Automobiles, including cars and light trucks, are the most held nonfinancial assets among Americans, which are often financed through loans. Peter Firsov works in the car loan division of a major commercial bank. He wants to use a data-driven strategy to identify borrowers likely to default on the automobile loan. The accompanying data file (Down below) includes historical data for 400 customers including information on whether the customer defaulted and the corresponding loan-to-value ratio (LTV in %), FICO credit score (FICO), and age.

a. Estimate the linear probability model to find the predicted probability of default given the average values of LTV, FICO, and Age,

b. What is the probability of default given LTV = 70, FICO = 600 and Age = 50.

c. Estmate the logistic regression model to find the predicted probability of default given the average values of LTV, FICO, and Age.

-----

Consider the logistic regression model for default for the following questions.

d. Extend the model to include Age-squared to find the corresponding predicted probability of default.

e. Is the Age-squared variable statistically significant at the 5% level?

f. What is the probability and odds of default given LTV = 70, FICO = 600 and Age = 50.

g. Find the corresponding probability and odds if FICO = 700.

h. Interpret the percentage change in the default odds when each predictor variable increases by one unit, holding the other variables constant.

-----

i. Compute and compare the accuracy rates of the LPM and logistic regression models.

j. Use the preferred model from (i) to predict the default probability with LTV = 80, FICO = 650, and Age = 40.

The Accompanying Data:

