Hello again stefnix, on Point A, you have a large sample size and therefore these tests become more sensitive. I know it's counter-intuitive. However, because you have such a large sample size they are basically meaningless also. So with those histograms and QQ plots as others said, no reason to hesitate to use linear regression. What I would do is to check normality of the residuals after fitting the model. If you use proc reg or proc glm you can save the residuals in an output and then check for their normality, This in my opinion is far more important for the fit of the model than normality of the outcome. On why you keep getting the same outcome for the normality test: Nothing wrong with your code or model. The p-values of these tests are an approximation.For example, for K-S you get a p-value of <0.01, that could be anything like 0.00049 or 0.0000000000000003. The output does not tell you the exact value, just that is smaller than 0.05. It doesn't mean it is not changing in the background. Hope that makes sense and eases your mind that you are not doing anything wrong. Please do ask again if you have any questions.
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