Homework3

# na.strings = "" will treat empty string as NA
loan_data <- read.csv('https://raw.githubusercontent.com/metis-macys-66898/data622_fa2021/main/hw3/data/Loan_approval.csv', header = TRUE, na.strings = "")

loan_raw <- read.csv('https://raw.githubusercontent.com/metis-macys-66898/data622_fa2021/main/hw3/data/Loan_approval.csv', header = TRUE)

1. Exploratory Data Analysis

Our loan data has 614 rows and 13 columns, 8 of which are categorical and 5 are numerical. The target variable is Loan_Status, which can be either Y (yes) or N (no). This let’s us know if the applicant’s loan is approved. There are 7 variables that have blank values. The one with the most blank values is Credit_History with 50 blanks.

loan_data %>% kbl() %>% kable_styling() %>% scroll_box(width = "750px", height = "250px")

Loan_ID	Gender	Married	Dependents	Education	Self_Employed	ApplicantIncome	CoapplicantIncome	LoanAmount	Loan_Amount_Term	Credit_History	Property_Area	Loan_Status
LP001002	Male	No	0	Graduate	No	5849	0.00	NA	360	1	Urban	Y
LP001003	Male	Yes	1	Graduate	No	4583	1508.00	128	360	1	Rural	N
LP001005	Male	Yes	0	Graduate	Yes	3000	0.00	66	360	1	Urban	Y
LP001006	Male	Yes	0	Not Graduate	No	2583	2358.00	120	360	1	Urban	Y
LP001008	Male	No	0	Graduate	No	6000	0.00	141	360	1	Urban	Y
LP001011	Male	Yes	2	Graduate	Yes	5417	4196.00	267	360	1	Urban	Y
LP001013	Male	Yes	0	Not Graduate	No	2333	1516.00	95	360	1	Urban	Y
LP001014	Male	Yes	3+	Graduate	No	3036	2504.00	158	360	0	Semiurban	N
LP001018	Male	Yes	2	Graduate	No	4006	1526.00	168	360	1	Urban	Y
LP001020	Male	Yes	1	Graduate	No	12841	10968.00	349	360	1	Semiurban	N
LP001024	Male	Yes	2	Graduate	No	3200	700.00	70	360	1	Urban	Y
LP001027	Male	Yes	2	Graduate	NA	2500	1840.00	109	360	1	Urban	Y
LP001028	Male	Yes	2	Graduate	No	3073	8106.00	200	360	1	Urban	Y
LP001029	Male	No	0	Graduate	No	1853	2840.00	114	360	1	Rural	N
LP001030	Male	Yes	2	Graduate	No	1299	1086.00	17	120	1	Urban	Y
LP001032	Male	No	0	Graduate	No	4950	0.00	125	360	1	Urban	Y
LP001034	Male	No	1	Not Graduate	No	3596	0.00	100	240	NA	Urban	Y
LP001036	Female	No	0	Graduate	No	3510	0.00	76	360	0	Urban	N
LP001038	Male	Yes	0	Not Graduate	No	4887	0.00	133	360	1	Rural	N
LP001041	Male	Yes	0	Graduate	NA	2600	3500.00	115	NA	1	Urban	Y
LP001043	Male	Yes	0	Not Graduate	No	7660	0.00	104	360	0	Urban	N
LP001046	Male	Yes	1	Graduate	No	5955	5625.00	315	360	1	Urban	Y
LP001047	Male	Yes	0	Not Graduate	No	2600	1911.00	116	360	0	Semiurban	N
LP001050	NA	Yes	2	Not Graduate	No	3365	1917.00	112	360	0	Rural	N
LP001052	Male	Yes	1	Graduate	NA	3717	2925.00	151	360	NA	Semiurban	N
LP001066	Male	Yes	0	Graduate	Yes	9560	0.00	191	360	1	Semiurban	Y
LP001068	Male	Yes	0	Graduate	No	2799	2253.00	122	360	1	Semiurban	Y
LP001073	Male	Yes	2	Not Graduate	No	4226	1040.00	110	360	1	Urban	Y
LP001086	Male	No	0	Not Graduate	No	1442	0.00	35	360	1	Urban	N
LP001087	Female	No	2	Graduate	NA	3750	2083.00	120	360	1	Semiurban	Y
LP001091	Male	Yes	1	Graduate	NA	4166	3369.00	201	360	NA	Urban	N
LP001095	Male	No	0	Graduate	No	3167	0.00	74	360	1	Urban	N
LP001097	Male	No	1	Graduate	Yes	4692	0.00	106	360	1	Rural	N
LP001098	Male	Yes	0	Graduate	No	3500	1667.00	114	360	1	Semiurban	Y
LP001100	Male	No	3+	Graduate	No	12500	3000.00	320	360	1	Rural	N
LP001106	Male	Yes	0	Graduate	No	2275	2067.00	NA	360	1	Urban	Y
LP001109	Male	Yes	0	Graduate	No	1828	1330.00	100	NA	0	Urban	N
LP001112	Female	Yes	0	Graduate	No	3667	1459.00	144	360	1	Semiurban	Y
LP001114	Male	No	0	Graduate	No	4166	7210.00	184	360	1	Urban	Y
LP001116	Male	No	0	Not Graduate	No	3748	1668.00	110	360	1	Semiurban	Y
LP001119	Male	No	0	Graduate	No	3600	0.00	80	360	1	Urban	N
LP001120	Male	No	0	Graduate	No	1800	1213.00	47	360	1	Urban	Y
LP001123	Male	Yes	0	Graduate	No	2400	0.00	75	360	NA	Urban	Y
LP001131	Male	Yes	0	Graduate	No	3941	2336.00	134	360	1	Semiurban	Y
LP001136	Male	Yes	0	Not Graduate	Yes	4695	0.00	96	NA	1	Urban	Y
LP001137	Female	No	0	Graduate	No	3410	0.00	88	NA	1	Urban	Y
LP001138	Male	Yes	1	Graduate	No	5649	0.00	44	360	1	Urban	Y
LP001144	Male	Yes	0	Graduate	No	5821	0.00	144	360	1	Urban	Y
LP001146	Female	Yes	0	Graduate	No	2645	3440.00	120	360	0	Urban	N
LP001151	Female	No	0	Graduate	No	4000	2275.00	144	360	1	Semiurban	Y
LP001155	Female	Yes	0	Not Graduate	No	1928	1644.00	100	360	1	Semiurban	Y
LP001157	Female	No	0	Graduate	No	3086	0.00	120	360	1	Semiurban	Y
LP001164	Female	No	0	Graduate	No	4230	0.00	112	360	1	Semiurban	N
LP001179	Male	Yes	2	Graduate	No	4616	0.00	134	360	1	Urban	N
LP001186	Female	Yes	1	Graduate	Yes	11500	0.00	286	360	0	Urban	N
LP001194	Male	Yes	2	Graduate	No	2708	1167.00	97	360	1	Semiurban	Y
LP001195	Male	Yes	0	Graduate	No	2132	1591.00	96	360	1	Semiurban	Y
LP001197	Male	Yes	0	Graduate	No	3366	2200.00	135	360	1	Rural	N
LP001198	Male	Yes	1	Graduate	No	8080	2250.00	180	360	1	Urban	Y
LP001199	Male	Yes	2	Not Graduate	No	3357	2859.00	144	360	1	Urban	Y
LP001205	Male	Yes	0	Graduate	No	2500	3796.00	120	360	1	Urban	Y
LP001206	Male	Yes	3+	Graduate	No	3029	0.00	99	360	1	Urban	Y
LP001207	Male	Yes	0	Not Graduate	Yes	2609	3449.00	165	180	0	Rural	N
LP001213	Male	Yes	1	Graduate	No	4945	0.00	NA	360	0	Rural	N
LP001222	Female	No	0	Graduate	No	4166	0.00	116	360	0	Semiurban	N
LP001225	Male	Yes	0	Graduate	No	5726	4595.00	258	360	1	Semiurban	N
LP001228	Male	No	0	Not Graduate	No	3200	2254.00	126	180	0	Urban	N
LP001233	Male	Yes	1	Graduate	No	10750	0.00	312	360	1	Urban	Y
LP001238	Male	Yes	3+	Not Graduate	Yes	7100	0.00	125	60	1	Urban	Y
LP001241	Female	No	0	Graduate	No	4300	0.00	136	360	0	Semiurban	N
LP001243	Male	Yes	0	Graduate	No	3208	3066.00	172	360	1	Urban	Y
LP001245	Male	Yes	2	Not Graduate	Yes	1875	1875.00	97	360	1	Semiurban	Y
LP001248	Male	No	0	Graduate	No	3500	0.00	81	300	1	Semiurban	Y
LP001250	Male	Yes	3+	Not Graduate	No	4755	0.00	95	NA	0	Semiurban	N
LP001253	Male	Yes	3+	Graduate	Yes	5266	1774.00	187	360	1	Semiurban	Y
LP001255	Male	No	0	Graduate	No	3750	0.00	113	480	1	Urban	N
LP001256	Male	No	0	Graduate	No	3750	4750.00	176	360	1	Urban	N
LP001259	Male	Yes	1	Graduate	Yes	1000	3022.00	110	360	1	Urban	N
LP001263	Male	Yes	3+	Graduate	No	3167	4000.00	180	300	0	Semiurban	N
LP001264	Male	Yes	3+	Not Graduate	Yes	3333	2166.00	130	360	NA	Semiurban	Y
LP001265	Female	No	0	Graduate	No	3846	0.00	111	360	1	Semiurban	Y
LP001266	Male	Yes	1	Graduate	Yes	2395	0.00	NA	360	1	Semiurban	Y
LP001267	Female	Yes	2	Graduate	No	1378	1881.00	167	360	1	Urban	N
LP001273	Male	Yes	0	Graduate	No	6000	2250.00	265	360	NA	Semiurban	N
LP001275	Male	Yes	1	Graduate	No	3988	0.00	50	240	1	Urban	Y
LP001279	Male	No	0	Graduate	No	2366	2531.00	136	360	1	Semiurban	Y
LP001280	Male	Yes	2	Not Graduate	No	3333	2000.00	99	360	NA	Semiurban	Y
LP001282	Male	Yes	0	Graduate	No	2500	2118.00	104	360	1	Semiurban	Y
LP001289	Male	No	0	Graduate	No	8566	0.00	210	360	1	Urban	Y
LP001310	Male	Yes	0	Graduate	No	5695	4167.00	175	360	1	Semiurban	Y
LP001316	Male	Yes	0	Graduate	No	2958	2900.00	131	360	1	Semiurban	Y
LP001318	Male	Yes	2	Graduate	No	6250	5654.00	188	180	1	Semiurban	Y
LP001319	Male	Yes	2	Not Graduate	No	3273	1820.00	81	360	1	Urban	Y
LP001322	Male	No	0	Graduate	No	4133	0.00	122	360	1	Semiurban	Y
LP001325	Male	No	0	Not Graduate	No	3620	0.00	25	120	1	Semiurban	Y
LP001326	Male	No	0	Graduate	NA	6782	0.00	NA	360	NA	Urban	N
LP001327	Female	Yes	0	Graduate	No	2484	2302.00	137	360	1	Semiurban	Y
LP001333	Male	Yes	0	Graduate	No	1977	997.00	50	360	1	Semiurban	Y
LP001334	Male	Yes	0	Not Graduate	No	4188	0.00	115	180	1	Semiurban	Y
LP001343	Male	Yes	0	Graduate	No	1759	3541.00	131	360	1	Semiurban	Y
LP001345	Male	Yes	2	Not Graduate	No	4288	3263.00	133	180	1	Urban	Y
LP001349	Male	No	0	Graduate	No	4843	3806.00	151	360	1	Semiurban	Y
LP001350	Male	Yes	NA	Graduate	No	13650	0.00	NA	360	1	Urban	Y
LP001356	Male	Yes	0	Graduate	No	4652	3583.00	NA	360	1	Semiurban	Y
LP001357	Male	NA	NA	Graduate	No	3816	754.00	160	360	1	Urban	Y
LP001367	Male	Yes	1	Graduate	No	3052	1030.00	100	360	1	Urban	Y
LP001369	Male	Yes	2	Graduate	No	11417	1126.00	225	360	1	Urban	Y
LP001370	Male	No	0	Not Graduate	NA	7333	0.00	120	360	1	Rural	N
LP001379	Male	Yes	2	Graduate	No	3800	3600.00	216	360	0	Urban	N
LP001384	Male	Yes	3+	Not Graduate	No	2071	754.00	94	480	1	Semiurban	Y
LP001385	Male	No	0	Graduate	No	5316	0.00	136	360	1	Urban	Y
LP001387	Female	Yes	0	Graduate	NA	2929	2333.00	139	360	1	Semiurban	Y
LP001391	Male	Yes	0	Not Graduate	No	3572	4114.00	152	NA	0	Rural	N
LP001392	Female	No	1	Graduate	Yes	7451	0.00	NA	360	1	Semiurban	Y
LP001398	Male	No	0	Graduate	NA	5050	0.00	118	360	1	Semiurban	Y
LP001401	Male	Yes	1	Graduate	No	14583	0.00	185	180	1	Rural	Y
LP001404	Female	Yes	0	Graduate	No	3167	2283.00	154	360	1	Semiurban	Y
LP001405	Male	Yes	1	Graduate	No	2214	1398.00	85	360	NA	Urban	Y
LP001421	Male	Yes	0	Graduate	No	5568	2142.00	175	360	1	Rural	N
LP001422	Female	No	0	Graduate	No	10408	0.00	259	360	1	Urban	Y
LP001426	Male	Yes	NA	Graduate	No	5667	2667.00	180	360	1	Rural	Y
LP001430	Female	No	0	Graduate	No	4166	0.00	44	360	1	Semiurban	Y
LP001431	Female	No	0	Graduate	No	2137	8980.00	137	360	0	Semiurban	Y
LP001432	Male	Yes	2	Graduate	No	2957	0.00	81	360	1	Semiurban	Y
LP001439	Male	Yes	0	Not Graduate	No	4300	2014.00	194	360	1	Rural	Y
LP001443	Female	No	0	Graduate	No	3692	0.00	93	360	NA	Rural	Y
LP001448	NA	Yes	3+	Graduate	No	23803	0.00	370	360	1	Rural	Y
LP001449	Male	No	0	Graduate	No	3865	1640.00	NA	360	1	Rural	Y
LP001451	Male	Yes	1	Graduate	Yes	10513	3850.00	160	180	0	Urban	N
LP001465	Male	Yes	0	Graduate	No	6080	2569.00	182	360	NA	Rural	N
LP001469	Male	No	0	Graduate	Yes	20166	0.00	650	480	NA	Urban	Y
LP001473	Male	No	0	Graduate	No	2014	1929.00	74	360	1	Urban	Y
LP001478	Male	No	0	Graduate	No	2718	0.00	70	360	1	Semiurban	Y
LP001482	Male	Yes	0	Graduate	Yes	3459	0.00	25	120	1	Semiurban	Y
LP001487	Male	No	0	Graduate	No	4895	0.00	102	360	1	Semiurban	Y
LP001488	Male	Yes	3+	Graduate	No	4000	7750.00	290	360	1	Semiurban	N
LP001489	Female	Yes	0	Graduate	No	4583	0.00	84	360	1	Rural	N
LP001491	Male	Yes	2	Graduate	Yes	3316	3500.00	88	360	1	Urban	Y
LP001492	Male	No	0	Graduate	No	14999	0.00	242	360	0	Semiurban	N
LP001493	Male	Yes	2	Not Graduate	No	4200	1430.00	129	360	1	Rural	N
LP001497	Male	Yes	2	Graduate	No	5042	2083.00	185	360	1	Rural	N
LP001498	Male	No	0	Graduate	No	5417	0.00	168	360	1	Urban	Y
LP001504	Male	No	0	Graduate	Yes	6950	0.00	175	180	1	Semiurban	Y
LP001507	Male	Yes	0	Graduate	No	2698	2034.00	122	360	1	Semiurban	Y
LP001508	Male	Yes	2	Graduate	No	11757	0.00	187	180	1	Urban	Y
LP001514	Female	Yes	0	Graduate	No	2330	4486.00	100	360	1	Semiurban	Y
LP001516	Female	Yes	2	Graduate	No	14866	0.00	70	360	1	Urban	Y
LP001518	Male	Yes	1	Graduate	No	1538	1425.00	30	360	1	Urban	Y
LP001519	Female	No	0	Graduate	No	10000	1666.00	225	360	1	Rural	N
LP001520	Male	Yes	0	Graduate	No	4860	830.00	125	360	1	Semiurban	Y
LP001528	Male	No	0	Graduate	No	6277	0.00	118	360	0	Rural	N
LP001529	Male	Yes	0	Graduate	Yes	2577	3750.00	152	360	1	Rural	Y
LP001531	Male	No	0	Graduate	No	9166	0.00	244	360	1	Urban	N
LP001532	Male	Yes	2	Not Graduate	No	2281	0.00	113	360	1	Rural	N
LP001535	Male	No	0	Graduate	No	3254	0.00	50	360	1	Urban	Y
LP001536	Male	Yes	3+	Graduate	No	39999	0.00	600	180	0	Semiurban	Y
LP001541	Male	Yes	1	Graduate	No	6000	0.00	160	360	NA	Rural	Y
LP001543	Male	Yes	1	Graduate	No	9538	0.00	187	360	1	Urban	Y
LP001546	Male	No	0	Graduate	NA	2980	2083.00	120	360	1	Rural	Y
LP001552	Male	Yes	0	Graduate	No	4583	5625.00	255	360	1	Semiurban	Y
LP001560	Male	Yes	0	Not Graduate	No	1863	1041.00	98	360	1	Semiurban	Y
LP001562	Male	Yes	0	Graduate	No	7933	0.00	275	360	1	Urban	N
LP001565	Male	Yes	1	Graduate	No	3089	1280.00	121	360	0	Semiurban	N
LP001570	Male	Yes	2	Graduate	No	4167	1447.00	158	360	1	Rural	Y
LP001572	Male	Yes	0	Graduate	No	9323	0.00	75	180	1	Urban	Y
LP001574	Male	Yes	0	Graduate	No	3707	3166.00	182	NA	1	Rural	Y
LP001577	Female	Yes	0	Graduate	No	4583	0.00	112	360	1	Rural	N
LP001578	Male	Yes	0	Graduate	No	2439	3333.00	129	360	1	Rural	Y
LP001579	Male	No	0	Graduate	No	2237	0.00	63	480	0	Semiurban	N
LP001580	Male	Yes	2	Graduate	No	8000	0.00	200	360	1	Semiurban	Y
LP001581	Male	Yes	0	Not Graduate	NA	1820	1769.00	95	360	1	Rural	Y
LP001585	NA	Yes	3+	Graduate	No	51763	0.00	700	300	1	Urban	Y
LP001586	Male	Yes	3+	Not Graduate	No	3522	0.00	81	180	1	Rural	N
LP001594	Male	Yes	0	Graduate	No	5708	5625.00	187	360	1	Semiurban	Y
LP001603	Male	Yes	0	Not Graduate	Yes	4344	736.00	87	360	1	Semiurban	N
LP001606	Male	Yes	0	Graduate	No	3497	1964.00	116	360	1	Rural	Y
LP001608	Male	Yes	2	Graduate	No	2045	1619.00	101	360	1	Rural	Y
LP001610	Male	Yes	3+	Graduate	No	5516	11300.00	495	360	0	Semiurban	N
LP001616	Male	Yes	1	Graduate	No	3750	0.00	116	360	1	Semiurban	Y
LP001630	Male	No	0	Not Graduate	No	2333	1451.00	102	480	0	Urban	N
LP001633	Male	Yes	1	Graduate	No	6400	7250.00	180	360	0	Urban	N
LP001634	Male	No	0	Graduate	No	1916	5063.00	67	360	NA	Rural	N
LP001636	Male	Yes	0	Graduate	No	4600	0.00	73	180	1	Semiurban	Y
LP001637	Male	Yes	1	Graduate	No	33846	0.00	260	360	1	Semiurban	N
LP001639	Female	Yes	0	Graduate	No	3625	0.00	108	360	1	Semiurban	Y
LP001640	Male	Yes	0	Graduate	Yes	39147	4750.00	120	360	1	Semiurban	Y
LP001641	Male	Yes	1	Graduate	Yes	2178	0.00	66	300	0	Rural	N
LP001643	Male	Yes	0	Graduate	No	2383	2138.00	58	360	NA	Rural	Y
LP001644	NA	Yes	0	Graduate	Yes	674	5296.00	168	360	1	Rural	Y
LP001647	Male	Yes	0	Graduate	No	9328	0.00	188	180	1	Rural	Y
LP001653	Male	No	0	Not Graduate	No	4885	0.00	48	360	1	Rural	Y
LP001656	Male	No	0	Graduate	No	12000	0.00	164	360	1	Semiurban	N
LP001657	Male	Yes	0	Not Graduate	No	6033	0.00	160	360	1	Urban	N
LP001658	Male	No	0	Graduate	No	3858	0.00	76	360	1	Semiurban	Y
LP001664	Male	No	0	Graduate	No	4191	0.00	120	360	1	Rural	Y
