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Re:Guide to Linear Regression (2015) by stdbrouw on Thursday January 21, 2016 @03:45PM (#10948171)
You're right, there is lots of confusion in the topic and not all texts on regression get it right. Theoretically, linear regression depends only on a normally distributed outcome variable, the predictors don't have to be normally distributed. Practically speaking even that requirement can mostly be ignored: OLS is fairly insensitive to non-normal outcomes. Violations of the assumptions of regression usually don't affect the estimates much, they mainly affect the uncertainty around those parameter estimates -- the standard errors. This too is easily solved: use bootstrapping to calculate the standard errors.

In short: you can't just throw linear regression at anything and expect to get reasonable results, but it's pretty damn close.

Re:Guide to Linear Regression (2015) by hooloovoo_zoo on Thursday January 21, 2016 @07:00PM (#10949601)
Even that normality is not required; see, for instance, https://en.wikipedia.org/wiki/Gauss%E2%80%93Markov_theorem.
Re:Guide to Linear Regression (2015) by stdbrouw on Friday January 22, 2016 @04:20AM (#10951698)
Good catch. Outcome (or error, which boils down to the same thing) can't just be anything either, though, e.g. a common pattern is that the variance in an outcome increases when the predictor increases (e.g. a machine behaves more erratically when it spins faster) and that can mess with estimates.