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 4,900 450 5,900 550 6,300 600 6,800 700 7,300 750 7,900

Compute b1 and b0 (to 1 decimal).

b1 b0 Complete the estimated regression equation (to 1 decimal).y= + x

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

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)? %

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

Solution: We can use the excel regression data analysis tool to answer the given questions. The excel output is given below:

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.9791
R Square	0.9587
Adjusted R Square	0.9484
Standard Error	241.5229
Observations	6
ANOVA
	df	SS	MS	F	Significance F
Regression	1	5415000.0000	5415000.0000	92.8286	0.0006
Residual	4	233333.3333	58333.3333
Total	5	5648333.3333
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	2146.67	464.1599	4.6248	0.0098	857.9521	3435.3812
Production Volume (units)	7.6	0.7888	9.6348	0.0006	5.4099	9.7901

Compute b1 and b0 (to 1 decimal).

Complete the estimated regression equation (to 1 decimal).

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

$7.6

Compute the coefficient of determination (to 3 decimals).

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

95.9%

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)?