What is the difference between RSE and MSE?

Question

I am going through Introduction to Statistical Learning in R by Hastie and Tibshirani. I came across two concepts: RSE and MSE. My understanding is like this:

RSE = sqrt(RSS/N-2)
MSE = RSS/N

Now I am building 3 models for a problem and need to compare them. While MSE come intuitively to me, I was also wondering if calculating RSS/N-2 will make any use which is according to above is RSE^2

I think I am not sure which to use where?

Answer 1

RSE is an estimate of the standard deviation of the residuals, and therefore also of the observations. Which is why it's equal to RSS/df. And in your case, as a simple linear model df = 2.

MSE is mean squared error observed in your models, and it's usually calculated using a test set to compare the predictive accuracy of your fitted models. Since we're concerned with the mean error of the model, we divide by n.

Answer 2

I think RSE ⊂ MSE (i.e. RSE is part of MSE). And MSE = RSS/ degree of freedom

MSE for a single set of data (X1,X2,....Xn) would be RSS over N or more accurately is RSS/N-1 (since your freedom to vary will be reduced by one when U have used up all the freedom)

But in linear regression concerning X and Y with binomial term, the degree of freedom is affected by both X and Y thus N-2 thus yr MSE = RSS/N-2 and one can also call this RSE

And in over parameterized model, meaning one have a collection of many ßs (more than 2 terms| y~ ß0 + ß1*X + ß2*X..), one can even penalize the model by reducing the denominator by including the number of parameters: MSE= RSS/N-p (p is the number of fitted parameters)