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	3,900
450	4,900
550	5,300
600	5,800
700	6,300
750	6,900

1. Compute b1 and b0 (to 1 decimal).
   b1
   b0
   
   Complete the estimated regression equation (to 1 decimal).
   = + x
   
2. What is the variable cost per unit produced (to 1 decimal)?
   $
   
3. Compute the coefficient of determination (to 3 decimals). Note: report r2 between 0 and 1.
   r2 =
   
   What percentage of the variation in total cost can be explained by the production volume (to 1 decimal)?
   %
   
4. 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

The statistical software output for this problem is:

Simple linear regression results:
Dependent Variable: y
Independent Variable: x
y = 1146.6667 + 7.6 x
Sample size: 6
R (correlation coefficient) = 0.9791271
R-sq = 0.95868988
Estimate of error standard deviation: 241.52295

Parameter estimates:

Parameter	Estimate	Std. Err.	Alternative	DF	T-Stat	P-value
Intercept	1146.6667	464.15993	≠ 0	4	2.4704129	0.0689
Slope	7.6	0.78881064	≠ 0	4	9.6347585	0.0006

Analysis of variance table for regression model:

Source	DF	SS	MS	F-stat	P-value
Model	1	5415000	5415000	92.828571	0.0006
Error	4	233333.33	58333.333
Total	5	5648333.3

Predicted values:

X value	Pred. Y	s.e.(Pred. y)	95% C.I. for mean	95% P.I. for new
500	4946.6667	114.98792	(4627.409, 5265.9243)	(4203.9712, 5689.3621)

Hence,

b1 = 7.6

bo = 1146.7

Estimated regression equation: y = 1146.7 + 7.6 x

Variable cose per unit produced = $ 7.6

Coefficient of determination = 0.959

Percentage of variation explained = 95.9%

Predicted total cost = $ 4947