9.1.3 Exploration 9A: Production Line Data
The WheelRight company manufactures parts for automobiles. The factory manager wants a
better understanding of overhead costs at her factory. She knows that the total overhead costs
include labor costs, electricity, materials, repairs, and various other quantities, but she
wants to understand how the total overhead costs are related to the way in which the
assembly line is used. For the past 36 months, she has tracked the overhead costs along
with two quantities that she suspects are relevant (see data file C09 Production.xls
[.rda]):
- MachHrs is the number of hours the assembly machines ran during the month
- ProdRuns is the number of different production runs during the month
MachHrs directly measures the amount of work being done. However, each time a new part
needs to be manufactured, the machines must be re-configured for production. This starts
a new production run, but it takes time to reset the machine and get the materials
prepared.
Your task is to assist the manager in understanding how each of these variables affects the
overhead costs in her factory.
- First, formulate and estimate two simple regression models to predict overhead, once
as a function of MachHrs and once as a function of ProdRuns. Which model is better?
- Would you expect that the combination of both variables will do a better job predicting
overhead? Why or why not? How much better would you estimate the multiple
regression model to be?
- Formulate and estimate a multiple regression model using the given data. Interpret each
of the estimated regression coefficients. Be sure to include the units of each coefficient.
- Compute and interpret the standard error of estimate and the coefficient of
determination . Examine the diagnostic graphs ”Fitted vs. Actual” and ”Residuals vs.
Fitted”. What do these tell you about the multiple regression model?
- Explain how having this information could help the manager in the future.