$($T$)53.$ PISTON RING ENTREPRENEUR. For his Master's degree thesis in Metallurgy at

McGill University, Larry developed an alloy that was flexible but also very hard, making

it ideal for piston rings in internal combustion engines. Upon graduation, Larry set up

his own production facility, and his piston rings were so popular that during some

quarters he ran out of production capacity and had to install new equipment. He has

now been in business for $11$ quarters and wants to forecast demand for the next year so

that he can plan upgrades to his production facilities ahead of time. His sales to date are:

a$.$ Fit a linear regression of demand against quarter.

b$.$ Sales grew quickly at first but are now slackening off like a log function. Fit a

linear regression of demand against $lo{g}_{10}($quarter$).$

c$.$ Compare the results of $($a$)$ and $($b$).$ Which do you prefer? Hint: The data are for

"sales." Larry wants to forecast "demand." In some quarters, sales were less than

demand because Larry had insufficient production equipment. LO $0,3$