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 R$2$ 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 R$2$ 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 CostsHours of InspectionNumber of Batches$$17,6891001018,3501202013,125601528,0003203030,5602402531,7552004040,7502803529,5002302247,5703505036,7402704543,5003503826,7802001828,5001402817,00016014$

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 X$1=$ hours of inspection, and X$2=$ number of batches.

Y $=$ $fill in the blank $1+$ $fill in the blank $2$ X$1+$ $fill in the blank $3$ X$2$

Are both activity drivers useful?

YesNo

What is the adjusted R$2?$ Round to the nearest whole percent.

fill in the blank $5\%$

$2.$ 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 $3\mathrm{.}14).$ In your computations, round X$1$ and X$2$ 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 $=$ $fill in the blank $6$

$fill in the blank $7$ Yf $$ $fill in the blank $8$