Let's simplify things a bit and consider two models with X1 and X2 as the only explanatory variables, both quantitative.

1) Y = b0 +b1X1 + b2X2 + error

2) Y = b0 +b1X1 + b2X2 + b3X1X2 + error

In model 1:

• b1 shows the effect (on the fitted value of Y) of increasing X1 by one unit while holding X2 constant (at any value you wish)
• b2 shows the effect (on the fitted value of Y) of increasing X2 by one unit while holding X1 constant (at any value you wish)

But those interpretations of b1 and b2 do not work for model 2. In model 2:

• b1 shows the effect (on the fitted value of Y) of increasing X1 by one unit while holding X2 constant at a value of 0
• b2 shows the effect (on the fitted value of Y) of increasing X2 by one unit while holding X1 constant at a value of 0

Putting it another way, b1 and b2 in model 2 are like simple main effects in a two-way ANOVA model, not like main effects in a two-way ANOVA model. Some authors describe them as "main effects", but I think that can cause confusion, and so I prefer to call them first order effects. HTH.

Bruce Weaver has given you some great advice. In addition, it does not make sense to analyze only the product (interaction) terms without also including the lower order terms ("main effects") in the regression model (it sounds a bit like you may have done this in your second step). When analyzing moderation (interaction effects), the lower-order terms must be included in addition to the interaction (product) terms.

When conducting a regression analysis, you can include both main effects and interaction effects to explore the relationship between predictors and the outcome variable. Main effects represent the independent contributions of individual predictors, while interaction effects capture how the relationship between predictors and the outcome varies depending on the combination of predictor values.

To include the main effects and interaction effects in a regression analysis, follow these steps:

Remember to consider the statistical significance of the coefficients and use appropriate methods to assess model fit, such as adjusted R-squared, F-tests, or likelihood ratio tests.

It's important to note that including interaction terms increases the complexity of the model, and interpretation can become more nuanced. Additionally, the inclusion of interaction effects requires larger sample sizes to obtain stable estimates and appropriate statistical power.