C$14-30.$ Estimating Machine Repair Costs

In an attempt to determine the best basis for predicting machine repair costs, the production su$-$

pervisor accumulated daily information on these costs and production over a one$-$month period.

Applying simple regression analysis to the data, she obtained the following estimating equation:

$Y=$$$800-$$$2\mathrm{.}60x$

where

$Y=$ total daily machine repair costs

$x=$ daily production in units

Because of the negative relationship between repair costs and production, she was somewhat skep$-$

tical of the results, even though the R$-$squared was a respectable $0\mathrm{.}765.$

REQUIRED

a$.$ What is the most likely explanation of the negative variable costs?

b$.$ Suggest an alternative procedure for estimating machine repair costs that might prove more

useful.