Variance-covariance matrix and correlation matrix for estimated parameters

[Whenry]

Hi all,

I would like some help understand the covariance and correlation matrix as it pertains to estimated parameters. I am performing logistic regression with just one independent variable and a constant term.

I am wondering if someone can help me understand the information these matrices are telling me. I found a lot of information about covariance and correlation between two variables, but not a lot on parameters. If someone could also help me understand how these matrices are calculated, that would be great.

This is what I have so far, please correct me where I am incorrect

the variance-covariance matrix describes how each beta could variance, either on it's own, or together with another parameter and have the model still produce the same (or nearly the same?) values. So for the values below, b0 = -2.4030 could vary +/-0.0036 and we would get estimated y's that are statistically the same, where Y = b0 + b1X.

the correlation matrix describes how you can change two variables together and produce the same fit? in this example, you could increase b0 by 1 and reduce b1 by -0.9035


betas

-2.4030
0.0201

covariance matrix

0.0035526 -3.4778e-05
-3.4778e-05 4.1704e-07



correlation matrix

1.0000 -0.9035
-0.9035 1.0000

 

[Jhero]

Thank you in advance for your help!The covariance matrix is a measure of how the estimated parameters (in this case b0 and b1) vary together. The higher the number, the more correlated the two parameters are. For example, if the covariance of b0 and b1 is 0.0036, that means that when one parameter increases, the other one has a tendency to increase as well. The correlation matrix is a measure of the strength of the relationship between two parameters. It ranges from -1 (perfect negative correlation) to 1 (perfect positive correlation). If the correlation between two parameters is 1, it means that when one parameter increases or decreases, the other one increases or decreases at the same rate.