The quantitative reasoning scores on the Graduate Record Examination (GRE)7 were recorded for students admitted to three different graduate programs at a local university. This data was analyzed in Exercise 11.27 using the analysis of variance for a completely randomized design.

a. Write the theoretical model relating the GRE score to the qualitative variable "graduate program" using two dummy (indicator) variables to represent the three graduate programs.
b. Use a computer package to analyze the data with a multiple regression analysis. Is there sufficient evidence to indicate a difference in the average scores between the students who have been admitted to the three graduate programs? Use a = .05.
c. Comment on the fit of the model and any regression assumptions that may have been violated. Summarize your results in a report, including printouts and graphs if possible.

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Graduate Program Life Sciences Physical Sciences 660 760 640 670 720 700 690 710 530 450 Social Sciences 630 660 640 660 470 480 600 650 580 710 440 540 330 450 670 570 570 530 590 630