Ms DOS

They say that, with children, it doesn't get "easier", it just gets "different". Well, I'm not so sure. I have four grown-up "children" - they're are all successfully following their dreams, and I couldn't be happier!

So, I hope that Emma doesn't mind if I share this story from the mid 1990's, when her age was in single digits.

The Adjusted R-Squared, Again

In an earlier post about the adjusted coefficient of determination, R_A², I mentioned the following results that a lot of students don't seem to be aware of, in the context of a linear regression model estimated by OLS:

1. Adding a regressor will increase (decrease) R_A² depending on whether the absolute value of the t-statistic associated with that regressor is greater (less) than one in value. R_A² is unchanged if that absolute t-statistic is exactly equal to one. If you drop a regressor from the model, the converse of the above result applies.
2. Adding a group of regressors to the model will increase (decrease) R_A² depending on whether the F-statistic for testing that their coefficients are all zero is greater (less) than one in value. R_A² is unchanged if that  F-statistic is exactly equal to one. If you drop a group of regressors from the model, the converse of the above result applies.

The first of these results is (effectively) stated as Therorem 3.1 in Greene (2012), but the proof is left as an exercise.

In a comment on my previous  post, I was asked if I could supply simple proofs of these results.

Connections Between Univariate Distributions

I've been enjoying Francis X. Diebold's blog, No Hesitations. The other day he had a nice post on statistical graphics, and I found myself nodding (affirmatively) as I read through it. I won't repeat his points here, save to say:

• I, too, am a great fan of Edward Tufte. I have a couple of his books, and I used to use Minard's Napoleon chart in my introductory descriptive statistics courses.
• I have a copy of the chart of univariate statistical distribution relationships (Leemis et al., 2008) on my office wall. I was delighted to learn, from Francis's blog, that an interactive version of this chart is available.

The interactive version is definitely worth taking a look at.

© 2013, David E. Giles