An important application of regression analysis in accounting is in the estimati

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.

Compute b1 and b0 (to 1 decimal).
b1  
b0  

Complete the estimated regression equation (to 1 decimal).
=  +  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)?
$

Production Volume (units) Total Cost ($) 400 4,600 450 5,600 550 6,000 600 6,500 700 7,000 750 7,600

Explanation / Answer

The statistical software output for this problem is:

Simple linear regression results:
Dependent Variable: Cost
Independent Variable: Volume (Units)
Cost = 1846.6667 + 7.6 Volume (Units)
Sample size: 6
R (correlation coefficient) = 0.9791271
R-sq = 0.95868988
Estimate of error standard deviation: 241.52295

Parameter estimates:

Analysis of variance table for regression model:

Predicted values:

Hence,

b1 = 7.6

bo = 1846.7

Regression equation:

y = 1846.7 + 7.6 x

Variable cost per unit = 7.6

r2 = 0.959

Percentage of variation explained = 95.9%

For x = 500, estimate total cost = $ 5647

Parameter Estimate Std. Err. Alternative DF T-Stat P-value Intercept 1846.6667 464.15993 ? 0 4 3.9785137 0.0164 Slope 7.6 0.78881064 ? 0 4 9.6347585 0.0006

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