Question

Required information Exercise 6A-2 Least-Squares Regression [L06-11] The following information applies to the questions displayed below.J 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 its car washing costs. The company operates its own car 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 2,500 2,800 3,200 3,700 5,200 5,600 5,700 4,800 4,700 2,300 3,200 $ 12,000 ş 13,600 $ 12,800 ş 15,800 17,200 $ 25,300 $ 23,200 $ 24,700 ş 23,800 $ 24,100 $ 11,700 $ 17,700 rcise 6A-2 Part 2

Answer 1

Month	Rental returns (X)	car wash cost (y)	XY	X^2
Jan	2500	12000	2500*12000= 30000000	2500*2500= 6250000
Feb	2500	13600	34000000	6250000
mar	2800	12800	35840000	7840000
Apr	3200	15800	50560000	10240000
May	3700	17200	63640000	13690000
Jun	5200	25300	131560000	27040000
Jul	5600	23200	129920000	31360000
Aug	5700	24700	140790000	32490000
Sep	4800	23800	114240000	23040000
Oct	4700	24100	113270000	22090000
Nov	2300	11700	26910000	5290000
Dec	3200	17700	56640000	10240000
Total(12 months)	46200	221900	927,370,000	195,820,000

unit variable cost = {n(Sum of XY)- (Sum of X)(Sum of Y)}/ {n(sum of x^2) - (sum of x)^2}

   ={12(927370000)-(46200)(221900)}/{12(195820000)-(46200)^2}

   ={111284400000- 10251780000}/{2349840000- 2134440000}

    = 876,660,000/215400000

    = 4.07

Fixed cost={ (Sum of Y) - b(sum of X) }/n

       ={221900- (4.07*46200) }/12

       = {221900- 188034]/12

      = 33866/12

      = $ 2822