Question

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	Rental Returns		Car Wash Costs
January	2,500		$	12,100
February	2,600		$	13,700
March	2,800		$	12,900
April	3,200		$	15,900
May	3,700		$	17,300
June	5,300		$	25,500
July	5,600		$	23,300
August	5,800		$	24,900
September	4,800		$	23,900
October	5,200		$	24,400
November	2,300		$	11,800
December	3,200		$	18,100

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.)

Answer 1

	Let it "X"	Let it "Y"
Month	Rental Returns	Car Wash Costs	X*Y	X(2)
January	2,500	12,100	3,02,50,000	62,50,000
February	2,600	13,700	3,56,20,000	67,60,000
March	2,800	12,900	3,61,20,000	78,40,000
April	3,200	15,900	5,08,80,000	1,02,40,000
May	3,700	17,300	6,40,10,000	1,36,90,000
June	5,300	25,500	13,51,50,000	2,80,90,000
July	5,600	23,300	13,04,80,000	3,13,60,000
August	5,800	24,900	14,44,20,000	3,36,40,000
September	4,800	23,900	11,47,20,000	2,30,40,000
October	5,200	24,400	12,68,80,000	2,70,40,000
November	2,300	11,800	2,71,40,000	52,90,000
December	3,200	18,100	5,79,20,000	1,02,40,000
Total	47,000	2,23,800	95,35,90,000	20,34,80,000
	no of months = 12
	y = total wash cost
	a = total fixed costs
	b = variable cost per level of rental returns
	x = level of returns
	Variable cost = {n∑xy – (∑x)(∑y)} /{n∑x² – (∑x)²}		i.e. = (12*953590000)-(47000*223800) / (12*203480000)-(47000*47000)	So variable cost = 3.97
	Fixed cost =( ∑y – b∑x)/n			i.e. = 223800-(3.97*47000) / 12	so, Fixed cost = 3100