For his Master’s degree thesis in Metallurgy at McGill University, Larry developed an alloy that was f lexible 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:

Quarter              Sales (million units)
1........................................................0.14
2........................................................0.31
3..........................................................1.1
4........................................................1.22
5........................................................1.67
6........................................................1.89
7........................................................1.91
8........................................................2.25
9........................................................2.41
10......................................................2.42
11.....................................................2.67

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 log10(quarter).

c) Compare the results of (a) and (b). Which do you prefer?