Is best model selection by RSS equivalent to best model selection by R2 value? I am trying to compare models using K-Fold-CV using the regsubsets function in R.
By default, it states that the ideal model is determined by the $RSS$.
I wished to change this parameter such that ideal model selection was performed on the basis of the $R^2$ value. However, I noticed that:
$R^2 = 1 - (RSS/TSS)$, and $TSS = \sum \big(y_i-\bar y\big)^2$. And therefore, is ideal model selection based on $RSS$ essentially equivalent to ideal model selection by $R^2$, given that the $TSS$ value is constant between test data-sets?

They are equivalent for the exact reason that you mention: one is a monotonic transformation of the other. Just keep in mind that we want to maximize $R^2$, while we want to minimize the residual sum of squares.
Since we typically want to find the best model for a set of data, we typically have a constant $TSS$.
