You should probably do moderated regression and include the interaction term in the model. That's telling you that the relationship between the CV and dv depends on the level of the IV. Depending on many things, that may be a more interesting story to tell.
If the p value of interaction of IV and CV is less than 0.01, should I be using the Type III sum of squares?
You should probably do moderated regression and include the interaction term in the model. That's telling you that the relationship between the CV and dv depends on the level of the IV. Depending on many things, that may be a more interesting story to tell.