Customer	Balance	Direct
1	122	No
2	289	No
3	365	Yes
4	398	No
5	409	No
6	491	No
7	524	No
8	573	No
9	617	No
10	628	No
11	652	No
12	670	No
13	674	Yes
14	680	No
15	685	Yes
16	698	No
17	726	Yes
18	776	No
19	778	Yes
20	810	Yes
21	975	Yes
22	1011	Yes
23	1019	Yes
24	1037	Yes
25	1169	No
26	1507	Yes
27	1845	Yes
28	2498	No
29	441	No
30	793	Yes
31	391	No
32	506	No
33	761	No
34	1463	Yes
35	628	Yes
36	706	No
37	289	No
38	654	No
39	557	No
40	1033	Yes
41	415	No
42	796	No
43	561	No
44	592	No
45	209	No
46	813	No
47	323	No
48	671	No
49	858	Yes
50	990	Yes
51	493	No
52	372	No
53	647	No
54	1295	Yes
55	1356	Yes
56	960	Yes
57	976	Yes
58	1176	Yes
59	426	No
60	333	No
61	1257	Yes
62	1144	Yes
63	938	Yes
64	620	No
65	361	No
66	300	No
67	596	No
68	527	No
69	1376	Yes
70	1509	Yes
71	263	No
72	324	No
73	850	Yes
74	786	No
75	363	No
76	990	Yes
77	164	No
78	582	No
79	553	No
80	432	No
81	468	No
82	438	No
83	512	No
84	451	No
85	1055	Yes
86	708	Yes
87	555	No
88	377	No
89	812	No
90	271	No
91	317	No
92	383	No
93	191	No
94	915	Yes
95	718	No
96	1001	Yes
97	674	Yes
98	1249	Yes
99	1422	Yes
100	696	No
101	676	No
102	570	No
103	554	No
104	509	No
105	603	No
106	356	No
107	505	No
108	503	No
109	2726	Yes
110	582	No
111	767	Yes
112	1078	Yes
113	629	No
114	831	No
115	505	No
116	697	Yes
117	972	Yes
118	341	No
119	664	Yes
120	1362	Yes
121	1068	Yes
122	1209	Yes
123	1127	Yes
124	1123	Yes
125	781	No
126	159	No
127	516	No
128	582	No
129	841	No
130	1196	Yes
131	550	No
132	458	No
133	1646	Yes
134	607	No
135	744	No
136	2578	Yes
137	589	No
138	540	No
139	340	No
140	542	No
141	335	No
142	377	No
143	263	No
144	221	No
145	1923	Yes
146	565	No
147	424	No
148	401	No
149	609	No
150	468	No
151	377	No
152	571	No
153	902	Yes
154	1337	Yes
155	305	No
156	572	No
157	365	No
158	1365	Yes
159	136	No
160	474	No
161	620	No
162	634	No
163	383	No
164	1299	Yes
165	164	No
166	984	Yes
167	388	No
168	654	No
169	494	No
170	445	No
171	605	No
172	659	No
173	879	No
174	579	No
175	741	No
176	176	No
177	916	Yes
178	987	Yes
179	890	Yes
180	1710	Yes
181	784	Yes
182	1335	Yes
183	375	No
184	1327	Yes
185	482	No
186	857	Yes
187	536	No
188	1108	Yes
189	263	No
190	1578	Yes
191	405	No
192	1312	Yes
193	1329	Yes
194	902	Yes
195	658	No
196	690	No
197	921	Yes
198	239	No
199	417	No
200	1666	Yes
201	348	No
202	455	No
203	556	No
204	808	Yes
205	1196	Yes
206	238	No
207	891	No
208	552	No
209	410	No
210	324	No
211	736	No
212	715	Yes
213	391	No
214	716	Yes
215	609	No
216	162	No
217	368	No
218	625	No
219	1500	Yes
220	1404	Yes
221	1813	Yes
222	635	No
223	353	No
224	699	No
225	652	No
226	560	No
227	663	No
228	569	No
229	362	No
230	687	No
231	1038	Yes
232	692	No
233	823	Yes
234	734	No
235	290	No
236	867	Yes
237	220	No
238	718	No
239	559	No
240	845	Yes
241	278	No
242	335	No
243	1732	Yes
244	633	No
245	393	No
246	229	No
247	158	No
248	1651	Yes
249	665	Yes
250	664	No
251	625	No
252	1359	Yes
253	246	No
254	310	No
255	1140	Yes
256	961	Yes
257	747	Yes
258	1104	Yes
259	536	No
260	962	No
