Question

Fine Tollowing information applies to the questions assplayed below 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 January February March April May June July August September October November December Rental Returns 2,500 2,500 2,800 3,100 3.700 5,200 5,600 5.700 4,800 4,900 2,300 Car Wash Costs $ 11,500 $ 13,500 $ 12,600 $ 15,500 $ 17,000 $ 24,900 $ 23,000 $ 24,200 $ 23,600 $ 23,500 $ 11,500 $ 17,000 2. Using least-squares regression, estimate the variable cost per rental return and the monthly fored 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 is complete but not entirely correct. 2 914 X Fixed cost per month Variable cost per rental return 3.96

Answer 1

Month		X	Y	XY	X^2
January		2,500	11,800	29500000	6250000
February		2,500	13,500	33750000	6250000
March		2800	12,600	35280000	7840000
April		3100	15,500	48050000	9610000
May		3700	17,000	62900000	13690000
June		5200	24,900	129480000	27040000
July		5,600	23,000	128800000	31360000
August		5,700	24,200	137940000	32490000
September	4,800	23,600	113280000	23040000
October		4,900	23,500	115150000	24010000
November	2,300	11,500	26450000	5290000
December	3,100	17,000	52700000	9610000
TOTAL		46,200	2,18,100	91,32,80,000	19,64,80,000

In a least square regression the variable cost elements of monthly cash wash costs is slope and fixed cost element is intercept.
The regression equation is
Y = a + bx
Where a is intercept
b is slope
Slope =3.95= VARIABLE COST PER RENTAL RETURN Unit variable cost = n * total of xy - (Total of x * total of y) n * total of x^2 -(Total of x)^2 =12*913280000-(46200*218100)/12*196480000-2134440000=3.95
Fixed cost = (Total of y - unit cost * toal of x)/n
(218100-3.95*46200)/12 =35610/12 = 2967.5