LP001665	Male	Yes	1	Graduate	No	3125	2583.00	170	360	1	Semiurban	N
LP001666	Male	No	0	Graduate	No	8333	3750.00	187	360	1	Rural	Y
LP001669	Female	No	0	Not Graduate	No	1907	2365.00	120	NA	1	Urban	Y
LP001671	Female	Yes	0	Graduate	No	3416	2816.00	113	360	NA	Semiurban	Y
LP001673	Male	No	0	Graduate	Yes	11000	0.00	83	360	1	Urban	N
LP001674	Male	Yes	1	Not Graduate	No	2600	2500.00	90	360	1	Semiurban	Y
LP001677	Male	No	2	Graduate	No	4923	0.00	166	360	0	Semiurban	Y
LP001682	Male	Yes	3+	Not Graduate	No	3992	0.00	NA	180	1	Urban	N
LP001688	Male	Yes	1	Not Graduate	No	3500	1083.00	135	360	1	Urban	Y
LP001691	Male	Yes	2	Not Graduate	No	3917	0.00	124	360	1	Semiurban	Y
LP001692	Female	No	0	Not Graduate	No	4408	0.00	120	360	1	Semiurban	Y
LP001693	Female	No	0	Graduate	No	3244	0.00	80	360	1	Urban	Y
LP001698	Male	No	0	Not Graduate	No	3975	2531.00	55	360	1	Rural	Y
LP001699	Male	No	0	Graduate	No	2479	0.00	59	360	1	Urban	Y
LP001702	Male	No	0	Graduate	No	3418	0.00	127	360	1	Semiurban	N
LP001708	Female	No	0	Graduate	No	10000	0.00	214	360	1	Semiurban	N
LP001711	Male	Yes	3+	Graduate	No	3430	1250.00	128	360	0	Semiurban	N
LP001713	Male	Yes	1	Graduate	Yes	7787	0.00	240	360	1	Urban	Y
LP001715	Male	Yes	3+	Not Graduate	Yes	5703	0.00	130	360	1	Rural	Y
LP001716	Male	Yes	0	Graduate	No	3173	3021.00	137	360	1	Urban	Y
LP001720	Male	Yes	3+	Not Graduate	No	3850	983.00	100	360	1	Semiurban	Y
LP001722	Male	Yes	0	Graduate	No	150	1800.00	135	360	1	Rural	N
LP001726	Male	Yes	0	Graduate	No	3727	1775.00	131	360	1	Semiurban	Y
LP001732	Male	Yes	2	Graduate	NA	5000	0.00	72	360	0	Semiurban	N
LP001734	Female	Yes	2	Graduate	No	4283	2383.00	127	360	NA	Semiurban	Y
LP001736	Male	Yes	0	Graduate	No	2221	0.00	60	360	0	Urban	N
LP001743	Male	Yes	2	Graduate	No	4009	1717.00	116	360	1	Semiurban	Y
LP001744	Male	No	0	Graduate	No	2971	2791.00	144	360	1	Semiurban	Y
LP001749	Male	Yes	0	Graduate	No	7578	1010.00	175	NA	1	Semiurban	Y
LP001750	Male	Yes	0	Graduate	No	6250	0.00	128	360	1	Semiurban	Y
LP001751	Male	Yes	0	Graduate	No	3250	0.00	170	360	1	Rural	N
LP001754	Male	Yes	NA	Not Graduate	Yes	4735	0.00	138	360	1	Urban	N
LP001758	Male	Yes	2	Graduate	No	6250	1695.00	210	360	1	Semiurban	Y
LP001760	Male	NA	NA	Graduate	No	4758	0.00	158	480	1	Semiurban	Y
LP001761	Male	No	0	Graduate	Yes	6400	0.00	200	360	1	Rural	Y
LP001765	Male	Yes	1	Graduate	No	2491	2054.00	104	360	1	Semiurban	Y
LP001768	Male	Yes	0	Graduate	NA	3716	0.00	42	180	1	Rural	Y
LP001770	Male	No	0	Not Graduate	No	3189	2598.00	120	NA	1	Rural	Y
LP001776	Female	No	0	Graduate	No	8333	0.00	280	360	1	Semiurban	Y
LP001778	Male	Yes	1	Graduate	No	3155	1779.00	140	360	1	Semiurban	Y
LP001784	Male	Yes	1	Graduate	No	5500	1260.00	170	360	1	Rural	Y
LP001786	Male	Yes	0	Graduate	NA	5746	0.00	255	360	NA	Urban	N
LP001788	Female	No	0	Graduate	Yes	3463	0.00	122	360	NA	Urban	Y
LP001790	Female	No	1	Graduate	No	3812	0.00	112	360	1	Rural	Y
LP001792	Male	Yes	1	Graduate	No	3315	0.00	96	360	1	Semiurban	Y
LP001798	Male	Yes	2	Graduate	No	5819	5000.00	120	360	1	Rural	Y
LP001800	Male	Yes	1	Not Graduate	No	2510	1983.00	140	180	1	Urban	N
LP001806	Male	No	0	Graduate	No	2965	5701.00	155	60	1	Urban	Y
LP001807	Male	Yes	2	Graduate	Yes	6250	1300.00	108	360	1	Rural	Y
LP001811	Male	Yes	0	Not Graduate	No	3406	4417.00	123	360	1	Semiurban	Y
LP001813	Male	No	0	Graduate	Yes	6050	4333.00	120	180	1	Urban	N
LP001814	Male	Yes	2	Graduate	No	9703	0.00	112	360	1	Urban	Y
LP001819	Male	Yes	1	Not Graduate	No	6608	0.00	137	180	1	Urban	Y
LP001824	Male	Yes	1	Graduate	No	2882	1843.00	123	480	1	Semiurban	Y
LP001825	Male	Yes	0	Graduate	No	1809	1868.00	90	360	1	Urban	Y
LP001835	Male	Yes	0	Not Graduate	No	1668	3890.00	201	360	0	Semiurban	N
LP001836	Female	No	2	Graduate	No	3427	0.00	138	360	1	Urban	N
LP001841	Male	No	0	Not Graduate	Yes	2583	2167.00	104	360	1	Rural	Y
LP001843	Male	Yes	1	Not Graduate	No	2661	7101.00	279	180	1	Semiurban	Y
LP001844	Male	No	0	Graduate	Yes	16250	0.00	192	360	0	Urban	N
LP001846	Female	No	3+	Graduate	No	3083	0.00	255	360	1	Rural	Y
LP001849	Male	No	0	Not Graduate	No	6045	0.00	115	360	0	Rural	N
LP001854	Male	Yes	3+	Graduate	No	5250	0.00	94	360	1	Urban	N
LP001859	Male	Yes	0	Graduate	No	14683	2100.00	304	360	1	Rural	N
LP001864	Male	Yes	3+	Not Graduate	No	4931	0.00	128	360	NA	Semiurban	N
LP001865	Male	Yes	1	Graduate	No	6083	4250.00	330	360	NA	Urban	Y
LP001868	Male	No	0	Graduate	No	2060	2209.00	134	360	1	Semiurban	Y
LP001870	Female	No	1	Graduate	No	3481	0.00	155	36	1	Semiurban	N
LP001871	Female	No	0	Graduate	No	7200	0.00	120	360	1	Rural	Y
LP001872	Male	No	0	Graduate	Yes	5166	0.00	128	360	1	Semiurban	Y
LP001875	Male	No	0	Graduate	No	4095	3447.00	151	360	1	Rural	Y
LP001877	Male	Yes	2	Graduate	No	4708	1387.00	150	360	1	Semiurban	Y
LP001882	Male	Yes	3+	Graduate	No	4333	1811.00	160	360	0	Urban	Y
LP001883	Female	No	0	Graduate	NA	3418	0.00	135	360	1	Rural	N
LP001884	Female	No	1	Graduate	No	2876	1560.00	90	360	1	Urban	Y
LP001888	Female	No	0	Graduate	No	3237	0.00	30	360	1	Urban	Y
LP001891	Male	Yes	0	Graduate	No	11146	0.00	136	360	1	Urban	Y
LP001892	Male	No	0	Graduate	No	2833	1857.00	126	360	1	Rural	Y
LP001894	Male	Yes	0	Graduate	No	2620	2223.00	150	360	1	Semiurban	Y
LP001896	Male	Yes	2	Graduate	No	3900	0.00	90	360	1	Semiurban	Y
LP001900	Male	Yes	1	Graduate	No	2750	1842.00	115	360	1	Semiurban	Y
LP001903	Male	Yes	0	Graduate	No	3993	3274.00	207	360	1	Semiurban	Y
LP001904	Male	Yes	0	Graduate	No	3103	1300.00	80	360	1	Urban	Y
LP001907	Male	Yes	0	Graduate	No	14583	0.00	436	360	1	Semiurban	Y
LP001908	Female	Yes	0	Not Graduate	No	4100	0.00	124	360	NA	Rural	Y
LP001910	Male	No	1	Not Graduate	Yes	4053	2426.00	158	360	0	Urban	N
LP001914	Male	Yes	0	Graduate	No	3927	800.00	112	360	1	Semiurban	Y
LP001915	Male	Yes	2	Graduate	No	2301	985.80	78	180	1	Urban	Y
LP001917	Female	No	0	Graduate	No	1811	1666.00	54	360	1	Urban	Y
LP001922	Male	Yes	0	Graduate	No	20667	0.00	NA	360	1	Rural	N
LP001924	Male	No	0	Graduate	No	3158	3053.00	89	360	1	Rural	Y
LP001925	Female	No	0	Graduate	Yes	2600	1717.00	99	300	1	Semiurban	N
LP001926	Male	Yes	0	Graduate	No	3704	2000.00	120	360	1	Rural	Y
LP001931	Female	No	0	Graduate	No	4124	0.00	115	360	1	Semiurban	Y
LP001935	Male	No	0	Graduate	No	9508	0.00	187	360	1	Rural	Y
LP001936	Male	Yes	0	Graduate	No	3075	2416.00	139	360	1	Rural	Y
LP001938	Male	Yes	2	Graduate	No	4400	0.00	127	360	0	Semiurban	N
LP001940	Male	Yes	2	Graduate	No	3153	1560.00	134	360	1	Urban	Y
LP001945	Female	No	NA	Graduate	No	5417	0.00	143	480	0	Urban	N
LP001947	Male	Yes	0	Graduate	No	2383	3334.00	172	360	1	Semiurban	Y
LP001949	Male	Yes	3+	Graduate	NA	4416	1250.00	110	360	1	Urban	Y
LP001953	Male	Yes	1	Graduate	No	6875	0.00	200	360	1	Semiurban	Y
LP001954	Female	Yes	1	Graduate	No	4666	0.00	135	360	1	Urban	Y
LP001955	Female	No	0	Graduate	No	5000	2541.00	151	480	1	Rural	N
LP001963	Male	Yes	1	Graduate	No	2014	2925.00	113	360	1	Urban	N
LP001964	Male	Yes	0	Not Graduate	No	1800	2934.00	93	360	0	Urban	N
LP001972	Male	Yes	NA	Not Graduate	No	2875	1750.00	105	360	1	Semiurban	Y
LP001974	Female	No	0	Graduate	No	5000	0.00	132	360	1	Rural	Y
LP001977	Male	Yes	1	Graduate	No	1625	1803.00	96	360	1	Urban	Y
LP001978	Male	No	0	Graduate	No	4000	2500.00	140	360	1	Rural	Y
LP001990	Male	No	0	Not Graduate	No	2000	0.00	NA	360	1	Urban	N
LP001993	Female	No	0	Graduate	No	3762	1666.00	135	360	1	Rural	Y
LP001994	Female	No	0	Graduate	No	2400	1863.00	104	360	0	Urban	N
LP001996	Male	No	0	Graduate	No	20233	0.00	480	360	1	Rural	N
LP001998	Male	Yes	2	Not Graduate	No	7667	0.00	185	360	NA	Rural	Y
LP002002	Female	No	0	Graduate	No	2917	0.00	84	360	1	Semiurban	Y
LP002004	Male	No	0	Not Graduate	No	2927	2405.00	111	360	1	Semiurban	Y
LP002006	Female	No	0	Graduate	No	2507	0.00	56	360	1	Rural	Y
LP002008	Male	Yes	2	Graduate	Yes	5746	0.00	144	84	NA	Rural	Y
LP002024	NA	Yes	0	Graduate	No	2473	1843.00	159	360	1	Rural	N
LP002031	Male	Yes	1	Not Graduate	No	3399	1640.00	111	180	1	Urban	Y
LP002035	Male	Yes	2	Graduate	No	3717	0.00	120	360	1	Semiurban	Y
LP002036	Male	Yes	0	Graduate	No	2058	2134.00	88	360	NA	Urban	Y
LP002043	Female	No	1	Graduate	No	3541	0.00	112	360	NA	Semiurban	Y
LP002050	Male	Yes	1	Graduate	Yes	10000	0.00	155	360	1	Rural	N
LP002051	Male	Yes	0	Graduate	No	2400	2167.00	115	360	1	Semiurban	Y
LP002053	Male	Yes	3+	Graduate	No	4342	189.00	124	360	1	Semiurban	Y
LP002054	Male	Yes	2	Not Graduate	No	3601	1590.00	NA	360	1	Rural	Y
LP002055	Female	No	0	Graduate	No	3166	2985.00	132	360	NA	Rural	Y
LP002065	Male	Yes	3+	Graduate	No	15000	0.00	300	360	1	Rural	Y
LP002067	Male	Yes	1	Graduate	Yes	8666	4983.00	376	360	0	Rural	N
LP002068	Male	No	0	Graduate	No	4917	0.00	130	360	0	Rural	Y
LP002082	Male	Yes	0	Graduate	Yes	5818	2160.00	184	360	1	Semiurban	Y
LP002086	Female	Yes	0	Graduate	No	4333	2451.00	110	360	1	Urban	N
LP002087	Female	No	0	Graduate	No	2500	0.00	67	360	1	Urban	Y
LP002097	Male	No	1	Graduate	No	4384	1793.00	117	360	1	Urban	Y
LP002098	Male	No	0	Graduate	No	2935	0.00	98	360	1	Semiurban	Y
LP002100	Male	No	NA	Graduate	No	2833	0.00	71	360	1	Urban	Y
LP002101	Male	Yes	0	Graduate	NA	63337	0.00	490	180	1	Urban	Y
LP002103	NA	Yes	1	Graduate	Yes	9833	1833.00	182	180	1	Urban	Y
LP002106	Male	Yes	NA	Graduate	Yes	5503	4490.00	70	NA	1	Semiurban	Y
LP002110	Male	Yes	1	Graduate	NA	5250	688.00	160	360	1	Rural	Y
LP002112	Male	Yes	2	Graduate	Yes	2500	4600.00	176	360	1	Rural	Y
LP002113	Female	No	3+	Not Graduate	No	1830	0.00	NA	360	0	Urban	N
LP002114	Female	No	0	Graduate	No	4160	0.00	71	360	1	Semiurban	Y
LP002115	Male	Yes	3+	Not Graduate	No	2647	1587.00	173	360	1	Rural	N
LP002116	Female	No	0	Graduate	No	2378	0.00	46	360	1	Rural	N
LP002119	Male	Yes	1	Not Graduate	No	4554	1229.00	158	360	1	Urban	Y
LP002126	Male	Yes	3+	Not Graduate	No	3173	0.00	74	360	1	Semiurban	Y
LP002128	Male	Yes	2	Graduate	NA	2583	2330.00	125	360	1	Rural	Y
LP002129	Male	Yes	0	Graduate	No	2499	2458.00	160	360	1	Semiurban	Y
LP002130	Male	Yes	NA	Not Graduate	No	3523	3230.00	152	360	0	Rural	N
LP002131	Male	Yes	2	Not Graduate	No	3083	2168.00	126	360	1	Urban	Y
LP002137	Male	Yes	0	Graduate	No	6333	4583.00	259	360	NA	Semiurban	Y
LP002138	Male	Yes	0	Graduate	No	2625	6250.00	187	360	1	Rural	Y
LP002139	Male	Yes	0	Graduate	No	9083	0.00	228	360	1	Semiurban	Y
LP002140	Male	No	0	Graduate	No	8750	4167.00	308	360	1	Rural	N
LP002141	Male	Yes	3+	Graduate	No	2666	2083.00	95	360	1	Rural	Y
LP002142	Female	Yes	0	Graduate	Yes	5500	0.00	105	360	0	Rural	N
LP002143	Female	Yes	0	Graduate	No	2423	505.00	130	360	1	Semiurban	Y
LP002144	Female	No	NA	Graduate	No	3813	0.00	116	180	1	Urban	Y
LP002149	Male	Yes	2	Graduate	No	8333	3167.00	165	360	1	Rural	Y
LP002151	Male	Yes	1	Graduate	No	3875	0.00	67	360	1	Urban	N
LP002158	Male	Yes	0	Not Graduate	No	3000	1666.00	100	480	0	Urban	N
LP002160	Male	Yes	3+	Graduate	No	5167	3167.00	200	360	1	Semiurban	Y
LP002161	Female	No	1	Graduate	No	4723	0.00	81	360	1	Semiurban	N
LP002170	Male	Yes	2	Graduate	No	5000	3667.00	236	360	1	Semiurban	Y
LP002175	Male	Yes	0	Graduate	No	4750	2333.00	130	360	1	Urban	Y
LP002178	Male	Yes	0	Graduate	No	3013	3033.00	95	300	NA	Urban	Y
LP002180	Male	No	0	Graduate	Yes	6822	0.00	141	360	1	Rural	Y
LP002181	Male	No	0	Not Graduate	No	6216	0.00	133	360	1	Rural	N
LP002187	Male	No	0	Graduate	No	2500	0.00	96	480	1	Semiurban	N
LP002188	Male	No	0	Graduate	No	5124	0.00	124	NA	0	Rural	N
LP002190	Male	Yes	1	Graduate	No	6325	0.00	175	360	1	Semiurban	Y
LP002191	Male	Yes	0	Graduate	No	19730	5266.00	570	360	1	Rural	N
LP002194	Female	No	0	Graduate	Yes	15759	0.00	55	360	1	Semiurban	Y
LP002197	Male	Yes	2	Graduate	No	5185	0.00	155	360	1	Semiurban	Y
LP002201	Male	Yes	2	Graduate	Yes	9323	7873.00	380	300	1	Rural	Y
LP002205	Male	No	1	Graduate	No	3062	1987.00	111	180	0	Urban	N
LP002209	Female	No	0	Graduate	NA	2764	1459.00	110	360	1	Urban	Y
LP002211	Male	Yes	0	Graduate	No	4817	923.00	120	180	1	Urban	Y
LP002219	Male	Yes	3+	Graduate	No	8750	4996.00	130	360	1	Rural	Y
LP002223	Male	Yes	0	Graduate	No	4310	0.00	130	360	NA	Semiurban	Y
LP002224	Male	No	0	Graduate	No	3069	0.00	71	480	1	Urban	N
LP002225	Male	Yes	2	Graduate	No	5391	0.00	130	360	1	Urban	Y
LP002226	Male	Yes	0	Graduate	NA	3333	2500.00	128	360	1	Semiurban	Y
LP002229	Male	No	0	Graduate	No	5941	4232.00	296	360	1	Semiurban	Y
LP002231	Female	No	0	Graduate	No	6000	0.00	156	360	1	Urban	Y
LP002234	Male	No	0	Graduate	Yes	7167	0.00	128	360	1	Urban	Y
LP002236	Male	Yes	2	Graduate	No	4566	0.00	100	360	1	Urban	N
LP002237	Male	No	1	Graduate	NA	3667	0.00	113	180	1	Urban	Y
LP002239	Male	No	0	Not Graduate	No	2346	1600.00	132	360	1	Semiurban	Y
LP002243	Male	Yes	0	Not Graduate	No	3010	3136.00	NA	360	0	Urban	N
LP002244	Male	Yes	0	Graduate	No	2333	2417.00	136	360	1	Urban	Y
LP002250	Male	Yes	0	Graduate	No	5488	0.00	125	360	1	Rural	Y
LP002255	Male	No	3+	Graduate	No	9167	0.00	185	360	1	Rural	Y
LP002262	Male	Yes	3+	Graduate	No	9504	0.00	275	360	1	Rural	Y
LP002263	Male	Yes	0	Graduate	No	2583	2115.00	120	360	NA	Urban	Y
LP002265	Male	Yes	2	Not Graduate	No	1993	1625.00	113	180	1	Semiurban	Y
LP002266	Male	Yes	2	Graduate	No	3100	1400.00	113	360	1	Urban	Y
LP002272	Male	Yes	2	Graduate	No	3276	484.00	135	360	NA	Semiurban	Y
LP002277	Female	No	0	Graduate	No	3180	0.00	71	360	0	Urban	N
LP002281	Male	Yes	0	Graduate	No	3033	1459.00	95	360	1	Urban	Y
LP002284	Male	No	0	Not Graduate	No	3902	1666.00	109	360	1	Rural	Y
LP002287	Female	No	0	Graduate	No	1500	1800.00	103	360	0	Semiurban	N
LP002288	Male	Yes	2	Not Graduate	No	2889	0.00	45	180	0	Urban	N
LP002296	Male	No	0	Not Graduate	No	2755	0.00	65	300	1	Rural	N
LP002297	Male	No	0	Graduate	No	2500	20000.00	103	360	1	Semiurban	Y
LP002300	Female	No	0	Not Graduate	No	1963	0.00	53	360	1	Semiurban	Y
LP002301	Female	No	0	Graduate	Yes	7441	0.00	194	360	1	Rural	N
