Question

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.)

Answer 1

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