Question

Companies in the U.S. car rental market vary greatly in terms of the size of the fleet, the number of locations, and annual revenue. In 2011, Hertz had 320,000 cars in service and annual revenue of approximately $4.2 billion. Suppose the following data show the number of cars in service (1,000s) and the annual revenue ($ millions) for six smaller car rental companies.

Company	Cars (1,000s)	Revenue ($ millions)
Company A	11.5	116
Company B	10.0	133
Company C	9.0	102
Company D	5.5	37
Company E	4.2	38
Company F	3.3	30

Use the least squares method to develop the estimated regression equation that can be used to predict annual revenue (in $ millions) given the number of cars in service (in 1,000s). (Round your numerical values to three decimal places.)

ŷ =   

For every additional car placed in service, estimate how much annual revenue will change (in dollars). (Round your answer to the nearest integer.)

Annual revenue will increase by $   , for every additional car placed in service.

A particular rental company has 4,000 cars in service. Use the estimated regression equation developed in part (c) to predict annual revenue (in $ millions) for this company. (Round your answer to the nearest integer.)

$  million

Answer 1

Sum of X = 43.5
Sum of Y = 456
Mean X = 7.25
Mean Y = 76
Sum of squares (SSX) = 56.655
Sum of products (SP) = 738.1

Regression Equation = ŷ = bX + a

b = SP/SSX = 738.1/56.66 = 13.028

a = MY - bMX = 76 - (13.03*7.25) = -18.453

ŷ = 13.028X - 18.453

Slope is additional car placed in service, and its value is 13.028

Annual revenue will increase by $ 13.028 , for every additional car placed in service.

Now for x=4, ŷ = (13.028*4) - 18.453=33.659