Question

Lacourse Inc.'s inspection costs are listed below:

	Units Produced			Inspection Costs
January	415			$	6,100
February	365			$	5,624
March	434			$	6,315
April	449			$	6,453
May	391			$	5,874
June	366			$	5,627
July	441			$	6,380
August	392			$	5,887

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

Answer:

Unit Variable Cost (b) =[nΣxy − (Σx)(Σy)]/[nΣx² − (Σx)^2]

Total Fixed Cost (a) =(Σy − bΣx)/n

Where,
n is number of pairs of units–total-cost used in the calculation;
Σy is the sum of total costs of all data pairs;
Σx is the sum of units of all data pairs;
Σxy is the sum of the products of cost and units of all data pairs; and
Σx² is the sum of squares of units of all data pairs.

Month	Units(x)	Cost(y)	x2	xy
January	415	6100	172225	2531500
February	365	5624	133225	2052760
March	434	6315	188356	2740710
April	449	6453	201601	2897397
May	391	5874	152881	2296734
June	366	5627	133956	2059482
July	441	6380	194481	2813580
August	392	5887	153664	2307704
TOTAL	3253	48260	1330389	19699867

We have,
n = 8;
Σx = 3253;
Σy = 48260;
Σx² = 1330389; and
Σxy = 19699867

Calculating the average variable cost per unit:

b=[(8*19699867) − (3253*48260)]/[(8*1330389) − 3253^2)]

^{=(157598936-156989780)/(10643112-10582009)}

^{=609156/61103}

=9.97

Calculating the approximate fixed cost:

a=(48260-9.97*3253)/8

=1978

fixed component of inspection cost per month is $1978.

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