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