A company makes parts for small engines. Its monthly sales in the two major Canadian provinces where it operates over the past year are:

British Columbia ($m)               Ontario ($m)
4.61...................................................................6.2
4.53.................................................................5.69
5.59.................................................................6.05
5.04.................................................................6.63
3.44......................................................................6
3.9...................................................................6.94
4.57.................................................................6.42
5.7...................................................................6.88
5.51.................................................................7.28
5.32.................................................................7.43
5.89.................................................................7.21
5.21.................................................................7.09

The vice president of Marketing awards bonuses to the marketing directors of provinces according to their sales growth as measured by the average increase in sales per month from a linear regression of the past year’s data. There are two bonuses: (i) for the province with the higher sales growth; and (ii) for the province whose sales growth is more significantly different from zero.

a) Critique this use of linear regression by the vice president as a general methodology to use in any year.

b) Perform the regressions. Does your critique in (a) apply this year? Indicate which provincial marketing director should receive bonus (i) and (ii).

c) The marketing director who does not receive bonus (ii) complains: “Although the other province had a sales growth more significantly different from zero, it is not significantly higher than my sales growth.” Confirm how true/false this statement is.