Confused on the definition of Residual standard error

I am confusing with the actuarial text book. It said the residual standard error is s =RSS/(n-2), why it is not $$\sqrt{\frac{RSS}{n-2}}$$? And also, what is the difference between the MSE and RSS, since $$MSE= \sum_{n}^{i=1}(y_i-\hat y)^2$$ and residual sum of square=$$(y_i-\hat y)^2$$? could I understand $$\sqrt{MSE}=RSE$$ ?

There is a $$\frac{1}{n}$$ missing in the MSE formula. Also, the summation subscript and supscript are swapped and the subscript $$i$$ of the prediction $$\hat{y}$$ is missing. It should read $$MSE = \frac{1}{n} \sum_{i=1}^n(y_i - \hat{y}_i)^2$$
Also, $$RSE = \sqrt{\frac{RSS}{dof}}$$ (the square root is required, since the standard error describes a standard deviation, so no idea why it should be $$RSE = \frac{RSS}{dof}$$), where $$RSS = \sum_{i=1}^n(y_i-\hat{y}_i)^2$$ and dof is your degree of freedom (dof $$= n - 2$$ for a $$2$$-parameter regression). Thus you have
$$MSE = \frac{1}{n}RSS = \frac{dof}{n}(RSE)^2$$