Complete mediation in the context of statistical analysis and regression models refers to a scenario where a mediating variable fully accounts for the relationship between an independent variable and a dependent variable. To clarify:

• An independent variable is something that you manipulate to see if it affects another variable.
• A dependent variable is the outcome you are interested in.
• A mediating variable (or mediator) is a variable that helps explain the relationship between the independent and dependent variables.

In the case of complete mediation, the path between the independent variable and the dependent variable becomes non-significant when the mediator is controlled for, which means the direct effect of the independent variable on the dependent variable is essentially zero. The independent variable influences the mediator, which in turn fully influences the dependent variable. This suggests that the independent variable does not have a direct effect on the dependent variable without the mediator.

The testing for mediation often involves several regression analyses:

1. Show that the independent variable significantly affects the dependent variable.
2. Show that the independent variable significantly affects the mediator.
3. Show that the mediator affects the dependent variable while controlling for the independent variable.
4. Demonstrate that the effect of the independent variable on the dependent variable drops to non-significance when the mediator is included in the model.

If these conditions are met, particularly the last one, then you have evidence of complete mediation. Partial mediation, on the other hand, occurs when the mediator reduces but does not completely eliminate the effect of the independent variable on the dependent variable.