A Researcher Is Investigating the Factors That Underlie Success or Failure

A researcher is investigating the factors that underlie success or failure in high school mathematics. She measures 30 predictor variables and five criterion variables relating to mathematics learning (e.g., gradepoint average in mathematics coursework, attitudes toward mathematics, and number of mathematics courses taken). What correlation technique should be used to determine (a) which combination of predictor variables best predicts mathematics gradepoint average, (b) which combination of predictor variables best predicts whether a student takes or does not take a course on calculus (which is a dichotomous variable), (c) whether the data support a theoretical model linking some of the predictor variables to one of the criterion variables, and (d) whether there are commonalities in the 30 predictor variables such that they can be reduced to a smaller number of underlying variables?