Which type of statistical test should I use for categorical and continuous IVs and continuous DV? I am conducting an experimental research. Research model shown as figure.

I hypothesized that X positively predicts Y. All participants were required to answer measurements of X and Y.
Meanwhile, three additional independent variables (conditions / wording of appeals: emotion, difficulty, effort) were manipulated and served as moderators of the X-Y direct relationship. There are eight conditions in total, and participants were randomly assigned to one of the eight conditions:

*

*guilt / easy / low effort

*guilt / easy / high effort

*guilt / difficult / low effort

*guilt / difficult / high effort

*shame / easy / low effort

*shame / easy / high effort

*shame / difficult / low effort

*shame / difficult / high effort

Put alternatively, my independent variable is a continuous variable and moderators are categorical variables whereas dependent variable is a continuous variable.
My question is: Which type of statistical test should I use?

I think using a regression model would be good and then to test if the coefficient estimate of $X$ is 0 or not. The tests can be wald test, likelihood ratio test, score test, etc. You can choose one suitable and easy to use for your model.
