Cost Control. Exercise 1 in Chapter 4 discussed in data available for a firm that produces...

Cost Control. Exercise 1 in Chapter 4 discussed in data available for a firm that produces corrugated paper for use in making boxes and other packing materials. The variables discussed were

y, total manufacturing cost per month in thousands of dollars (COST)

x1, total production of paper per month in tons (PAPER)

x2, total machine hours used per month (MACHINE)

x3, total variable overhead costs per month in thousands of dollars (OVERHEAD)

x4, total direct labor hours used each month (LABOR)

The data, available in a file named COST8 on the CD, are monthly and refer to the time period from January 2001 to March 2003. Use the backward elimination procedure to analyze these data, then answer the following questions:

a. What is the regression equation chosen by the backward elimination procedure?

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b. What is the R2 for the chosen equation?

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c. What is the adjusted R2 for the chosen equation?

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d. What is the standard error of the chosen equation?

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e. What variables were omitted? Do you feel these variables are unrelated to COST? Why or why not? Do you feel the omitted variables are necessary in the regression equation? Why or why not?

Exercise 1:

Cost Control. Ms. Karen Ainsworth is an employee of a well-known accounting find’s management services division. She is currently on a consulting assignment to the Apex Corporation, a firm that produces corrugated paper for use in making boxes and other packing materials. Apex called in consulting help to improve its cost control program, and Ms. Ainsworth is analyzing manufacturing costs to understand more fully the important influences on these costs. She has assembled monthly data on a group of variables, and she is using regression analysis to help assess how these variables are related to total manufacturing cost. The variables Ms. Ainsworth has selected to study, the data for which are contained in the file COST4 on the CD, are

y, total manufacturing cost per month in thousands of dollars (COST)

x1, total production of paper per month in tons (PAPER)

x2, total machine hours used per month (MACHINE)

x3, total variable overhead costs per month in thousands of dollars (OVERHEAD)

x4, total direct labor hours used each month (LABOR)

The data shown in Table 4.2 refer to the period January 2001 through March 2003. Ms. Ainsworth wants to use a cost function developed by means of regression analysis that initially includes all four of the explanatory variables. Use the regression results in Figure 4.8 to help answer the following questions:

a. What is the equation that is determined using all four explanatory variables?

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b. Conduct the F test for overall fit of the regression. State the hypotheses to be tested, the decision rule, the test statistic, and your decision. Use a 5% level of significance. What conclusion can be drawn from the result of the test?

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c. In the cost accounting literature, the sample regression coefficient corresponding to xk is regarded as an estimate of the true marginal cost of output associated with the variable xk. Find a point estimate of the true marginal cost associated with total machine hours per month. Also, find a 95% confidence interval estimate of the true marginal cost associated with total machine hours.

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d. Test the hypothesis that the true marginal cost of output associated with total production of paper is 1.0. Use a 5% level of significance and a two- tailed test procedure. State the hypotheses to be tested, the decision rule, the test statistic, and your decision. What conclusion can be drawn from the result of the test?

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e. What percentage of the variation in y has been explained by the regression?

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f. What is the adjusted R2 for this regression?

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g. Based on the regression equation, what actions might be taken to control costs?

Table 4.2: Data for Cost Control Exercise

Source: These data were created by Dr. Roger L. Wright, RLW Analytics. Inc., Sonoma, CA. and are used (with modification) with his permission.

FIGURE 4.8: Regression Results for Cost Control Exercise