As part of its ongoing testing and reporting program, the Insurance Institute for Highway Safety has crashed vehicles into a barrier intended to represent another vehicle’s bumper, then recorded the cost of repairs necessary to fix whatever damage has occurred.

In these tests, the simulated bumper was set at 16 inches from the ground in the corner tests, and at 18 inches from the ground in the full-width tests. In crash-testing a sample of mini and micro-cars at 6 mph, the repair costs were as shown in the table.

a. Based on these data, determine the least-squares regression equation for predicting rear full-width crash repair cost on the basis of rear corner crash repair cost.

b. Determine and interpret the coeffi cients of correlation and determination.

c. Based on these data, if a mini or micro-car like the ones tested were to incur $800 in damages in the rear corner test, what level of repairs would be predicted for the rear full-width test?

Vehicle Tested Rear Full-Width Rear Corner Smart Fortwo $631 $507 Chevrolet Aveo 1370 612 Mini Cooper 929 743 Toyota Yaris 3345 474 Honda Fit 3648 999 Hyundai Accent 2057 831 Kia Rio 3148 773