{Exercise 12.21 (Algorithmic)} An important application of regression analysis i
ID: 3061972 • Letter: #
Question
{Exercise 12.21 (Algorithmic)}
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. Predict the total cost for this operation? (to the nearest whole number)?
$
Explanation / Answer
The statistical software output for this problem is:
Simple linear regression results:
Dependent Variable: Total Cost ($)
Independent Variable: Production Volume (units)
Total Cost ($) = 1846.6667 + 7.6 Production 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%
Predicted total cost for operation = 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 0.0006Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.