261	220	No
262	795	No
263	1213	Yes
264	943	No
265	548	No
266	352	No
267	295	No
268	633	No
269	1380	Yes
270	1268	Yes
271	1567	Yes
272	659	No
273	191	No
274	462	No
275	613	No
276	382	No
277	989	Yes
278	336	No
279	700	No
280	1045	Yes
281	1452	Yes
282	516	No
283	615	No
284	1108	Yes
285	613	No
286	935	Yes
287	734	No
288	76	No
289	470	No
290	1198	Yes
291	561	No
292	1053	Yes
293	902	No
294	828	Yes
295	819	Yes
296	1726	Yes
297	1178	Yes
298	419	No
299	447	No
300	904	Yes
301	573	No
302	830	No
303	497	No
304	1182	Yes
305	1194	Yes
306	940	Yes
307	466	No
308	273	No
309	687	No
310	398	No
311	373	No
312	817	No
313	529	No
314	425	No
315	795	No
316	329	No
317	991	Yes
318	603	No
319	1389	Yes
320	379	No
321	471	No
322	553	No
323	1397	Yes
324	958	Yes
325	236	No
326	403	No
327	1185	Yes
328	740	No
329	493	No
330	614	Yes
331	658	No
332	498	No
333	293	No
334	442	No
335	306	No
336	518	No
337	382	No
338	554	No
339	793	No
340	1262	Yes
341	446	No
342	519	No
343	862	No
344	327	No
345	1755	Yes
346	361	No
347	490	No
348	601	No
349	239	No
350	421	No
351	521	No
352	445	No
353	717	No
354	612	No
355	664	No
356	293	No
357	1253	Yes
358	240	No
359	452	No
360	612	No
361	841	Yes
362	1261	Yes
363	749	No
364	567	No
365	1049	Yes
366	947	Yes
367	801	Yes
368	259	No
369	1730	Yes
370	462	No
371	704	No
372	556	No
373	1264	Yes
374	422	No
375	1436	Yes
376	1358	Yes
377	268	No
378	165	No
379	818	Yes
380	856	Yes
381	486	No
382	1321	Yes
383	1345	Yes
384	387	No
385	1331	Yes
386	1028	Yes
387	766	No
388	839	Yes
389	267	No
390	988	Yes
391	423	No
392	823	No
393	813	No
394	1338	Yes
395	459	No
396	244	No
397	572	No
398	1231	Yes
399	348	No
400	313	No
401	716	No
402	480	No
403	281	No
404	427	No
405	384	No
406	1017	Yes
407	442	No
408	476	No
409	861	No
410	427	No
411	220	No
412	788	No
413	641	No
414	463	No
415	884	Yes
416	1030	Yes
417	531	No
418	772	No
419	402	No
420	482	No
421	658	Yes
422	339	No
423	1339	Yes
424	333	No
425	123	No
426	365	No
427	661	No
428	212	No
429	834	Yes
430	1520	Yes
431	639	No
432	297	No
433	369	No
434	874	Yes
435	799	No
436	336	No
437	222	No
438	587	No
439	422	No
440	1045	Yes
441	260	No
442	1011	Yes
443	708	Yes
444	814	No
445	492	No
446	485	No
447	1165	Yes
448	512	No
449	1574	Yes
450	464	No
451	655	No
452	806	Yes
453	1355	Yes
454	298	No
455	1029	Yes
456	981	Yes
457	990	No
458	834	No
459	951	Yes
460	863	No
461	275	No
462	432	No
463	2178	Yes
464	280	No
465	1159	Yes
466	500	No
467	274	No
468	489	No
469	322	No
470	167	No
471	267	No
472	1152	Yes
473	787	No
474	707	Yes
475	616	No
476	1297	Yes
477	362	No
478	1164	Yes
479	1431	Yes
480	641	No
481	518	No
482	309	No
483	564	No
484	671	No
485	587	No
486	391	No
487	410	No
488	1394	Yes
489	541	No
490	261	No
491	376	No
492	193	No
493	996	No
494	678	Yes
495	488	No
496	494	No
497	612	No
498	965	Yes
499	1146	Yes
500	578	No
501	738	Yes
502	369	No
503	1074	Yes
504	198	No
505	771	No
506	446	No
507	1147	Yes
508	540	No
509	556	No
510	905	Yes
511	431	No
512	836	No
513	1159	Yes
514	339	No
