To relate the stopping distance of a car to its speed, ten cars were tested at five different speeds, two cars at each speed. The following data were obtained. Speed (x) 20 20 30 30 40 50 50 60 60
Stop. Dist. y (ft) 16.3 26.7 39.2 63.5 65.7 98.4 104.1 155.6 217.2

Required:
a. Fit a least-squares linear equation to these data. Plot the residuals against the speed.
b. Comment on the goodness of the fit based on the overall F-statistic and the residual plot. Which two assumptions of the linear regression model seem to be violated?
c. Based on the residual plot, what transformation of stopping distance should be used to lin- earize the relationship with respect to speed? A clue to find this transformation is provided by the following engineering argument: In bringing a car to a stop, its kinetic energy is dissipated as its braking energy, and the two are roughly equal. The kinetic energy is pro- portional to the square of the car's speed, while the breaking energy is proportional to the stopping distance, assuming a constant braking force.
d. Make this linearizing transformation and check the goodness of fit. What is the predicted stopping distance according to this model if the car is traveling at 40 mph?