Stats nerd post

I try not to complain too much (in this forum) about my students, but I couldn't resist a quick rant about an answer I just read on the stats test. Now to preface this, I should point out that most of the students handled this questioned just as well as I'd hoped.

This test covered regression analysis -- the MOST important topic in stats 2 in my opinion. Most regression analysis today is performed by computer, but I make them do one by hand just to show they understand the process. The more important (to me) task, though, is to make sure they understand the results. Hence, after having them determine the OLS regression line, I asked them to interpret the results and then I asked the following:

JUST GIVEN WHAT YOU'VE DONE IN THIS PROBLEM, can you say whether experience is an important predictor of sales? Why or why not?

The correct answer would be something like, "While experience does appear to be positively correlated to sales, one would have to test the significance of this relationship before reaching a valid conclusion about the link." Most students gave me a rather terse version of that answer, but a few fell for the "obvious" conclusion that since the correlation was positive, experience MUST be important. Then I read this answer:

Experience is an important predictor of sales because common sense says the more experience one has selling something the better he/she gets. [Emphasis added.]

I couldn't believe it -- someone actually invoked the "common sense theorem" (the grad school version is known as the "obvious theorem") as evidence in my stats class! ARGH! You know, the longer I do this, the more sympathy I have for my old grad school profs -- bless their hearts.