Why should errors be normally distributed in linear regression?

Usually, there are 2 reasons why this issue(error does not follow a normal distribution) would occur: Dependent or independent variables are too non-normal(can see from skewness or kurtosis of the variable) Existence of a few outliers/extreme values which disrupt the model prediction.

Does data need to be normally distributed for linear regression?

4 Answers. You don’t need to assume Normal distributions to do regression. Least squares regression is the BLUE estimator (Best Linear, Unbiased Estimator) regardless of the distributions.

Do errors need to be normally distributed?

The normality assumption is needed for the error rates we are willing to accept when making decisions about the process. If the random errors are not from a normal distribution, incorrect decisions will be made more or less frequently than the stated confidence levels for our inferences indicate.

Why is the normality assumption important?

The Assumption of Normality says that if you repeat the above sequence many many many times and plot the sample means, the distribution would be normal. Therefore, we must estimate the sampling distribution of the mean. The sample, itself, does not provide enough information for us to do this.

What if error is not normally distributed?

When faced with non-normally in the error distribution, one option is to transform the target space. With the right function f, it may be possible to achieve normality when we replace the original target values y with f(y). Specifics of the problem can sometimes lead to a natural choice for f.

Why data should be normally distributed?

It is the most important probability distribution in statistics because it accurately describes the distribution of values for many natural phenomena. Characteristics that are the sum of many independent processes frequently follow normal distributions.