Is attending class regularly positively associated with college students’ academic performance? A professor has been telling students for years that the most important thing they can do as college students is to show up to class, whether or not they have completed their work. Noticing that some students continue to disregard her advice, the professor decides to analyze the empirical relationship between class attendance and GPA in a sample of twenty students who are all taking the same courses during their first semester of college. Table 14.1 presents the number of classes that each student attended during their first semester of college and their first-semester GPA. The mean and standard deviation are noted for each variable.

a. For each student, calculate the difference between the number of classes that the student attended and the mean number of classes that all twenty students attended.

b. For each student, calculate the difference between the student’s GPA and the mean GPA for all twenty students.

c. Calculate the cross product for each student.

d. Find the sum of cross products for these twenty students.

e. What is the covariance between number of classes attended and GPA?

f. What is the correlation between number of classes attended and GPA?
g. Does the correlation support the professor’s advice to students about the importance of attending class?