Cost function using multiple regression (appendix 2A) Refer to the data and requirements of Problem 2.23. Required (a) Perform multiple re
Cost function using multiple regression (appendix 2A)
Refer to the data and requirements of Problem 2.23.
Required
(a) Perform multiple regression using all three cost drivers. Compare the adjusted R-squares and cost functions for the multiple regression with the results of simple regressions for each potential cost driver.
(b) Which cost drivers do the best job of explaining manufacturing overhead costs? Explain.
(c) Select only the cost drivers that do the best job of explaining manufacturing overhead costs. Perform multiple regression analysis for those cost drivers and write the cost function.
(d) Explain why more than one cost driver is plausible for manufacturing overhead costs.
(a) Multiple regression with all three potential cost drivers:
Regression Statistics |
|
Multiple R |
0.9092294 |
R Square |
0.8266982 |
Adjusted R Square |
0.8067018 |
Standard Error |
4832.5558 |
Observations |
30 |
|
Coefficients |
Standard Error |
t Stat |
P-value |
Intercept |
60988.489 |
10361.2349 |
5.886218 |
3.3E-06 |
Labour Hours |
-0.1959303 |
3.333162437 |
-0.05878 |
0.953575 |
Machine Hours |
48.778501 |
5.291558412 |
9.218173 |
1.12E-09 |
Raw Materials |
82.976635 |
10.10654585 |
8.210187 |
1.08E-08 |
Comparison of simple and multiple regression results:
(b) Labour hours does not appear to be a cost driver when using either simple regression or multiple regression; its coefficient is not significantly different from zero in either regression. Also, its coefficient is negative rather than positive in the multiple regression. Thus, labour hours can be eliminated as a potential cost driver.
Both machine hours and raw materials are positive and significantly different from zero when using simple regression and also when using multiple regression. The adjusted R-Square is far higher in the multiple regression (0.806) than in either of the simple regressions (0.352 and 0.226) for these two cost drivers. A combination of cost drivers does a much better job of explaining the variation in manufacturing overhead costs than either cost driver alone.
(c) Multiple regression using machine hours and raw materials as cost drivers:
Regression Statistics |
|
Multiple R |
0.90921678 |
R Square |
0.82667515 |
Adjusted R Square |
0.81383627 |
Standard Error |
4742.5348 |
Observations |
30 |
|
Coefficients |
Standard Error |
t Stat |
P-value |
Intercept |
60677.5902 |
8743.664851 |
6.939606 |
1.86E-07 |
Machine Hours |
48.7422519 |
5.157604083 |
9.450561 |
4.71E-10 |
Raw Materials |
82.925842 |
9.881964042 |
8.391636 |
5.29E-09 |
The cost function is: TC = $60 678 + $48.74×Machine hours + $82.93×Raw materials
(d) Manufacturing can be a complex activity requiring a number of different tasks. Each task includes different activities. Costs for these activities are likely related to specific cost drivers. In this example, machine hours and raw materials explain different activity costs, such as machining work on units, and materials handling for the units. A better understanding of the manufacturing process improves the ability to determine the types and number of cost drivers that can be used in a more complete cost function.