Problem 3-30
The management of Wheeler Company has decided to develop cost formulas for its major overhead activities. Wheeler uses a highly automated manufacturing process, and power costs are a significant manufacturing cost. Cost analysts have decided that power costs are mixed; thus, they must be broken into their fixed and variable elements so that the cost behavior of the power usage activity can be properly described. Machine hours have been selected as the activity driver for power costs. The following data for the past eight quarters have been collected:
[pic]
.:.
For the following requirements, round the fixed cost to the nearest dollar and round the variable rates to the nearest cent.
Required:
1. Prepare a scattergraph by plotting power costs against machine hours. Does the scattergraph show a linear relationship between machine hours and power cost?
2. Using the high and low points, compute a power cost formula.
3. Use the method of least squares to compute a power cost formula. Evaluate the coefficient of determination.
4. Rerun the regression, and drop the point (20,000, $26,000) as an outlier. Compare the results from this regression to those for the regression in Requirement 3. Which is better?
SOLUTION:
1.
[pic]
The overall relationship looks reasonably linear—although the data point for the first quarter may be an outlier.
2. Using the high-low method:
Variable power cost = [pic] = $1.13 (rounded)
Fixed power cost = $42,500 – ($1.13 × 30,000) = $8,600
Total power cost = $8,600 + ($1.13 × Number of machine hours)
3. Output of regression program:
|SUMMARY OUTPUT | | | | | | | |
| | | | | | | | |
|Multiple R |0.89336
[pic]
.:.
For the following requirements, round the fixed cost to the nearest dollar and round the variable rates to the nearest cent.
Required:
1. Prepare a scattergraph by plotting power costs against machine hours. Does the scattergraph show a linear relationship between machine hours and power cost?
2. Using the high and low points, compute a power cost formula.
3. Use the method of least squares to compute a power cost formula. Evaluate the coefficient of determination.
4. Rerun the regression, and drop the point (20,000, $26,000) as an outlier. Compare the results from this regression to those for the regression in Requirement 3. Which is better?
SOLUTION:
1.
[pic]
The overall relationship looks reasonably linear—although the data point for the first quarter may be an outlier.
2. Using the high-low method:
Variable power cost = [pic] = $1.13 (rounded)
Fixed power cost = $42,500 – ($1.13 × 30,000) = $8,600
Total power cost = $8,600 + ($1.13 × Number of machine hours)
3. Output of regression program:
|SUMMARY OUTPUT | | | | | | | |
| | | | | | | | |
|Multiple R |0.89336