The data from data297.dat contains information on 78 seventh-grade students. We

Question

The data from data297.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.)

Every space that seperates each number is in the order of OBS, GPA, Iq, gender, concept. Put these numbers in a chart.

obs gpa iq gender concept 1 7.94 123 2 63 2 8.292 117 2 70 3 4.643 98 2 29 4 7.47 114 2 38 5 8.882 115 1 51 6 7.585 122 2 31 7 7.65 118 2 25 8 2.412 83 2 53 9 6 100 1 38 10 8.833 118 2 59 11 7.47 104 1 46 12 5.528 101 1 41 13 7.167 95 2 60 14 7.571 115 1 59 15 4.7 96 1 66 16 8.167 106 1 62 17 7.822 106 1 56 18 7.598 95 1 51 19 4 86 2 23 20 6.231 117 1 60 21 7.643 109 2 59 22 1.76 102 2 40 24 6.419 105 1 48 26 9.648 131 2 43 27 10.7 114 1 61 28 10.58 138 2 51 29 9.429 114 2 75 30 8 117 2 45 31 9.585 113 2 91 32 9.571 103 1 68 33 8.998 112 1 65 34 8.333 115 1 56 35 8.175 121 2 55 36 8 117 2 41 37 9.333 118 1 32 38 9.5 120 2 54 39 9.167 121 2 90 40 10.14 116 1 49 41 9.999 116 1 52 43 10.76 113 2 87 44 9.763 131 2 81 45 9.41 124 2 57 46 9.167 136 2 63 47 9.348 128 2 62 48 8.167 114 2 55 50 3.647 84 2 37 51 3.408 83 1 37 52 3.936 86 2 27 53 7.167 108 2 58 54 7.647 108 2 53 55 .53 86 2 31 56 6.173 116 2 45 57 7.295 113 2 48 58 7.295 113 1 72 59 8.938 109 1 81 60 7.882 113 1 74 61 8.353 106 2 58 62 5.062 91 2 54 63 8.175 91 2 71 64 8.235 125 2 33 65 7.588 96 2 40 68 7.647 103 2 58 69 5.237 80 1 72 71 7.825 113 2 70 72 7.333 103 1 53 74 9.167 130 2 59 76 7.996 116 2 47 77 8.714 102 1 64 78 7.833 96 1 92 79 4.885 109 2 49 80 7.998 115 1 43 83 3.82 84 2 49 84 5.936 107 1 70 85 9 119 1 56 86 9.5 133 1 56 87 6.057 115 2 52 88 6.057 106 1 55 89 6.938 98 2 59

Regressor: IQ) R 2 = __________

(Regressor: Self-Concept) R 2 = _____________

Which variable is the better predictor?

IQ or selfconcept?

Explanation / Answer

Rcode:

> df<-read.csv("Book8.csv")
> model1<-lm(gpa~iq,data=df)
> model2<-lm(gpa~concept,data=df)
> summary(model1)

Call:
lm(formula = gpa ~ iq, data = df)

Residuals:
Min 1Q Median 3Q Max
-4.8325 -0.7770 -0.1392 0.8806 2.8998

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -5.1628 1.3669 -3.777 0.000313 ***
iq 0.1153 0.0124 9.291 3.7e-14 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 1.446 on 76 degrees of freedom
Multiple R-squared: 0.5318,   Adjusted R-squared: 0.5257
F-statistic: 86.33 on 1 and 76 DF, p-value: 3.699e-14

> summary(model2)

Call:
lm(formula = gpa ~ concept, data = df)

Residuals:
Min 1Q Median 3Q Max
-5.4540 -0.9900 0.2798 1.2670 3.3733

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 4.08877 0.80456 5.082 2.6e-06 ***
concept 0.06114 0.01412 4.330 4.5e-05 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 1.893 on 76 degrees of freedom
Multiple R-squared: 0.1979,   Adjusted R-squared: 0.1873
F-statistic: 18.75 on 1 and 76 DF, p-value: 4.497e-05

Answer:

R square is a measure of goodness of fit. It means who variance of the dependent variable can be explained by the independent variables. Here for IQ R square is 0.5318 and for Concept R square is 0.1979. So, it is quite evident from the result that IQ is a better choice for predicting GPA of students.

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