A college teacher decided to do an experiment to see whether the position her students sat in the classroom had an effect on their performance in the class. At the beginning of the semester, she randomly assigned each student to one of three classroom positions: Front, Middle, or Back. As it turned out, 10 students were assigned to the front of the room, 14 students to the Middle, and 10 to the Back. The teacher also observed each student’s GPA previous to taking this course and included that variable in the model. At the end of the semester, the teacher measured the numerical overall grade in the course for each student.
Based on the data, determine whether the previous GPA significantly affected course grade: Was the teacher wise to include that variable in the model?
Based on your model, interpret what the relevant parameter estimates tell you about how the three classroom positions compare in terms of mean course grade. Formally assess whether or not the estimated differences in the mean scores for the three positions are statistically significant, providing numerical justification (test statistic and P-value) for your conclusion. If you find a significant difference among the positions, then investigate which positions differ significantly from each other. Finally, formally assess whether the model that assumes that the effect of previous GPA on grade is the same for all positions is appropriate, again providing numerical justification (test statistic and P-value) for your conclusion.

DATA two;
INPUT grade position $ prevGPA;
cards;
93.2 front 3.78
88.4 front 3.52
65.4 front 2.67
56.3 front 2.23
73.6 front 3.21
44.3 front 1.96
89.4 front 3.45
92.7 front 3.77
75.4 front 2.99
86.5 front 3.26
95.6 middle 4.00
77.3 middle 3.12
91.1 middle 3.59
87.2 middle 3.19
75.3 middle 2.65
97.4 middle 3.82
67.4 middle 2.87
93.6 middle 3.67
86.2 middle 3.42
88.3 middle 3.44
56.6 middle 1.76
94.3 middle 3.98
99.3 middle 3.93
76.4 middle 3.17
70.8 back 2.43
78.5 back 3.11
98.2 back 3.89
89.3 back 3.24
71.2 back 3.12
46.3 back 2.11
65.5 back 2.34
81.2 back 3.24
85.4 back 3.23
78.3 back 2.93
;
run;