When we conduct linear regression, there are several assumptions. The assumption of normality is whether the residual errors are normally distributed, not whether a predictor is normal?
Correct. The normality assumption is that the residuals are normally distributed, not the values of the predictor.
Just to say it, before Bruce Weaver will do it: it is about the normality of the errors, not the residuals, but we only have the residuals, so this is fine ;-)
But it is not recommended to only rely on statistical tests to check this assumption. In small samples they won't detect deviations from normality, due to power problems, and in large samples, they will flag even small deviations. Therefore, use QQ plots and histograms to evaluate the shape and causes of (non-) normality. There is not true normal distribution in nature.
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