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A measure of the degree of association among a pair of variables.
1
vote
Covariance matrix for multivariate normal random variable
You can write $Y$ as
$$
Y = WX
$$
where
$$W = \begin{pmatrix}1 &0&0&1\\0&1&0&-1\end{pmatrix}.$$
Then,
$$\text{cov}(Y)=W\text{cov}(X)W'.$$
2
votes
Multiple Linear Regression and Correlation of two beta estimates
From there, you can compute the correlation between $\hat\beta_1$ and $\hat\beta_3$ by standardizing appropriately, using the variances of $\hat\beta_1$ and $\hat\beta_3$, which you get from the elements …