Contents
What is a non normal residual?
When the residuals are not normally distributed, then the hypothesis that they are a random dataset, takes the value NO. This means that in that case your (regression) model does not explain all trends in the dataset.
What is Fisher R to Z transformation?
The Fisher Z-Transformation is a way to transform the sampling distribution of Pearson’s r (i.e. the correlation coefficient) so that it becomes normally distributed. The “z” in Fisher Z stands for a z-score. If r1 is larger than r2, the z-value will be positive; If r1 is smaller than r2, the z-value will be negative.
What do you do if your variables are not normally distributed?
Many practitioners suggest that if your data are not normal, you should do a nonparametric version of the test, which does not assume normality. From my experience, I would say that if you have non-normal data, you may look at the nonparametric version of the test you are interested in running.
Is there an assumption about the normality of residuals?
However, there is an assumption about the normality of the residuals. Check different kind of models. Another model might be better to explain your data (for example, non-linear regression, etc). You would still have to check that the assumptions of this “new model” are not violated.
How are residuals validated in a second model?
So in a second model, dismissing variables following a backward selection procedure I got normal residuals validated both graphically with a qqplot and by hypotesis testing with a Shapiro-Wilk test. Check if this could be your case. Thanks for contributing an answer to Cross Validated!
What can I do if my residuals are not normally distributed?
That slightly differs from a normal distribution and the shapiro.test also rejects the null hypothesis that the residuals are from a normal distribution: What can I do if my residuals are not normally distributed? Does it mean the linear model is entirely useless?
When to remove outliers from a regression model?
You should not remove outliers just because they make the distribution of the residuals non-normal. You may examine the case that has that high residual and see if there are problems with it (the easiest would be if it is a data entry error) but you must justify your deletion on substantive grounds.