testing for the change in correlation between 2 variables over a 3rd linear variable


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I have a hypothesis that the strength of correlation between two continuous variables will decrease with higher levels of a third variable. To give an applied example of the problem, looking at the correlation between mothers weight and their adult child's weight, I expect the correlation to decrease as the difference in age between child and mother increases.

At first I was modeling this in a regression as:
Childweight = mom'sWeight + ageDifference + mom'sWeight*ageDifference
(with centering of independent variables)

However, I realized this is really testing whether the beta values of mom'sWeight changes as ageDifference varies. I am not predicting that the slope of the association will change, but instead that the tightness of the association (correlation coefficient) will change.

So, what's the best way to test this (without loosing power by turning continuous variables into categorical)?

One thought I have is that if I z-score all of my variables (except my interaction term which will be the product of the two z-scores), I'll standardize the beta and make it equivalent to a correlation coefficient. Would this do the trick?

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