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Cost analysis for a shipping department. Multiple
Chapter 12, Problem 24E(choose chapter or problem)
Cost analysis for a shipping department. Multiple regression is used by accountants in cost analysis to shed light on the factors that cause costs to be incurred and the magnitudes of their effects. Sometimes, it is desirable to use physical units instead of cost as the dependent variable in a cost analysis (e.g., if the cost associated with the activity of interest is a function of some physical unit, such as hours of labor). The advantage of this approach is that the regression model will provide estimates of the number of labor hours required under different circumstances, and these hours can then be costed at the current labor rate (Horngren, Foster, and Datar, Cost Accounting, 2006). The sample data shown in the table below have been collected from a firm’s accounting and production records to provide cost information about the firm’s shipping department. These data are saved in the file. Consider the model
\(y=\beta_{0}+\beta_{1} x_{1}+\beta_{2} x_{2}+\beta_{3} x_{3}+\varepsilon\)
a. Find the least squares prediction equation.
b. Use an F-test to investigate the usefulness of the model specified in part a. Use \(\alpha=.01\) and state your conclusion in the context of the problem.
c. Test \(H_{0}: \beta_{2}=0\) versus \(H_{\mathrm{a}}: \beta_{2} \neq 0\) using \(\alpha=.05\). What do the results of your test suggest about the magnitude of the effects of \(x_{2}\) on labor costs?
d. Find \(R^{2}\) and interpret its value in the context of the problem.
e. If shipping department employees are paid $7.50 per hour, how much less, on average, will it cost the company per week if the average number of pounds per shipment increases from a level of 20 to 21? Assume that \(x_1\) and \(x_2\) remain unchanged. Your answer is an estimate of what is known in economics as the expected marginal cost associated with a 1-pound increase in \(x_3\).
f. With what approximate precision can this model be used to predict the hours of labor? [Note: The precision of multiple regression predictions is discussed in Section 12.4.]
g. Can regression analysis alone indicate what factors cause costs to increase? Explain.
Date for Exercise 12.24
\(\begin{array}{ccccc}
\hline \text { Week } & \text { Labor, } y(\mathrm{hr}) & \begin{array}{c}
\text { Pounds Shipped, } \\
x_{1}(1,000 \mathrm{~s})
\end{array} & \begin{array}{c}
\text { Percentage of Units } \\
\text { Shipped by Truck, } x_{2}
\end{array} & \begin{array}{c}
\text { Average Shipment Weight, } \\
x_{3} /(\mathrm{b})
\end{array} \\
\hline 1 & 100 & 5.1 & 90 & 20 \\
2 & 85 & 3.8 & 99 & 22 \\
3 & 108 & 5.3 & 58 & 19 \\
4 & 116 & 7.5 & 16 & 15 \\
5 & 92 & 4.5 & 54 & 20 \\
6 & 63 & 3.3 & 42 & 26 \\
7 & 79 & 5.3 & 12 & 25 \\
8 & 101 & 5.9 & 32 & 21 \\
9 & 88 & 4.0 & 56 & 24 \\
10 & 71 & 4.2 & 64 & 29 \\
11 & 122 & 6.8 & 78 & 10 \\
12 & 85 & 3.9 & 90 & 30 \\
13 & 50 & 3.8 & 74 & 28 \\
14 & 114 & 7.5 & 89 & 14 \\
15 & 104 & 4.5 & 90 & 21 \\
16 & 111 & 6.0 & 40 & 20 \\
17 & 110 & 8.1 & 55 & 16 \\
18 & 100 & 2.9 & 64 & 19 \\
19 & 82 & 4.0 & 35 & 23 \\
20 & 85 & 4.8 & 58 & 25 \\
\hline
\end{array}\)
Questions & Answers
QUESTION:
Cost analysis for a shipping department. Multiple regression is used by accountants in cost analysis to shed light on the factors that cause costs to be incurred and the magnitudes of their effects. Sometimes, it is desirable to use physical units instead of cost as the dependent variable in a cost analysis (e.g., if the cost associated with the activity of interest is a function of some physical unit, such as hours of labor). The advantage of this approach is that the regression model will provide estimates of the number of labor hours required under different circumstances, and these hours can then be costed at the current labor rate (Horngren, Foster, and Datar, Cost Accounting, 2006). The sample data shown in the table below have been collected from a firm’s accounting and production records to provide cost information about the firm’s shipping department. These data are saved in the file. Consider the model
\(y=\beta_{0}+\beta_{1} x_{1}+\beta_{2} x_{2}+\beta_{3} x_{3}+\varepsilon\)
a. Find the least squares prediction equation.
