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:

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 + 428.69

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 ????????$

I want this part. what is ???

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