Suppose I want to see if Gaussian linear regression is an appropriate model for my data. Then let X be the design matrix (with each column corresponding to an explanatory variable). and let e be the vector containing my residuals. We then have transpose(X)e = 0.
My course says that this implies that "no correlation should appear between explanatory variables and residuals".
I do not understand what is meant by correlation here as the definition I know involves two random variables. But X is not a random variable.
Also, given the right definition, how does he arrive at this conclusion of "no correlation"?
Thank you in advance! I hope my question was adequate as this is my first time posting.