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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:
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 | |||
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
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
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 |
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