Question

An important application of regression analysis in accounting is in the estimation of cost. By collecting data on volume and cost and using the least squares method to develop an estimated regression equation relating volume and cost, an accountant can estimate the cost associated with a particular manufacturing volume. Consider the following sample of production volumes and total cost data for a manufacturing operation.

Production Volume (units)	Total Cost ($)
400	3,500
450	4,500
550	4,900
600	5,400
700	5,900
750	6,500

a. Compute b₁ and b₀ (to 1 decimal).



Complete the estimated regression equation (to 1 decimal).
y^=___+___x

b. What is the variable cost per unit produced (to 1 decimal)?


c. Compute the coefficient of determination (to 3 decimals). Note: report r² between 0 and 1.


What percentage of the variation in total cost can be explained by the production volume (to 1 decimal)?


d. The company's production schedule shows 500 units must be produced next month. What is the estimated total cost for this operation (to the nearest whole number)?

Answer 1

	Production Volume X	Total Cost Y	X * Y
	400	3500	1400000	160000	12250000
	450	4500	2025000	202500	20250000
	550	4900	2695000	302500	24010000
	600	5400	3240000	360000	29160000
	700	5900	4130000	490000	34810000
	750	6500	4875000	562500	42250000
Total	3450	30700	18365000	2077500	1.63E+08

Equation of regression line is


b = 7.6


a = 746.7
Equation of regression line becomes

b0 = 746.7

b1 = 7.6

Part b)

$7.6 is the variable cost per unit produced

r = 0.979

Coefficient of Determination

Explained variation = 0.959* 100 = 95.9%
Unexplained variation = 1 - 0.959* 100 = 4.1%

When X = 500
= 746.667 + 7.6 X
= 746.667 + 7.6 * 500
= 4546.67

= 4547