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From what I know, linear regression is a parametric model (as mentioned in here). Parametric tests requires normality of the variables. My first question is that this is an assumption of the linear regression? Should we have features, or target, that are normally distributed?

I'm asking this because I've seen plenty of models with nonlinear features and target. So what's the meaning of the "parametric" on linear regression?

I know that we talk about the normality of the residuals. But not even this is required for a regression if what you want is the prediction. From what I know, the normality is just for the BLUE estimator (you can see the math on this post.

To sum up, I'm confused regarding these two things:

  1. What's the meaning of the word "parametric" that people use to talk about Linear Regression?
  2. You can have a model that makes good prediction without any kind of normality (not even from the residuals). Should we still use the word "parametric" when talking about this regression?

Thanks in advance. I hope the questions aren't too confuse.

Aldla E Aoepql
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  • Parametric models do not require normality of the variables. – Tim Sep 03 '22 at 19:33
  • 'Parametric tests requires normality of the variables.' is untrue in general, this appears to be a widespread misunderstanding. See https://en.wikipedia.org/wiki/Parametric_statistics to see what 'parametric' means. In the derivation of the 'usual' forms of inference in linear regression there's an assumption of normality for something but neither the IVs nor DVs are assumed to be normal, and there's also a large sample argument which indicates that the significance level at least should be close to correct. ... ctd – Glen_b Sep 04 '22 at 15:47
  • ctd ... Thrse issues are discussed in a number if posts already on site. There's also forms of inference that use different parametric assumptions, and some that rely on no parametric distributional assumptions. – Glen_b Sep 04 '22 at 15:49

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