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Do errors need to be normally distributed?
Yes, you should check normality of errors AFTER modeling. In linear regression, errors are assumed to follow a normal distribution with a mean of zero. Let’s do some simulations and see how normality influences analysis results and see what could be consequences of normality violation.
How do you tell if regression errors are normally distributed?
The easiest way to check for normality is to measure the Skewness and the Kurtosis of the distribution of residual errors. The Skewness of a perfectly normal distribution is 0 and its kurtosis is 3.0. Any departures, positive or negative from these values indicates a departure from normality.
What happens when errors are not normally distributed?
When errors are not normally distributed, estimations are not normally distributed and we can no longer use p-values to decide if the coefficient is different from zero. In short, if the normality assumption of the errors is not met, we cannot draw a valid conclusion based on statistical inference in linear regression analysis.
When to use normal distribution in data analysis?
When I first learned data analysis, I always checked normality for each variable and made sure they were normally distributed before running any analyses, such as t-test, ANOVA, or linear regression. I thought normal distribution of variables was the important assumption to proceed to analyses.
Do we need normal distribution of dependent variable when working with?
1) It is not the distribution of the variable that needs to be normal (or, better: Gaussian). If a distribution matters at all (e.g. in the Newman-Pearson framework of hyposesis testing) then it is the distribution of the residuals.
Do you check the normality of errors after modeling?
Yes, you should check normality of errors AFTER modeling. In linear regression, errors are assumed to follow a normal distribution with a mean of zero.