Speed	Mileage
20	24.67
22	24.47
24	25.93
26	27.2
28	28.35
30	28.69
32	28.12
34	29.14
36	30.9
38	30.03
40	29.43
42	29.96
44	30.99
46	29.98
48	30.06
50	31.37
52	30.17
54	30.61
56	29.64
58	28.45
60	27.09
62	26.84
64	27.67
66	26.47
68	24.75
70	26.72

1) A study was done to compare the speed x (in miles per hour) with the mileage y (in miles per gallon) of a particular automobile. (File: Mileage).

a) Find an appropriate regression model for the prediction of mileage based on speed. Provide all the necessary model diagnostics to demonstrate the appropriateness of fit.

b) Predict mileage when the speed is 37 miles per hour. Report your answer to the nearest hundredth place. Show the hand computation.

c) Based on the fitted regression model, find the speed that is associated with the greatest mileage. Report your answer to the nearest hundredth place. Show the hand computation. (Hint: you are simply finding the xcoordinate value for the vertex of the function. A simple Google search will give you many sites telling you the formula for the xcoordinate value.)

solve with proper calculation and show screeenshot of excel