Verbal Description Of The RSE I'm reading An Introduction to Statistical Learning, currently on page 69, the chapter on Simple Linear Regression.
The text says:

In the case of the advertising data, we see from the linear regression output in Table 3.2 that the RSE is 3.26. In other words, actual sales in each market deviate from the true regression line by approximately 3,260 units, on average. Another way to think about this is that even if the model were correct and the true values of the unknown coefficients $\beta_0$ and $\beta_1$ were known exactly, any prediction of sales on the basis of TV advertising would still be off by about 3,260 units on average.

I was a bit puzzled by the last sentence, isn't what's described here the approximation of the average absolute deviation instead of the RSE, which is an approximation of the standard deviation?
 A: Consider a simple linear regressor of the form
$Y=\beta_0+\beta_1X+\epsilon$ where $\epsilon$ is an error term, independent of $X$.
The consequence of this relation is that knowing $\beta_0$ and $\beta_1$ is insufficient to know exactly the value of $Y$.
If we assume that the population error term $\epsilon$ has some distribution with $\operatorname{E}[\epsilon]=0$ and constant variance $\sigma_\epsilon^2$, then $\sigma_\epsilon^2=\operatorname{RSE}^2$
The RSE is simply the square root of the sum of the squares of the residuals, divided by the number of degrees of freedom $n-p-1$ where $n$ is the sample size and $p$ the number of variables (excluding the intercept, accounted for by the $-1$ term)
$$
\operatorname{SSR}=\sum_i^n{(y_i-\hat{y_i})^2}\\
\operatorname{RSE} = \sqrt{\frac{\operatorname{SSR}}{n-p-1}}\
$$
This answer could be expanded upon, and I do hope that someone will correct / further this explanation where necessary. 
A: You're correct but for any given error distribution the two are related by a simple scaling constant; for example, with normal errors and large samples the  mean (absolute) deviation, MD of the residuals, is $\sqrt{\frac{2}{\pi}}$ (~80%) of the standard deviation or equivalently the standard deviation is about 25% larger than the mean deviation. 
As such, under some assumption about the error distribution, the standard deviation of the errors does in fact tell you something about the average distance of observations from the mean.
More generally, the RMS distance is always at least as large as the mean absolute distance, but it's typically only a moderate percentage larger; such relationships can be useful.
RMS distance (i.e. standard deviation) is also arguably a sort of weighted-average-distance where the observation weights are proportional to the individual distances.
