Introductory Econometrics: A Modern Approach 6th Edition by Jeffrey M Wooldridge

Exercise 10

Suppose that at a large university, college grade point average, GPA, and SAT score, SAT, are related by the conditional expectation E(GPA|SAT) = .70 + .002 SAT.

(i) Find the expected GPA when SAT = 800. Find E(GP|SAT = 1,400). Comment on the difference.

(ii) If the average SAT in the university is 1,100, what is the average GPA? (Hint: Use Property CE.4.)

(iii) If a student’s SAT score is 1,100, does this mean he or she will have the GPA found in part (ii)? Explain.

Step 1 of 3

The conditional expectation of GPA and SAT is given as:

(i) The expected GPA when SAT is 800 is equal to:

The expected GPA when SAT is 1400 is equal to:

This shows that SAT score is directly correlated to GPA score. The higher the Sat score, the higher is the GPA.