In: Math
obs gpa iq gender concept 1 7.94 121 2 69 2 8.292 120 2 71 3 4.643 111 2 44 4 7.47 106 2 44 5 8.882 108 1 69 6 7.585 98 2 72 7 7.65 121 2 53 8 2.412 75 2 26 9 6 109 1 47 10 8.833 122 2 64 11 7.47 109 1 46 12 5.528 106 1 62 13 7.167 105 2 53 14 7.571 89 1 68 15 4.7 85 1 62 16 8.167 117 1 50 17 7.822 119 1 46 18 7.598 98 1 64 19 4 100 2 35 20 6.231 104 1 49 21 7.643 129 2 50 22 1.76 98 2 43 24 6.419 109 1 44 26 9.648 128 2 53 27 10.7 126 1 72 28 10.58 123 2 51 29 9.429 120 2 65 30 8 96 2 57 31 9.585 126 2 67 32 9.571 134 1 68 33 8.998 124 1 51 34 8.333 122 1 53 35 8.175 104 2 60 36 8 118 2 46 37 9.333 112 1 62 38 9.5 125 2 67 39 9.167 114 2 61 40 10.14 111 1 65 41 9.999 133 1 55 43 10.76 106 2 95 44 9.763 109 2 72 45 9.41 121 2 65 46 9.167 119 2 84 47 9.348 109 2 43 48 8.167 88 2 55 50 3.647 82 2 41 51 3.408 89 1 56 52 3.936 111 2 30 53 7.167 104 2 71 54 7.647 114 2 59 55 .53 81 2 16 56 6.173 74 2 42 57 7.295 101 2 72 58 7.295 123 1 65 59 8.938 124 1 55 60 7.882 96 1 32 61 8.353 118 2 68 62 5.062 102 2 45 63 8.175 121 2 65 64 8.235 115 2 56 65 7.588 113 2 71 68 7.647 112 2 47 69 5.237 79 1 28 71 7.825 96 2 48 72 7.333 95 1 64 74 9.167 100 2 90 76 7.996 106 2 56 77 8.714 101 1 65 78 7.833 102 1 63 79 4.885 88 2 52 80 7.998 118 1 74 83 3.82 89 2 56 84 5.936 88 1 73 85 9 93 1 65 86 9.5 122 1 88 87 6.057 102 2 52 88 6.057 101 1 61 89 6.938 117 2 39
The data from data216.dat contains information on 78 seventh-grade students. We want to know how well each of IQ score and self-concept score predicts GPA using least-squares regression. We also want to know which of these explanatory variables predicts GPA better. Give numerical measures that answer these questions. (Round your answers to three decimal places.)
(Regressor: IQ) R 2 =
(Regressor: Self-Concept) R 2 =
Which variable is the better predictor?
-IQ
-Self Concept
Solution:
We can use the excel regression data analysis tool to find R-square values. The excel output is given below:
(Regressor: IQ)
(Regressor: Self-Concept)
Which variable is the better predictor?
Answer: IQ
Because R-square is greater when IQ is regressor as compared when Self-concept is regressor