LP002305	Female	No	0	Graduate	No	4547	0.00	115	360	1	Semiurban	Y
LP002308	Male	Yes	0	Not Graduate	No	2167	2400.00	115	360	1	Urban	Y
LP002314	Female	No	0	Not Graduate	No	2213	0.00	66	360	1	Rural	Y
LP002315	Male	Yes	1	Graduate	No	8300	0.00	152	300	0	Semiurban	N
LP002317	Male	Yes	3+	Graduate	No	81000	0.00	360	360	0	Rural	N
LP002318	Female	No	1	Not Graduate	Yes	3867	0.00	62	360	1	Semiurban	N
LP002319	Male	Yes	0	Graduate	NA	6256	0.00	160	360	NA	Urban	Y
LP002328	Male	Yes	0	Not Graduate	No	6096	0.00	218	360	0	Rural	N
LP002332	Male	Yes	0	Not Graduate	No	2253	2033.00	110	360	1	Rural	Y
LP002335	Female	Yes	0	Not Graduate	No	2149	3237.00	178	360	0	Semiurban	N
LP002337	Female	No	0	Graduate	No	2995	0.00	60	360	1	Urban	Y
LP002341	Female	No	1	Graduate	No	2600	0.00	160	360	1	Urban	N
LP002342	Male	Yes	2	Graduate	Yes	1600	20000.00	239	360	1	Urban	N
LP002345	Male	Yes	0	Graduate	No	1025	2773.00	112	360	1	Rural	Y
LP002347	Male	Yes	0	Graduate	No	3246	1417.00	138	360	1	Semiurban	Y
LP002348	Male	Yes	0	Graduate	No	5829	0.00	138	360	1	Rural	Y
LP002357	Female	No	0	Not Graduate	No	2720	0.00	80	NA	0	Urban	N
LP002361	Male	Yes	0	Graduate	No	1820	1719.00	100	360	1	Urban	Y
LP002362	Male	Yes	1	Graduate	No	7250	1667.00	110	NA	0	Urban	N
LP002364	Male	Yes	0	Graduate	No	14880	0.00	96	360	1	Semiurban	Y
LP002366	Male	Yes	0	Graduate	No	2666	4300.00	121	360	1	Rural	Y
LP002367	Female	No	1	Not Graduate	No	4606	0.00	81	360	1	Rural	N
LP002368	Male	Yes	2	Graduate	No	5935	0.00	133	360	1	Semiurban	Y
LP002369	Male	Yes	0	Graduate	No	2920	16.12	87	360	1	Rural	Y
LP002370	Male	No	0	Not Graduate	No	2717	0.00	60	180	1	Urban	Y
LP002377	Female	No	1	Graduate	Yes	8624	0.00	150	360	1	Semiurban	Y
LP002379	Male	No	0	Graduate	No	6500	0.00	105	360	0	Rural	N
LP002386	Male	No	0	Graduate	NA	12876	0.00	405	360	1	Semiurban	Y
LP002387	Male	Yes	0	Graduate	No	2425	2340.00	143	360	1	Semiurban	Y
LP002390	Male	No	0	Graduate	No	3750	0.00	100	360	1	Urban	Y
LP002393	Female	NA	NA	Graduate	No	10047	0.00	NA	240	1	Semiurban	Y
LP002398	Male	No	0	Graduate	No	1926	1851.00	50	360	1	Semiurban	Y
LP002401	Male	Yes	0	Graduate	No	2213	1125.00	NA	360	1	Urban	Y
LP002403	Male	No	0	Graduate	Yes	10416	0.00	187	360	0	Urban	N
LP002407	Female	Yes	0	Not Graduate	Yes	7142	0.00	138	360	1	Rural	Y
LP002408	Male	No	0	Graduate	No	3660	5064.00	187	360	1	Semiurban	Y
LP002409	Male	Yes	0	Graduate	No	7901	1833.00	180	360	1	Rural	Y
LP002418	Male	No	3+	Not Graduate	No	4707	1993.00	148	360	1	Semiurban	Y
LP002422	Male	No	1	Graduate	No	37719	0.00	152	360	1	Semiurban	Y
LP002424	Male	Yes	0	Graduate	No	7333	8333.00	175	300	NA	Rural	Y
LP002429	Male	Yes	1	Graduate	Yes	3466	1210.00	130	360	1	Rural	Y
LP002434	Male	Yes	2	Not Graduate	No	4652	0.00	110	360	1	Rural	Y
LP002435	Male	Yes	0	Graduate	NA	3539	1376.00	55	360	1	Rural	N
LP002443	Male	Yes	2	Graduate	No	3340	1710.00	150	360	0	Rural	N
LP002444	Male	No	1	Not Graduate	Yes	2769	1542.00	190	360	NA	Semiurban	N
LP002446	Male	Yes	2	Not Graduate	No	2309	1255.00	125	360	0	Rural	N
LP002447	Male	Yes	2	Not Graduate	No	1958	1456.00	60	300	NA	Urban	Y
LP002448	Male	Yes	0	Graduate	No	3948	1733.00	149	360	0	Rural	N
LP002449	Male	Yes	0	Graduate	No	2483	2466.00	90	180	0	Rural	Y
LP002453	Male	No	0	Graduate	Yes	7085	0.00	84	360	1	Semiurban	Y
LP002455	Male	Yes	2	Graduate	No	3859	0.00	96	360	1	Semiurban	Y
LP002459	Male	Yes	0	Graduate	No	4301	0.00	118	360	1	Urban	Y
LP002467	Male	Yes	0	Graduate	No	3708	2569.00	173	360	1	Urban	N
LP002472	Male	No	2	Graduate	No	4354	0.00	136	360	1	Rural	Y
LP002473	Male	Yes	0	Graduate	No	8334	0.00	160	360	1	Semiurban	N
LP002478	NA	Yes	0	Graduate	Yes	2083	4083.00	160	360	NA	Semiurban	Y
LP002484	Male	Yes	3+	Graduate	No	7740	0.00	128	180	1	Urban	Y
LP002487	Male	Yes	0	Graduate	No	3015	2188.00	153	360	1	Rural	Y
LP002489	Female	No	1	Not Graduate	NA	5191	0.00	132	360	1	Semiurban	Y
LP002493	Male	No	0	Graduate	No	4166	0.00	98	360	0	Semiurban	N
LP002494	Male	No	0	Graduate	No	6000	0.00	140	360	1	Rural	Y
LP002500	Male	Yes	3+	Not Graduate	No	2947	1664.00	70	180	0	Urban	N
LP002501	NA	Yes	0	Graduate	No	16692	0.00	110	360	1	Semiurban	Y
LP002502	Female	Yes	2	Not Graduate	NA	210	2917.00	98	360	1	Semiurban	Y
LP002505	Male	Yes	0	Graduate	No	4333	2451.00	110	360	1	Urban	N
LP002515	Male	Yes	1	Graduate	Yes	3450	2079.00	162	360	1	Semiurban	Y
LP002517	Male	Yes	1	Not Graduate	No	2653	1500.00	113	180	0	Rural	N
LP002519	Male	Yes	3+	Graduate	No	4691	0.00	100	360	1	Semiurban	Y
LP002522	Female	No	0	Graduate	Yes	2500	0.00	93	360	NA	Urban	Y
LP002524	Male	No	2	Graduate	No	5532	4648.00	162	360	1	Rural	Y
LP002527	Male	Yes	2	Graduate	Yes	16525	1014.00	150	360	1	Rural	Y
LP002529	Male	Yes	2	Graduate	No	6700	1750.00	230	300	1	Semiurban	Y
LP002530	NA	Yes	2	Graduate	No	2873	1872.00	132	360	0	Semiurban	N
LP002531	Male	Yes	1	Graduate	Yes	16667	2250.00	86	360	1	Semiurban	Y
LP002533	Male	Yes	2	Graduate	No	2947	1603.00	NA	360	1	Urban	N
LP002534	Female	No	0	Not Graduate	No	4350	0.00	154	360	1	Rural	Y
LP002536	Male	Yes	3+	Not Graduate	No	3095	0.00	113	360	1	Rural	Y
LP002537	Male	Yes	0	Graduate	No	2083	3150.00	128	360	1	Semiurban	Y
LP002541	Male	Yes	0	Graduate	No	10833	0.00	234	360	1	Semiurban	Y
LP002543	Male	Yes	2	Graduate	No	8333	0.00	246	360	1	Semiurban	Y
LP002544	Male	Yes	1	Not Graduate	No	1958	2436.00	131	360	1	Rural	Y
LP002545	Male	No	2	Graduate	No	3547	0.00	80	360	0	Rural	N
LP002547	Male	Yes	1	Graduate	No	18333	0.00	500	360	1	Urban	N
LP002555	Male	Yes	2	Graduate	Yes	4583	2083.00	160	360	1	Semiurban	Y
LP002556	Male	No	0	Graduate	No	2435	0.00	75	360	1	Urban	N
LP002560	Male	No	0	Not Graduate	No	2699	2785.00	96	360	NA	Semiurban	Y
LP002562	Male	Yes	1	Not Graduate	No	5333	1131.00	186	360	NA	Urban	Y
LP002571	Male	No	0	Not Graduate	No	3691	0.00	110	360	1	Rural	Y
LP002582	Female	No	0	Not Graduate	Yes	17263	0.00	225	360	1	Semiurban	Y
LP002585	Male	Yes	0	Graduate	No	3597	2157.00	119	360	0	Rural	N
LP002586	Female	Yes	1	Graduate	No	3326	913.00	105	84	1	Semiurban	Y
LP002587	Male	Yes	0	Not Graduate	No	2600	1700.00	107	360	1	Rural	Y
LP002588	Male	Yes	0	Graduate	No	4625	2857.00	111	12	NA	Urban	Y
LP002600	Male	Yes	1	Graduate	Yes	2895	0.00	95	360	1	Semiurban	Y
LP002602	Male	No	0	Graduate	No	6283	4416.00	209	360	0	Rural	N
LP002603	Female	No	0	Graduate	No	645	3683.00	113	480	1	Rural	Y
LP002606	Female	No	0	Graduate	No	3159	0.00	100	360	1	Semiurban	Y
LP002615	Male	Yes	2	Graduate	No	4865	5624.00	208	360	1	Semiurban	Y
LP002618	Male	Yes	1	Not Graduate	No	4050	5302.00	138	360	NA	Rural	N
LP002619	Male	Yes	0	Not Graduate	No	3814	1483.00	124	300	1	Semiurban	Y
LP002622	Male	Yes	2	Graduate	No	3510	4416.00	243	360	1	Rural	Y
LP002624	Male	Yes	0	Graduate	No	20833	6667.00	480	360	NA	Urban	Y
LP002625	NA	No	0	Graduate	No	3583	0.00	96	360	1	Urban	N
LP002626	Male	Yes	0	Graduate	Yes	2479	3013.00	188	360	1	Urban	Y
LP002634	Female	No	1	Graduate	No	13262	0.00	40	360	1	Urban	Y
LP002637	Male	No	0	Not Graduate	No	3598	1287.00	100	360	1	Rural	N
LP002640	Male	Yes	1	Graduate	No	6065	2004.00	250	360	1	Semiurban	Y
LP002643	Male	Yes	2	Graduate	No	3283	2035.00	148	360	1	Urban	Y
LP002648	Male	Yes	0	Graduate	No	2130	6666.00	70	180	1	Semiurban	N
LP002652	Male	No	0	Graduate	No	5815	3666.00	311	360	1	Rural	N
LP002659	Male	Yes	3+	Graduate	No	3466	3428.00	150	360	1	Rural	Y
LP002670	Female	Yes	2	Graduate	No	2031	1632.00	113	480	1	Semiurban	Y
LP002682	Male	Yes	NA	Not Graduate	No	3074	1800.00	123	360	0	Semiurban	N
LP002683	Male	No	0	Graduate	No	4683	1915.00	185	360	1	Semiurban	N
LP002684	Female	No	0	Not Graduate	No	3400	0.00	95	360	1	Rural	N
LP002689	Male	Yes	2	Not Graduate	No	2192	1742.00	45	360	1	Semiurban	Y
LP002690	Male	No	0	Graduate	No	2500	0.00	55	360	1	Semiurban	Y
LP002692	Male	Yes	3+	Graduate	Yes	5677	1424.00	100	360	1	Rural	Y
LP002693	Male	Yes	2	Graduate	Yes	7948	7166.00	480	360	1	Rural	Y
LP002697	Male	No	0	Graduate	No	4680	2087.00	NA	360	1	Semiurban	N
LP002699	Male	Yes	2	Graduate	Yes	17500	0.00	400	360	1	Rural	Y
LP002705	Male	Yes	0	Graduate	No	3775	0.00	110	360	1	Semiurban	Y
LP002706	Male	Yes	1	Not Graduate	No	5285	1430.00	161	360	0	Semiurban	Y
LP002714	Male	No	1	Not Graduate	No	2679	1302.00	94	360	1	Semiurban	Y
LP002716	Male	No	0	Not Graduate	No	6783	0.00	130	360	1	Semiurban	Y
LP002717	Male	Yes	0	Graduate	No	1025	5500.00	216	360	NA	Rural	Y
LP002720	Male	Yes	3+	Graduate	No	4281	0.00	100	360	1	Urban	Y
LP002723	Male	No	2	Graduate	No	3588	0.00	110	360	0	Rural	N
LP002729	Male	No	1	Graduate	No	11250	0.00	196	360	NA	Semiurban	N
LP002731	Female	No	0	Not Graduate	Yes	18165	0.00	125	360	1	Urban	Y
LP002732	Male	No	0	Not Graduate	NA	2550	2042.00	126	360	1	Rural	Y
LP002734	Male	Yes	0	Graduate	No	6133	3906.00	324	360	1	Urban	Y
LP002738	Male	No	2	Graduate	No	3617	0.00	107	360	1	Semiurban	Y
LP002739	Male	Yes	0	Not Graduate	No	2917	536.00	66	360	1	Rural	N
LP002740	Male	Yes	3+	Graduate	No	6417	0.00	157	180	1	Rural	Y
LP002741	Female	Yes	1	Graduate	No	4608	2845.00	140	180	1	Semiurban	Y
LP002743	Female	No	0	Graduate	No	2138	0.00	99	360	0	Semiurban	N
LP002753	Female	No	1	Graduate	NA	3652	0.00	95	360	1	Semiurban	Y
LP002755	Male	Yes	1	Not Graduate	No	2239	2524.00	128	360	1	Urban	Y
LP002757	Female	Yes	0	Not Graduate	No	3017	663.00	102	360	NA	Semiurban	Y
LP002767	Male	Yes	0	Graduate	No	2768	1950.00	155	360	1	Rural	Y
LP002768	Male	No	0	Not Graduate	No	3358	0.00	80	36	1	Semiurban	N
LP002772	Male	No	0	Graduate	No	2526	1783.00	145	360	1	Rural	Y
LP002776	Female	No	0	Graduate	No	5000	0.00	103	360	0	Semiurban	N
LP002777	Male	Yes	0	Graduate	No	2785	2016.00	110	360	1	Rural	Y
LP002778	Male	Yes	2	Graduate	Yes	6633	0.00	NA	360	0	Rural	N
LP002784	Male	Yes	1	Not Graduate	No	2492	2375.00	NA	360	1	Rural	Y
LP002785	Male	Yes	1	Graduate	No	3333	3250.00	158	360	1	Urban	Y
LP002788	Male	Yes	0	Not Graduate	No	2454	2333.00	181	360	0	Urban	N
LP002789	Male	Yes	0	Graduate	No	3593	4266.00	132	180	0	Rural	N
LP002792	Male	Yes	1	Graduate	No	5468	1032.00	26	360	1	Semiurban	Y
LP002794	Female	No	0	Graduate	No	2667	1625.00	84	360	NA	Urban	Y
LP002795	Male	Yes	3+	Graduate	Yes	10139	0.00	260	360	1	Semiurban	Y
LP002798	Male	Yes	0	Graduate	No	3887	2669.00	162	360	1	Semiurban	Y
LP002804	Female	Yes	0	Graduate	No	4180	2306.00	182	360	1	Semiurban	Y
LP002807	Male	Yes	2	Not Graduate	No	3675	242.00	108	360	1	Semiurban	Y
LP002813	Female	Yes	1	Graduate	Yes	19484	0.00	600	360	1	Semiurban	Y
LP002820	Male	Yes	0	Graduate	No	5923	2054.00	211	360	1	Rural	Y
LP002821	Male	No	0	Not Graduate	Yes	5800	0.00	132	360	1	Semiurban	Y
LP002832	Male	Yes	2	Graduate	No	8799	0.00	258	360	0	Urban	N
LP002833	Male	Yes	0	Not Graduate	No	4467	0.00	120	360	NA	Rural	Y
LP002836	Male	No	0	Graduate	No	3333	0.00	70	360	1	Urban	Y
LP002837	Male	Yes	3+	Graduate	No	3400	2500.00	123	360	0	Rural	N
LP002840	Female	No	0	Graduate	No	2378	0.00	9	360	1	Urban	N
LP002841	Male	Yes	0	Graduate	No	3166	2064.00	104	360	0	Urban	N
LP002842	Male	Yes	1	Graduate	No	3417	1750.00	186	360	1	Urban	Y
LP002847	Male	Yes	NA	Graduate	No	5116	1451.00	165	360	0	Urban	N
LP002855	Male	Yes	2	Graduate	No	16666	0.00	275	360	1	Urban	Y
LP002862	Male	Yes	2	Not Graduate	No	6125	1625.00	187	480	1	Semiurban	N
LP002863	Male	Yes	3+	Graduate	No	6406	0.00	150	360	1	Semiurban	N
LP002868	Male	Yes	2	Graduate	No	3159	461.00	108	84	1	Urban	Y
LP002872	NA	Yes	0	Graduate	No	3087	2210.00	136	360	0	Semiurban	N
LP002874	Male	No	0	Graduate	No	3229	2739.00	110	360	1	Urban	Y
LP002877	Male	Yes	1	Graduate	No	1782	2232.00	107	360	1	Rural	Y
LP002888	Male	No	0	Graduate	NA	3182	2917.00	161	360	1	Urban	Y
LP002892	Male	Yes	2	Graduate	No	6540	0.00	205	360	1	Semiurban	Y
LP002893	Male	No	0	Graduate	No	1836	33837.00	90	360	1	Urban	N
LP002894	Female	Yes	0	Graduate	No	3166	0.00	36	360	1	Semiurban	Y
LP002898	Male	Yes	1	Graduate	No	1880	0.00	61	360	NA	Rural	N
LP002911	Male	Yes	1	Graduate	No	2787	1917.00	146	360	0	Rural	N
LP002912	Male	Yes	1	Graduate	No	4283	3000.00	172	84	1	Rural	N
LP002916	Male	Yes	0	Graduate	No	2297	1522.00	104	360	1	Urban	Y
LP002917	Female	No	0	Not Graduate	No	2165	0.00	70	360	1	Semiurban	Y
LP002925	NA	No	0	Graduate	No	4750	0.00	94	360	1	Semiurban	Y
LP002926	Male	Yes	2	Graduate	Yes	2726	0.00	106	360	0	Semiurban	N
LP002928	Male	Yes	0	Graduate	No	3000	3416.00	56	180	1	Semiurban	Y
LP002931	Male	Yes	2	Graduate	Yes	6000	0.00	205	240	1	Semiurban	N
LP002933	NA	No	3+	Graduate	Yes	9357	0.00	292	360	1	Semiurban	Y
LP002936	Male	Yes	0	Graduate	No	3859	3300.00	142	180	1	Rural	Y
LP002938	Male	Yes	0	Graduate	Yes	16120	0.00	260	360	1	Urban	Y
LP002940	Male	No	0	Not Graduate	No	3833	0.00	110	360	1	Rural	Y
LP002941	Male	Yes	2	Not Graduate	Yes	6383	1000.00	187	360	1	Rural	N
LP002943	Male	No	NA	Graduate	No	2987	0.00	88	360	0	Semiurban	N
LP002945	Male	Yes	0	Graduate	Yes	9963	0.00	180	360	1	Rural	Y
LP002948	Male	Yes	2	Graduate	No	5780	0.00	192	360	1	Urban	Y
LP002949	Female	No	3+	Graduate	NA	416	41667.00	350	180	NA	Urban	N
LP002950	Male	Yes	0	Not Graduate	NA	2894	2792.00	155	360	1	Rural	Y
LP002953	Male	Yes	3+	Graduate	No	5703	0.00	128	360	1	Urban	Y
LP002958	Male	No	0	Graduate	No	3676	4301.00	172	360	1	Rural	Y
LP002959	Female	Yes	1	Graduate	No	12000	0.00	496	360	1	Semiurban	Y
LP002960	Male	Yes	0	Not Graduate	No	2400	3800.00	NA	180	1	Urban	N
LP002961	Male	Yes	1	Graduate	No	3400	2500.00	173	360	1	Semiurban	Y
LP002964	Male	Yes	2	Not Graduate	No	3987	1411.00	157	360	1	Rural	Y
LP002974	Male	Yes	0	Graduate	No	3232	1950.00	108	360	1	Rural	Y
LP002978	Female	No	0	Graduate	No	2900	0.00	71	360	1	Rural	Y
LP002979	Male	Yes	3+	Graduate	No	4106	0.00	40	180	1	Rural	Y
LP002983	Male	Yes	1	Graduate	No	8072	240.00	253	360	1	Urban	Y
LP002984	Male	Yes	2	Graduate	No	7583	0.00	187	360	1	Urban	Y
LP002990	Female	No	0	Graduate	Yes	4583	0.00	133	360	0	Semiurban	N

