A Researcher Has Collected a Large Amount of Data on a Sample

A researcher has collected a large amount of data on a sample of college students: scores on the Stanford-Binet Intelligence Scale, scores on the Wechsler Adult Intelligence Scale, scores on the Scholastic Aptitude Test (SAT), high school class rank, scores on a test anxiety scale, and whether the students successfully completed the first year of college (pass-fail and gradepoint average). Answer the following questions about the appropriate correlational analyses to be conducted on these data:
a. What correlational technique should be used to determine whether scores on the Stanford-Binet are related to scores on the Wechsler scale? Why this technique?
b. The researcher finds that test anxiety correlates significantly with the criterion variable of gradepoint average in the first year of college. The SAT also correlates significantly with test anxiety and the criterion. What statistical technique should be used to determine the correlation between test anxiety and college gradepoint average after the influence of SAT on both variables has been removed?
c. What correlational technique should be used to determine whether all of the tests used in this study, when intercorrelated, measure a common factor?
d. What correlational technique should be used to determine whether the relationship between scores on the test anxiety scale and high school class rank is nonlinear?