Question

Chapter 6 Homework

Required information

Exercise 6A-2 Least-Squares Regression [LO6-11]

[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 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		$	11,900
February	2,500		$	13,600
March	2,800		$	12,700
April	3,100		$	15,600
May	3,700		$	17,100
June	5,200		$	25,100
July	5,600		$	23,100
August	5,700		$	24,400
September	4,800		$	23,700
October	4,500		$	23,800
November	2,300		$	11,600
December	3,100		$	17,400

Exercise 6A-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 your Fixed cost to the nearest whole dollar amount and the Variable cost per unit to 2 decimal places.)

Answer 1

	Rental Returns (X)	Car Wash Costs (Y)	X * Y	X2	Y2
	2500	11900	29750000	6250000	141610000
	2500	13600	34000000	6250000	184960000
	2800	12700	35560000	7840000	161290000
	3100	15600	48360000	9610000	243360000
	3700	17100	63270000	13690000	292410000
	5200	25100	130520000	27040000	630010000
	5600	23100	129360000	31360000	533610000
	5700	24400	139080000	32490000	595360000
	4800	23700	113760000	23040000	561690000
	4500	23800	107100000	20250000	566440000
	2300	11600	26680000	5290000	134560000
	3100	17400	53940000	9610000	302760000
Total	45800	220000	911380000	192720000	4348060000

Equation of regression line is Ŷ = a + bX

b = ( 12 * 911380000 - 45800 * 220000 ) / ( 12 * 192720000 - ( 45800 )²)
b = 4.003
a =( Σ Y - ( b * Σ X) ) / n
a =( 220000 - ( 4.0026 * 45800 ) ) / 12
a = 3056.726
Equation of regression line becomes Ŷ = 3057 + 4.00X