I’ve got some data (158 cases) which was derived from a Likert scale answer to 21 questionnaire items. I really want/need to perform a regression analysis to see which items on the questionnaire predict the response to an overall item (satisfaction). The responses are not normally distributed (according to K-S tests) and I’ve transformed it in every way I can think of (inverse, log, log10, sqrt, squared) and it stubbornly refuses to be normally distributed.

The residual plot looks all over the place so I believe it really isn’t legitimate to do a linear regression and pretend it’s behaving normally (it’s also not a Poisson distribution). I think this is because the answers are very closely clustered (mean is 3.91, 95% CI 3.88 to 3.95).So, I am thinking I either need a new way of transforming my data or need some sort of non-parametric regression but I don’t know of any that I can do in SPSS.

**Answer**

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. See the Gauss-Markov Theorem (e.g. wikipedia) A normal distribution is only used to show that the estimator is also the maximum likelihood estimator. It is a common misunderstanding that OLS somehow assumes normally distributed data. It does not. It is far more general.

**Attribution***Source : Link , Question Author : rachel S , Answer Author : Dave31415*