I have the following model with 23 observations (n = 23):
$Y_{i}=\beta_{1}+\beta_{2} X_{2 i}+\beta_{3} X_{3 i}+\varepsilon_{i}$
and the following information which is available in the form of deviations from the mean:
$\sum_{i=1}^{23} x_{3 i}^{2}=12 ; \sum_{i=1}^{23} x_{2 i}^{2}=12 ; \sum_{i=1}^{23} y_{i}^{2}=10$
$\sum_{i=1}^{23} x_{3 i} * x_{2 i}=8 ; \sum_{i=1}^{23} y_{i} * x_{3 i}=10 ; \sum_{i=1}^{23} y_{i} * x_{2 i}=8$
where:
$y_{i}=\left(Y_{i}-\bar{Y}\right) ; x_{2 i}=\left(X_{2 i}-\bar{X}_{2}\right) ; x_{3 i}=\left(X_{3 i}-\bar{X}_{3}\right)$
I had already estimated $\beta_{2}$ and $\beta_{3}$ with sample variance and covariance, but I cannot find the standard deviations of $\beta_{2}$ and $\beta_{3}$ without $\sigma_{u}^{2}$, meaning the error variance.
Knowing that:
$\operatorname{var}\left[\widehat{\beta}_{1} \mid X_{1}, \ldots, X_{n}\right]=\frac{\sigma_{u}^{2}}{\sum_{i=1}^{n}\left(X_{i}-\bar{X}\right)^{2}}$
I would really appreciate the help.
