Juniors at New City High School were offered the opportunity to participate in a free after-school tutoring program to help them prepare for the SAT exam. A total of 40 one-hour tutoring sessions were offered, and all students were invited drop in to any number of sessions. Students who did participate were asked to sign in, and the school kept track of who participated and for how many hours.

Principal Parker is trying to decide whether to keep investing resources in the free program and wants to know if it is having a positive impact on students. After the SAT exams were completed, she took a random sample of 25 New City HS juniors. She put together a data set (in the "Tutoring" tab) including observations of the following for each sampled student: (1) combined SAT score in critical reading and math, (2) grade point average (GPA), and (3) number of hours spent in the free SAT prep tutoring program. She has asked you to investigate whether participation in the tutoring program is associated with higher SAT scores, while accounting for the potential impact of a student's GPA on SAT score.

4. In a multiple regression analysis of association, which would be the primary independent (x) variable of interest and which would be the dependent (y) variable? What is the other independent (x) variable in the model?

5. (a) In your Excel file, show an example of a scatterplot to show the relationship between the dependent variable and the primary independent variable of interest. (b) Based on a visual assessment, is the association roughly linear? (c) Use Excel to find measures of association (specifically, sample slope, r², and correlation) for the association between the dependent variable and primary independent variable of interest. Interpret these measures of association in context.

6. (a) In your Excel file show an example of a scatterplot to show the relationship between the dependent variable and the other independent variable. (b) Based on a visual assessment, is the association roughly linear? (c) Use Excel to find measures of association (specifically, sample slope, r2, and correlation) for the association between the dependent variable and other independent variable. Interpret these measures of association in context.

7. Use Excel to generate a multiple regression output for all three variables.

8. (a) What are the null and alternative hypotheses for the relationship between the dependent variable and the primary independent variable of interest? State them using notation, and in words. (b) Interpret the slope coefficient for the primary independent variable, in context. (c) What are the t statistic and p value for this hypothesis test? Interpret the p-value. (d) Do you have evidence to reject the null hypothesis? If so, at what level? State your conclusion.

9. (a) What are the null and alternative hypotheses for the relationship between the dependent variable and the other independent variable? State them using notation, and in words. (b) Interpret the slope coefficient for the other independent variable, in context. (c) What are the t statistic and p value for this hypothesis test? Interpret the p-value. (d) Do you have evidence to reject the null hypothesis? If so, at what level? State your conclusion.

10. Interpret the R and Adjusted R² for the multiple regression model.

11. draft a letter to Principal Parker explaining the results of your analysis and giving your informed opinion as to whether the free SAT tutoring program is having a positive impact on student SAT scores.

Variables Operational Form GPA and TV hours Description positive numbers from 1-60 Name points, ranging from 2.0-4.0 subject student identification number high_sch_gpa student's high school GPA hours , ranging from 0-37 tv tv hours of television watched by student per week subject high_sch_GPA 2.2 3.3 3.5 3.1 3.5 3.6 3 3 4 2.3 3.5 3.3 3.2 mmmMmmMMM Mmmmmmmmmsmiteumm gTutoring hours, GPA, and SAT score data Variables Name Description Operational Form student sat score gpa tutoring hours student student identification number positive numbers from 1-25 980 3. 15.0 sat score combined SAT score points, ranging from 400-1600 1550 3.9 22.0 gpa high school grade point average points, ranging from 1.0-4.0 1100 3.6 0.0 tutoring hours hours spent in tutoring program hours, ranging from 0-40 840 2.9 10.0 380 1.9 0.0 770 3.5 15.0 850 3.0 5.0 910 2.6 10.0 1300 3.9 15.0 1400 3.5 10.0 680 3.0 4.0 930 3.3 5.0 1010 3.5 8.0 1230 3.4 10.0 1120 2.9 26.0 690 3.2 5. 990 3.8 0.0 790 3.1 12.0 830 3.0 7.0 1020 3.0 22.0 1200 3.7 5.0 500 2.7 0.0 1260 2.9 20.0 740 2.9 5.0 1410 3.2 20.0