Question

Exercise 5A-2 Least-Squares Regression (LO5-11) [The following Information applies to the questions displayed 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 belleves 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 2,380 2,421 2,586 2,725 2,968 3,281 3,353 3,489 3,057 2,876 2,735 2,983 Car Wash Costs $ 10,825 $ 11,865 $ 11,332 $ 12,422 $ 13,850 $ 14,419 $ 14,935 $ 15,738 $ 13,563 $ 11,889 $ 12,683 $ 13,796 Exercise 5A-2 Part 2 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 Varlable cost per unit to 2 decimal places.) Fixed cost per month Variable cost per rental return

Answer 1

Answer :-

First we calculate x² and xy then Sum all x, y, x² and xy, which gives us Σx, Σy, Σx² and Σxy to find out Variable cost per rental return and Fixed Cost per month.

Month January February March April May June Rental returns(x) Car Wash costs (y) xy 2,380 10,825 25763500 5664400 2,421 11,865 28725165 5861241 2,586 11,332 29304552 6687396 2,725 12,422 33849950 7425625 2,968 13,850 41106800 8809024 3,281 14,419 47308739 10764961 3,353 14,935 50077055 11242609 3,489 15,738 54909882 12173121 3,057 13,563 41462091 9345249 2,876 11,889 34192764 8271376 2,735 12,683 34688005 7480225 2,983 13,796 41153468 8898289 34854 157317 462541971 102623516 July August September October November December Total

Σx = 34,854

Σy = 157,317

Σxy = 462,541,971

Σx² = 102,623,516

N = number of months = 12

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

Variable cost per rental return ={( 12 × 462,541,971) - (34,854 × 157,317) } / {(12 ×102,623,516) - (34,854)²}

Variable cost per rental return = (5,550,503,652 - 5,483,126,718) / (1231482192 - 1214801316)

Variable cost per rental return = 67,376,934 / 16680876

Variable cost per rental return = $4.04

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

Fixed Cost per month = {157,317 - (4.04 × 34,854)} /12

Fixed Cost per month = ( 157,317 - 140,810.16) /12

Fixed Cost per month = $1376