Dr. jones hopes to demonstrate that children who eat a more nutritious breakfast also tend to have more academic success than their peers. if this result is obtained, then would be the predictor variable and would be the criterion variable for the study.

Then the consumption of nutritious breakfast by children would be the predictor variable and academic success would be the criterion variable for the study. 

Consumption of nutritious breakfast is the variable being manipulated or used to predict another variable. Academic success is the variable being predicted.