Consider simple linear regression with $n$ pairs of numbers $x_i,y_i$. Let ${\hat\beta}_0 +{\hat\beta}_1x$ be the least squares line where ${\hat\beta}_0={\overline y}-{\hat\beta}_1{\overline x}$ and ${\hat\beta}_1 = r_{xy}s_y/s_x$. In terms of the summary statistics, derive a simple expression for the residual standard deviation $[\sum_{i=1}^n e_i^2/(n-2)]^{1/2}$, where
$\sum_{i=1}^n e_i^2 = \sum_{i=1}^n (y_i-{\hat\beta}_0-{\hat\beta_1}x_i)^2$
For a question like this one that involves a derivation, after you formulate an algebraic solution, check its validity on some numerical regression examples with small data sets. If you match numerically in some instances, your answer is likely correct. If your theoretical answer doesn't match the numerical cases, go back to review your "derivation".

Part a)
To validate whether you have the correct expression, suppose $n=34$, $r_{xy}=0.7$, $s_y=0.5$ and $s_x=1.6$. What is your value of the residual SD:

Hint: