# Finding regression coefficient only with matrix correlation

How do I find Regression coefficient if data provided is only matrix correlation table?

Here is example for x1 matrix correlation. ( I also have x2,x3,x4, but only provided x1 in here) for the sake of simplicity.

                                       x1       x2          x3        x4

Pearson Correlation                   1       -.519       .855       .859

Sig. (2tailed)                                 .019       .000       .000

Sum of squares & Cross products     88.800   -56.000     80.800    156.400

Covariance                           4.674    -2.947      4.253      8.232

N                                   20        20         20         20


with regard to data provided, is there any way to find coefficient regression?

Would be so grateful, if an answer could be provided using simple explanation. I am so newbie in this part.

The correlation coefficient is defined as $\rho = \frac{Cov(X_1, X_2)}{\sqrt{V(X_1)} \sqrt{V(X_2)}}$, while the regression coefficient is defined as $\beta = \frac{Cov(X_1, X_2)}{V(X_2)}$, if $X_1$ is your dependent variable.