515	243	No
516	525	No
517	529	No
518	1334	Yes
519	946	Yes
520	681	No
521	898	Yes
522	770	No
523	802	No
524	983	Yes
525	537	No
526	793	No
527	757	No
528	782	No
529	346	No
530	1265	Yes
531	818	No
532	182	No
533	475	No
534	830	Yes
535	314	No
536	1375	Yes
537	494	No
538	509	No
539	1556	Yes
540	329	No
541	496	No
542	525	No
543	559	No
544	1287	Yes
545	821	Yes
546	675	No
547	371	No
548	140	No
549	1092	Yes
550	2605	Yes
551	964	Yes
552	373	No
553	871	Yes
554	86	No
555	426	No
556	451	No
557	298	No
558	583	No
559	663	No
560	734	No
561	894	Yes
562	255	No
563	406	No
564	633	No
565	350	No
566	1009	Yes
567	883	Yes
568	161	No
569	378	No
570	1815	Yes
571	262	No
572	258	No
573	573	No
574	217	No
575	167	No
576	849	Yes
577	1365	Yes
578	815	No
579	634	No
580	933	No
581	561	No
582	720	No
583	182	No
584	283	No
585	893	Yes
586	141	No
587	1130	Yes
588	1152	Yes
589	156	No
590	712	Yes
591	249	No
592	389	No
593	1282	Yes
594	386	No
595	1025	Yes
596	688	No
597	268	No
598	798	No
599	1229	Yes
600	536	No
601	572	No
602	719	No
603	222	No
604	157	No
605	898	No
606	309	No
607	553	No
608	1518	Yes
609	779	No
610	806	No
611	559	No
612	878	Yes
613	753	No
614	722	No
615	174	No
616	717	No
617	378	No
618	389	No
619	419	No
620	910	No
621	1829	Yes
622	1346	Yes
623	540	No
624	1165	Yes
625	639	No
626	610	No
627	439	No
628	683	Yes
629	1312	Yes
630	344	No
631	809	No
632	552	No
633	433	No
634	663	No
635	248	No
636	426	No
637	541	No
638	617	No
639	606	No
640	1028	Yes
641	667	No
642	298	No
643	491	No
644	893	Yes
645	390	No
646	853	Yes
647	500	No
648	920	Yes
649	559	No
650	979	No
651	625	No
652	723	No
653	936	Yes
654	537	No
655	126	No
656	899	No
657	270	No
658	961	Yes
659	418	No
660	783	No
661	287	No
662	766	No
663	725	No
664	372	No
665	633	No
666	693	No
667	583	No
668	1468	Yes
669	1245	Yes
670	673	Yes
671	866	No
672	525	No
673	461	No
674	457	No
675	616	No
676	752	Yes
677	349	No
678	558	No
679	554	No
680	642	No
681	723	No
682	1454	Yes
683	767	No
684	225	No
685	689	No
686	675	Yes
687	956	Yes
688	421	No
689	386	No
690	215	No
691	130	No
692	922	Yes
693	680	Yes
694	523	No
695	613	No
696	638	No
697	1092	No
698	1524	Yes
699	763	Yes
700	437	No
701	1754	Yes
702	688	No
703	337	No
704	860	No
705	693	No
706	718	No
707	424	No
708	737	Yes
709	554	No
710	1151	Yes
711	1093	Yes
712	1490	Yes
713	313	No
714	535	No
715	690	No
716	538	No
717	282	No
718	388	No
719	355	No
720	437	No
721	397	No
722	629	No
723	895	Yes
724	665	No
725	733	Yes
726	1078	Yes
727	943	No
728	1097	Yes
729	680	No
730	310	No
731	1179	Yes
732	713	No
733	1135	Yes
734	357	No
735	585	No
736	119	No
737	652	No
738	686	Yes
739	1645	Yes
740	924	No
741	241	No
742	630	No
743	1138	Yes
744	600	No
745	367	No
746	1000	No
747	256	No
748	1058	Yes
749	138	No
750	1009	Yes
751	655	No
752	575	No
753	593	No
754	304	No
755	1078	Yes
756	510	No
757	941	No
758	328	No
759	376	No
760	1009	Yes
761	276	No
762	509	No
763	606	No
764	1553	Yes
765	1298	Yes
766	1534	Yes
767	1744	Yes
768	699	Yes
