Is there any assumption that states that X and Y have to be correlated (and forget about the significance statement, this is a whole other topic and concerned with power to detect any difference, since sample data will almost always show a descriptve non-null correlation!!)?

No! By contrast, a null correlation may be the result of a strong (disordinal) interaction. E.g you have two groups, where one group has a positive effect and the other the same, but negative effect. This may cancel each other out so that you see a null correlation in the bivariate analysis and bivariate scatterplot, if you do not account for the moderator.

Hi Rainer

Thank you so much for your response.

No there is no assumption that states that X and Y should be correlated . I just assumed that for one to test whether W moderates the relationship between X and Y then there actually has to be a significant relationship between X and Y. Is this not the case? Please elaborate and also advise if there is any article that I can cite or read to better understand. Would truly appreciate your assistance

You are mixing different statistical concepts in your post but you do not say what your research question is!

If you are interested in the interaction then include it in a model and focus your conclusions on the estimated effects not the pvalues.

If you computed a correlation coefficient between X and Y and obtained a large pvalue, then the conclusion is not that X and Y are not correlated: that is simply put not how you interpret statistical tests

Sequential tests (like the approach you are using: if A happens than I test B) are a deprecated approach to data analysis

@rainer already explained that observational data the correlation will (almost) always be there

To better understand you can get any introductory statistics book

Tarryn Smith if there is no asumption, as you stated yourself, that X and Y have to be correlated, why do YOU assume it in the first place? I think there is no paper or book needed to demonstrate it (and I think it is more difficult to find a text that explicitly states, which assumption a model does NOT have....). I think my explanation should suffice to see, why it cannot be a necessary condition. Maybe you should consult a textbook about this topic to get familiar with multiple regression in general, e.g. Darlington & Hayes (2016), Hayes (2022) or Cohen, Cohen, West & Aiken (2014).

Darlington, R. B., & Hayes, A. F. (2016). Regression analysis and linear models: Concepts, applications, and implementation. Guilford Publications.

Hayes, A. F. (2022). Introduction to mediation, moderation, and conditional process analysis: A regression-based approach. Guilford publications.

Cohen, J., Cohen, P., West, S. G., & Aiken, L. S. (2014). Applied multiple regression/correlation analysis for the behavioral sciences. Psychology press.

For illustration, see the results of simulated data, no bivariate correlations, in the multiple regression model no weights for x and the grouping factor (effect coding), but an interaction, which is disordinal, as you can see, so that the effects from group 1 and 2 cancel each other out --> no bivariate correlation between X and Y

If moderators correlate with Y, then it might moderate (affect) the relationship between X and Y.

They may still be correlated on one level or more of the moderator. If the moderation is theoretically established, it should be done for further investigation.