Several research workers associated with the Office of Highway Safety were evaluating the relationship between driving speed

Question:

Several research workers associated with the Office of Highway Safety were evaluating the relationship between driving speed (MPH) and the distance a vehicle travels once brakes are applied (DIST). The results of 19 experimental tests are displayed in the following table.
a. Determine the least-squares estimates of the slope and intercept for each of the following straight-line regressions: Y1 (DIST) on X and Y2 (ˆšDIST) on X. Draw the estimated lines on the appropriate scatter diagrams.
b. Which of the two variable pairs mentioned in part (a) seems to be better suited for straight-line regression?
c. For the variable pair Y2 and X, test the hypothesis that the true slope is equal to 1 (use Î± = .01). Be sure to interpret your result.
d. Construct a 99% confidence interval for the true slope in part (c). Interpret your result.
e. For the same variable pair considered in parts (c) and (d), calculate and sketch 95% confidence bands on the appropriate scatter diagram. Using the confidence bands, estimate the mean value of Y2 when X = 45. Interpret your result.