Question

In: Statistics and Probability

Find the accuracy of the linear predicted probability model. Write your answer using two decimal places...

Find the accuracy of the linear predicted probability model. Write your answer using two decimal places in the format xx.xx%

STEM GPA SAT White Female Asian
1 2.90 1550 1 1 0
0 4.50 1360 0 0 0
0 4.40 1090 0 1 1
1 2.50 1520 1 0 0
0 4.10 1200 0 1 1
1 2.90 1490 1 0 0
0 4.30 1260 1 1 0
1 4.50 1430 0 0 0
0 4.40 1250 0 0 0
1 2.80 1590 1 0 0
1 3.10 1410 0 0 1
1 4.00 1230 1 0 0
0 2.50 1010 1 1 0
0 2.60 1240 0 1 0
0 4.10 1120 0 1 0
0 2.70 1100 0 0 1
0 4.00 1240 0 0 1
0 3.60 1510 0 1 0
0 2.70 1290 0 1 0
1 3.40 1580 0 1 0
1 3.60 1410 0 0 1
0 2.70 1050 0 1 1
1 4.00 1480 0 1 1
0 4.40 1090 0 0 0
1 3.20 1590 0 0 1
1 2.80 1530 1 1 0
1 4.20 1570 1 1 0
0 2.60 1050 0 1 0
0 3.80 1030 1 0 0
1 3.60 1330 0 0 1
1 2.50 1330 1 0 0
0 3.30 1350 1 1 0
1 2.50 1220 0 0 1
0 3.70 1270 0 1 1
1 4.10 1390 0 0 0
1 2.60 1560 0 1 1
0 4.30 1020 0 0 0
0 4.40 1050 0 0 1
0 2.90 1050 1 0 0
0 2.50 1050 1 1 0
0 3.90 1300 0 1 1
0 3.80 1390 0 1 0
1 2.70 1520 0 1 0
1 3.90 1440 0 1 1
0 3.90 1180 1 1 0
0 3.70 1440 1 1 0
0 3.40 1190 1 1 0
1 3.20 1380 1 0 0
0 2.80 1430 0 1 0
1 3.80 1270 1 0 0
0 3.60 1210 1 0 0
1 4.40 1470 0 1 0
1 2.90 1560 1 1 0
1 4.50 1500 0 0 0
1 3.80 1380 0 0 1
0 2.60 1020 0 1 0
0 4.40 1460 1 1 0
1 3.30 1550 1 1 0
1 4.00 1400 0 1 1
0 2.60 1200 0 0 0
1 4.10 1190 1 0 0
1 2.80 1410 1 0 0
0 4.50 1190 1 1 0
0 2.80 1010 0 1 0
0 3.00 1030 0 0 1
0 3.30 1080 1 0 0
1 3.80 1520 0 0 0
0 4.50 1380 1 1 0
0 3.90 1030 0 1 1
0 3.60 1240 0 1 1
1 3.60 1200 0 0 1
1 4.00 1320 0 1 0
0 4.30 1300 0 1 0
0 3.90 1070 0 1 0
1 3.30 1430 0 1 1
1 4.40 1400 0 0 1
0 2.70 1420 1 1 0
1 3.30 1310 1 1 0
1 3.90 1450 1 1 0
1 2.70 1470 0 0 0
1 3.40 1560 0 0 0
1 4.20 1550 0 0 0
1 3.70 1350 0 0 0
0 2.60 1240 0 0 1
0 2.90 1170 0 1 1
1 2.60 1370 0 0 0
1 3.00 1470 0 1 0
0 3.80 1030 1 1 0
1 3.10 1600 0 1 0
0 4.00 1170 0 1 1
0 4.10 1070 0 0 0
1 4.30 1420 0 0 0
0 3.90 1080 1 1 0
0 3.80 1250 0 0 1
0 3.80 1030 0 0 0
1 3.70 1210 0 0 1
0 4.30 1340 0 1 0
0 3.60 1340 0 1 0
0 4.40 1190 0 0 0
0 2.80 1120 1 1 0

Solutions

Expert Solution

The multiple linear regression output is obtained as

SUMMARY OUTPUT
Regression Statistics
Multiple R 0.761486
R Square 0.579861
Adjusted R Square 0.557514
Standard Error 0.333202
Observations 100
ANOVA
df SS MS F Significance F
Regression 5 14.40376 2.880752 25.94714 2.27E-16
Residual 94 10.43624 0.111024
Total 99 24.84
Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
Intercept -1.84172 0.32883 -5.60081 2.11E-07 -2.49462 -1.18882 -2.49462 -1.18882
GPA -0.05828 0.052515 -1.10979 0.269922 -0.16255 0.045989 -0.16255 0.045989
SAT 0.002001 0.000191 10.47626 1.79E-17 0.001622 0.00238 0.001622 0.00238
White 0.080644 0.080424 1.00274 0.318561 -0.07904 0.240327 -0.07904 0.240327
Female -0.30211 0.067396 -4.48268 2.08E-05 -0.43593 -0.1683 -0.43593 -0.1683
Asian 0.131925 0.083311 1.583529 0.11666 -0.03349 0.297341 -0.03349 0.297341

The measures of accuracy of the predicted model is given by R2 and adjusted R2. The value of R2 is obtained as 57.99% and the adjusted R2 is obtained as 55.75%

Hopefully this will help you. In case of any query, do comment. If you are satisfied with the answer, give it a like. Thanks.

orchestra answered 1 year ago
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