According to the formula of RMSE which is square root of mean sum of errors, the df for RMSE calculation is n, however, the df of MSE calculation which is SSE/df is square root of SSE/df, and df is n-k-1. can anyone explain the difference between n and n-k-1 in RMSE and MSE? Appreciated.

This is a question that I have often thought about and spent too much time on the internet not understanding. My formal statistc does not go further than 1st year degree (it was by 2nd degree and children came along) so I am always feel a little on the back foot.

RSME - is often used with out of sample data to test the effectiveness of the model. sometimes known as root square mean predicted error. It will include it errors due to unobservable errors and poor predictions of the slope and intercept in the model. We are are combiing both these errors and using “n”

RSME is considerd to be biased. The adjsutment in ANOVA is try and remove that bias by dividing by the degrees of freedom. Exactly why it is baised is beyond my explainable grasp - I think If I can’t explain it I don’t really know. BUt for example If we have a model with 2 variables (inercept and slope) and 2 data items there can be be not error it is only when we introduce more data items to we introduce the possibility of error. It is better to divide your sum of square of residuals by df = n- k - 1 (ie of this case 1) then n (3).

Not as n increases the two values will converge

Try this article

2nd paragraph under regression

Stockexchange and reddit statistics are also good places to try and learn.