Question

Lacourse Inc.'s inspection costs are listed below: Units Produced Inspection Costs

January 433 $ 6,136

February 383 $ 5,642

March 452 $ 6,351

April 467 $ 6,489

May 409 $ 5,892

June 384 $ 5,645

July 459 $ 6,416

August 410 $ 5,905

Management believes that inspection cost is a mixed cost that depends on units produced. Using the least-squares regression method, the estimate of the fixed component of inspection cost per month is closest to:

Answer 1

UNIT VARIABLE COST(b)= [nExy- (Ex)(Ey)]/[nEx² - (Ex)²]

TOTAL FIXED COST(a)= (Ey- bEx)/n

where,n= number of pairs of units total cost used in calculation

Ey= Sum of total cost of all data pairs

Ex= Sum of units of all data pairs

Exy= Sum of the products of cost and units of all data pairs

Ex² = Sum of squares of units of all data pairs.

MONTH	UNITS(x)	COST(y)	x2	xy
Jan	433	6136	187489	2656888
Feb	383	5642	146689	2160886
Mar	452	6351	204304	2870652
Apr	467	6489	218089	3030363
May	409	5892	167281	2409828
June	384	5645	147456	2167680
July	459	6416	210681	2944944
Aug	410	5905	168100	2421050
Total	3397	48476	1450089	20662291

So, we have

n= 8

Ex= 3397

Ey=48476

Ex²= 1450089

Exy= 20662291

Calculating the average variable cost per unit:-

b= [(8*20662291) - (3397*48476)]/ [8*1450089) - (3397)²]

= (165298328-164672972)/ (11600712- 11539609)

=625356/61003= 10.25

Calculating the approximate fixed cost:-

a= (48476- 10.25*3397)/8

= 13656.75/8= $1707

Fixed cost of inspection cost per month is $1707.