summary(loan_data) %>% kbl() %>% kable_styling() %>% scroll_box(width = "750px", height = "250px")

Loan_ID	Gender	Married	Dependents	Education	Self_Employed	ApplicantIncome	CoapplicantIncome	LoanAmount	Loan_Amount_Term	Credit_History	Property_Area	Loan_Status
Length:614	Length:614	Length:614	Length:614	Length:614	Length:614	Min. : 150	Min. : 0	Min. : 9.0	Min. : 12	Min. :0.0000	Length:614	Length:614
Class :character	Class :character	Class :character	Class :character	Class :character	Class :character	1st Qu.: 2878	1st Qu.: 0	1st Qu.:100.0	1st Qu.:360	1st Qu.:1.0000	Class :character	Class :character
Mode :character	Mode :character	Mode :character	Mode :character	Mode :character	Mode :character	Median : 3812	Median : 1188	Median :128.0	Median :360	Median :1.0000	Mode :character	Mode :character
NA	NA	NA	NA	NA	NA	Mean : 5403	Mean : 1621	Mean :146.4	Mean :342	Mean :0.8422	NA	NA
NA	NA	NA	NA	NA	NA	3rd Qu.: 5795	3rd Qu.: 2297	3rd Qu.:168.0	3rd Qu.:360	3rd Qu.:1.0000	NA	NA
NA	NA	NA	NA	NA	NA	Max. :81000	Max. :41667	Max. :700.0	Max. :480	Max. :1.0000	NA	NA
NA	NA	NA	NA	NA	NA	NA	NA	NA’s :22	NA’s :14	NA’s :50	NA	NA

