[CTcard]

OK, if we are really going to nerd out

All I can say in my defense for what follows is ... you started it.

(and like Winflop, I also taught introductory stats, though I am not a statistician, and the students were Pharmacy students),

Unlike you and Winflop, I have never taught introductory stats, but I have taught statistical mechanics and data analysis.

one thing that needs to be pointed out is that the observations are not independent, which is one of the requirements for performing an OLS regression. 

Really, whether data points are independent or not is irrelevant for performing a least squares linear fit, at least as done here. The least squares fitting done will tell us the most likely values of the parameters of the line IF there is a linear relationship in the data set. It doesn't really tell you whether there actually is a linear relationship, though goodness of fit parameters certainly weigh in on the matter.

Basically, there is an internal correlation structure between the datapoints, because consecutive seasons in a given season are more likely to have similar results than seasons with more time between them.  The bottom line is that Harbaugh came to Stanford one year before Dawkins, and the revival of Stanford football (including 10 consecutive bowl games between 2009 and 2018 coincided with the relative decline of basketball with only one NCAA tournament over that time).

BC

The question of interest is independent of whether year to year results are independent in each sport alone. The hypothesis clearly includes the idea that there is a cosmic force that ensures that if we manage to hire a good football coach that makes year on year results good, then we will be forced into a bad basketball coach for a similar period of time. Thus the Harbaugh/Dawkins association you note is part of the theory.

However, the actual data set appears to indicate no real relationship, at least by my eye. The data looks roughly like a cloud. A linear fit will give SOME slope by definition, which happens to be negative in this case.

[CTcard]

OK, if we are really going to nerd out

All I can say in my defense for what follows is ... you started it.

(and like Winflop, I also taught introductory stats, though I am not a statistician, and the students were Pharmacy students),

Unlike you and Winflop, I have never taught introductory stats, but I have taught statistical mechanics and data analysis.

one thing that needs to be pointed out is that the observations are not independent, which is one of the requirements for performing an OLS regression. 

Really, whether data points are independent or not is irrelevant for performing a least squares linear fit, at least as done here. The least squares fitting done will tell us the most likely values of the parameters of the line IF there is a linear relationship in the data set. It doesn't really tell you whether there actually is a linear relationship, though goodness of fit parameters certainly weigh in on the matter.

Basically, there is an internal correlation structure between the datapoints, because consecutive seasons in a given season are more likely to have similar results than seasons with more time between them.  The bottom line is that Harbaugh came to Stanford one year before Dawkins, and the revival of Stanford football (including 10 consecutive bowl games between 2009 and 2018 coincided with the relative decline of basketball with only one NCAA tournament over that time).

BC

The question of interest is independent of whether year to year results are independent in each sport alone. The hypothesis clearly includes the idea that there is a cosmic force that ensures that if we manage to hire a good football coach that makes year on year results good, then we will be forced into a bad basketball coach for a similar period of time. Thus the Harbaugh/Dawkins association you note is part of the theory.

However, the actual data set appears to indicate no real relationship, at least by my eye. The data looks roughly like a cloud. A linear fit will give SOME slope by definition, which happens to be negative in this case.