I have read in many places, including stack exchange, that in order to carry linear regression analysis the residuals have to be normal. This is required because most of the statistical results, parameter estimates, and prediction intervals rely on normality assumption. Thus, we carry appropriate tests to determine whether the residual is normal and, if the residual is not normal, we can either transform the observations data (or the residuals?) or we can take more data samples such that $N$$>$$30$. PLEASE CORRECT ME IF I'M WRONG ON ANY OF THIS.
However, I have also read in other places that for most models ,including linear regression, one also usually assumes normality of our variables for two main reasons(Toby Mordkoff, 2016):
1) "To prevent us from having to use one set of statistical procedures for large ($30+$) samples and another set of procedures for smaller samples... we assume that the population is normal"
2) "Therefore, if we are going to assume that our estimates of the population mean and variance are independent (in order to simplify the mathematics involved, as we do), and we are going to use the sample mean and the sample variance to make these estimates (as we do), then we need the sample mean and sample variance to be independent. The only distribution for which this is true is the normal. Therefore, we assume that populations are normal."
So should the independent (or dependent) variables in a linear regression model be normal or just the residual? Please explain.