missing <- loan_data %>% mutate_if(is.character, list(~na_if(.,""))) 

missing%>%
  summarise_all(list(~sum(is.na(.)))) %>%
  gather(key="Variable", value="Number_Missing") %>%
  arrange(desc(Number_Missing)) %>% kbl() %>% kable_styling() %>% scroll_box(width = "750px", height = "250px")

Variable	Number_Missing
Credit_History	50
Self_Employed	32
LoanAmount	22
Dependents	15
Loan_Amount_Term	14
Gender	13
Married	3
Loan_ID	0
Education	0
ApplicantIncome	0
CoapplicantIncome	0
Property_Area	0
Loan_Status	0

Factors

loan_data <- loan_data %>% mutate_if(is.character, factor)

The following section we’ll continue to look at the data from the raw perspective (loan_raw).

Categorical Variables

There are several variables which have blank values "". These data points may have been intentionally skipped by customers from banks during the data collection process or they may just be missing. We will handle this later on.
* Loan_ID: unique identifier
* Gender: either Male or Female or blank
* Married: either No or Yes or blank
* Dependents: how many dependents does someone have? 0, 1, 2, 3+ or blank
* Education: Graduate or Not Graduate
* Self_Employed: No or Yes or blank
* Property_Area: Urban, Rural or Semiurban
* Loan_status: Y (yes) or N (no)
* Credit_History: does the credit history meet the guidelines? 1 = Yes, 0 = No

Married

Married applicants have a higher approval rate than non married applicants. It will be useful to look into if this has any correlation with income.

married_loan_status_count <- table(loan_raw$Married,loan_raw$Loan_Status)
married_loan_status_perct <- married_loan_status_count
married_loan_status_perct[1,] <- round(married_loan_status_perct[1,]/3 * 100, 2)
married_loan_status_perct[2,] <- round(married_loan_status_perct[2,]/213 * 100, 2)
married_loan_status_perct[3,] <- round(married_loan_status_perct[3,]/398 * 100, 2)

#set column names for married_loan_status_count
married_loan_status_count <- data.frame(married_loan_status_count)
colnames(married_loan_status_count) <- c('Married','Loan_Status','Count')

#set column names and row names for gender_loan_status_perct
rownames(married_loan_status_perct) <-  c("Blank", "Not Married", "Married")
colnames(married_loan_status_perct) <-  c("% Applications Not Approved", "% Applications Approved")

loan_data_Married <- loan_raw
loan_data_Married[loan_data_Married$Married == '',] <- "Blank"

t1 <- loan_data_Married %>% group_by(Married) %>% tally 
colnames(t1) <- c("Married","Count Loan Applications")
t2 <- married_loan_status_perct

knitr::kable(list(t1, t2))

Married	Count Loan Applications
Blank	3
No	213
Yes	398

	% Applications Not Approved	% Applications Approved
Blank	0.00	100.00
Not Married	37.09	62.91
Married	28.39	71.61

ggplot(data=married_loan_status_count, aes(x=Married, y=Count, fill=Loan_Status)) + geom_bar(stat="identity",position="dodge")

Dependents

Applicants with 2 dependents appear to have the highest loan approval rate. It’d be interesting to see if the income per dependent has any impact on loan approval if we assume having more income makes it more likely to get a loan approved.

dep_loan_status_count <- table(loan_raw$Dependents,loan_raw$Loan_Status)
dep_loan_status_perct <- dep_loan_status_count
dep_loan_status_perct[1,] <- round(dep_loan_status_perct[1,]/15 * 100, 2)
dep_loan_status_perct[2,] <- round(dep_loan_status_perct[2,]/345 * 100, 2)
dep_loan_status_perct[3,] <- round(dep_loan_status_perct[3,]/102 * 100, 2)
dep_loan_status_perct[4,] <- round(dep_loan_status_perct[4,]/101 * 100, 2)
dep_loan_status_perct[5,] <- round(dep_loan_status_perct[5,]/51 * 100, 2)

#set column names for dep_loan_status_count
dep_loan_status_count <- data.frame(dep_loan_status_count)
colnames(dep_loan_status_count) <- c('Dependents','Loan_Status','Count')

