# OLS variance estimators - multiple linear regression

I got a three-dimensional point set ($X1$, $X2$, $Y$) which can be described by a regression equation of the form

$y_c = a + b_1x_1 + b_2x_2$.

Now I want to calculate $Var(b_1)$ and $Var(b_2)$ but I have no idea how to do this. So could someone give me a hint, please?

Thanks in advance - I'd appreciate it if someone could help me please. Greetings

$$\begin{array}{|l|c|r|} X_1 & X_2 & Y \\ \hline 36 & 8 & 990 \\ 40 & 8 & 1140 \\ 44 & 9 & 1230 \\ 47 & 9 & 1320 \\ 50 & 10 & 1370 \end{array}$$

$a = 120\\ b_1 = \frac{75}{2}\\ b_2 = -60$

$\sigma^2 = 378$

$$R^2 = \frac{SSE}{SST} = \frac{90266}{91400} \approx 0.988$$ $$Var(b_j)=\frac{\sigma^2}{(1-R^2)\sum_{i=1}^{n} (x_{ij}-\bar{x}_j)^2}$$

$Var(b_1) \approx 35.57 \\ Var(b_2) \approx 1125$

What about my soultion? Are there any mistakes?

You missed the error in your formula. $y = a + b_1x_1+b_2x_2+e$.