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I found the estimation of S and $\overline{x}$ of a data set to be approximately $\overline{x} = \begin{pmatrix} 185 & 151 & 183 & 149 \\ \end{pmatrix}'.$ and $S = \begin{pmatrix} 95 & 52 & 69 & 46 \\ 52 & 54 & 52 & 35 \\ 69 & 51 & 100 & 56 \\ 46 & 35 & 56 & 45 \end{pmatrix}.$

How do I now calculate the sample multiple correlation coefficients between $x_3$ and $(x_1, x_2)$, and $x_4$ and $(x_1, x_2)$. Moreover, how do I then test the hypothesis that $x_3$ is independent of $(x_1, x_2)$. If someone could help with a forumla or direct me to any reading, it would be helpful!

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