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Why do error values in linear regression have to be normally distributed and why not in logistic regression?

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Lets clarify with a simpler question

Why points on a circle must be equally distanced from center, but not points on a square?

Because of how circle and square are "defined". The same goes for linear and logistic regression, we cannot pose a "why?" question when errors are "defined" in a certain way (or a better word here "assumed"). We may design a new version of linear regression by replacing Normal distribution with some other distribution, and then proceed to derive a formula or algorithm for estimating the parameters. Then use it in a real-world scenario to see how it works, and so on.

Also here is a list of good posts on stats.stackexchange.com related to characteristics of those errors:

  1. Error distribution for linear and logistic regression,

  2. Logistic Regression - Error Term and its Distribution.

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