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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 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	Rental Returns		Car Wash Costs
January	2,400		$	11,400
February	2,500		$	13,300
March	2,800		$	12,200
April	3,100		$	14,900
May	3,700		$	16,600
June	5,100		$	24,100
July	5,600		$	22,600
August	5,600		$	23,200
September	4,800		$	23,200
October	4,100		$	22,300
November	2,200		$	11,100
December	3,000		$	15,600

2. Using least-squares regression, estimate the variable cost per rental return and the monthly fixed cost incurred to wash cars. (Round Fixed cost to the nearest whole dollar amount and the Variable cost per unit to 2 decimal places.)

fixed cost per month:

variable cost per rental return:

Answer 1

Month	Rental Returns(X)	Total Cost(Y)(in $)	Square of X	X*Y(in $)
Jan	2,400	11,400	57,60,000	2,73,60,000
Feb	2,500	13,300	62,50,000	3,32,50,000
Mar	2,800	12,200	78,40,000	3,41,60,000
Apr	3,100	14,900	96,10,000	4,61,90,000
May	3,700	16,600	1,36,90,000	6,14,20,000
Jun	5,100	24,100	2,60,10,000	12,29,10,000
Jul	5,600	22,600	3,13,60,000	12,65,60,000
Aug	5,600	23,200	3,13,60,000	12,99,20,000
Sep	4,800	23,200	2,30,40,000	11,13,60,000
Oct	4,100	22,300	1,68,10,000	9,14,30,000
Nov	2,200	11,100	48,40,000	2,44,20,000
Dec	3,000	15,600	90,00,000	4,68,00,000
Total	44,900	2,10,500	18,55,70,000	85,57,80,000
	Unit Variable Cost (b) = nΣxy − (Σx)(Σy) /nΣx^2 − (Σx)^2		Total Fixed Cost (a) = Σy − bΣx / n
So here n =12 ,Σx =44.900, Σy =210,500, Σx^2=18,55,70,000 ,Σxy =85,57,80,000
Variable cost per unit(b) =12*85,57,80,000 - (44,900*210,500) / 12*18,55,70,000 - 44,900^2
Variable cost per unit(b) =10,26,93,60,000 - 9,45,14,40,000 / 2,03,18,40,000 - 2,01,60,10,000
Variable cost per unit(b) =81,79,10,000 / 21,08,30,000 =$3.88
Total Fixed cost =210,500 - ($3.88*44,900) / 12
Total Fixed cost =(210,500 - 174,212) / 12
Total Fixed cost =$36,288 /12 =$3,024
The cost volume formula is:
y =$3,024 + $3.88X