After fitting a line or curve, it is easy to compute each residual as the difference between the actual Y value and the Y value predicted by the model fit by regression. For standard regression, the goal is to minimize the sum of the square of these residuals.
What is the standard deviation of the residuals? I've always summed the square of all the residuals, divided by (N - K). where N is the number of points and K is the number of parameters fit by regression, and then taking the square root of that quotient. This is called Sy.x or Se.
In a few places I've seen a value called the Root Mean Square Error (RMSE) computed by using N-1 rather than N-K in the denominator. Except for the very special case where you are only fitting one parameter (K=1) this RMSE will differ from Sy.x.
Is there any justification for computing RMSE with a denominator of N-1, or should it always be computed with N-K?