In: Statistics and Probability
1 7.94 111 2 54 2 8.292 119 2 63 3 4.643 96 2 36 4 7.47 115 2 50 5 8.882 117 1 46 6 7.585 101 2 67 7 7.65 129 2 47 8 2.412 82 2 43 9 6 108 1 54 10 8.833 112 2 67 11 7.47 120 1 41 12 5.528 93 1 35 13 7.167 110 2 50 14 7.571 100 1 80 15 4.7 101 1 38 16 8.167 114 1 45 17 7.822 113 1 54 18 7.598 113 1 61 19 4 108 2 42 20 6.231 107 1 72 21 7.643 120 2 54 22 1.76 78 2 58 24 6.419 112 1 53 26 9.648 123 2 69 27 10.7 119 1 56 28 10.58 124 2 60 29 9.429 114 2 64 30 8 120 2 40 31 9.585 120 2 63 32 9.571 106 1 51 33 8.998 124 1 46 34 8.333 102 1 45 35 8.175 114 2 63 36 8 119 2 44 37 9.333 108 1 65 38 9.5 108 2 67 39 9.167 118 2 66 40 10.14 106 1 72 41 9.999 114 1 57 43 10.76 132 2 51 44 9.763 114 2 67 45 9.41 117 2 63 46 9.167 138 2 78 47 9.348 127 2 60 48 8.167 102 2 64 50 3.647 92 2 47 51 3.408 102 1 36 52 3.936 90 2 36 53 7.167 101 2 51 54 7.647 117 2 72 55 .53 90 2 39 56 6.173 87 2 54 57 7.295 94 2 57 58 7.295 122 1 63 59 8.938 101 1 55 60 7.882 118 1 53 61 8.353 120 2 64 62 5.062 108 2 49 63 8.175 104 2 56 64 8.235 109 2 75 65 7.588 122 2 52 68 7.647 100 2 82 69 5.237 101 1 49 71 7.825 117 2 73 72 7.333 91 1 59 74 9.167 130 2 60 76 7.996 103 2 54 77 8.714 95 1 41 78 7.833 106 1 80 79 4.885 89 2 49 80 7.998 118 1 48 83 3.82 74 2 68 84 5.936 91 1 49 85 9 105 1 59 86 9.5 125 1 54 87 6.057 119 2 46 88 6.057 100 1 43 89 6.938 107 2 82
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.)
Taking IQ as independent variable,
The regression equation is defined as,
Where, Dependent variable, Y = GPA and independent variable, X = IQ Score
The regression analysis is done in excel by following steps
Step 1: Write the data values in excel. The screenshot is shown below,
Step 2: DATA > Data Analysis > Regression > OK. The screenshot is shown below,
Step 3: Select Input Y Range: 'GPA' column, Input X Range: 'IQ Score' column then OK. The screenshot is shown below,
The result is obtained. The screenshot is shown below,
The R-square value is,
Taking Self-Concept score as independent variable,
The regression equation is defined as,
Where, Dependent variable, Y = GPA and independent variable, X = Self-Concept score
The regression analysis is done in excel by following steps
Step 1: Write the data values in excel. The screenshot is shown below,
Step 2: DATA > Data Analysis > Regression > OK.
Step 3: Select Input Y Range: 'GPA' column, Input X Range: 'Self-Concept score' column then OK. The screenshot is shown below,
The result is obtained. The screenshot is shown below,
The R-square value is,
The R square value define how well the data fit the model. By comparing R square value for both the model,
Which means, IQ explains the 46.14% variance of the model
Which means, Self-Concept score explains the 17.79% variance of the model
Hence IQ is better predictor for GPA compare to Self-Concept score