#set column names and row names for gender_loan_status_perct
rownames(dep_loan_status_perct) <-  c("Blank", "0", "1","2","3+")
colnames(dep_loan_status_perct) <-  c("% Applications Not Approved", "% Applications Approved")

loan_data_Dep <- loan_raw
loan_data_Dep[loan_data_Dep$Dependents == '',] <- "Blank"

t1 <- loan_data_Dep %>% group_by(Dependents) %>% tally 
colnames(t1) <- c("Dependents","Count Loan Applications")
t2 <- dep_loan_status_perct

knitr::kable(list(t1, t2))

Dependents	Count Loan Applications
0	345
1	102
2	101
3+	51
Blank	15

	% Applications Not Approved	% Applications Approved
Blank	40.00	60.00
0	31.01	68.99
1	35.29	64.71
2	24.75	75.25
3+	35.29	64.71

ggplot(data=dep_loan_status_count, aes(x=Dependents, y=Count, fill=Loan_Status)) + geom_bar(stat="identity",position="dodge")

Education

Applicants with Graduate education have a higher loan approval rate here.

edu_loan_status_count <- table(loan_raw$Education,loan_raw$Loan_Status)
edu_loan_status_perct <- edu_loan_status_count
edu_loan_status_perct[1,] <- round(edu_loan_status_perct[1,]/480 * 100, 2)
edu_loan_status_perct[2,] <- round(edu_loan_status_perct[2,]/134 * 100, 2)

#set column names for edu_loan_status_count
edu_loan_status_count <- data.frame(edu_loan_status_count)
colnames(edu_loan_status_count) <- c('Education','Loan_Status','Count')

#set column names for edu_loan_status_perct
colnames(edu_loan_status_perct) <-  c("% Applications Not Approved", "% Applications Approved")

t1 <- loan_raw %>% group_by(Education) %>% tally 
colnames(t1) <- c("Education","Count Loan Applications")
t2 <- edu_loan_status_perct

knitr::kable(list(t1, t2))

Education	Count Loan Applications
Graduate	480
Not Graduate	134

	% Applications Not Approved	% Applications Approved
Graduate	29.17	70.83
Not Graduate	38.81	61.19

ggplot(data=edu_loan_status_count, aes(x=Education, y=Count, fill=Loan_Status)) + geom_bar(stat="identity",position="dodge")

Property Area

Semiurban applicants have the highest approval loan rating over rural and urban.

proparea_loan_status_count <- table(loan_raw$Property_Area,loan_raw$Loan_Status)
proparea_loan_status_perct <- proparea_loan_status_count
proparea_loan_status_perct[1,] <- round(proparea_loan_status_perct[1,]/179  * 100, 2)
proparea_loan_status_perct[2,] <- round(proparea_loan_status_perct[2,]/233  * 100, 2)
proparea_loan_status_perct[3,] <- round(proparea_loan_status_perct[3,]/202  * 100, 2)

#set column names for proparea_loan_status_count
proparea_loan_status_count <- data.frame(proparea_loan_status_count)
colnames(proparea_loan_status_count) <- c('Property_Area','Loan_Status','Count')

#set column names for proparea_loan_status_perct
colnames(proparea_loan_status_perct) <-  c("% Applications Not Approved", "% Applications Approved")

t1 <- loan_raw %>% group_by(Property_Area) %>% tally 
colnames(t1) <- c("Property_Area","Count Loan Applications")
t2 <- proparea_loan_status_perct

knitr::kable(list(t1, t2))

Property_Area	Count Loan Applications
Rural	179
Semiurban	233
Urban	202

	% Applications Not Approved	% Applications Approved
Rural	38.55	61.45
Semiurban	23.18	76.82
Urban	34.16	65.84

ggplot(data=proparea_loan_status_count, aes(x=Property_Area, y=Count, fill=Loan_Status)) + geom_bar(stat="identity",position="dodge")

Credit History

Having an a credit history that meets the guidelines appears to be extremely important in whether the loan status is approved or not.

credhist_loan_status_count <- table(loan_raw$Credit_History,loan_raw$Loan_Status)
credhist_loan_status_perct <- credhist_loan_status_count
credhist_loan_status_perct[1,] <- round(credhist_loan_status_perct[1,]/89  * 100, 2)
credhist_loan_status_perct[2,] <- round(credhist_loan_status_perct[2,]/475  * 100, 2)

#set column names for credhist_loan_status_count
credhist_loan_status_count <- data.frame(credhist_loan_status_count)
colnames(credhist_loan_status_count) <- c('Credit_History','Loan_Status','Count')

#set column names for credhist_loan_status_perct
colnames(credhist_loan_status_perct) <-  c("% Applications Not Approved", "% Applications Approved")

t1 <- loan_raw %>% group_by(Credit_History) %>% tally 
colnames(t1) <- c("Credit_History","Count Loan Applications")
t2 <- credhist_loan_status_perct

knitr::kable(list(t1, t2))

Credit_History	Count Loan Applications
0	89
1	475
NA	50

	% Applications Not Approved	% Applications Approved
0	92.13	7.87
1	20.42	79.58

ggplot(data=credhist_loan_status_count, aes(x=Credit_History, y=Count, fill=Loan_Status)) + geom_bar(stat="identity",position="dodge")

Numerical Variables

ApplicantIncome: how much money does the applicant make?
CoapplicantIncome: how much money does the coapplicant make? if there is no coapplicant this is 0.
LoanAmount: how much is the loan worth in thousands?
Loan_Amount_Term: how many months is the loan?

Now let’s use the pairs.panels function to see a lot of important information related to our numeric data:

Applicant income and loan_amount are strongly correlated
The most common Loan_Amount_Term is 360 months

numeric_loan_data <- dplyr::select(loan_data,ApplicantIncome,CoapplicantIncome,LoanAmount,Loan_Amount_Term)
pairs.panels(numeric_loan_data, 
             method = "pearson", # correlation method
             hist.col = "#00AFBB",
             density = TRUE,  # show density plots
             ellipses = TRUE # show correlation ellipses
             )

Inspecting ApplicantIncome and Loan Income

Here we can see that the ApplicantIncome does not have a huge effect on whether the Loan_Status was approved (Y) or not. The average ApplicantIncome is about the same for both groups is similar. There are a fewer more outliers of high incomes in the group where the loan status was approved.

approved <- loan_data[loan_data$Loan_Status == 'Y',]
denied <- loan_data[loan_data$Loan_Status == 'N',]

a <- ggplot(loan_data,aes(x=ApplicantIncome,color=Loan_Status))  + geom_boxplot()
b <- ggplot(approved,aes(x=ApplicantIncome,y=LoanAmount,color=Loan_Status)) + geom_point(color='blue') + xlab('Approved Applicant Income') + scale_x_continuous(limits = c(0, 25000)) + scale_y_continuous(limits = c(0, 650))
grid.arrange(a,b,nrow=2)#,nrow=2,ncol=2,layout_matrix=c(1,1,2,3))

c <- ggplot(denied,aes(x=ApplicantIncome,y=LoanAmount,color=Loan_Status)) + geom_point(color='red') + xlab('Denied Applicant Income') + scale_x_continuous(limits = c(0, 25000)) + scale_y_continuous(limits = c(0, 650))

grid.arrange(c)

In addition, upon investigating the sum of ApplicantIncome and CoapplicantIncome, we observe that it does not appear to have much prediction power with Loan_Status.

ggplot(data = loan_data, aes(x = Loan_Status, y = ApplicantIncome+CoapplicantIncome, fill=Loan_Status)) +
  geom_boxplot() +
  coord_flip()

LoanAmount Per ApplicantIncome

Now let’s see if the rate of the LoanAmount divided by ApplicantIncome has any prediction power when trying to deteremine if a Loan_Status will be approved or not. This would indicate that perhaps someone who is requesting a LoanAmount 5 times their income, they might not be approved but if they requested 3 times their income they could get approved.

Looking at the boxplots below, the average LoanAmtPerSalary is roughly the same for approved and not approved applications so this disbunks this theory. This variable might prove helpful in our modeling so we will keep it.

loan_data$LoanAmtPerSalary <- loan_data$LoanAmount*100000/loan_data$ApplicantIncome
ggplot(loan_data,aes(x=LoanAmtPerSalary,color=Loan_Status)) + geom_boxplot() + scale_x_continuous(limits = c(0, 30000))

## Warning: Removed 25 rows containing non-finite values (stat_boxplot).

Data Prep for Model-fitting

I explicitly recoded the Y/N values into 1/0’s

Since credit history is a categorical value and fewer than 50 rows are missing it’s better to delete these data points rather than to try to interpret a value for them. For loan amount term and loan amount we will use the mice package to impute a value where it is missing.

Additional Data Processing / Manipulation Steps

So, first off, I need to convert Credit_History to factors so that the mice model that I’m going to use can detect that column as a categorical variable.

Combining ApplicantIncome and CoapplicantIncome into a new variable TotalIncome, and dropping the respective input columns. Loan_ID doesn’t help with the prediction obviously. So dropping it as well.

loan_knn_pre_imp <- loan_knn
loan_knn_pre_imp$Credit_History <- as.factor(loan_knn_pre_imp$Credit_History)

loan_knn_pre_imp <- loan_knn_pre_imp %>% mutate(TotalIncome = ApplicantIncome + CoapplicantIncome)
loan_knn_pre_imp <- loan_knn_pre_imp %>% dplyr::select(-c('Loan_ID','ApplicantIncome','CoapplicantIncome'))

# loan_knn_pre_imp[loan_knn_pre_imp$Dependents = "3+"] <- "3"

# recode dependents 3+ to 3
loan_knn_pre_imp$Dependents <- revalue(loan_knn_pre_imp$Dependents, c("3+"="3"))


str(loan_knn_pre_imp)

## 'data.frame':    614 obs. of  12 variables:
##  $ Gender          : Factor w/ 2 levels "Female","Male": 2 2 2 2 2 2 2 2 2 2 ...
##  $ Married         : Factor w/ 2 levels "No","Yes": 1 2 2 2 1 2 2 2 2 2 ...
##  $ Dependents      : Factor w/ 4 levels "0","1","2","3": 1 2 1 1 1 3 1 4 3 2 ...
##  $ Education       : Factor w/ 2 levels "Graduate","Not Graduate": 1 1 1 2 1 1 2 1 1 1 ...
##  $ Self_Employed   : Factor w/ 2 levels "No","Yes": 1 1 2 1 1 2 1 1 1 1 ...
##  $ LoanAmount      : int  NA 128 66 120 141 267 95 158 168 349 ...
##  $ Loan_Amount_Term: int  360 360 360 360 360 360 360 360 360 360 ...
##  $ Credit_History  : Factor w/ 2 levels "0","1": 2 2 2 2 2 2 2 1 2 2 ...
##  $ Property_Area   : Factor w/ 3 levels "Rural","Semiurban",..: 3 1 3 3 3 3 3 2 3 2 ...
##  $ Loan_Status     : num  1 0 1 1 1 1 1 0 1 0 ...
##  $ LoanAmtPerSalary: num  NA 2793 2200 4646 2350 ...
##  $ TotalIncome     : num  5849 6091 3000 4941 6000 ...

Status quo of missing data

clean_loan_data <- loan_data

vis_dat(clean_loan_data)

I’ve set up a predictorMatrix where I can instruct mice to use which method for which column for imputation.

Set seed = 501. Retrieved the results.

# clean_loan_data <- complete(mice(clean_loan_data,m=5,meth='pmm',print=FALSE))
init <- mice(loan_knn_pre_imp, maxit=0) 
meth <- init$method
predM <- init$predictorMatrix
meth[c('LoanAmount','Loan_Amount_Term')] <- 'norm'
meth[c('Credit_History','Self_Employed','Gender','Married')] <- 'logreg'
meth[c('Dependents')] <- 'polyreg'
meth[c('Loan_Status','TotalIncome','Property_Area','Education')] = ''
loan_knn_imp1 <- mice(loan_knn_pre_imp, method=meth, predictorMatrix=predM, seed=501)

## 
##  iter imp variable
##   1   1  Gender  Married  Dependents  Self_Employed  LoanAmount  Loan_Amount_Term  Credit_History  LoanAmtPerSalary
##   1   2  Gender  Married  Dependents  Self_Employed  LoanAmount  Loan_Amount_Term  Credit_History  LoanAmtPerSalary
##   1   3  Gender  Married  Dependents  Self_Employed  LoanAmount  Loan_Amount_Term  Credit_History  LoanAmtPerSalary
##   1   4  Gender  Married  Dependents  Self_Employed  LoanAmount  Loan_Amount_Term  Credit_History  LoanAmtPerSalary
##   1   5  Gender  Married  Dependents  Self_Employed  LoanAmount  Loan_Amount_Term  Credit_History  LoanAmtPerSalary
##   2   1  Gender  Married  Dependents  Self_Employed  LoanAmount  Loan_Amount_Term  Credit_History  LoanAmtPerSalary
##   2   2  Gender  Married  Dependents  Self_Employed  LoanAmount  Loan_Amount_Term  Credit_History  LoanAmtPerSalary
##   2   3  Gender  Married  Dependents  Self_Employed  LoanAmount  Loan_Amount_Term  Credit_History  LoanAmtPerSalary
##   2   4  Gender  Married  Dependents  Self_Employed  LoanAmount  Loan_Amount_Term  Credit_History  LoanAmtPerSalary
##   2   5  Gender  Married  Dependents  Self_Employed  LoanAmount  Loan_Amount_Term  Credit_History  LoanAmtPerSalary
##   3   1  Gender  Married  Dependents  Self_Employed  LoanAmount  Loan_Amount_Term  Credit_History  LoanAmtPerSalary
##   3   2  Gender  Married  Dependents  Self_Employed  LoanAmount  Loan_Amount_Term  Credit_History  LoanAmtPerSalary
##   3   3  Gender  Married  Dependents  Self_Employed  LoanAmount  Loan_Amount_Term  Credit_History  LoanAmtPerSalary
##   3   4  Gender  Married  Dependents  Self_Employed  LoanAmount  Loan_Amount_Term  Credit_History  LoanAmtPerSalary
##   3   5  Gender  Married  Dependents  Self_Employed  LoanAmount  Loan_Amount_Term  Credit_History  LoanAmtPerSalary
##   4   1  Gender  Married  Dependents  Self_Employed  LoanAmount  Loan_Amount_Term  Credit_History  LoanAmtPerSalary
##   4   2  Gender  Married  Dependents  Self_Employed  LoanAmount  Loan_Amount_Term  Credit_History  LoanAmtPerSalary
##   4   3  Gender  Married  Dependents  Self_Employed  LoanAmount  Loan_Amount_Term  Credit_History  LoanAmtPerSalary
##   4   4  Gender  Married  Dependents  Self_Employed  LoanAmount  Loan_Amount_Term  Credit_History  LoanAmtPerSalary
##   4   5  Gender  Married  Dependents  Self_Employed  LoanAmount  Loan_Amount_Term  Credit_History  LoanAmtPerSalary
##   5   1  Gender  Married  Dependents  Self_Employed  LoanAmount  Loan_Amount_Term  Credit_History  LoanAmtPerSalary
##   5   2  Gender  Married  Dependents  Self_Employed  LoanAmount  Loan_Amount_Term  Credit_History  LoanAmtPerSalary
##   5   3  Gender  Married  Dependents  Self_Employed  LoanAmount  Loan_Amount_Term  Credit_History  LoanAmtPerSalary
##   5   4  Gender  Married  Dependents  Self_Employed  LoanAmount  Loan_Amount_Term  Credit_History  LoanAmtPerSalary
##   5   5  Gender  Married  Dependents  Self_Employed  LoanAmount  Loan_Amount_Term  Credit_History  LoanAmtPerSalary

Manual Examinations

After some manual examinations of the different imputed results, I’ve decided to go with imputed column #3.

