OBS AP APENG APMATH ESL GEND GPA PREP RACE SAT Family Income 1 1 1 0 0 0 3.74 0

Question

OBS AP APENG APMATH ESL GEND GPA PREP RACE SAT Family Income 1 1 1 0 0 0 3.74 0 0 1060 99800 2 0 0 0 0 0 2.71 1 0 740 47800 3 1 1 0 0 0 3.92 1 0 1070 96700 4 1 1 0 0 0 3.43 1 0 1070 99000 5 1 1 1 0 0 4.35 1 0 1330 204900 6 1 1 0 0 1 3.02 1 0 1220 156380 7 1 1 1 1 0 3.98 1 0 1130 89700 8 0 0 0 0 0 2.94 1 0 770 55000 9 1 1 0 0 0 3.49 1 0 1050 84650 10 1 1 1 0 1 3.87 1 0 1250 89670 11 0 0 0 0 0 3.49 1 0 1000 64800 12 1 1 0 0 0 3.24 1 0 1010 73560 13 1 1 1 1 1 4.22 0 1 1320 187590 14 1 1 1 1 1 3.61 1 1 1230 68790 15 1 0 1 1 1 2.48 0 1 840 189700 16 1 0 1 1 0 2.26 0 1 940 167900 17 0 0 0 1 1 2.32 1 1 910 76000 18 1 1 1 0 1 3.89 1 0 1240 258390 19 0 0 0 0 1 3.67 0 0 1020 68790 20 0 0 0 0 0 2.54 1 0 630 37800 21 0 0 0 0 0 3.16 1 0 850 54000 22 1 1 1 1 1 4.16 1 0 1300 189700 23 0 0 0 0 1 2.94 1 0 950 123000 24 1 1 1 0 1 3.79 1 0 1350 197800 25 0 0 0 0 1 2.56 0 0 1070 103900 26 0 0 0 0 1 3 1 0 1000 104000 27 0 0 0 0 0 2.79 1 0 770 64890 28 1 0 1 1 0 3.7 1 1 1280 165980 29 0 0 0 1 0 3.23 1 1 590 29800 30 1 1 1 1 1 3.98 0 1 1060 112000 31 1 0 1 0 0 2.64 0 0 1050 93870 32 1 1 1 1 1 4.15 1 1 1220 74650 33 0 0 0 0 1 2.73 1 0 930 64890 34 1 1 1 1 0 3.1 0 1 940 56300 35 0 0 0 1 1 2.7 1 1 980 57900 36 1 1 1 0 1 3.73 1 0 1280 117860 37 0 0 0 1 0 1.64 1 1 700 35600 38 1 1 1 1 0 4.03 1 1 1040 75800 39 1 1 0 0 1 3.24 1 0 1070 98470 40 0 0 0 0 1 3.42 1 0 900 57000 41 1 1 1 0 1 4.29 0 0 1430 246500 42 0 0 0 0 1 3.33 0 0 1290 108000 43 1 0 1 1 0 3.61 1 1 1070 67930 44 1 1 1 0 0 3.58 1 0 1100 110390 45 1 1 0 0 0 3.52 1 0 1030 68790 46 0 0 0 0 1 2.94 1 0 1070 98470 47 1 1 1 1 1 3.98 1 0 1170 98600 48 1 1 1 0 1 3.89 0 0 1300 125600 49 1 1 1 1 0 4.34 1 1 1410 99000 50 1 1 1 0 1 3.43 1 0 1160 84700 51 1 1 1 0 0 3.56 0 0 1170 119970 52 1 1 1 0 0 4.11 1 0 1280 99000 53 1 1 1 1 0 3.58 1 0 1060 102030 54 1 1 1 0 1 3.47 1 0 1250 109000 55 1 0 1 1 1 2.92 1 1 1020 73800 56 1 1 0 1 0 4.05 0 1 1000 95800 57 1 1 1 1 1 3.24 1 1 1090 183690 58 1 1 1 1 0 4.38 0 1 1430 98700 59 1 0 1 1 0 2.62 0 1 860 55000 60 0 0 0 0 1 2.37 0 0 1050 87400 61 0 0 0 0 0 2.77 1 0 920 56890 62 0 0 0 0 1 2.54 1 0 1100 74690 63 1 0 1 1 1 3.55 1 1 1160 82930 64 1 1 0 1 0 2.98 1 0 1360 245890 65 1 1 1 0 0 3.64 1 0 970 64700 Many articles maintain that SAT is biased against women ana minorities. Yet there are a few articles arguing family income as a key determinant of a student's SAT score. Indeed the College Board reveals some descriptive data every year and it shows the same result: The richer the parent, the higher the children's SAT scores. One plausible explanation provided is that parental IQ is correlated with children's IQ everywhere. In all advanced societies, income is correlated with IQ. Scores on academic achievement tests are always correlated with the test-takers' IQ. Therefore, those three correlations guarantee that every standardized academic-achievement test shows higher average test scores as parental income increases. In this question, please test the family income argument. You will need to make a decision on which other variables to include and which should be excluded given the natural of the data. Are there possible interaction relationships in the data? Is the income effect distributed evenly?

Explanation / Answer

SUMMARY OUTPUT Regression Statistics Multiple R 0.840270579 R Square 0.706054645 Adjusted R Square 0.657954496 Standard Error 111.9165389 Observations 65 ANOVA df SS MS F Significance F Regression 9 1654714.012 183857.1124 14.6788453 9.1503E-12 Residual 55 688892.1422 12525.31168 Total 64 2343606.154 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 427.0537224 108.3001011 3.943243987 0.000229537 210.0154698 644.091975 210.0154698 644.091975 AP 62.32015956 69.681234 0.894360734 0.375026107 -77.32415393 201.964473 -77.32415393 201.964473 APENG 15.21690131 58.11529411 0.261839874 0.79442304 -101.2487507 131.6825533 -101.2487507 131.6825533 APMATH 26.57717102 46.60072301 0.57031671 0.570785538 -66.81276483 119.9671069 -66.81276483 119.9671069 ESL -3.520706982 57.10350733 -0.061654829 0.951061221 -117.958693 110.917279 -117.958693 110.917279 GEND 86.14156496 31.02019528 2.776951086 0.007487976 23.97570443 148.3074255 23.97570443 148.3074255 GPA 134.0494593 34.2985971 3.908307354 0.000257051 65.31353467 202.7853838 65.31353467 202.7853838 PREP -13.79637187 33.57593557 -0.410900594 0.682742007 -81.08405039 53.49130665 -81.08405039 53.49130665 RACE -37.68418886 61.95383319 -0.608262426 0.545517275 -161.8424451 86.47406734 -161.8424451 86.47406734 Family Income 0.001103422 0.00033607 3.283307844 0.001787004 0.000429922 0.001776921 0.000429922 0.001776921 Family income is a significant independent variable in determining the change in SAT scores as we can see that the p-value is less than 0.005. Apart from that, we can see that Gender and GPA also have a significant impact on the SAT scores

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