Class 8. Executive compensation review example.

What you need to have learnt from Class 7.

Two types of model.

Parallel lines model: different intercepts - same slopes.

Non-parallel lines: different intercepts and different slopes.

Two key facts in understanding the JMP output.

JMP always makes comparisons to the ``average'' of the groups.

JMP always leaves one group out - you figure out the missing difference (easy).

Non-parallel slopes, an interaction model.

Interaction. A three variable concept (Y,X1,X2). Generic description: the impact of X1 on Y depends on the value of X2.

Tests: the null hypothesis is always that the differences are zero, that is no difference between the groups. Three types of test: (a) Slope or intercept differences non-zero. (b) Slope differences non-zero? (c) Intercept differences non-zero?

Are any of the slope or intercept differences non-zero. (i.e. does adding the categorical variable and its interaction buy us any explanatory power?). Use the partial-F. You have to calculate this one yourself, see p. 232 of the BulkPack.

Are any of the slope differences non-zero? Do we need separate slopes (i.e. do we need an interaction term)? Use the partial-F as given on the interaction term in the ``effect test''.

Are any of the intercept differences non-zero? Given we don't need interaction, do we need separate intercepts? Use the partial-F as given on the categorical variable term in the ``effect test'' from a model excluding the interaction.

A model with different intercepts and same slopes is OK. A model with different intercepts and different slopes is OK. A model with same intercepts but different slopes is not desirable.

Our rule: if you have an interaction term in the model (i.e. different slopes) then make sure you have the variables that make up the interaction in the model as well (even if they are not significant).

We know the rule for calculating the missing group on the output. It's difference is the number that makes all the differences sum to zero. What about it's t-statistic and p-value? Rule of thumb - (so long as the missing group has roughly as many observations as the included groups and the X-values are similar) use the standard error from the included groups to calculate an approximate t-statistic. Alternatively recode the categorical variable so that the missing group has a coding that comes first in the alphabet and re-run the regression.

New material for today: NONE. It's a review example.

Some comments on the analysis.

The main question is ``what difference does an MBA make'' to your total compensation given you are a CEO.

What is the population here? To be in the spreadsheet you have to be a CEO, so another interesting, but unanswered question is ``what difference does having an MBA make on your chances of becoming a CEO''?

Severe outliers in total compensation make graphics too compressed to reveal structure. Taking logs remedies this.

Taking logs of both Y and X gives elasticity interpretation.

Note the partial-F calculation on p.232 testing both a categorical variable and its interaction term simultaneously.

The term on p.236 after a bit of trial and error disguises a large amount of exploratory analysis.

Note the highly leveraged point for Return over 5 years identified on p.238.

A non-linear relationship is identified for the marginal association between Profits and Log 10 TotComp, p.240.

See how the difficulty of taking logs of negative numbers is handled with the incorporation of an ``offset'' on p.241.

Check out the residual plots on pp. 247-248. Remember that p-values only have credibility if assumptions are satisfied.

Note the bottom line calculation on p.249 estimating what an MBA is worth (the initial question).