Finding regression coefficient only with matrix correlation

Question

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.

Answer 1

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.

You know the covariance terms, and you know the correlation coefficients, which means that you can calculate the denominators (the product of standard deviations). Since you have these tables for all four variables, this allows you to calculate the individual standard deviations, which in turn lets you calculate the regression coefficients.