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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

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

choice=f(0+1Age65+ 2Urban+ 3ColGrad).

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 approach.

(2) Report exp(1), exp(2), and exp(3) using the estimated values in (1). 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=1 when in fact the choice=1

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