The regression coefficients, the slopes, or, the B values represent the unique variants explained in the outcome by each predictor.
- For a simple regression: Statistics - (Univariate|Simple|Basic) Linear Regression
- For a multiple regression: Statistics - Multiple Linear Regression
The regression coefficient, <math>B_1</math> is the slope for <math>X_1</math> . assuming an average score on any other predictor <math> X_2, X_3, \dots, X_n</math> . If there's no moderation, it's representative of all the other values on all the other predictors. Like the mean is representative of the entire sample, if you don't have any skew or outliers effects.
No moderation effect implies that <math>B_1</math> is consistent across the entire distribution of others predictors.
Having a moderation effect, implies that a single regression coefficient relating x to y is not sufficient. Because the slope representing X to Y is actually changing as a function of this moderator variable, Z. So one regression coefficient B1 is not sufficient to count for the true relationship that exists between X and Y. A moderator variable is needed to show that the relationship is changing as a function of it. That's the power of a moderation analysis.
While interpreting the slopes, you have to take the units of the variables into account.