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Exercise 5A-2 (Algo) Least-Squares Regression [LO5-11]

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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 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		$	12,000
February	2,500		$	13,600
March	2,800		$	12,800
April	3,200		$	15,800
May	3,700		$	17,200
June	5,200		$	25,300
July	5,600		$	23,200
August	5,700		$	24,700
September	4,800		$	23,800
October	4,700		$	24,100
November	2,300		$	11,700
December	3,200		$	17,700

Exercise 5A-2 Part 2 (Algo)

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.)

Answer 1

Month	x=rental returns	y = car wash costs	xy	X2
Jan	2,500	12,000	3,00,00,000	62,50,000
Feb	2,500	13,600	3,40,00,000	62,50,000
Mar	2800	12,800	3,58,40,000	78,40,000
April	3200	15,800	5,05,60,000	1,02,40,000
May	3700	17,200	6,36,40,000	1,36,90,000
June	5200	25,300	13,15,60,000	2,70,40,000
July	5600	23,200	12,99,20,000	3,13,60,000
Aug	5700	24,700	14,07,90,000	3,24,90,000
Sep	4800	23,800	11,42,40,000	2,30,40,000
Oct	4700	24,100	11,32,70,000	2,20,90,000
Nov	2300	11,700	2,69,10,000	52,90,000
Dec	3200	17,700	5,66,40,000	1,02,40,000
Total	46,200	2,21,900	92,73,70,000	19,58,20,000

N = number of months = 12

Variable cost per rental return =( N Σxy − Σx Σy)/{(N Σx²) − (Σx)²}

Variable cost per rental return ={( 12 × 92,73,70,000) - (46,200× 2,21,900) } / {(12 ×19,58,20,000) - (46,200)²}

On solving VC per Rental return = 4.0699 or 4.07

Fixed Cost per month = {Σy - ( Variable cost per rental return × Σx )/N

Fixed Cost per month = {2,21,900 - (4.07 × 46,200)} /12

Fixed cost Per month = 33,866/12 = 2822.17