Question
choice =f( 0 + 1 Age65+ 2 Urban+ 3 ColGrad) We want to apply the logistic regression model, where choice is notated as 0 or
choice =f( 0 + 1 Age65+ 2 Urban+ 3 ColGrad) We want to apply the logistic regression model, where choice is notated as 0 or 1 and Age65, Urban, ColGrad are predictor variables. (1) Estimate 1 2 , 3 using MLE method, and report the estimated values. After that, carry out the test for their significance at 10% significance level using p value approa ch (2) Report exp( 1 ), 2 )), and exp( 3 using the estimated values in ( After that, explain the meaning of each value. Hint : as 1 unit of x increase, odds of success increase xx times
(3) Using the threshold 0.5, report the proportion of predicting that choice=1when in fact the choice=1.
State | choice | Age65 | Urban | ColGrad | Union | MidWest | Neast | West | Seast |
AL | 1 | 13 | 69.9 | 20.4 | 9.6 | 0 | 0 | 0 | 1 |
AK | 1 | 5.7 | 41.5 | 28.1 | 21.9 | 0 | 0 | 1 | 0 |
AZ | 1 | 13 | 88.2 | 24.6 | 6.4 | 0 | 0 | 1 | 0 |
AR | 1 | 14 | 49.9 | 18.4 | 5.8 | 0 | 0 | 0 | 1 |
CA | 0 | 10.6 | 96.7 | 27.5 | 16 | 0 | 0 | 1 | 0 |
CO | 1 | 9.7 | 83.9 | 34.6 | 9 | 0 | 0 | 1 | 0 |
CT | 0 | 13.8 | 95.6 | 31.6 | 16.3 | 0 | 1 | 0 | 0 |
DE | 0 | 13 | 80 | 24 | 13.3 | 0 | 1 | 0 | 0 |
FL | 0 | 17.6 | 92.8 | 22.8 | 6.8 | 0 | 0 | 0 | 1 |
GA | 1 | 9.6 | 69.2 | 23.1 | 6.3 | 0 | 0 | 0 | 1 |
HI | 0 | 13.3 | 72.3 | 26.3 | 24.8 | 0 | 0 | 1 | 0 |
ID | 1 | 11.3 | 39.9 | 20 | 7.6 | 0 | 0 | 1 | 0 |
IL | 0 | 12.1 | 84.9 | 27.1 | 18.6 | 1 | 0 | 0 | 0 |
IN | 1 | 12.4 | 72.2 | 17.1 | 15.6 | 1 | 0 | 0 | 0 |
IA | 0 | 14.9 | 45.3 | 25.5 | 13.6 | 1 | 0 | 0 | 0 |
KS | 1 | 13.3 | 56.6 | 27.3 | 9 | 1 | 0 | 0 | 0 |
KY | 1 | 12.5 | 48.8 | 20.5 | 12 | 0 | 0 | 0 | 1 |
LA | 1 | 11.6 | 75.4 | 22.5 | 7.1 | 0 | 0 | 0 | 1 |
ME | 0 | 14.4 | 36.6 | 24.1 | 14 | 0 | 1 | 0 | 0 |
MD | 0 | 11.3 | 92.7 | 32.3 | 14.6 | 0 | 1 | 0 | 0 |
MA | 0 | 13.5 | 95.9 | 32.7 | 14.3 | 0 | 1 | 0 | 0 |
MI | 0 | 12.3 | 82.2 | 23 | 20.8 | 1 | 0 | 0 | 0 |
MN | 0 | 12.1 | 70.4 | 31.2 | 18.2 | 1 | 0 | 0 | 0 |
MS | 1 | 12.1 | 36 | 18.7 | 6 | 0 | 0 | 0 | 1 |
MO | 1 | 13.5 | 67.8 | 26.2 | 13.2 | 1 | 0 | 0 | 0 |
MT | 1 | 13.4 | 33.9 | 23.8 | 13.9 | 0 | 0 | 1 | 0 |
NE | 1 | 13.6 | 52.6 | 24.6 | 8.4 | 1 | 0 | 0 | 0 |
NV | 0 | 11 | 87.5 | 19.3 | 17.1 | 0 | 0 | 1 | 0 |
NH | 0 | 12 | 59.9 | 30.1 | 10.4 | 0 | 1 | 0 | 0 |
NJ | 0 | 13.2 | 100 | 30.1 | 20.8 | 0 | 1 | 0 | 0 |
NM | 0 | 11.7 | 56.9 | 23.6 | 8.1 | 0 | 0 | 1 | 0 |
NY | 0 | 12.9 | 92.1 | 28.7 | 25.5 | 0 | 1 | 0 | 0 |
NC | 1 | 12 | 67.5 | 23.2 | 3.6 | 0 | 0 | 0 | 1 |
ND | 1 | 14.7 | 44.2 | 22.6 | 6.5 | 1 | 0 | 0 | 0 |
OH | 0 | 13.3 | 81.2 | 24.6 | 17.3 | 1 | 0 | 0 | 0 |
OK | 1 | 13.2 | 60.8 | 22.5 | 6.8 | 1 | 0 | 0 | 0 |
OR | 0 | 12.8 | 73.1 | 27.2 | 16.1 | 0 | 0 | 1 | 0 |
PA | 0 | 15.6 | 84.6 | 24.3 | 16.9 | 0 | 1 | 0 | 0 |
RI | 0 | 14.5 | 94.1 | 26.4 | 18.2 | 0 | 1 | 0 | 0 |
SC | 1 | 12.1 | 70 | 19 | 4 | 0 | 0 | 0 | 1 |
SD | 1 | 14.3 | 34.6 | 25.7 | 5.5 | 1 | 0 | 0 | 0 |
TN | 1 | 12.4 | 67.9 | 22 | 8.9 | 0 | 0 | 0 | 1 |
TX | 1 | 9.9 | 84.8 | 23.9 | 5.8 | 0 | 0 | 1 | 0 |
UT | 1 | 8.5 | 76.5 | 26.4 | 7.3 | 0 | 0 | 1 | 0 |
VT | 0 | 12.7 | 27.8 | 28.8 | 10.3 | 0 | 1 | 0 | 0 |
VA | 1 | 11.2 | 78.1 | 31.9 | 5.6 | 0 | 0 | 0 | 1 |
WA | 0 | 11.2 | 83.1 | 28.6 | 18.2 | 0 | 0 | 1 | 0 |
WV | 1 | 15.3 | 42.3 | 15.3 | 14.3 | 0 | 0 | 0 | 1 |
WI | 0 | 13.1 | 67.9 | 23.8 | 17.6 | 1 | 0 | 0 | 0 |
WY | 1 | 11.7 | 30 | 20.6 | 8.3 | 0 | 0 | 1 | 0 |
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