RMSE formula

Question

If you fit a regression model, you can get the RMSE of the model.  From our documentation, RMSE is the standard deviation of the random error.  To me that would imply if you took the stdev of the residuals of the model, it would equal the RMSE, but this is not true.  The values are close but not exact, see the below example (RMSE = 3.03, Stdev of Residuals = 2.99):

So I'm wondered what I'm missing here as my assumption is not correct.

DonMcCormack · Accepted Answer

For the regression model, root MSE = Sqrt(SSe/df) = Sqrt(348.9/38), for the sample standard deviation, SD = Sqrt(SSe/(n-1)) = Sqrt(SSe/39)). In the regression model, you're losing an extra degree of freedom by estimating the slope.

andreacoombs · Accepted Answer

If you were just calculating the mean, the RMSE would be the SD of the residuals.  But you need one DF for the model to calculate slope.