Today, I had an epiphany. As I was reading a book on statistical modeling, I read a statement I had read dozens of times before about how beta-weights are partial derivatives and the light went off as I thought,
“Duh, of course! I can’t believe I have never realized this. It is so obvious. OF COURSE, the beta-weight has to be a partial derivative. A derivative is the rate of change and the partial derivative is the rate of change with other variables held constant and so of course a beta-weight in a multiple regression is the same thing.”
In my defense I should point out that my last Calculus course was probably ten years before my first inferential statistics course, so it is not completely stupid that I did not put two and two together at once. (My niece would comment that this is actually far beyond two plus two. Humph!) Still, it is embarrassing to relate that for twenty years I have been using matrix algebra to solve these equations without really thinking very deeply about the underlying mathematics.
Of all of the people I know, Dennis is the only one who, instead of,
“What the hell are you talking about?”
“That is so obvious. I can’t believe you never thought of that before,”
In fact, that is exactly what he said. Well, he didn’t add that he couldn’t believe I hadn’t thought of it, because he wants peace and marital bliss in the house.
Why did it take me so long to put these obvious facts together, even if they were learned ten years apart? The embarrassing truth is, like everyone else, I often did not learn more than I had to. There were courses to pass, children to raise, articles to write. Today, for the first time, I had the leisure of sitting down with no intent other than to completely understand the mathematical underpinnings of the statistical techniques that I use, even if it took reading the same page ten times or reading a hundred different books until I got it completely. It didn’t take a hundred books or even reading one book ten times. All it took was giving my complete, undivided attention to understanding it instead of ‘getting through it’.
What a concept.