## Question

###### The data from data95.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 t...

The data from data95.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?

IQSelf Concept

obs gpa iq gender concept 1 7.94 105 2 59 2 8.292 122 2 63 3 4.643 87 2 43 4 7.47 105 2 55 5 8.882 91 1 46 6 7.585 109 2 72 7 7.65 108 2 78 8 2.412 90 2 43 9 6 102 1 58 10 8.833 113 2 60 11 7.47 132 1 71 12 5.528 94 1 12 13 7.167 103 2 67 14 7.571 101 1 70 15 4.7 119 1 31 16 8.167 117 1 65 17 7.822 124 1 51 18 7.598 104 1 51 19 4 98 2 47 20 6.231 117 1 35 21 7.643 111 2 59 22 1.76 88 2 36 24 6.419 109 1 36 26 9.648 115 2 62 27 10.7 123 1 77 28 10.58 127 2 61 29 9.429 113 2 63 30 8 112 2 59 31 9.585 112 2 87 32 9.571 130 1 90 33 8.998 122 1 57 34 8.333 131 1 77 35 8.175 93 2 45 36 8 97 2 62 37 9.333 119 1 80 38 9.5 116 2 68 39 9.167 114 2 53 40 10.14 134 1 86 41 9.999 117 1 51 43 10.76 123 2 43 44 9.763 119 2 61 45 9.41 125 2 68 46 9.167 126 2 65 47 9.348 119 2 69 48 8.167 131 2 54 50 3.647 75 2 59 51 3.408 87 1 52 52 3.936 109 2 27 53 7.167 89 2 57 54 7.647 104 2 34 55 .53 75 2 18 56 6.173 110 2 47 57 7.295 108 2 71 58 7.295 101 1 51 59 8.938 118 1 63 60 7.882 100 1 76 61 8.353 117 2 60 62 5.062 96 2 35 63 8.175 113 2 52 64 8.235 101 2 43 65 7.588 122 2 65 68 7.647 112 2 55 69 5.237 118 1 42 71 7.825 121 2 52 72 7.333 112 1 46 74 9.167 130 2 57 76 7.996 95 2 69 77 8.714 112 1 59 78 7.833 119 1 68 79 4.885 91 2 42 80 7.998 117 1 54 83 3.82 115 2 44 84 5.936 113 1 49 85 9 103 1 69 86 9.5 130 1 61 87 6.057 107 2 52 88 6.057 117 1 50 89 6.938 109 2 46

## Answers

Using IQ as predictor

in Excel

data -> data analysis -> regression

SUMMARY OUTPUT Regression StatisticsMultiple R 0.646809885 R Square0.4184Adjusted R Square 0.4107 Standard Error 1.6117 Observations 78 ANOVA dfSSMSFSignificance FRegression 1 142.0037 142.0037 54.6657 0.0000 Residual 76 197.4232 2.5977 Total 77 339.4269 CoefficientsStandard Errort StatP-valueLower 95%Intercept -3.8983 1.5452 -2.5228 0.0137 -6.9759 iq 0.1027 0.0139 7.3936 0.0000 0.0751 R^2 = 0.4184

Using Self-concept as predictor

SUMMARY OUTPUT Regression StatisticsMultiple R 0.6256 R Square0.3914Adjusted R Square 0.3834 Standard Error 1.6487 Observations 78 ANOVA dfSSMSFSignificance FRegression 1 132.8474 132.8474 48.8742 0.0000 Residual 76 206.5795 2.7182 Total 77 339.4269 CoefficientsStandard Errort StatP-valueLower 95%Intercept 2.4952 0.7324 3.4067 0.0011 1.0364 concept 0.0884 0.0126 6.9910 0.0000 0.0632

R^2 = 0.3914we see that R^2 is larger with IQ as predictor

hence

IQis is the better predictorPlease rate

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