I thought the discussion of the regression anatomy theorem was good and wouldn’t mind working through some of the implications for the theorem in applied work, thinking here of the inevitable conversation which goes: “That’s nice, why should i care?”

It may be of very little importance, but I was just wondering about the choice of the word explained as in ‘explained sum of square’ or ‘explained variance’, when it actually does not explain anything in the sense of give the reason or the cause.

Hi @lacopoff, any bit of learning is important. You’re right the word explained is a bit overloaded. He’s using this term.

But really I think a visual does more justice. If I use my own words the explained variance is the amount of variance “reduced” once you use a linear regression to estimate the data.

If you’re like me I learn more hands on, what you could do is

Simulate some data with a linear trend,

Calculate the variance without a regression

Run a regression

Calculate the residual

Measure the variance of those

If that sounds interesting to you we can start another topic and walk through it! Great question