Suppose that, for one semester, you can collect the following data on a random sample of college juniors and seniors for each class taken: a standardized final exam score, percentage of lectures attended, a dummy variable indicating whether the class is within the student's major, cumulative grade point average prior to the start of the semester, and SAT score.
(i) Why would you classify this data set as a cluster sample? Roughly, how many obser- vations would you expect for the typical student?
(ii) Write a model that explains final exam performance in terms of attendance and the other characteristics. Use s to subscript student and c to subscript class. Which variables do not change within a student?
(iii) If you pool all of the data and use OLS, what are you assuming about unobserved stu- dent characteristics that affect performance and attendance rate? What roles do SAT score and prior GPA play in this regard?
(iv) If you think SAT score and prior GPA do not adequately capture student ability, how would you estimate the effect of attendance on final exam performance?