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 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 April Rental Returns 2.500 2.500 2.800 31200 3.200 5.200 5.600 5.700 4.800 4.700 Car Wash Costs $ 12.000 $ 13.600 $ 12.800 $15.800 $ 17.200 $25.900 23,200 $ 24.700 $ 23.800 $ 24,100 $11.700 $ 17.700 August September October November December 3.200 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

The linear regression equation is given as

y = a + bx

where a = intercept ; b = slope

y = dependent variable = Car washing costs

x = independent variable = number of rental returns

13600 uary Rental Car Wash Month Returns(x) costs (Y) XY January 2500 12000 30000000 6250000 February 2500 34000000 6250000 March 2800 12800 35840000 7840000 April 3200 15800| 50560000 10240000 May 1 3700 17200 63640000 13690000 June 520025300 131560000 27040000 July 5600 23200 129920000 31360000 August 5700 247001 140790000 32490000 September 48001 23800 114240000 23040000 October 4700 24100 113270000 22090000 November 2300 11700 26910000 5290000 December 3200 17700 56640000 10240000 |EX = 46200 XY = 221900 EXY = 927370000 Ex² = 195820000 * = * = 420 = 3850 y = xy = 21900 = 18,291.66667

The value of the  slope is found using the following equation

ΣΧΥ – ηXY Σχ2 – ηX2

b= 927370000 - 12 x 3850 x 18491.66667 195820000 - 12 x 38502

b = 4.07

a = 18491.66667 - 4.07 $\times$ 3850

a = $ 2823

Fixed cost per month	$2,823
Variable cost per rental return	$4.07