GPA ACT 21 14 28 22 21 31 32 27 29 26 24 30 24 24 33 27 25 MAJOR DO yes no yes no yes yes yes yes no no yes yes yes no yes yes no no yes MAJOR yes no yes yes no yes no yes yes no yes yes yes yes yes yes 33 GPA 3.897 3.885 3.278 2.540 3.828 3.865 2.962 3.961 8.500 3.178 3.310 3.538 3.883 3.013 3.245 2.963 3.522 3.013 2.947 2.118 2.563 3.357 3.731 3.925 3.556 3.101 2.428 2.579 3.871 3.860 3.927 2.375 2.929 3.375 2.857 3.872 3.381 3.299 3.549 3.646 2.978 2.654 GPA 2.540 2.250 2.869 2.617 2.183 2.000 2.952 3.826 2.871 3.352 3.305 2.952 3.547 3.691 3.160 2.194 3.323 3.936 2.922 2.716 3.370 3.686 2.642 2.452 2.655 3.714 1.826 3.516 3.939 2.966 2.482 2.700 3.920 2.834 3.222 3.884 4.800 3.511 3.323 3.872 2.879 3.875 yes ACT 24 26 29 24 31 15 19 18 27 16 27 26 24 30 21 28 30 29 25 23 25 23 30 21 24 32 18 23 20 23 18 18 29 20 23 26 28 34 20 20 26 32 3.288 2.920 3.345 3.956 3.888 2.586 3.886 2.183 3.429 3.824 3.750 3.833 3.113 2.875 2.747 2.311 1.841 1.583 2.879 3.591 2.914 3.716 2.880 3.621 3.792 2.867 3.419 3.600 2.394 2.286 1.486 3.885 3.888 3.914 1.860 2.948 25 20 24 21 28 27 28 26 28 22 26 21 25 16 28 26 22 24 21 3e 27 26 26 38 MAJOR yes no yes no no yes yes yes yes no yes yes yes yes yes yes yes no no yes no no no yes no no yes yes no yes yes yes yes no yes yes yes yes no yes yes no ACT 25 27 27 29 19 21 24 27 25 18 29 24 27 21 19 18 25 18 2e 32 24 35 25 28 28 25 22 30 2e 20 31 20 29 28 16 28 no yes yes no no yes yes yes yes no no yes no yes no yes no yes yes yes yes yes yes yes yes yes yes yes yes no no yes yes no yes no yes yes no 4 For the subset of the students who have already declared a major, what is the estimated difference in the mean GPA when the ACT score differs by five points? Compare your answer to this question, to the answer you got in Project 1 for the same model fit to all 120 students' data combined in one group. GPA ACT 21 14 28 22 21 31 32 27 29 26 24 30 24 24 33 27 25 MAJOR DO yes no yes no yes yes yes yes no no yes yes yes no yes yes no no yes MAJOR yes no yes yes no yes no yes yes no yes yes yes yes yes yes 33 GPA 3.897 3.885 3.278 2.540 3.828 3.865 2.962 3.961 8.500 3.178 3.310 3.538 3.883 3.013 3.245 2.963 3.522 3.013 2.947 2.118 2.563 3.357 3.731 3.925 3.556 3.101 2.428 2.579 3.871 3.860 3.927 2.375 2.929 3.375 2.857 3.872 3.381 3.299 3.549 3.646 2.978 2.654 GPA 2.540 2.250 2.869 2.617 2.183 2.000 2.952 3.826 2.871 3.352 3.305 2.952 3.547 3.691 3.160 2.194 3.323 3.936 2.922 2.716 3.370 3.686 2.642 2.452 2.655 3.714 1.826 3.516 3.939 2.966 2.482 2.700 3.920 2.834 3.222 3.884 4.800 3.511 3.323 3.872 2.879 3.875 yes ACT 24 26 29 24 31 15 19 18 27 16 27 26 24 30 21 28 30 29 25 23 25 23 30 21 24 32 18 23 20 23 18 18 29 20 23 26 28 34 20 20 26 32 3.288 2.920 3.345 3.956 3.888 2.586 3.886 2.183 3.429 3.824 3.750 3.833 3.113 2.875 2.747 2.311 1.841 1.583 2.879 3.591 2.914 3.716 2.880 3.621 3.792 2.867 3.419 3.600 2.394 2.286 1.486 3.885 3.888 3.914 1.860 2.948 25 20 24 21 28 27 28 26 28 22 26 21 25 16 28 26 22 24 21 3e 27 26 26 38 MAJOR yes no yes no no yes yes yes yes no yes yes yes yes yes yes yes no no yes no no no yes no no yes yes no yes yes yes yes no yes yes yes yes no yes yes no ACT 25 27 27 29 19 21 24 27 25 18 29 24 27 21 19 18 25 18 2e 32 24 35 25 28 28 25 22 30 2e 20 31 20 29 28 16 28 no yes yes no no yes yes yes yes no no yes no yes no yes no yes yes yes yes yes yes yes yes yes yes yes yes no no yes yes no yes no yes yes no 4 For the subset of the students who have already declared a major, what is the estimated difference in the mean GPA when the ACT score differs by five points? Compare your answer to this question, to the answer you got in Project 1 for the same model fit to all 120 students' data combined in one group