# Manual examination 
#Credit_History
loan_knn_imp1$imp$Credit_History

##     1 2 3 4 5
## 17  1 1 1 1 1
## 25  0 1 1 0 1
## 31  1 1 1 1 1
## 43  1 1 1 1 1
## 80  1 1 1 1 1
## 84  0 0 1 0 0
## 87  1 1 1 1 1
## 96  0 0 1 0 1
## 118 1 1 1 1 1
## 126 1 1 1 1 1
## 130 1 0 1 0 1
## 131 1 1 1 1 1
## 157 1 1 1 1 1
## 182 0 1 1 0 1
## 188 1 1 1 1 1
## 199 1 1 1 1 1
## 220 1 1 1 1 1
## 237 1 0 0 1 1
## 238 1 1 1 1 1
## 260 0 0 1 1 0
##  [ reached 'max' / getOption("max.print") -- omitted 30 rows ]

loan_knn[96:118,]

##      Loan_ID Gender Married Dependents    Education Self_Employed
## 96  LP001326   Male      No          0     Graduate          <NA>
## 97  LP001327 Female     Yes          0     Graduate            No
## 98  LP001333   Male     Yes          0     Graduate            No
## 99  LP001334   Male     Yes          0 Not Graduate            No
## 100 LP001343   Male     Yes          0     Graduate            No
## 101 LP001345   Male     Yes          2 Not Graduate            No
## 102 LP001349   Male      No          0     Graduate            No
##     ApplicantIncome CoapplicantIncome LoanAmount Loan_Amount_Term
## 96             6782                 0         NA              360
## 97             2484              2302        137              360
## 98             1977               997         50              360
## 99             4188                 0        115              180
## 100            1759              3541        131              360
## 101            4288              3263        133              180
## 102            4843              3806        151              360
##     Credit_History Property_Area Loan_Status LoanAmtPerSalary
## 96              NA         Urban           0               NA
## 97               1     Semiurban           1         5515.298
## 98               1     Semiurban           1         2529.084
## 99               1     Semiurban           1         2745.941
## 100              1     Semiurban           1         7447.413
## 101              1         Urban           1         3101.679
## 102              1     Semiurban           1         3117.902
##  [ reached 'max' / getOption("max.print") -- omitted 16 rows ]

#Married
loan_knn_imp1$imp$Married

##       1   2   3   4   5
## 105 Yes Yes Yes  No Yes
## 229  No Yes Yes Yes Yes
## 436 Yes Yes  No  No  No

loan_knn[430:436,]

##      Loan_ID Gender Married Dependents    Education Self_Employed
## 430 LP002370   Male      No          0 Not Graduate            No
## 431 LP002377 Female      No          1     Graduate           Yes
## 432 LP002379   Male      No          0     Graduate            No
## 433 LP002386   Male      No          0     Graduate          <NA>
## 434 LP002387   Male     Yes          0     Graduate            No
## 435 LP002390   Male      No          0     Graduate            No
## 436 LP002393 Female    <NA>       <NA>     Graduate            No
##     ApplicantIncome CoapplicantIncome LoanAmount Loan_Amount_Term
## 430            2717                 0         60              180
## 431            8624                 0        150              360
## 432            6500                 0        105              360
## 433           12876                 0        405              360
## 434            2425              2340        143              360
## 435            3750                 0        100              360
## 436           10047                 0         NA              240
##     Credit_History Property_Area Loan_Status LoanAmtPerSalary
## 430              1         Urban           1         2208.318
## 431              1     Semiurban           1         1739.332
## 432              0         Rural           0         1615.385
## 433              1     Semiurban           1         3145.387
## 434              1     Semiurban           1         5896.907
## 435              1         Urban           1         2666.667
## 436              1     Semiurban           1               NA

#Dependents
loan_knn_imp1$imp$Dependents

##     1 2 3 4 5
## 103 2 1 3 1 0
## 105 0 3 0 2 0
## 121 2 2 3 2 0
## 227 2 2 1 1 1
## 229 0 0 2 1 2
## 294 0 0 3 0 0
## 302 0 0 1 3 1
## 333 0 0 0 0 0
## 336 0 0 1 2 2
## 347 0 0 3 0 1
## 356 1 0 0 0 0
## 436 2 2 0 0 0
## 518 0 2 0 1 2
## 572 0 0 1 1 2
## 598 0 0 0 0 0

loan_knn[227:229,]

##      Loan_ID Gender Married Dependents    Education Self_Employed
## 227 LP001754   Male     Yes       <NA> Not Graduate           Yes
## 228 LP001758   Male     Yes          2     Graduate            No
## 229 LP001760   Male    <NA>       <NA>     Graduate            No
##     ApplicantIncome CoapplicantIncome LoanAmount Loan_Amount_Term
## 227            4735                 0        138              360
## 228            6250              1695        210              360
## 229            4758                 0        158              480
##     Credit_History Property_Area Loan_Status LoanAmtPerSalary
## 227              1         Urban           0         2914.467
## 228              1     Semiurban           1         3360.000
## 229              1     Semiurban           1         3320.723

Decision

We picked impute #3.

loan_knn2 <- complete(loan_knn_imp1, 3) # 2nd argument if not provided is defaulted to 1

clean_loan_data <- loan_knn2

# have to redo loan_status as loan_knn's loan status had been recoded to numeric on purpose
clean_loan_data$Loan_Status <- as.factor(clean_loan_data$Loan_Status)
str(clean_loan_data)

## 'data.frame':    614 obs. of  12 variables:
##  $ Gender          : Factor w/ 2 levels "Female","Male": 2 2 2 2 2 2 2 2 2 2 ...
##  $ Married         : Factor w/ 2 levels "No","Yes": 1 2 2 2 1 2 2 2 2 2 ...
##  $ Dependents      : Factor w/ 4 levels "0","1","2","3": 1 2 1 1 1 3 1 4 3 2 ...
##  $ Education       : Factor w/ 2 levels "Graduate","Not Graduate": 1 1 1 2 1 1 2 1 1 1 ...
##  $ Self_Employed   : Factor w/ 2 levels "No","Yes": 1 1 2 1 1 2 1 1 1 1 ...
##  $ LoanAmount      : num  21.1 128 66 120 141 ...
##  $ Loan_Amount_Term: num  360 360 360 360 360 360 360 360 360 360 ...
##  $ Credit_History  : Factor w/ 2 levels "0","1": 2 2 2 2 2 2 2 1 2 2 ...
##  $ Property_Area   : Factor w/ 3 levels "Rural","Semiurban",..: 3 1 3 3 3 3 3 2 3 2 ...
##  $ Loan_Status     : Factor w/ 2 levels "0","1": 2 1 2 2 2 2 2 1 2 1 ...
##  $ LoanAmtPerSalary: num  403 2793 2200 4646 2350 ...
##  $ TotalIncome     : num  5849 6091 3000 4941 6000 ...

Imbalanced Dataset

Notice that the response variable is 31/69 split on the binary response, No and Yes, respectively.

imb_dat <- as.data.frame(prop.table(x = table(clean_loan_data$Loan_Status)))
colnames(imb_dat) <- c("Loan Status", "Freq")
imb_dat

##   Loan Status      Freq
## 1           0 0.3127036
## 2           1 0.6872964

Splitting Data into Training & Testing

Here we are going to use 80% of our data to train the model and reserve 20% to test the model we pick.

set.seed(1042)
sample_size <- floor(nrow(clean_loan_data)*0.8)
indices <- sample(1:nrow(clean_loan_data),sample_size)
train <- clean_loan_data[c(indices),]
test <- clean_loan_data[-c(indices),]

2. Linear Discriminant Analysis

LDA does not seem to be a good approach with this data set as the points provided by the available data are not linearly separable

train%>%
  ggplot(aes(x = log(LoanAmount), y= log(TotalIncome), color = Loan_Status)) + geom_point()

lda Cross Validation

predictions with the LDA model are less accurate than if we just used the binary classifier Credit_History to determine weather or not a loan would be approved

# cross validation 
ctrl <- trainControl(method = 'repeatedcv', repeats = 11)

lda model results

lda.fit <- train(Loan_Status ~ TotalIncome + LoanAmount,
             data = train,
             method = 'lda',
             trControl = ctrl
             )
test$lda <- predict(lda.fit, test)
confusionMatrix(test$lda, test$Loan_Status)

## Confusion Matrix and Statistics
## 
##           Reference
## Prediction  0  1
##          0  0  0
##          1 33 90
##                                           
##                Accuracy : 0.7317          
##                  95% CI : (0.6443, 0.8076)
##     No Information Rate : 0.7317          
##     P-Value [Acc > NIR] : 0.5467          
##                                           
##                   Kappa : 0               
##                                           
##  Mcnemar's Test P-Value : 2.54e-08        
##                                           
##             Sensitivity : 0.0000          
##             Specificity : 1.0000          
##          Pos Pred Value :    NaN          
##          Neg Pred Value : 0.7317          
##              Prevalence : 0.2683          
##          Detection Rate : 0.0000          
##    Detection Prevalence : 0.0000          
##       Balanced Accuracy : 0.5000          
##                                           
##        'Positive' Class : 0               
##

3. K-nearest Neighbor

First off, set seed = 688.

Create training/test partitions by calling createDataPartition. p is set to .8 to mean 80/20 split for train/test set.

Checking the structure of the train set (knn_train)

Checking the structure of the test set (knn_test)

str(knn_test)

## 'data.frame':    122 obs. of  12 variables:
##  $ Gender          : Factor w/ 2 levels "Female","Male": 2 2 2 2 2 2 2 2 1 2 ...
##  $ Married         : Factor w/ 2 levels "No","Yes": 1 2 2 2 2 1 1 2 2 2 ...
##  $ Dependents      : Factor w/ 4 levels "0","1","2","3": 1 3 2 3 3 2 4 3 2 1 ...
##  $ Education       : Factor w/ 2 levels "Graduate","Not Graduate": 1 1 1 2 2 1 1 1 1 1 ...
##  $ Self_Employed   : Factor w/ 2 levels "No","Yes": 1 2 1 1 1 2 1 1 2 1 ...
##  $ LoanAmount      : num  141 267 349 112 110 106 320 134 286 96 ...
##  $ Loan_Amount_Term: num  360 360 360 360 360 360 360 360 360 360 ...
##  $ Credit_History  : Factor w/ 2 levels "0","1": 2 2 2 1 2 2 2 2 1 2 ...
##  $ Property_Area   : Factor w/ 3 levels "Rural","Semiurban",..: 3 3 2 1 3 1 1 3 3 2 ...
##  $ Loan_Status     : Factor w/ 2 levels "0","1": 2 2 1 1 2 1 1 1 1 2 ...
##  $ LoanAmtPerSalary: num  2350 4929 2718 3328 2603 ...
##  $ TotalIncome     : num  6000 9613 23809 5282 5266 ...

Cross Validation

Perform a repeated 11-fold cross-validation, meaning the number of complete sets of folks to compute is 11. For this classification problem, we assigned our fitted model to knn.fit. The cross-validated results is plugged in the form of trControl.

# cleaning up some parallel computing
# https://stackoverflow.com/questions/25097729/un-register-a-doparallel-cluster
registerDoSEQ()

trControl <- trainControl(method  = "repeatedcv",
                          repeats  = 11)
knn.fit <- train(Loan_Status ~ .,
             method     = "knn",
             tuneGrid   = expand.grid(k = 1:10),
             trControl  = trControl,
             preProcess = c("center","scale"),
             data       = knn_train
             )

knn.fit

## k-Nearest Neighbors 
## 
## 492 samples
##  11 predictor
##   2 classes: '0', '1' 
## 
## Pre-processing: centered (14), scaled (14) 
## Resampling: Cross-Validated (10 fold, repeated 11 times) 
## Summary of sample sizes: 442, 444, 443, 443, 442, 444, ... 
## Resampling results across tuning parameters:
## 
##   k   Accuracy   Kappa    
##    1  0.7122390  0.3217246
##    2  0.7089797  0.3061592
##    3  0.7694411  0.4090793
##    4  0.7605727  0.3808163
##    5  0.7838922  0.4188985
##    6  0.7732961  0.3882704
##    7  0.7848086  0.4070143
##    8  0.7832899  0.4023703
##    9  0.7912427  0.4176016
##   10  0.7873503  0.4063482
## 
## Accuracy was used to select the optimal model using the largest value.
## The final value used for the model was k = 9.

