# Manual calculation of variance-covariance from published confidence intervals

I would like to obtain the variance-covariance matrix from a published set of regression outputs. These outputs provide a mean value and confidence intervals. I will convert the confidence intervals into standard errors.

I plan to use these standard errors to calculate the variance-covariance matrix. Before doing the calculation on 'real' data, I did a simple regression with two right hand side variables and used a popular statistics package to output the post-estimation variance-covariance matrix to check my calculations. The diagonals are easy to calculate being the product of the estimated standard errors. I had (naively) thought that the off diagonals would be simply the product of the std error of variable 1 and the standard error of variable 2.

This is not the case and I am somewhat stuck as to where to go next. I will be very grateful for any advice.

• I am wondering where in the outputs you will find any information about covariances: that's not a standard part of most regression summaries and it's not available solely from means and CIs. It is conceivable you could infer something about the covariances from the nature of the model itself (for instance, many experimental designs guarantee covariances are zero), but you would have to provide those details in your question. – whuber Sep 18 '14 at 20:59
• Thank you. No indeed, the regression outputs do not provide information on covariances. The regressions are hazard ratios with mean and 95% confidence interval. The information of the model is that they are certainly not equal to zero. – Covquestion Sep 18 '14 at 21:11

## 1 Answer

Did you take into account the degrees of freedom when converting CIs into standard errors? Anyway, you won't be able to back out the variance-covariance matrix because you have no information about the correlations.

• Thanks James - the degrees of freedom are not reported. I had been proceeding according to the advice here: handbook.cochrane.org/chapter_7/… – Covquestion Sep 18 '14 at 20:55
• That advice assumes that the test statistic is normal, but it doesn't have to be. – James Sep 18 '14 at 22:16