Question

Check my work Required information [The following information applies to the Bargain Rental Car offers rental cars in an off-airport location near a major tourist destination in Californ would like to better understand the variable and fixed portions of it car washing costs. The company operates its wash facility in which each rental car that is returned is thorough customer. Management bel Accordingly, the following data have been compiled: own car before being released for rental to another lieves that the variable portion of its car washing costs relates to the number of rental returns r Wash Costs January February March April Hay June uly August September October November December 2,480 2,589 2,880 3,800 3,780 5,100 5,5e0 5,50e 4,780 4,180 2,200 2,908 11,206e 13,200 12,00e s 14,600 16,400 s 23,700 s 22,480 s 22,780 23,000 s 21,700 5 18,908 s 14,900 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

2. Variable cost per rental return = $3.92

Month	Rental Returns	Car wash costs
	x	y	x^2	x*y
January	2400	11200	5760000	26880000
February	2500	13200	6250000	33000000
March	2800	12000	7840000	33600000
April	3000	14600	9000000	43800000
May	3700	16400	13690000	60680000
June	5100	23700	26010000	120870000
July	5500	22400	30250000	123200000
August	5500	22700	30250000	124850000
September	4700	23000	22090000	108100000
October	4100	21700	16810000	88970000
November	2200	10900	4840000	23980000
December	2900	14900	8410000	43210000
Total	44400	206700	181200000	831140000
?x = 44,400
?y = 206,700
?xy = 831,140,000
?x^2 = 181,200,000
Unit variable cost = b = (n*?xy - ?x*?y)/(n?x^2 - (?x)^2)
=(12*831,140,000 - 44,400*206,700) /
(12*181,200,000 - 44,400*44,000)
=796,200,000 / 203,040,000
=3.92
Total Fixed Cost = a = (?y -b*?x)/n
=(206,700 - 3.92*44,400)/12
=2,852