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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

EXHIBIT 3.14 Table of Selected Values: t Distribution* Degrees of Freedom 90% 95% 99% 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 30 00** 6.314 2.920 2.353 2.132 2.015 1.943 1.895 1.860 1.833 1.812 1.796 1.782 1.771 1.761 1.753 1.746 1.740 1.734 1.729 1.725 1.697 1.645 12.708 4.303 3.182 2.776 2.571 2.447 2.365 2.306 2.262 2.228 2.201 2.179 2.160 2.145 2.131 2.120 2.110 2.101 2.093 2.086 2.042 1.960 63.657 9.925 5.841 4.604 4.032 3.707 3.499 3.355 3.250 3.169 3.106 3.055 3.055 3.012 2.947 2.921 2.898 2.878 2.861 2.845 2.750 2.5761 Values are based on the assumption that two tails are importantas they would be with confidence intervals and 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 = $ 5,289 + $ 55.82 X1 + $ 428.69 X2 Are both activity drivers useful? Yes What is the adjusted R?? 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, Yf 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 = $ 34,896 $ X = Yf