# Why square root for RSE?

$$\text{RSE}=\sqrt{\frac{1}{n-2}\text{RSS}}=\sqrt{\frac{1}{n-2}\sum_{i=1}^n (y_i-\hat{y_i})^2}$$

Why should we put square root to get RSE ? what for?

Suppose that $y$ is in units of meters. Then the squared errors $\sum (y_i - \hat y_i)^2$ are in units of meters squared, whereas RSE is in units of meters again. This puts it on a comparable scale to the data points, making the resulting numbers much more interpretable.