Question

Grawburg Inc. maintains a call center to take orders, answer questions, and handle complaints. The costs of the call center for a number of recent months are listed below:

	Calls Taken	Call Center Cost
April	8,460	$	91,717
May	8,429	$	91,548
June	8,470	$	91,777
July	8,469	$	91,759
August	8,433	$	91,567
September	8,444	$	91,605
October	8,486	$	91,831
November	8,474	$	91,787

Management believes that the cost of the call center is a mixed cost that depends on the number of calls taken.

Required:

Estimate the variable cost per call and fixed cost per month using the least-squares regression method.

Answer 1

April May June July August September October November Calls Taken Call Center Cost 8,460 $ 91,717 8,429 $ 91,548 8,470 $ 91,777 8,469 $ 91,759 8,433 $ 91,567 8,444 $ 91,605 8,486 $ 91,831 8,474 $ 91,787 8,460 $ 8,429 $ 8,470 $ 8,469 $ 8,433 $ 8,444 $ 8,486 $ 8,474 $ 67,665 $ 91,717 91,548 91,777 91,759 91,567 91,605 91,831 91,787 733,591 | x^2 71,571,600 71,048,041 71,740,900 71,723,961 71,115,489 71,301,136 72,012,196 71,808,676 572,321,999 xy 775,925,820 771,658,092 777,351,190 777,106,971 772,184,511 773,512,620 779,277,866 777,803,038 6,204,820,108 Sigma (Sum) Computation of variable cost per unit (b): b-n(Exy)-(2x) Ey) n(2x2)-(2x)2

Let us take the number of months as (n = 8) b = 8 x 6,204,820,108 - 67,665 x 733,591 8 x 572,321,999 - (67,665)^2 = 49,638,560,864 - 49,638,435,015 4,578,575,992 - 4,578,552,225 125,849 23,767 Total Variable costb = $ 5.295 The value of 'b' i.e., per unit variable cost) is $5.295 which can be substituted in fixed cost formula to find the value of 'a' (i.e., the total fixed cost).

Computation of total fixed cost (a): – b(2x) n 733,591 - 5.295 x 67,665 375,297.04 Total Fixed cost a = $ 46,912.13

Variable and fixed cost can be estimated using least squares regression method using the above steps in the images for this question.