b. Use an F-test to investigate the usefulness of the model specified in part a. Use \(\alpha=.01\) and state your conclusion in the context of the problem.
c. Test \(H_{0}: \beta_{2}=0\) versus \(H_{\mathrm{a}}: \beta_{2} \neq 0\) using \(\alpha=.05\). What do the results of your test suggest about the magnitude of the effects of \(x_{2}\) on labor costs?
d. Find \(R^{2}\) and interpret its value in the context of the problem.
e. If shipping department employees are paid $7.50 per hour, how much less, on average, will it cost the company per week if the average number of pounds per shipment increases from a level of 20 to 21? Assume that \(x_1\) and \(x_2\) remain unchanged. Your answer is an estimate of what is known in economics as the expected marginal cost associated with a 1-pound increase in \(x_3\).
f. With what approximate precision can this model be used to predict the hours of labor? [Note: The precision of multiple regression predictions is discussed in Section 12.4.]
g. Can regression analysis alone indicate what factors cause costs to increase? Explain.
Date for Exercise 12.24
\(\begin{array}{ccccc}
\hline \text { Week } & \text { Labor, } y(\mathrm{hr}) & \begin{array}{c}
\text { Pounds Shipped, } \\
x_{1}(1,000 \mathrm{~s})
\end{array} & \begin{array}{c}
\text { Percentage of Units } \\
\text { Shipped by Truck, } x_{2}
\end{array} & \begin{array}{c}
\text { Average Shipment Weight, } \\
x_{3} /(\mathrm{b})
\end{array} \\
\hline 1 & 100 & 5.1 & 90 & 20 \\
2 & 85 & 3.8 & 99 & 22 \\
3 & 108 & 5.3 & 58 & 19 \\
4 & 116 & 7.5 & 16 & 15 \\
5 & 92 & 4.5 & 54 & 20 \\
6 & 63 & 3.3 & 42 & 26 \\
7 & 79 & 5.3 & 12 & 25 \\
8 & 101 & 5.9 & 32 & 21 \\
9 & 88 & 4.0 & 56 & 24 \\
10 & 71 & 4.2 & 64 & 29 \\
11 & 122 & 6.8 & 78 & 10 \\
12 & 85 & 3.9 & 90 & 30 \\
13 & 50 & 3.8 & 74 & 28 \\
14 & 114 & 7.5 & 89 & 14 \\
15 & 104 & 4.5 & 90 & 21 \\
16 & 111 & 6.0 & 40 & 20 \\
17 & 110 & 8.1 & 55 & 16 \\
18 & 100 & 2.9 & 64 & 19 \\
19 & 82 & 4.0 & 35 & 23 \\
20 & 85 & 4.8 & 58 & 25 \\
\hline
\end{array}\)
Step 1 of 11
The collected information is about firm’s accounting and production records to provide
cost information about the ?rm’s shipping department. In this study the factors believed
to be related to the cost is independent variable and in cost analysis it is desirable to use
physical units instead of the cost is dependent variable.
These are given in the following table.
\(\begin{array}{|c|c|c|c|c|}
\hline \text { Week } & \begin{array}{c}
\text { Labor, } \\
Y(\mathrm{hr})
\end{array} & \begin{array}{c}
\text { Pounds } \\
\text { Shipped, } \\
X_{1}(1,000 \mathrm{~s})
\end{array} & \begin{array}{c}
\text { Percentage } \\
\text { of Units } \\
\text { Shipped } \\
\text { by Truck, } \\
X_{2}
\end{array} & \begin{array}{c}
\text { Average } \\
\text { shipment } \\
\text { Weight } \\
X_{3}(\mathbf{l b})
\end{array} \\
\hline 1 & 100 & 5.1 & 90 & 20 \\
\hline 2 & 85 & 3.8 & 99 & 22 \\
\hline 3 & 108 & 5.3 & 58 & 19 \\
\hline- & - & - & - & - \\
\hline & - & - & & \\
\hline & & & & \\
\hline 17 & 110 & 8.1 & 55 & 16 \\
\hline 18 & 100 & 2.9 & 64 & 19 \\
\hline 19 & 82 & 4 & 35 & 23 \\
\hline 20 & 85 & 4.8 & 58 & 25 \\
\hline
\end{array}\)