The Philly Company manufactures widgets and digits. Philly assembles the widgets in batches but makes digits one at a time. Philly believes that the cost of producing widgets is independent of the number of digits produced in a week. The firm gathered cost data for 156 weeks. The following notation is used:
C = Total manufacturing costs per week
N = Number of widgets produced during a week
B = Average number of widgets in a batch during the week
D = Number of digits produced during the week
A multiple linear regression fitted to the observations gave the following results:
C = $265:80 + $8:21N – $7:83B + $12:32D
a. According to the regression results, how much are weekly costs expected to increase if the number of widgets increases by 1?
b. What are the expected costs for the week if Philly produces 500 widgets in batches of 20 each and produces 300 digits during the week?
c. Interpret the negative coefficient $(7.83) estimated for the variable B.