Question: At State University, a study was done to establish - whether a relationship existed between a student's GPA when graduating and SAT score when entering 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

1. Develop a scatter plot for these data and describe what, if any, relationship exists between the two variables, GPA and SAT score.
2. (i) Compute the correlation coefficient.
   (ii) Does it appear that the success of students at State University is related to the SAT scores of those students? Conduct a statistical procedure to answer this question. Use a significance level of 0.01.
3. (i) Compute the regression equation based on these sample data if you wish to predict the university GPA using the students' SAT scores.

(ii) Interpret the regression coefficients.

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