PPD 558 multivariate statistics analysis

Problem Set #1

1. A university administrator is exploring the effect of time pressure on final exam scores within a particular department. The professors in this department all give similar exams and use the same grading scheme, but different professors allow their students different amounts of time to complete the exam. Let Yi denote the number of points scored on the exam by student i(with possible scores ranging from 0 to 100), let Xi denote the amount of time (in minutes) that this student was given to complete the exam, and consider the regression model Yi = 0 + lXi + at. a. [0.32 points] Explain what the term 81- represents (simply stating what it is caiied wiii not be sumcient). What are a few reasons that different students will have different values of q? b. Estimation of the regression model above produces the following result: 1"; = 49 + 0.24-Xi. i, [0.32 points] What exam score would be predicted for a student given 90 minutes to complete the exam? ii. [0.32 points] Suppose that a student is given an additional 10 minutes to complete the exam. What change in test score would be predicted for this student? [Note that you do not need to know how much time they were initiaiiy given; this instead reiies on your understanding of how the regression estimates above are interpreted. ]