The estimated correlation between $\hat{\beta}_1$ and $\hat{\beta}_2$ is $0.988$. Note that

$\hat{\beta}_1 = (Y_{1,1} + Y_{2,1} + \dots + Y_{10,1})/10=10.360$

and

$\hat{\beta}_2 = (Y_{1,2} + Y_{2,2} + \dots + Y_{10,2})/10 = 11.040$

From this we can recover the correlation $0.988$ as follows:

By comparison, in the linear model version of the above:

because $Var(\hat{\beta}) = \hat{\sigma}^2 (X^T X)^{-1}$.

## 2 comments:

Cool!

This is great!

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