Could someone please explain the difference between the root mean square error and the standard error of the estimate? I have run a multiple regression in SPSS and have got a standard error of estimate value but when I do the same regression in R and ask for the RMSE I get the same value as the standard error of estimate value. They seem like the same thing to me or am I wrong?
They are not the same. The root mean square error (RMSE) represents the average distance between predicted values and actual values while the residual standard error represents the standard deviation of the residual values, i.e. it gives us an idea of how much-projected value could vary from the mean of the actual value.