769	375	No
770	1002	Yes
771	650	No
772	512	No
773	131	No
774	341	No
775	772	Yes
776	1135	Yes
777	1116	Yes
778	276	No
779	1044	Yes
780	900	No
781	730	No
782	519	No
783	1247	Yes
784	210	No
785	1131	Yes
786	390	No
787	865	Yes
788	1039	Yes
789	614	No
790	108	No
791	760	Yes
792	364	No
793	960	Yes
794	639	No
795	963	Yes
796	515	No
797	588	No
798	982	Yes
799	1991	Yes
800	984	Yes
801	775	No
802	162	No
803	778	No
804	1508	Yes
805	478	No
806	505	No
807	1298	Yes
808	931	Yes
809	759	Yes
810	485	No
811	763	No
812	277	No
813	1601	Yes
814	484	No
815	595	No
816	402	No
817	1769	Yes
818	1025	Yes
819	666	No
820	1063	Yes
821	987	Yes
822	545	No
823	338	No
824	1027	Yes
825	1104	Yes
826	967	No
827	466	No
828	224	No
829	376	No
830	841	No
831	469	No
832	535	No
833	464	No
834	375	No
835	343	No
836	356	No
837	541	No
838	483	No
839	323	No
840	507	No
841	2087	Yes
842	342	No
843	963	Yes
844	742	No
845	566	No
846	332	No
847	767	No
848	563	No
849	711	No
850	373	No
851	452	No
852	879	Yes
853	955	Yes
854	932	Yes
855	596	No
856	441	No
857	323	No
858	253	No
859	773	Yes
860	714	No
861	491	No
862	538	No
863	1115	Yes
864	1036	Yes
865	417	No
866	513	No
867	651	Yes
868	1015	No
869	1051	Yes
870	713	No
871	1382	Yes
872	944	Yes
873	553	No
874	641	Yes
875	1048	Yes
876	490	No
877	974	Yes
878	415	No
879	827	No
880	1124	Yes
881	805	Yes
882	720	No
883	617	Yes
884	352	No
885	583	No
886	343	No
887	450	No
888	1282	Yes
889	534	No
890	528	No
891	480	No
892	485	No
893	1443	Yes
894	192	No
895	538	No
896	377	No
897	355	No
898	714	No
899	918	Yes
900	423	No
901	668	No
902	935	Yes
903	707	No
904	525	No
905	575	No
906	626	No
907	486	No
908	407	No
909	584	No
910	573	No
911	1008	Yes
912	455	No
913	856	No
914	1307	Yes
915	583	No
916	550	No
917	461	No
918	539	No
919	775	No
920	1108	Yes
921	1264	Yes
922	887	Yes
923	1653	Yes
924	684	No
925	776	No
926	1140	Yes
927	444	No
928	517	No
929	883	No
930	615	No
931	611	No
932	1450	Yes
933	467	No
934	1568	Yes
935	471	No
936	1657	Yes
937	317	No
938	127	No
939	768	No
940	920	Yes
941	565	No
942	527	No
943	365	No
944	971	Yes
945	452	No
946	570	No
947	837	No
948	559	No
949	509	No
950	476	No
951	658	No
952	356	No
953	898	Yes
954	247	No
955	895	No
956	481	No
957	571	No
958	946	Yes
959	951	Yes
960	238	No
961	457	No
962	743	No
963	961	Yes
964	576	No
965	372	No
966	1070	Yes
967	763	No
968	872	Yes
969	493	No
970	794	No
971	465	No
972	594	No
973	305	No
974	346	No
975	1818	Yes
976	842	Yes
977	753	No
978	1406	Yes
979	715	Yes
980	1102	Yes
981	1171	Yes
982	532	No
983	368	No
984	782	No
985	335	No
986	327	No
987	203	No
988	394	No
989	185	No
990	534	No
991	587	No
992	609	No
993	1178	Yes
994	509	No
995	268	No
996	521	No
997	483	No
998	847	Yes
999	1024	Yes
1000	682	No
1001	624	No
1002	962	No
1003	196	No
1004	866	No
1005	656	No
1006	1616	No
1007	880	No
1008	1777	No
1009	821	No
1010	541	No
1011	2039	No
1012	902	No
1013	1143	No
1014	1097	No
1015	532	No
1016	214	No
1017	858	No
1018	466	No
1019	949	No
1020	998	No
1021	555	No
