Below are cost and activity data for a particular cost over the last four periods. Your boss has asked you to analyze this cost so that management will have a better understanding of how this cost changes in response to changes in activity. ActivityCostPeriod 146 $791Period 240 $738Period 347 $807Period 441 $746 Required:Using the least-squares regression method, estimate the cost formula for this cost.
What will be an ideal response?
The solution using Microsoft Excel functions is:
Variable cost = Slope = $9.57
Fixed cost = Intercept = $354.31
Therefore, the cost formula is $354.31 per period plus $9.57 per unit of activity or:
Y = $354.31 + $9.57X
The solution using the formulas in the text is:
n = 4
?X = 174
?Y = 3,082
?XY = 134,421
?X^2 = 7,606
b = [n(?XY)-(?X)(?Y)]/[n(?X^2)-(?X)^2]
= [4(134,421)-(174)(3,082)]/[4(7,606)-(174)^2]
= $9.57 (rounded to nearest whole cent)
a = [(?Y)-b(?X)]/n
= [(3,082)- 9.57(174)]/4
= $354 (rounded to nearest whole dollar)
Cost formula: Y = $354 + $9.57X.
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