Suppose we deal with the linear regression model $Y=X\beta+\epsilon$, where $X$ is determined matrix, $\beta$ - the vector of coefficents, $\epsilon$ - the vector of errors.
I often meet the statement that the coefficient of determination increases as the number of regressors does. How can it be explained? Obviously, $TSS$ does not change (observed values do not change). How can I prove that $ESS$ decreases?
Thanks in advance!