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

Lacourse Inc.'s inspection costs are listed below:

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:

Multiple Choice

$1,759

$1,801

$5,639

$5,813

Units Produced Inspection Costs January 430 $ 6,130 February 380 $ 5,639 March 449 $ 6,345 April 464 $ 6,483 May 406 $ 5,889 June 381 $ 5,642 July 456 $ 6,410 August 407 $ 5,902

Explanation / Answer

Let ’X’ be No of units produced and

Let ‘Y’ be Inspection costs for that month.

Unit variable cost = V = [n(Sum of (X*Y)) – (Sum of X * Sum of Y)]/[n(sum of X2) – (sum of X)2 ]

Total Fixed cost = F = [(sum of Y) – V * (Sum of X)]/ n

We have,

N = 8,

Sum of X = 3373

Sum of Y = 48440

Sum of X2 = 1429779

Sum of XY = 20501347

Calculating the average variable cost per unit=

[n(Sum of (X*Y)) – (Sum of X * Sum of Y)]/[n(sum of X2) – (sum of X)2 ]

= [(8*20501347) – (3373*48440)] / [(8*1429779) – (3373)2]

=622656/61103

=10.19

Calculating the approximate total Fixed cost:

F = [(sum of Y) – V * (Sum of X)]/ n

=[48440-(10.19*3373)]/8

=(48440-34370.87)/8

=14069.13/8

=1758.64 approximately equals to $1759

Month X Y X2 XY Jan 430 6130 184900 79507000 Feb 380 5639 144400 54872000 Mar 449 6345 201601 90518849 Apr 464 6483 215296 99897344 May 406 5889 164836 66923416 Jun 381 5642 145161 55306341 Jul 456 6410 207936 94818816 Aug 407 5902 165649 67419143 3373 48440 1429779 609262909

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