1022	69	No
1023	921	No
1024	489	No
1025	462	No
1026	710	No
1027	1015	No
1028	581	No
1029	639	No
1030	440	No
1031	187	No
1032	1044	No
1033	760	No
1034	592	No
1035	940	No
1036	86	No
1037	391	No
1038	654	No
1039	101	No
1040	321	No
1041	678	No
1042	763	No
1043	823	No
1044	509	No
1045	667	No
1046	695	No
1047	1497	No
1048	1239	No
1049	276	No
1050	1075	No
1051	1322	No
1052	1110	No
1053	1424	No
1054	211	No
1055	1364	No
1056	867	No
1057	407	No
1058	646	No
1059	395	No
1060	902	No
1061	427	No
1062	1228	No
1063	1008	No
1064	537	No
1065	444	No
1066	451	No
1067	857	No
1068	118	No
1069	688	No
1070	1564	No
1071	2754	No
1072	1011	No
1073	435	No
1074	795	No
1075	1064	No
1076	1307	No
1077	443	No
1078	1104	No
1079	564	No
1080	1106	No
1081	305	No
1082	660	No
1083	407	No
1084	1329	No
1085	1085	No
1086	513	No
1087	429	No
1088	1327	No
1089	1023	No
1090	94	No
1091	988	No
1092	1323	No
1093	1050	No
1094	794	No
1095	769	No
1096	834	No
1097	603	No
1098	488	No
1099	608	No
1100	168	No
1101	1015	No
1102	1203	No
1103	1418	No
1104	1439	No
1105	934	No
1106	1014	No
1107	974	No
1108	1226	No
1109	632	No
1110	2070	No
1111	708	No
1112	411	No
1113	837	No
1114	1450	No
1115	1358	No
1116	1982	No
1117	908	No
1118	873	No
1119	957	No
1120	1677	No
1121	582	No
1122	1195	No
1123	713	No
1124	1136	No
1125	397	No
1126	2252	No
1127	436	No
1128	449	No
1129	569	No
1130	1135	No
1131	1108	No
1132	532	No
1133	251	No
1134	1241	No
1135	254	No
1136	241	No
1137	847	No
1138	1033	No
1139	883	No
1140	834	No
1141	986	No
1142	879	No
1143	1876	No
1144	825	No
1145	752	No
1146	1317	No
1147	656	No
1148	1717	No
1149	1382	No
1150	1359	No
1151	1420	No
1152	749	No
1153	557	No
1154	472	No
1155	461	No
1156	114	No
1157	691	No
1158	984	No
1159	399	No
1160	563	No
1161	1101	No
1162	427	No
1163	1308	No
1164	196	No
1165	1096	No
1166	470	No
1167	499	No
1168	720	No
1169	1282	No
1170	1095	No
1171	473	No
1172	612	No
1173	737	No
1174	572	No
1175	251	No
1176	884	No
1177	611	No
1178	1316	No
1179	722	No
1180	1267	No
1181	256	No
1182	1207	No
1183	493	No
1184	275	No
1185	694	No
1186	1078	No
1187	701	No
1188	1220	No
1189	1295	No
1190	1193	No
1191	963	No
1192	963	No
1193	1069	No
1194	1070	No
1195	173	No
1196	329	No
1197	1261	No
1198	358	No
1199	665	No
1200	1179	No

Sandhills Bank would like to increase the number of customers who use payroll direct deposit as part of the rollout of its new e-banking platform. Management has proposed offering an increased interest rate on a savings account if customers sign up for direct deposit into a checking account. To determine whether this proposal is a good idea, management would like to estimate how many of the 200 current customers who do not use direct deposit would accept the offer. The IT company that handles Sandhills Bank's e-banking has provided anonymized data for 1,000 customers from one of its other client banks that made a similar promotion to increase direct deposit participation. For these 1,000 customers (which correspond to the first 1,000 observations in the fileSandhills), each observation consists of the average monthly checking account balance and whether the customer signed up for direct deposit. Sandhills has designated the data corresponding to its 200 current customers as the test set and these customers are the last 200 observations in the fileSandhills(observations 1,001 to 1,200). As Sandhills has not yet launched its promotion to any of these 200 customers, it has entered an artificial value of zero (i.e., "No") for whether they have signed up for direct deposit. As some of these 200 customers will be the target of the direct-deposit promotion, Sandhills would like to estimate the likelihood of these customers signing up for direct deposit based on their average monthly balance. Classify the data usingk-nearest neighbors for a range of values ofk. Use Balance as the input variable and Direct as the target (or response) variable.

Use the following steps to classify observations using thek-nearest neighbor method in R:

Step 1:	Load and activate the necessary packages.
	library(caret)
Step 2:	Read in data from the file located in the working directory.
	df <- read.csv("sandhills.csv")
Step 3:	Remove the Customer variable which indexes the data set.
	df <- df[,-1]
Step 4:	Set the random number seed (to ensure reproducibility of code).
	set.seed(1975)
Step 5:	Partition the data using the first 1,000 observations for the train set and the last 200 observations for the test set.
	training <- df[1:1000,] testing <- df[1001:1200,]
Step 6:	View the percentage of no's and yes's in the Direct variable in the train set.
	prop.table(table(training$Direct))
Step 7:	Specify repeated cross-validation with 10 folds, repeated 1 time, with oversampling to address the class imbalance issue.
	ctrl <- trainControl(method = "repeatedcv", number = 10, repeats = 1, sampling = "up")
Step 8:	Identify the value ofkthat maximizes accuracy fork-NN.
	knnFit <- train(Direct ~ ., data = training, method = "knn", trControl = ctrl, preProcess = c("center","scale"), tuneLength = 30)
Step 9:	List the output of the cross-validation and plot the classification accuracy (averaged over 10 cross-validation iterations) for various values ofk.
	knnFit plot(knnFit)
Step 10:	Generate thek-NN classification of each observation in the test set.
	knnPredict <- predict(knnFit, newdata = testing)
Step 11:	Compute performance measures ofk-NN on the test set using "Yes" as the positive class.
	confusionMatrix(knnPredict, testing$Direct, positive = "Yes")

(a)	For a default cutoff value of 0.5, what value ofkminimizes the overall error rate on a static validation set or through a 10-fold cross-validation procedure?
(b)	For a cutoff value of 0.5 and the value ofkidentified in part (a), how many of Sandhills Bank's 200 customers (in the test set) doesk-nearest neighbors classify as enrolling in direct deposit?