Question

1.-Given are five observations for two variables, x and y.

xi	1	2	3	4	5
yi	4	7	4	10	15

(d) Develop the estimated regression equation by computing the values of b₀ and b₁ using b₁ =(Σ(x_i − x)(y_i − y))/Σ(x_i − x)² and b₀ =  y − b₁x.

(e)Use the estimated regression equation to predict the value of y when x = 2.

2.-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	118
Company B	10.0	135
Company C	9.0	100
Company D	5.5	37
Company E	4.2	42
Company F	3.3	30

(c) 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 =_____

(d) 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.

(e) A particular rental company has 6,000 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

1)

d) from above bo= 0.5

b1= 2.50

y^ =0.5+2.5x

e)predicted value =0.5+2.5*2 =5.5

2)

c)

d)

Annual revenue will increase by $ 12998 for every additional car placed in service.

e)

predcited value =-17.235+12.998*6 = $ 61 million