# How to calculate multiple correlation coefficients and test hypothesis?

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!