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 (√DIST) 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 α = .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.