Confidence intervals in multivariate linear regression I am fitting my data to a multivariate linear regression $Y = BX + \Xi$, where the response is bivariate $Y\in R^{n\times 2}$, and the predictor is uni-variate but elevated to the projective plane to account for the intercept $X\in R^{n\times 2}$.

Now, finding the best fit reduces to $\hat B = (X^T X)^{-1}X^T Y$.

But I am interested in finding a $0.7$ confidence region around $\hat B$. How do I do that?
Looking at https://en.wikipedia.org/wiki/Simple_linear_regression :

This t-value has a Student's t-distribution with $n-2$ degrees of freedom. Using it we can construct a confidence interval for $\beta$:

$$ \beta \in \left[\widehat\beta - s_{\widehat\beta} t^*_{n - 2},\ \widehat\beta + s_{\widehat\beta} t^*_{n - 2}\right] $$

at confidence level $1-\gamma$, where $t^*_{n - 2}$ is the $(1-\frac{\gamma}{2})$-th quantile of the $t_{n−2}$ distribution.