the speed Xmax at which the average mileage E {Y} is maximized. It can be shown for second-order model (8.2) that Xmax =
c. Using fixed X sampling, obtain 1,000 bootstrap samples of size 12. For each bootstrap sample, fit regression model (8.2) and obtain the bootstrap estimate 
d. Construct a histogram of the 1,000 bootstrap estimates Does the bootstrap sampling distribution of appear to approximate a normal distribution?
e. Construct a 90 percent bootstrap confidence interval for 
using reflection method (11.56). How precisely has been estimated?