Multiple Regression, Confidence Intervals, Reliability of Cost Formulas

Randy Harris, controller, has been given the charge to implement an advanced cost management system. As part of this process, he needs to identify activity drivers for the activities of the firm. During the past four months, Randy has spent considerable effort identifying activities, their associated costs, and possible drivers for the activities' costs.

Initially, Randy made his selections based on his own judgment using his experience and input from employees who perform the activities. Later, he used regression analysis to confirm his judgment. Randy prefers to use one driver per activity, provided that an R² of at least 80 percent can be produced. Otherwise, multiple drivers will be used, based on evidence provided by multiple regression analysis. For example, the activity of inspecting finished goods produced an R² of less than 80 percent for any single activity driver. Randy believes, however, that a satisfactory cost formula can be developed using two activity drivers: the number of batches and the number of inspection hours. Data collected for a 14-month period are as follows:

Inspection Costs Hours of Inspection Number of Batches

$17,689            100                  10

18,350            120                  20

13,125            60                  15

28,000            320                  30

30,560            240                  25

31,755            200                  40

40,750            280                  35

29,500            230                  22

47,570            350                  50

36,740            270                  45

43,500            350                  38

26,780            200                  18

28,500            140                  28

17,000            160                  14

Required:

1. Calculate the cost formula for inspection costs using the two drivers, inspection hours and number of batches. In the formula, round your answer for the intercept to the nearest whole number and round the X variables 1 and 2 to the nearest cent. Where X₁ = hours of inspection, and X₂ = number of batches.

Y = $ 5289 + $ 55.82 X₁ + $428.69 X₂

Are both activity drivers useful?

Yes

What is the adjusted R²? Round to the nearest whole percent.

87%

2. Using the formula developed in Requirement 1, calculate the inspection cost when 300 inspection hours are used and 30 batches are produced. Prepare a 90 percent confidence interval for this prediction. (Refer to Exhibit 3.14). In your computations, round X₁ and X₂ to 2 decimals, round intercept, Y_f and the standard error to the nearest dollar and round t-values to three decimals. Enter the final answers rounded to the nearest dollar.

Y = $ 34896

$ ≤ Y_f ≤ $
Transcribed Image Text:Table of Selected Values: t Distribution* Degrees of Freedom 90% 95% 99% 1 6.314 12.708 63.657 2.920 2.353 2 4.303 9.925 3 3.182 5.841 2.132 2.015 2.776 2.571 4.604 4.032 2.447 2.365 6 1.943 3.707 7 1.895 3.499 8. 1.860 2.306 3.355 1.833 2.262 2.228 2.201 3.250 3.169 10 1.812 11 1.796 3.106 12 1.782 2.179 3.055 13 1.771 2.160 3.055 14 1.761 2.145 3.012 15 1.753 2.131 2.947 16 17 18 1.746 2.120 2.921 1.740 2.110 2.898 1.734 2.101 2.878 2.093 2.086 19 1.729 2.861 20 1.725 2.845 1.697 1.645 30 2.042 2.750 00** 1.960 2.576| * Values are based on the assumption that two tails are important-as they would be with confidence intervals and hypothesis tests of regression coefficients. **For values above 30, simply use the last row.

Question

Multiple Regression, Confidence Intervals, Reliability of Cost Formulas

Randy Harris, controller, has been given the charge to implement an advanced cost management system. As part of this process, he needs to identify activity drivers for the activities of the firm. During the past four months, Randy has spent considerable effort identifying activities, their associated costs, and possible drivers for the activities' costs.

Initially, Randy made his selections based on his own judgment using his experience and input from employees who perform the activities. Later, he used regression analysis to confirm his judgment. Randy prefers to use one driver per activity, provided that an R² of at least 80 percent can be produced. Otherwise, multiple drivers will be used, based on evidence provided by multiple regression analysis. For example, the activity of inspecting finished goods produced an R² of less than 80 percent for any single activity driver. Randy believes, however, that a satisfactory cost formula can be developed using two activity drivers: the number of batches and the number of inspection hours. Data collected for a 14-month period are as follows:

Inspection Costs	Hours of Inspection	Number of Batches
$17,689		100	10
18,350		120	20
13,125		60	15
28,000		320	30
30,560		240	25
31,755		200	40
40,750		280	35
29,500		230	22
47,570		350	50
36,740		270	45
43,500		350	38
26,780		200	18
28,500		140	28
17,000		160	14

Required:

1. Calculate the cost formula for inspection costs using the two drivers, inspection hours and number of batches. In the formula, round your answer for the intercept to the nearest whole number and round the X variables 1 and 2 to the nearest cent. Where X₁ = hours of inspection, and X₂ = number of batches.

Y = $ 5289 + $ 55.82 X₁ + $428.69 X₂

Are both activity drivers useful?

Yes

What is the adjusted R²? Round to the nearest whole percent.

87%

2. Using the formula developed in Requirement 1, calculate the inspection cost when 300 inspection hours are used and 30 batches are produced. Prepare a 90 percent confidence interval for this prediction. (Refer to Exhibit 3.14). In your computations, round X₁ and X₂ to 2 decimals, round intercept, Y_f and the standard error to the nearest dollar and round t-values to three decimals. Enter the final answers rounded to the nearest dollar.

Y = $ 34896

$ ≤ Y_f ≤ $

Table of Selected Values: t Distribution*
Degrees of Freedom
90%
95%
99%
1
6.314
12.708
63.657
2.920
2.353
2
4.303
9.925
3
3.182
5.841
2.132
2.015
2.776
2.571
4.604
4.032
2.447
2.365
6
1.943
3.707
7
1.895
3.499
8.
1.860
2.306
3.355
1.833
2.262
2.228
2.201
3.250
3.169
10
1.812
11
1.796
3.106
12
1.782
2.179
3.055
13
1.771
2.160
3.055
14
1.761
2.145
3.012
15
1.753
2.131
2.947
16
17
18
1.746
2.120
2.921
1.740
2.110
2.898
1.734
2.101
2.878
2.093
2.086
19
1.729
2.861
20
1.725
2.845
1.697
1.645
30
2.042
2.750
00**
1.960
2.576|
* Values are based on the assumption that two tails are important-as they would be with confidence intervals and
hypothesis tests of regression coefficients.
**For values above 30, simply use the last row.

Accepted Answer

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