Question

Required information Exercise 5A-2 Least-Squares Regression [LO5-11) (The following information applies to the questions displayed below.) Bargain Rental Car offers rental cars in an off-airport location near a major tourist destination in California. Management would like to better understand the variable and fixed portions of it car washing costs. The company operates its own cal wash facility in which each rental car that is returned is thoroughly cleaned before being released for rental to another customer. Management believes that the variable portion of its car washing costs relates to the number of rental returns. Accordingly, the following data have been compiled: Month January February March April May June July August September October November December Rental Returns Car Wash Costs 2,500 $ 12, 100 2,600 $ 13, 700 2,800 $ 12,900 3,200 $ 15,900 3,700 $ 17,300 5,300 $ 25,500 5,600 $ 23, 300 5,800 $ 24,900 4,800 $ 23,900 5, 200 $ 24,400 2,300 $ 11,800 3,200 $ 18, 100

Answer 1

Solution:

X 2500 2600 2800 3200 3700 5300 5600 5800 4800 5200 2300 3200 47000 Y X*Y $12,100 $ 30,250,000 $13,700 $ 35,620,000 $12,900 $ 36,120,000 $15,900 $ 50,880,000 $17,300 $ 64,010,000 $25,500 $ 135,150,000 $23,300 $ 130,480,000 $24,900 $ 144,420,000 $23,900 $ 114,720,000 $24,400 $ 126,880,000 $11,800 $ 27,140,000 $18,100 $ 57,920,000 $223,800 $ 953,590,000 Square of X 6,250,000 6,760,000 7,840,000 10,240,000 13,690,000 28,090,000 31,360,000 33,640,000 23,040,000 27,040,000 5,290,000 10.240.000 203,480,000

Here ΣX = $47,000, ΣΥ = $223,800, ΣΧΥ = $953,590,000 and Σχ' = $203,480,000 Variable cost per rental return ηΣxy - (Σx)(Σy) ηΣx? - (Σκ)? = [12x953,590,000 - 47,000*223,800](12*203,480,000 - 47,000^2) = $3.97 Σy - bΣx Fixed cost per month = . =(223,800-3.97*47,000)/12 = $3,094