Question: At State University, a study was done to establish whether a relationship exists between students' graduating grade point average (GPA) and the SAT verbal score when the student originally entered the university. The sample data are reported as follows:
GPA 2.5 3.2 3.5 2.8 3.0 2.4 3.4 2.9 2.7 3.8
SAT 640 700 550 540 620 490 710 600 505 710
a. Develop a scatter plot for these data and describe what, if any, relationship exists between the two variables, GPA and SAT score.
b. (1) Compute the correlation coefficient.
(2) Does it appear that the success of students at State University is related to the SAT verbal scores of those students? Conduct a statistical procedure to answer this question. Use a significance level of 0.01.
c. (1) Compute the regression equation based on these sample data if you wish to predict the university GPA using the student SAT score.
(2) Interpret the regression coefficients.