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John Hall

These past two posts focus a lot on the "regression doesn't know". I think what you needed to spell out more clearly is that the naive process is to estimate the regression and then use the estimate of the intercept to infer the population average. You're obviously right that this is mistaken when the groups in the population are unbalanced. It would make for a good introduction to posterior predictive checks or Gelman's Mr. P. (multi-level regression with post-stratification)

Kaiser

JH: Yes, one of the next posts will explain what regression is good for and why we do what we do.

"You're obviously right that this is mistaken when the groups in the population are unbalanced." Couldn't have said it better - and when in the real world do we have populations that are balanced?

And yes, what is in this post directly relates to Mr. P.

Clur

Thanks again for this well-explained post. It would be nice if you could make a post in this serie on multi-level regression with post-stratification. So far I have not been able to develop a good intuitive understanding of it. I am asking you that because I really like how you explain difficult ideas, by using examples that directly show the mistakes we make if we don't have a good understanding of how it works. Your examples are simple and yet very powerful. You are really gifted for explaining all this!

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Kaiser Fung. Business analytics and data visualization expert. Author and Speaker.
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