I'm in a machine learning class right now and having difficulty with some problems.

I'm pretty much trying to figure out the correlation between model coefficient estimates over different folds during cross-validation.

The assumption of the model is Y = β + e such that E(e) = 0, Var(e) = σ^2.

If we use K-fold CV, how can I determine the correlation between the least sq. est of β estimate using the first fold and the least sq. est of β estimate using the second fold?

I know since β_1 = 0 by the model assumption, the estimate of β is just the mean of the observations. And I know that as K goes towards n (n = # of observations), the correlation will increase as both training sets will have more and more overlap. I'm just unsure where to start to derive the exact correlation.

Any help is greatly appreciated!
Thank you