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The project template on sports won-loss records suggests using an F test to compare the regression equations for years before and after the free agency rule in baseball. This student project gives an example, using the sports statistics on the NEAS web site.

As the candidate notes, the free agency rules changed in 1976 and 1981. He choose two twenty years periods: 1961-1980 and 1981-2000. He examines ten teams in the American League that span the 40 years. This design is good. Note the following:

You don’t have to use both Leagues or all the data on the NEAS web site. With 40 years, 10 teams, and 10 independent variables, the regression has about 300 data points. The candidate concludes that two past years gives the optimal regression equation, so we have about 350 data points for the F test. We need about 80 points to get credible results.

You can choose other time periods, such as 1961-1975 vs 1981-2005. This candidate chooses time periods with equal numbers of years. This is a good choice, since it gives enough data points for each time period. But the time periods don’t have to be the same length. The M and N parameters in the F test may differ. Choose time periods that make the most sense.]

The candidate explains why the optimal regression equations may differ for the two time periods. This is good statistical practice. If we examine all possible F tests, some will seem significant by random fluctuation. We combine intuition and statistical evidence to draw conclusions from the data.

Explain your intuition for the student project. This shows you understand the meaning of the regression equations. Candidates who understand the material worry that repeating simple definitions from the textbook or the course modules is not useful. The opposite is true. We want to see that you understand what the statistical technique shows. Explain the null hypothesis, and say how it is tested.

Numerous factors cause differences between two time periods. Even the change in the free agency rule might have offsetting effects. This candidate reasons that before free agency, a team retained its good players for many years, so the beta coefficients are high. Another candidate might reason that

We do not judge the truth of your hypothesis. We look at how you test the hypothesis and if you understand the implications you draw about the optimal regression equation.