If you are talking about standard (OLS) regression, the assumption about normality is about the regression residuals, not about the distribution of your outcome (e.g. see: https://www.theanalysisfactor.com/assumptions-about-residuals/). Checking the distribution of the residuals is much more informative than checking normality of your data.

With respect to Kolmogorov-Smirnove and Shapiro-Wilk: these being ordinary significance tests, their "significance" is depends on, among other things the size of the deviation from normality and the size of your data. Chances are that at a large sample it can signal deviation from normality even when so small it would never pose a problem. The reverse is true for small data.

Hello. As far as i know, normality isn't an issue for regression analysis. You may look at http://www.statisticssolutions.com/normality/

And the following paper will help you

Article Linear regression and the normality assumption

If you are talking about standard (OLS) regression, the assumption about normality is about the regression residuals, not about the distribution of your outcome (e.g. see: https://www.theanalysisfactor.com/assumptions-about-residuals/). Checking the distribution of the residuals is much more informative than checking normality of your data.

With respect to Kolmogorov-Smirnove and Shapiro-Wilk: these being ordinary significance tests, their "significance" is depends on, among other things the size of the deviation from normality and the size of your data. Chances are that at a large sample it can signal deviation from normality even when so small it would never pose a problem. The reverse is true for small data.

The assumption of normality is about the residuals not the variables as Maarten already stated.

Graphical approaches to testing for normality in the residuals are more effective, and might assist you in making a good transformation. A q-q plot (normality) and a plot of the residuals against the predicted (heteroscedasticity) will be helpful.

A plot of observed data, regression line and 95% confidence interval might help. With that figure do you believe the outcome?

The test for normality will get you into trouble. It is an important issue and you should look at how well the model fits the data. Yet if the test for normality is significant then you either need to transform the data or use a non-parametric model. If the test for normality is not significant then you are going to behave as if such a test proves that the data are normally distributed. Sadly, failing to reject the null hypothesis is not proof that the null hypothesis is true. It is also generally possible to make tests like the test for normality produce a significant outcome by increasing sample size. So the end result is an unsatisfying mess.

The problem with the graphical approach is that it requires some experience to look at the graphs and decide if corrective measures are needed. The only way to gain experience is to look at a great deal of data.

Hello Ehab. I've attached some notes summarizing what Jeffrey Wooldridge says about the assumptions for OLS linear regression in his book Introductory Econometrics: A Modern Approach. One of the key points he makes, I think, is that as the sample size gets large, normality of the errors is not required. What is required is that the sampling distributions of the parameters (i.e., the regression coefficients) be approximately normal.

Here's how I think about it: Provided that the errors are independently and identically distributed (i.i.d.), normality of the errors is a sufficient condition, but not a necessary condition for the model to be a good model. The necessary condition, as noted above, is that the sampling distributions of the parameters be approximately normal. (I say approximately normal, because as George Box famously noted, normal distributions don't exist in the real world, nor do straight lines.)

Finally, when lecturing on the assumptions of OLS linear regression, I always point out that the i.i.d. assumptions are about the errors, not the residuals. The Wikipedia page linked below has a nice discussion of this important distinction. (Note that residuals can never be truly independent, for example, because if n-1 of them are known, the last one is completely determined.)

• https://en.wikipedia.org/wiki/Errors_and_residuals

HTH.