I want to calculate MPSE, mean square prediction error, to compare the performance of several regression models that I developed with training data on new testing data.
Is the mean square prediction error simply calculated as the mean of (Predicted Values - Observed Values)^2? The observed values here are the response variable from the testing dataset.
Also, can the predicted values be obtained from the R code below?
predict(lm.fit, newdata=testing, interval="prediction")
Yes, you simply take the mean of the squared errors. This is often simply called Mean Squared Error (mse - take a look at the tag), since the P often refers to percentages, e.g. in the mape. I'd argue that "prediction" is redundant, since you should always evaluate your prediction on holdout data, anyway.
And yes, you can obtain your predictions from an lm object by using predict(). (More precisely, predict.lm().) However, since the MSE is a point accuracy measure, you only need point predictions, not intervals, so you can go with the default parameter interval="none".
