I love these great examples but having the animation with half the speed would be easier on my eyes

Thanks and yeah I think you're right 😅… I've slowed most of them down and added the Scrubber's loopDelay option so they pause for a second before starting over.

I believe this should show the distribution of the errors. The error is measured only in the y dimension (the residual). The graphic is meant to show the non-normality of the error terms under heteroskedasticity, which is a violation of the Gauss-Markov assumptions for OLS.

Exactly! The least squares solution is only correct for a model where the error bars are assumed correct, Gaussian and independent (the standard way to fit a line to these data). We know, of course, that this isn't the right model in general. Unfortunately, there isn't a generalization of least squares that supports a model without the above-mentioned assumption. Instead, we need to write down the likelihood function and numerically optimize it - see this example: https://cadasa.github.io/LQR-MLR.png

Also I was incorrect on what it shows.. the author is bootstrapping the confidence intervals: selecting a subset of points to estimate, then generating 1000 samples (or so) from this subset and estimating the coefficients for each. The histogram is the distribution of coefficients. The best fit line is the average coefficients from all the fit samples.