Default	LTV	FICO	Age
0	70.50	705	61
0	73.91	586	20
0	80.33	779	67
0	91.06	764	55
0	68.45	776	32
0	90.75	721	52
1	92.23	633	35
0	83.15	735	65
1	82.13	543	35
0	63.98	775	20
0	68.59	788	36
0	67.65	629	37
0	83.98	727	36
0	74.29	738	66
0	86.63	716	37
1	77.93	659	45
1	84.96	664	64
0	93.74	617	64
0	74.16	714	30
0	86.88	746	54
0	91.91	649	35
0	68.79	669	46
0	82.85	706	55
0	66.02	576	59
0	70.55	626	61
0	74.36	641	20
0	62.43	561	29
0	74.24	773	36
1	89.83	750	33
0	72.89	760	54
0	77.43	774	53
0	81.19	558	64
0	77.79	635	60
0	67.96	674	57
1	88.48	566	38
0	83.39	740	47
0	87.42	725	22
0	65.45	553	62
0	85.16	661	66
0	75.16	770	43
1	88.27	550	64
0	82.71	613	25
0	87.05	665	30
0	79.70	692	42
1	78.95	606	42
1	87.26	646	40
0	62.75	632	20
0	77.27	776	50
1	85.43	571	54
1	84.17	558	36
0	77.28	781	65
0	89.56	651	55
0	76.02	633	21
0	69.83	583	67
0	64.26	554	29
0	65.18	704	20
0	72.12	685	31
0	78.60	787	54
0	83.18	691	30
0	75.02	556	30
0	91.21	581	19
0	71.40	659	31
1	76.69	540	53
0	72.64	650	20
0	82.83	605	21
0	70.26	775	38
0	77.31	719	43
0	86.52	581	50
0	64.70	659	54
0	90.01	713	22
0	72.85	655	39
0	88.86	779	67
0	73.09	718	59
0	72.68	639	29
1	77.24	569	42
0	90.55	600	19
0	89.66	756	31
0	74.48	649	41
0	86.87	664	55
0	92.74	713	68
0	75.91	730	35
0	84.80	579	65
0	74.80	752	66
0	72.41	777	63
0	86.23	687	43
0	68.49	666	57
1	84.76	587	58
0	65.89	540	52
0	69.86	759	47
0	66.59	574	35
0	69.67	546	18
0	63.89	775	21
0	82.55	613	22
0	90.04	581	19
0	86.93	640	35
0	87.51	655	24
0	76.57	649	48
0	75.12	669	20
0	87.95	752	18
0	81.36	554	26
0	82.95	679	60
0	73.30	712	56
0	70.65	705	32
0	93.77	706	27
0	82.27	658	29
0	68.82	782	21
0	66.14	641	21
0	77.30	752	25
0	91.57	729	22
0	81.16	673	20
0	93.24	759	44
0	85.42	657	57
0	73.42	542	53
0	75.81	722	21
0	66.74	719	19
0	62.42	587	40
0	84.90	702	26
0	65.30	675	54
0	76.28	624	53
0	82.48	699	62
0	93.74	747	34
0	77.86	717	67
0	77.50	627	67
0	67.55	572	20
0	86.15	637	63
0	76.52	772	59
0	78.36	741	54
0	68.64	730	32
0	69.32	779	43
0	81.06	788	39
0	80.40	692	49
0	64.47	547	64
0	63.14	624	30
0	82.57	609	32
1	91.72	569	55
1	81.14	551	56
0	79.95	633	65
1	78.83	624	41
0	93.52	583	61
0	78.24	695	34
0	83.85	639	28
0	81.25	779	64
0	69.64	703	21
0	70.26	622	39
1	85.34	589	41
0	76.48	569	39
0	67.60	789	52
0	85.89	635	56
0	65.36	680	64
0	89.67	723	59
0	81.67	758	23
0	79.83	683	27
0	72.52	543	50
0	76.50	767	62
0	78.01	733	48
0	67.79	636	31
0	78.95	564	62
0	64.41	552	27
0	70.89	745	42
0	68.81	747	18
0	71.11	704	36
0	90.64	573	40
0	76.28	625	24
0	86.96	723	49
0	90.18	767	33
0	75.22	714	30
0	64.04	600	36
0	72.74	701	63
0	85.16	610	68
0	72.80	779	55
0	82.17	580	68
0	88.90	645	45
1	89.40	603	40
0	74.52	564	66
0	74.18	747	25
0	90.65	671	21
0	82.62	707	19
1	85.71	642	49
0	81.37	751	53
0	90.90	724	58
0	71.40	627	25
0	68.12	777	26
0	90.37	702	67
0	78.11	549	38
0	90.07	689	27
0	68.05	644	42
1	86.26	559	45
0	85.18	672	34
0	92.20	781	68
0	79.52	717	44
0	84.78	678	25
0	74.44	601	40
0	65.23	735	49
0	91.67	703	28
0	71.06	748	25
0	80.90	702	57
0	65.53	660	50
0	88.90	664	32
0	72.17	635	28
0	87.05	653	31
0	70.56	744	45
0	69.00	772	52
1	78.54	577	37
0	70.61	727	66
0	67.80	784	24
0	78.59	784	20
0	80.01	628	43
0	66.13	638	47
0	70.20	778	60
1	84.97	567	51
0	92.77	774	65
0	65.20	627	44
0	86.42	673	22
0	92.33	675	68
0	88.20	719	38
0	71.87	641	63
1	82.79	578	62
0	92.51	625	33
0	92.52	697	25
0	72.88	554	31
0	70.40	753	18
0	67.29	593	59
0	72.31	675	27
0	78.32	574	60
0	91.57	621	26
0	78.35	695	56
0	70.24	604	44
0	63.49	699	32
0	75.37	661	35
0	89.33	775	53
0	73.11	754	48
0	66.21	633	41
0	73.98	619	35
0	82.21	747	66
0	74.48	653	50
0	84.07	619	28
0	84.06	564	36
0	79.76	556	44
0	75.75	712	62
0	76.49	707	26
0	71.81	766	30
0	80.51	615	26
0	91.13	773	49
0	66.56	590	43
0	75.28	738	27
0	68.75	596	38
1	75.72	548	47
0	66.25	756	33
0	76.72	711	42
0	92.17	776	65
0	86.38	709	20
0	91.85	751	45
0	77.06	630	40
0	81.31	638	63
0	77.52	682	62
0	65.48	564	26
0	69.93	588	56
0	77.95	687	38
0	73.93	728	46
0	91.91	757	22
0	78.77	633	24
0	72.15	740	64
0	70.89	555	62
0	87.20	696	26
0	84.48	629	45
0	67.28	687	64
0	64.06	768	34
0	86.15	590	26
0	81.85	632	65
0	67.43	708	41
0	63.99	732	29
0	65.49	671	18
0	74.21	747	49
0	67.42	672	38
0	71.56	665	63
0	68.15	645	43
0	70.23	631	54
0	67.80	571	19
0	77.27	615	37
1	86.66	609	37
0	62.89	733	35
0	78.87	735	36
1	90.17	576	50
0	73.94	669	20
0	63.53	689	53
0	66.44	666	59
0	72.29	637	43
0	66.95	647	24
0	66.23	543	63
0	69.08	770	39
0	69.24	560	42
0	66.21	667	54
0	93.41	745	30
0	72.46	690	33
0	78.22	646	53
0	83.81	680	57
0	65.17	737	19
0	65.80	582	46
0	63.61	783	51
0	91.74	658	65
0	83.56	772	53
0	65.04	765	31
0	77.76	728	39
0	76.77	709	24
0	74.01	702	25
1	93.72	558	50
0	67.64	646	35
0	88.03	673	39
0	64.19	776	65
0	74.81	718	37
0	66.52	721	29
0	68.19	658	53
0	88.92	570	18
0	85.04	736	52
0	70.55	650	58
0	77.84	648	43
0	64.66	547	33
0	73.32	577	55
0	93.01	646	33
0	81.99	732	57
0	83.27	541	24
0	72.00	691	58
0	74.98	766	43
1	93.87	717	60
1	89.36	606	56
0	92.51	753	63
0	87.99	623	32
0	87.03	685	40
0	70.57	648	32
0	86.39	553	34
1	93.56	722	61
0	71.40	677	23
0	74.78	728	38
1	87.99	553	38
0	64.47	719	40
0	73.64	614	27
0	76.16	611	31
0	67.01	747	51
0	80.63	562	59
1	93.05	551	39
0	93.66	627	26
0	67.65	676	32
0	79.35	692	58
0	74.30	608	26
1	83.64	591	57
0	70.62	635	44
0	77.02	658	34
0	67.50	749	32
0	73.81	570	58
0	85.21	709	23
0	77.56	664	60
0	64.04	766	22
1	87.11	678	54
0	75.39	572	61
0	93.39	651	67
0	71.05	588	30
0	89.13	649	19
0	64.63	596	29
0	90.37	780	24
0	77.10	652	37
0	65.49	734	22
0	72.66	580	32
0	88.80	757	46
0	70.86	592	34
0	80.79	584	65
0	88.78	581	37
0	64.28	681	66
0	84.49	722	32
0	84.36	759	52
0	76.85	717	25
0	75.98	659	59
0	79.99	745	56
1	91.71	544	40
0	69.37	789	41
0	69.10	699	52
0	75.45	647	22
1	72.67	547	50
0	89.67	728	57
0	67.67	592	29
0	77.79	790	20
0	75.75	767	37
0	80.06	718	35
0	83.00	723	40
1	93.31	658	37
0	69.43	756	64
0	69.71	581	27
0	87.50	695	25
1	88.61	613	49
0	65.63	654	19
0	92.83	551	21
0	66.71	584	57
0	66.60	554	65
0	91.61	776	28
0	78.23	626	50
0	66.96	669	35
0	73.15	696	66
0	83.11	599	59
0	71.98	669	55
0	73.25	742	29
0	66.73	627	20