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# Consider the model P t = 0 + 1 S t + u t, where P and S are profits and sales of a company at time t.

1. Consider the model Pt = β0 + β1 St + ut,

where P and S are profits and sales of a company at time t. The company's sales manager believes that this relationship is different across the fall, winter, spring and summer seasons. She gives you data for each season for 20 years (n = 80) and wants you to test the null hypothesis that there is no difference in the parameters across the seasons.

i. Derive another model that will enable you to test this hypothesis.

ii. Write down the null and alternative hypotheses.

iii. Describe how you would test the hypothesis using the F-test. In particular, state what regressions you would run, how you would compute the test statistic, its distribution and degrees of freedom, and the criterion for acceptance or rejection of the null hypotheses.