I am reading the book " An Introduction to Statistical Learning " and I have trouble understanding their explanation of RSE(Residual Standard Error ) . This is what the book says :

"The RSE is an estimate of the standard deviation of \epsilon . Roughly speaking, it is the average amount that the response will deviate from the true regression line. It is computed using the formula :"

[![enter image description here](https://i.stack.imgur.com/P3S4z.png)](https://i.stack.imgur.com/P3S4z.png)

What I don't understand here is definition of RSE as " Standard deviation of \epsilon " .

If Residual = y(i) - yHat(i)

and going by my assumption that \epsilon is also = y(i) - yHat(i)

Isn't the formula of RSE just computing the "root(squared mean)" of \epsilon ?

If \epsilon = y(i) - yHat(i) ,

Then , standard deviation of \epsilon would be
`sum[y(i) - yHat(i) - mean(Y - Yhat)] / n-2` which is not what the above formula does .

So , Technically , I think RSE is just squared mean of the Residuals or \epsilon and would be wrong to call it " Standard deviation of \epsilon " , if we go by the actual formula for standard deviation .

Or , In my opinion this should mean the standard deviation of predicted yHat values rather than \epsilon .

So , is this a misuse of the term " standard deviation " in the book or Am I missing something ?

Please correct or help me understand .