# Least squares regression coefficient with minimal information

If I only have a correlation matrix of 4 variables and the sample size, is it possible to predict 1 variables from the other 3 while using information about sample size? I’m trying to use lm but my degrees of freedom are 0 because I’m unable to incorporate the sample size information somehow. Can anyone help?

• If you mean the R function lm will not be possible. Regression coefficients cannot be calculated only from the correlation matrix (but you can get the coefficients for the regression based on the standardized variables, though. For the coefficients for regression based on original variables you will need also means and variances. Why don't you have access to full dataset? explain, and some more details. Mar 9, 2019 at 13:20
• Is there any chance that you mean covariance matrix rather than correlation matrix? Mar 9, 2019 at 13:29

If all you have is a correlation matrix and $$N$$, then you are able to create simulated data but not much else. To do this, make a $$N \times 4$$ matrix $$Z$$ consisting of random standard normals. Then calculate the square root of your correlation matrix $$R$$ using Cholesky decomposition. The matrix $$X=ZR^{1/2}$$ will correspond to 4 variables in the standardized form that @kjetil is referring to in his comment. That is as far as we can go without means and standard deviations.