Key Information on the value of K

Since our target variable is a binary factor of 2, by default, we use Accuracy as the determining performance metric. The optimal K is thus determined by Accuracy. K = 9 was finally selected. # of neighbors is 9.

plot(knn.fit)

Model Results

knn_pred <- predict(knn.fit, newdata = knn_test)
# options('max.print' = 100)  
# getOption("max.print")
confusionMatrix(knn_pred, knn_test$Loan_Status)

## Confusion Matrix and Statistics
## 
##           Reference
## Prediction  0  1
##          0 15  3
##          1 23 81
##                                           
##                Accuracy : 0.7869          
##                  95% CI : (0.7035, 0.8558)
##     No Information Rate : 0.6885          
##     P-Value [Acc > NIR] : 0.0104406       
##                                           
##                   Kappa : 0.4195          
##                                           
##  Mcnemar's Test P-Value : 0.0001944       
##                                           
##             Sensitivity : 0.3947          
##             Specificity : 0.9643          
##          Pos Pred Value : 0.8333          
##          Neg Pred Value : 0.7788          
##              Prevalence : 0.3115          
##          Detection Rate : 0.1230          
##    Detection Prevalence : 0.1475          
##       Balanced Accuracy : 0.6795          
##                                           
##        'Positive' Class : 0               
##

Accuracy is 78.69% while balanced accuracy is only 67.95%.

4. Decision Trees

Now we will use a decision tree to see how well it will perform on our data.
* Our decision tree starts by splitting users based on their Credit_History. This makes sense based on our exploratory data analysis.
* Other variables used in the decision tree include LoanAmount, PropertyArea, etc.

loan_tree = tree(Loan_Status ~., train)
plot(loan_tree)
text(loan_tree)
title(main = "Unpruned Decision Tree")

Decision Tree Performance

Training Data

Now we will use our model to see how it performs on the training data. We see that the model predicted Loan_Status with an accuracy of ~83%. 81 instances were incorrectly classified.

pred_tree_train <- predict(loan_tree,train,type="class")
test_table <- table(pred_tree_train,train$Loan_Status) %>% kbl() %>% kable_styling()
test_table

	0	1
0	89	11
1	70	321

mean(pred_tree_train == train$Loan_Status)

## [1] 0.8350305

Cross-validation for better performance

The first version of our model was a full, unpruned tree. Now we are going to prune it back to get the optimal tree using cross validation. We have plotted the number of misclassifications with the different trees. As we can see, the trees with size 2-4 have the fewest misclassifications. We will choose size 4 to have the fewest misclassifications.

set.seed(2311)
cv_trees = cv.tree(loan_tree,FUN = prune.misclass)
cv_trees

## $size
## [1] 15 10  4  2  1
## 
## $dev
## [1] 108 108 101  97 159
## 
## $k
## [1]      -Inf  0.000000  1.333333  2.500000 65.000000
## 
## $method
## [1] "misclass"
## 
## attr(,"class")
## [1] "prune"         "tree.sequence"

plot(cv_trees)

Using a size = 4, our decision tree looks like the following:

loan_tree_pruned = prune.misclass(loan_tree,best=4)
plot(loan_tree_pruned)
text(loan_tree_pruned)

Testing Data

Now let’s see how our pruned performs on our testing data. The accuracy for our test data was ~82%, which was almost the same as our training data. 21 of the total observations were misclassified.

pred_tree_test  <- predict(loan_tree_pruned,test, type="class")
test_table <- table(pred_tree_test,test$Loan_Status) %>% kbl() %>% kable_styling()
test_table

	0	1
0	14	2
1	19	88

mean(pred_tree_test == test$Loan_Status)

## [1] 0.8292683

confusionMatrix(pred_tree_test, test$Loan_Status)

## Confusion Matrix and Statistics
## 
##           Reference
## Prediction  0  1
##          0 14  2
##          1 19 88
##                                           
##                Accuracy : 0.8293          
##                  95% CI : (0.7509, 0.8911)
##     No Information Rate : 0.7317          
##     P-Value [Acc > NIR] : 0.0075806       
##                                           
##                   Kappa : 0.4804          
##                                           
##  Mcnemar's Test P-Value : 0.0004803       
##                                           
##             Sensitivity : 0.4242          
##             Specificity : 0.9778          
##          Pos Pred Value : 0.8750          
##          Neg Pred Value : 0.8224          
##              Prevalence : 0.2683          
##          Detection Rate : 0.1138          
##    Detection Prevalence : 0.1301          
##       Balanced Accuracy : 0.7010          
##                                           
##        'Positive' Class : 0               
##

5. Random Forests

Now we will develop a random forest model to see how well it will performs with our data. Parameters for a random forest include: mtry : Number of variables randomly sampled as candidates at each split. Note that the default values are different for classification (sqrt(p) where p is number of variables in x) and regression (p/3) ntree : Number of trees to grow. This should not be set to too small a number, to ensure that every input row gets predicted at least a few times

Our initial model will have default parameters of mtry=sqrt(13) and ntree=500.

# find out no of cores 
no_cores <- detectCores() - 1

cl<-makePSOCKcluster(no_cores)
  
registerDoParallel(cl)
  
# start.time<-proc.time()
  
# model<-train(target~., data=trainingset, method='rf')

#drop loan id
train_rf1 <- train
test_rf1 <- test 

# Create model with default parameters
control <- trainControl(method="repeatedcv", number=10, repeats=3)
mtry <- sqrt(ncol(train_rf1))
tunegrid <- expand.grid(.mtry=mtry)
rf_default <- train(Loan_Status~., data=train_rf1, method="rf", metric="Accuracy", tuneGrid=tunegrid, trControl=control)
print(rf_default)

## Random Forest 
## 
## 491 samples
##  11 predictor
##   2 classes: '0', '1' 
## 
## No pre-processing
## Resampling: Cross-Validated (10 fold, repeated 3 times) 
## Summary of sample sizes: 443, 442, 441, 442, 442, 442, ... 
## Resampling results:
## 
##   Accuracy   Kappa    
##   0.8011678  0.4879166
## 
## Tuning parameter 'mtry' was held constant at a value of 3.464102

# stop.time<-proc.time()
# 
# run.time<-stop.time -start.time
# 
# print(run.time)
#   
# stopCluster(cl)

Our inital model has accuracy of about 80%. Let’s see if we can improve accuracy by finding an optimal mtry value. We will test different mtry values 1-10 by using gridsearch. We see from our results that the optimal mtry value for accuracy is 2.

control <- trainControl(method="repeatedcv", number=10, repeats=3, search="grid")
set.seed(123)
tunegrid <- expand.grid(.mtry=c(1:10))
rf_gridsearch <- train(Loan_Status~., data=train_rf1, method="rf", metric="Accuracy", tuneGrid=tunegrid, trControl=control)
print(rf_gridsearch)

## Random Forest 
## 
## 491 samples
##  11 predictor
##   2 classes: '0', '1' 
## 
## No pre-processing
## Resampling: Cross-Validated (10 fold, repeated 3 times) 
## Summary of sample sizes: 442, 442, 441, 442, 442, 441, ... 
## Resampling results across tuning parameters:
## 
##   mtry  Accuracy   Kappa    
##    1    0.6795697  0.0138783
##    2    0.8003464  0.4745384
##    3    0.8030964  0.4913187
##    4    0.7983611  0.4853485
##    5    0.7895170  0.4665550
##    6    0.7874632  0.4625780
##    7    0.7881434  0.4672603
##    8    0.7847562  0.4591980
##    9    0.7846871  0.4605619
##   10    0.7820074  0.4550405
## 
## Accuracy was used to select the optimal model using the largest value.
## The final value used for the model was mtry = 3.

plot(rf_gridsearch)

Next let’s find the optimal value for ntree. Again we’ll use gridsearch to test different ntree values. It’s evident from our results that optimal ntree value for accuracy is 1500.

control <- trainControl(method="repeatedcv", number=10, repeats=3, search="grid")
tunegrid <- expand.grid(.mtry=2)
modellist <- list()
for (ntree in c(500, 1000, 1500, 2000, 2500)) {
  set.seed(124)
    fit <- train(Loan_Status~., data=train_rf1, method="rf", metric="Accuracy", tuneGrid=tunegrid, trControl=control, ntree=ntree)
    key <- toString(ntree)
    modellist[[key]] <- fit
}
# compare results
results <- resamples(modellist)
summary(results)

## 
## Call:
## summary.resamples(object = results)
## 
## Models: 500, 1000, 1500, 2000, 2500 
## Number of resamples: 30 
## 
## Accuracy 
##           Min.   1st Qu.    Median      Mean   3rd Qu.      Max. NA's
## 500  0.7346939 0.7755102 0.7959184 0.8025006 0.8190816 0.8958333    0
## 1000 0.7346939 0.7755102 0.7959184 0.8011400 0.8163265 0.8958333    0
## 1500 0.7346939 0.7755102 0.7959184 0.8018203 0.8163265 0.8979592    0
## 2000 0.7346939 0.7755102 0.7959184 0.8011400 0.8163265 0.8958333    0
## 2500 0.7346939 0.7755102 0.7959184 0.8018203 0.8163265 0.8979592    0
## 
## Kappa 
##           Min.   1st Qu.    Median      Mean  3rd Qu.      Max. NA's
## 500  0.2669735 0.4038375 0.4688651 0.4828621 0.545829 0.7435897    0
## 1000 0.2669735 0.4035402 0.4688651 0.4794511 0.541709 0.7435897    0
## 1500 0.2669735 0.4035402 0.4688651 0.4813131 0.541709 0.7476828    0
## 2000 0.2669735 0.4035402 0.4688651 0.4794511 0.541709 0.7435897    0
## 2500 0.2669735 0.4035402 0.4688651 0.4813131 0.541709 0.7476828    0

dotplot(results)

Our final random forest model will have mtry=2 and ntree=1500.

rf_final <- randomForest(Loan_Status ~ ., 
                        data = train_rf1, 
                        ntree = 1500, 
                        mtry = 2,
                        importance = TRUE,
                        proximity = TRUE)

print(rf_final)

## 
## Call:
##  randomForest(formula = Loan_Status ~ ., data = train_rf1, ntree = 1500,      mtry = 2, importance = TRUE, proximity = TRUE) 
##                Type of random forest: classification
##                      Number of trees: 1500
## No. of variables tried at each split: 2
## 
##         OOB estimate of  error rate: 20.16%
## Confusion matrix:
##    0   1 class.error
## 0 73  86  0.54088050
## 1 13 319  0.03915663

#variable importance
round(importance(rf_final), 2)

##                      0     1 MeanDecreaseAccuracy MeanDecreaseGini
## Gender           -3.23  7.74                 4.91             3.08
## Married          -3.14  7.90                 5.27             3.78
## Dependents       -4.43 10.80                 6.82             8.80
## Education         0.92  2.94                 3.06             3.91
## Self_Employed    -4.98  8.16                 4.25             3.06
## LoanAmount       -3.72 24.77                20.67            25.34
## Loan_Amount_Term  7.10  9.66                11.98             8.48
## Credit_History   93.68 95.74               104.16            50.51
## Property_Area     1.28  3.23                 3.38             8.43
## LoanAmtPerSalary  3.34 17.43                16.68            27.54
## TotalIncome      -4.38 23.64                19.72            27.19

prediction <-predict(rf_final, test_rf1)
confusionMatrix(prediction, test_rf1$Loan_Status)

## Confusion Matrix and Statistics
## 
##           Reference
## Prediction  0  1
##          0 14  1
##          1 19 89
##                                           
##                Accuracy : 0.8374          
##                  95% CI : (0.7601, 0.8978)
##     No Information Rate : 0.7317          
##     P-Value [Acc > NIR] : 0.0039800       
##                                           
##                   Kappa : 0.4994          
##                                           
##  Mcnemar's Test P-Value : 0.0001439       
##                                           
##             Sensitivity : 0.4242          
##             Specificity : 0.9889          
##          Pos Pred Value : 0.9333          
##          Neg Pred Value : 0.8241          
##              Prevalence : 0.2683          
##          Detection Rate : 0.1138          
##    Detection Prevalence : 0.1220          
##       Balanced Accuracy : 0.7066          
##                                           
##        'Positive' Class : 0               
##

# stop.time<-proc.time()

# run.time<-stop.time -start.time

# print(run.time)

# Stopping Cluster
stopCluster(cl)

Accuracy of our final random forest model is about 83% on the test data with 19 instances misclassified. 2 are false negatives and 17 are false positives. Credit_history is the most important feature.

6. Model Performance

Model Performance Matrix
Metric	LDA	K-Nearest Neighbor (KNN)	Decision Trees	Random Forest
Accuracy	0.7317	0.7869	0.8293	0.8374
Balanced Accuracy	0.5000	0.6795	0.7010	0.7066
Sensitivity	0	0.3947	0.4242	0.4242

Notice that the sensitivity between Decision Trees, and RF is the same at 42.42%. It’s surprising to see that LDA and Random Forest ended up having the highest accuracy, which is usually the go-to metric to go for in an unbalanced dataset with the binary response that are not 50/50. The model we picked is Random Forest.

Homework3

Homework3

1. Exploratory Data Analysis

Factors

The following section we’ll continue to look at the data from the raw perspective (loan_raw).

Categorical Variables

Married

Dependents

Education

Property Area

Credit History

Numerical Variables

Inspecting ApplicantIncome and Loan Income

LoanAmount Per ApplicantIncome

Data Prep for Model-fitting

Additional Data Processing / Manipulation Steps

Status quo of missing data

Manual Examinations

Decision

Imbalanced Dataset

Splitting Data into Training & Testing

2. Linear Discriminant Analysis

lda Cross Validation

lda model results

3. K-nearest Neighbor

Cross Validation

Key Information on the value of K

Model Results

4. Decision Trees

Decision Tree Performance

Training Data

Cross-validation for better performance

Testing Data

5. Random Forests

6. Model Performance

Resources: