December 1, 2020 494 min to read

Linear Regression Example

Machine Learning in R

<!DOCTYPE html>

2020-12-01-Multiple-Regressions-Example-1.utf8

TAYKO SOFTWARE

Business Problem

Predicting Software Reselling Profits

Tayko is a software catalog firm. It sells games and educational software. Initially it began as a software manufacturer and later it added third-party titles to its offerings. It has recently put together a revised collection of items in a new catalog. Tayko is preparing to roll out the catalog in a mailing.

Tayko has joined a consortium of catalog firms that specialize in computer and software products. Through this it gets to send its cataloges to a names drawn from a pooled list of customers. It supplies a list of customers to the consortium and in return can get a list of new customers. Members can do predictive modeling on the available records in the pool to get a good set of names generating profits to the company.

In this regard, Tayko has supplied 200000 names to the pool of 5000000 names. It is entitled to draw 200000 names. To draw the best names, it tests with 2000 names for its new catalog. The work presented here uses Logistics Regression Model to help Tayko decide if the drawn list is good for its revenue generation.

OBJECTIVE: From the dataset Tayko.csv, Purchase output variable is considered for the analysis and prediction. The objective of the model is to classify records into ‘PURCHASE’ or "NO PURCHASE’.

The following list explains the details for the independent variables in the dataset:

Variable Name Description

US Is the address in US?

Freq Number of transactions in the last year

last_update_days_ago How many days ago last update was made

1st_update_days_ago How many days ago first update was made

Web_Order Customer placed at least one order via web

Gender Customer is male or not

Address_is_res Address is a residence

Purchase Person made purchase in testing mailing or not

Read in data

library(tibble)
library(kableExtra)
rm(list = ls())
Tayko.df <- read.csv("https://raw.githubusercontent.com/HenryBernreuter/test_data/main/CSV_Tayko.csv")


Tayko.df %>%
  kbl() %>%
  scroll_box(width = "750px", height = "500px")

sequence_number	Address_US	Freq	last_update	Web	Gender	Address_RES	Purchase	Spending
1	1	2	3662	1	0	1	1	128
2	1	0	2900	1	1	0	0	0
3	1	2	3883	0	0	0	1	127
4	1	1	829	0	1	0	0	0
5	1	1	869	0	0	0	0	0
6	1	1	1995	0	0	1	0	0
7	1	2	1498	0	0	1	0	0
8	1	1	3397	0	1	0	0	0
9	1	4	525	1	1	0	1	489
10	1	1	3215	0	0	0	1	174
11	1	0	734	0	1	0	0	0
12	1	2	1275	0	0	1	0	0
13	1	1	2802	1	1	0	0	0
14	1	5	2081	0	1	0	1	1416
15	0	1	1465	0	0	1	1	192
16	0	1	2523	1	0	0	0	0
17	1	2	1801	1	0	1	0	0
18	0	0	3694	1	0	0	0	0
19	1	2	1879	1	1	1	1	130
20	1	0	3120	0	1	0	0	0
21	1	2	2943	1	0	0	1	386
22	1	2	1928	0	1	0	1	161
23	1	1	310	0	0	1	0	0
24	1	2	1463	0	0	1	1	174
25	1	3	3613	1	1	0	1	131
26	1	1	2460	1	0	0	1	189
27	0	0	3394	0	0	0	0	0
28	1	0	1569	1	0	0	0	0
29	1	1	3299	0	0	0	1	90
30	1	2	3744	0	1	0	1	354
31	1	0	3090	0	0	0	0	0
32	0	2	2947	1	0	0	1	352
33	0	1	2123	0	1	0	0	0
34	1	0	2905	1	1	0	0	0
35	0	0	2005	0	1	1	0	0
36	1	1	1158	0	1	1	0	0
37	1	2	2478	0	1	0	1	185
38	0	1	1058	0	0	0	0	0
39	1	1	1774	0	0	0	0	0
40	1	0	3694	1	0	0	0	0
41	1	2	1752	1	0	1	0	0
42	1	2	3698	0	1	0	1	34
43	1	2	1318	0	1	1	1	161
44	1	9	868	1	0	1	1	639
45	1	2	2752	0	1	0	1	638
46	1	1	3338	0	1	1	1	159
47	1	0	3747	0	0	0	0	0
48	1	0	2905	1	0	0	0	0
49	1	2	1786	0	0	0	1	41
50	0	1	316	1	1	0	0	0
51	1	2	2226	0	1	0	1	232
52	1	2	1920	0	0	1	0	0
53	1	8	106	1	0	0	1	1030
54	1	0	1822	1	1	0	0	0
55	1	1	1170	1	1	0	1	375
56	1	0	3157	0	1	1	0	0
57	1	5	1856	0	0	1	1	362
58	0	1	2212	0	0	0	1	95
59	1	2	3338	0	1	0	1	109
60	1	0	3367	0	1	0	0	0
61	1	3	2957	1	1	0	1	136
62	1	1	834	0	1	0	0	0
63	1	3	2908	0	1	0	1	261
64	1	1	906	1	1	0	1	43
65	1	6	1408	0	1	1	1	389
66	1	3	1835	1	0	0	1	80
67	1	1	2803	0	0	0	0	0
68	1	4	479	1	1	0	1	394
69	1	6	1470	0	1	0	1	588
70	1	1	3654	1	1	0	0	0
71	1	1	3716	0	0	1	1	298
72	1	0	3125	0	0	0	0	0
73	1	4	1995	0	1	1	0	0
74	1	0	3747	0	1	0	0	0
75	1	1	2438	0	1	1	0	0
76	1	1	2848	1	1	0	0	0
77	0	1	3125	1	1	0	1	160
78	1	2	541	1	1	1	1	50
79	1	1	2859	1	0	0	1	161
80	1	1	1095	1	0	1	0	0
81	1	1	2508	0	1	0	1	233
82	1	1	2862	0	0	0	1	129
83	1	0	3745	1	0	0	0	0
84	1	2	3698	1	0	0	1	98
85	1	0	3746	0	1	0	0	0
86	1	2	2962	1	0	0	1	132
87	1	2	841	1	0	1	1	158
88	1	1	2912	1	1	0	0	0
89	0	2	458	1	0	0	1	248
90	1	1	1269	1	0	0	1	277
91	1	1	2982	1	1	0	0	0
92	1	1	1415	1	0	1	0	0
93	1	0	4005	0	0	0	0	0
94	1	1	2102	1	1	0	1	54
95	1	1	2872	0	1	0	0	0
96	1	1	2548	1	0	0	1	230
97	1	0	2740	0	0	0	0	0
98	1	0	217	0	0	0	0	0
99	0	1	366	0	1	0	0	0
100	1	3	822	1	0	1	1	287
101	1	0	3746	0	0	0	0	0
102	1	1	3772	0	1	0	0	0
103	1	0	2781	0	1	0	0	0
104	1	1	511	0	0	0	0	0
105	1	1	1112	0	1	0	1	164
106	0	1	2807	1	0	0	1	405
107	1	0	1011	0	1	0	0	0
108	1	1	2907	0	1	0	1	160
109	1	1	3724	0	1	0	1	305
110	1	1	3356	0	0	0	0	0
111	0	3	3791	1	1	1	1	534
112	1	2	3642	1	0	0	0	0
113	0	1	4005	1	1	0	1	105
114	1	1	1130	1	1	0	1	79
115	1	6	1128	1	0	1	1	404
116	1	2	1521	0	1	1	0	0
117	1	2	1882	0	1	1	0	0
118	0	2	1529	0	1	0	1	186
119	1	1	2404	0	0	0	1	114
120	1	1	667	0	1	0	1	324
121	1	1	4157	1	1	0	1	69
122	1	2	3436	1	1	0	1	225
123	1	1	1154	0	0	1	1	205
124	1	1	1263	1	1	0	0	0
125	1	1	1863	0	1	1	1	167
126	1	3	731	0	0	1	0	0
127	1	0	1816	1	0	0	0	0
128	1	1	1302	1	1	0	1	67
129	1	2	785	1	0	0	1	206
130	1	1	3883	0	1	0	1	67
131	1	1	2960	0	1	1	1	120
132	1	5	617	0	0	0	1	356
133	1	1	3009	0	0	1	1	129
134	1	1	2404	0	1	0	0	0
135	1	1	1968	0	1	0	0	0
136	1	4	1121	1	1	0	1	420
137	1	0	2879	1	0	0	0	0
138	1	1	2648	1	1	0	1	130
139	1	0	2891	1	1	0	0	0
140	1	3	1240	1	1	1	1	141
141	1	1	2856	0	1	0	0	0
142	1	0	2977	0	0	0	0	0
143	1	1	2960	1	1	0	1	129
144	1	1	3047	0	1	1	0	0
145	1	0	2765	1	0	0	0	0
146	1	1	1109	0	0	0	1	21
147	1	5	2268	0	0	0	1	605
148	1	1	1147	1	0	0	1	164
149	1	2	2425	0	0	0	1	130
150	1	1	2296	0	0	0	1	161
151	1	0	3619	0	0	0	0	0
152	1	2	1016	1	0	0	1	451
153	1	1	723	0	1	1	0	0
154	1	2	841	0	1	1	0	0
155	1	1	890	0	1	0	0	0
156	1	3	1242	1	1	1	1	432
157	1	0	3747	1	1	0	0	0
158	1	1	2060	0	1	0	0	0
159	1	2	3074	1	0	0	1	163
160	1	3	2024	0	1	0	1	547
161	1	0	3138	1	0	1	0	0
162	1	1	3334	1	0	0	0	0
163	0	0	90	0	1	0	0	0
164	1	1	2632	1	0	0	1	140
165	1	1	3451	1	0	0	0	0
166	0	2	3543	0	0	0	1	129
167	1	1	169	1	1	0	1	163
168	1	3	3662	0	1	1	1	310
169	1	2	582	1	1	0	1	326
170	1	2	969	0	0	1	1	43
171	1	1	1968	1	1	0	0	0
172	0	1	364	1	0	0	1	249
173	0	0	2185	0	1	0	0	0
174	1	0	91	0	0	0	0	0
175	1	0	3502	0	1	0	0	0
176	1	1	3485	0	1	0	0	0
177	1	1	2855	0	1	0	0	0
178	1	1	1890	1	0	0	1	77
179	1	1	3944	1	1	0	1	68
180	1	3	2347	0	0	0	1	219
181	1	1	3237	0	1	1	0	0
182	1	2	3772	1	0	0	1	149
183	0	2	3583	1	0	0	1	140
184	0	1	140	0	1	1	0	0
185	1	1	2960	0	1	1	1	129
186	1	1	1598	1	1	0	1	40
187	1	3	1689	0	0	1	1	108
188	1	1	2675	0	1	0	1	30
189	1	4	1989	0	1	0	1	130
190	1	1	1569	1	1	0	1	32
191	1	1	1906	1	0	0	1	50
192	1	1	2408	1	0	0	1	54
193	1	2	1864	0	1	0	1	243
194	1	1	2947	0	0	0	1	80
195	0	2	2723	1	1	0	1	237
196	1	1	3660	1	1	0	0	0
197	1	1	2893	0	1	0	0	0
198	1	3	2466	1	1	0	1	145
199	1	2	1882	0	0	1	0	0
200	0	1	2502	0	0	1	0	0
201	1	3	2024	1	1	0	1	437
202	1	2	2080	1	1	1	1	35
203	1	2	1856	0	0	1	0	0
204	1	1	583	0	0	0	1	412
205	0	0	3369	0	0	0	0	0
206	1	0	181	0	0	0	0	0
207	1	1	50	1	1	0	1	25
208	1	1	3270	1	0	0	1	153
209	0	1	1926	0	1	0	1	62
210	1	1	1567	1	0	0	1	32
211	1	2	2404	1	0	0	1	187
212	1	1	906	0	0	0	1	80
213	1	2	1577	1	0	0	1	277
214	1	2	1037	0	1	0	1	278
215	0	1	2768	0	0	0	0	0
216	1	1	3522	0	0	0	0	0
217	0	4	511	1	0	0	1	268
218	1	1	833	0	0	0	0	0
219	1	3	191	1	1	0	1	363
220	1	1	182	1	1	0	1	1075
221	1	2	2201	0	0	0	1	164
222	1	3	1962	1	1	1	0	0
223	1	1	3236	1	1	0	1	128
224	0	2	583	1	0	0	1	69
225	1	1	3453	1	0	0	0	0
226	1	0	3746	0	1	0	0	0
227	1	1	2081	1	0	1	1	130
228	0	1	2541	0	0	0	1	174
229	1	3	2205	0	0	0	1	36
230	1	1	3263	0	0	0	0	0
231	1	1	2918	1	1	0	0	0
232	1	1	2996	1	0	0	1	184
233	0	1	1701	0	0	0	1	110
234	1	1	3883	1	1	0	1	33
235	1	2	2802	1	0	0	1	130
236	1	1	1946	1	0	0	1	130
237	1	1	2562	1	1	0	1	35
238	1	1	2705	0	1	0	1	130
239	1	1	2333	1	1	1	1	161
240	1	2	2933	1	1	0	1	54
241	1	1	290	1	1	0	1	163
242	1	0	3745	0	1	0	0	0
243	1	1	3517	0	0	0	0	0
244	1	1	890	0	1	0	0	0
245	0	1	42	0	0	1	0	0
246	0	1	772	0	0	0	1	80
247	1	2	2194	0	0	1	1	161
248	0	2	1141	0	1	0	1	208
249	1	1	3011	0	1	0	1	80
250	1	2	2080	1	0	1	1	35
251	1	0	3507	0	0	0	0	0
252	1	1	1968	1	1	0	0	0
253	1	1	962	0	0	0	1	141
254	1	1	2212	0	0	0	0	0
255	1	1	2648	1	1	0	1	130
256	1	2	1415	0	1	1	0	0
257	1	2	1758	1	1	0	1	167
258	1	1	2383	0	1	0	0	0
259	0	1	814	1	1	0	1	172
260	1	1	58	1	0	0	1	99
261	0	0	3528	1	1	0	0	0
262	1	1	2960	0	0	0	1	130
263	1	2	1882	1	0	0	1	210
264	1	0	2737	0	1	1	0	0
265	1	2	2163	0	0	0	1	107
266	0	1	1683	0	0	0	1	85
267	1	6	800	1	1	0	1	1294
268	1	2	304	1	0	0	1	303
269	1	4	1134	1	0	0	1	271
270	1	1	1361	0	0	0	1	1250
271	1	2	1204	0	0	0	1	81
272	1	1	4065	0	0	0	1	32
273	1	0	616	1	0	1	0	0
274	1	1	1415	0	1	1	0	0
275	0	0	2705	0	1	0	0	0
276	1	1	107	1	1	0	1	129
277	0	2	2009	0	1	0	1	163
278	1	1	833	0	1	0	0	0
279	0	3	1086	0	1	1	1	135
280	1	4	1879	0	0	0	1	164
281	1	0	744	1	0	0	0	0
282	1	2	1786	1	0	0	1	95
283	1	4	1129	0	0	0	1	280
284	1	2	1899	0	0	1	1	166
285	1	0	301	0	1	0	0	0
286	1	1	1162	1	0	1	1	164
287	1	0	2735	0	1	0	0	0
288	1	1	2478	0	0	0	1	136
289	1	1	7	0	1	0	1	129
290	0	2	1130	0	0	0	1	309
291	0	0	1035	1	1	1	0	0
292	1	2	2891	1	0	1	1	143
293	1	1	2599	1	0	0	1	130
294	0	3	1415	0	1	1	0	0
295	1	2	1120	1	1	0	1	200
296	1	1	833	0	1	0	0	0
297	0	3	283	0	0	0	1	405
298	1	2	1752	1	1	0	0	0
299	1	1	3025	1	0	0	1	153
300	1	2	1175	0	0	0	1	44
301	1	2	3791	1	1	0	1	88
302	0	1	2767	1	0	0	1	124
303	1	1	1690	0	0	0	1	90
304	1	1	1666	0	0	0	1	165
305	0	1	2793	1	0	0	1	170
306	1	1	512	0	0	1	0	0
307	1	0	3914	0	0	0	0	0
308	1	1	1290	0	0	0	1	112
309	0	1	1626	0	0	0	1	165
310	1	1	1968	1	0	0	1	255
311	1	1	2305	1	0	0	1	60
312	1	0	1505	0	1	0	0	0
313	1	4	526	1	0	1	1	427
314	1	0	3394	0	1	0	0	0
315	1	1	1991	0	1	0	1	261
316	0	1	3453	0	1	0	0	0
317	0	1	408	0	0	1	1	188
318	1	1	2102	1	1	0	1	161
319	1	4	2100	0	1	0	1	204
320	0	3	3398	1	0	0	1	192
321	0	2	3479	0	0	1	1	189
322	1	0	441	1	1	0	0	0
323	1	2	520	1	1	0	1	212
324	1	2	2194	0	1	1	1	30
325	1	2	217	1	1	0	0	0
326	1	0	3401	0	1	0	0	0
327	1	2	1582	1	0	1	1	3
328	1	1	2380	1	1	0	0	0
329	1	0	3522	0	0	0	0	0
330	1	1	868	1	0	0	0	0
331	1	1	2758	1	0	0	1	161
332	1	3	2481	1	1	0	1	619
333	1	0	3522	0	0	0	0	0
334	1	0	2943	0	1	0	0	0
335	1	1	2404	0	1	0	1	114
336	1	1	2278	1	1	0	0	0
337	1	0	1710	1	0	0	0	0
338	1	1	833	0	0	0	0	0
339	1	1	2529	0	0	0	0	0
340	1	1	868	0	1	0	0	0
341	1	2	916	1	0	1	1	43
342	1	0	2539	0	1	0	0	0
343	1	1	2299	0	1	0	0	0
344	1	1	1864	0	0	0	1	30
345	0	2	295	0	0	0	1	164
346	1	2	1128	0	1	0	1	248
347	1	4	492	1	1	1	1	139
348	1	1	3334	0	1	0	0	0
349	1	1	2962	1	1	0	1	96
350	1	1	4157	0	1	0	1	98
351	1	1	891	1	1	0	1	81
352	1	3	2065	0	1	0	1	197
353	1	1	1346	0	1	1	0	0
354	1	2	2054	1	1	0	1	25
355	0	3	1134	0	0	1	1	314
356	1	1	2831	1	1	0	0	0
357	1	2	681	0	0	1	0	0
358	1	1	3185	0	1	1	0	0
359	1	1	3548	0	0	0	0	0
360	1	0	304	0	1	1	0	0
361	1	2	3382	0	0	0	0	0
362	0	3	841	1	1	1	1	50
363	1	0	2744	1	0	0	0	0
364	0	1	2073	0	0	0	0	0
365	1	2	3655	0	1	0	1	35
366	0	1	1463	1	1	0	0	0
367	1	1	3011	0	1	0	0	0
368	1	1	2802	1	1	0	1	161
369	1	3	2016	1	0	0	1	1353
370	1	10	430	1	1	0	1	1184
371	1	1	3146	1	0	0	1	10
372	1	0	3507	0	0	0	0	0
373	1	2	1536	0	1	0	1	1500
374	1	1	3248	0	0	1	1	132
375	1	1	3095	0	0	0	0	0
376	0	1	3235	1	1	1	1	110
377	1	2	1031	0	1	0	1	191
378	1	3	2201	0	0	0	1	99
379	1	1	2529	1	0	0	1	35
380	1	3	3129	0	1	0	1	217
381	1	2	3283	1	0	0	1	128
382	1	1	1646	1	0	1	0	0
383	1	0	3401	0	0	0	0	0
384	0	3	479	0	0	0	1	459
385	1	1	1192	1	1	0	1	44
386	1	1	314	0	1	0	1	149
387	0	2	506	1	1	0	1	282
388	1	2	2072	0	0	0	1	105
389	1	1	2618	1	1	1	1	6
390	1	1	9	0	1	1	1	196
391	1	1	3278	1	0	0	1	153
392	1	1	217	0	0	1	0	0
393	1	3	1529	0	1	1	1	424
394	1	3	3583	0	0	0	1	205
395	1	2	1856	0	0	1	0	0
396	1	0	2632	0	1	0	0	0
397	1	2	1415	0	1	1	0	0
398	1	0	1249	0	0	0	0	0
399	1	0	3159	1	0	0	0	0
400	0	2	458	1	1	0	1	114
401	0	2	864	0	1	0	1	163
402	1	0	3747	0	0	0	0	0
403	1	2	3975	1	1	0	1	170
404	1	2	2044	1	1	1	1	136
405	1	2	1646	0	1	1	1	83
406	1	0	1709	0	0	0	0	0
407	1	1	2404	0	0	0	1	114
408	1	0	2765	0	0	0	0	0
409	1	1	906	1	0	1	1	141
410	1	2	1498	1	0	1	1	40
411	0	0	2891	0	1	0	0	0
412	0	2	2744	1	0	0	1	86
413	1	1	1646	0	1	1	0	0
414	1	1	1240	0	0	0	0	0
415	1	0	2802	0	1	0	0	0
416	1	0	534	0	1	1	0	0
417	1	2	1346	0	0	1	0	0
418	1	3	1842	1	1	1	1	169
419	1	2	1780	0	0	1	0	0
420	1	2	247	0	0	0	1	324
421	1	1	2919	0	1	1	0	0
422	1	0	2735	0	1	0	0	0
423	1	1	758	0	1	0	1	83
424	1	4	1122	0	0	0	1	274
425	0	3	1137	0	0	1	1	287
426	1	1	644	0	1	1	0	0
427	0	4	1794	1	1	1	1	259
428	1	1	3125	1	0	0	1	103
429	1	1	974	0	0	0	0	0
430	0	0	3747	0	1	0	0	0
431	1	2	216	1	0	0	1	134
432	1	4	1498	0	1	1	1	209
433	1	3	1739	0	1	0	1	226
434	1	0	345	1	1	0	0	0
435	1	2	1801	1	1	0	0	0
436	1	1	216	1	1	0	0	0
437	1	2	1130	0	0	0	1	252
438	0	1	1612	0	0	0	1	43
439	1	3	1568	1	0	0	1	344
440	1	1	2102	1	1	0	1	54
441	1	1	2863	0	0	0	0	0
442	1	1	535	0	1	1	1	149
443	1	1	3430	0	0	0	0	0
444	0	1	1207	0	1	0	0	0
445	1	1	486	0	1	0	1	30
446	1	1	3262	1	1	0	1	158
447	1	1	2249	0	0	0	1	54
448	0	3	2647	0	1	0	1	1255
449	1	2	3593	0	1	0	1	98
450	1	1	1890	0	0	0	1	85
451	1	1	3306	0	0	0	0	0
452	1	0	3747	0	0	0	0	0
453	0	1	4188	1	1	0	1	137
454	1	1	2772	1	0	0	1	135
455	1	2	1261	0	0	0	1	44
456	1	1	827	1	1	0	1	163
457	1	2	3590	1	0	0	1	116
458	1	2	1120	1	0	1	1	172
459	1	3	1570	1	0	0	1	104
460	1	2	1253	0	1	0	0	0
461	1	1	2977	0	0	0	1	70
462	0	2	458	1	0	0	1	271
463	1	1	1962	1	1	1	0	0
464	1	1	3255	1	1	0	0	0
465	0	1	1091	0	0	0	0	0
466	1	1	1010	0	0	0	0	0
467	1	1	2991	1	0	1	1	184
468	1	0	2740	0	0	0	0	0
469	1	0	2728	1	1	0	0	0
470	1	1	4065	0	1	0	0	0
471	1	1	2102	1	0	0	1	161
472	0	0	220	0	1	0	0	0
473	1	1	216	0	1	0	0	0
474	1	2	2950	0	1	0	0	0
475	1	1	23	0	1	0	0	0
476	1	1	2999	1	0	0	1	34
477	1	3	463	1	1	0	1	322
478	1	1	743	0	0	0	0	0
479	1	1	700	1	1	1	0	0
480	1	2	197	1	0	0	0	0
481	1	3	301	0	0	0	1	1249
482	1	0	2905	1	0	0	0	0
483	0	1	665	0	1	1	0	0
484	1	1	308	0	1	0	1	40
485	1	0	2735	0	0	0	0	0
486	1	1	2415	1	1	0	1	35
487	1	1	113	1	0	0	1	308
488	1	4	1653	1	0	1	1	192
489	1	0	3507	0	1	0	0	0
490	1	2	1708	1	1	0	1	122
491	1	1	3822	0	1	0	0	0
492	0	2	1976	0	0	0	1	43
493	1	5	240	0	0	1	1	588
494	1	4	2481	1	0	0	1	160
495	1	0	2877	0	1	0	0	0
496	1	2	2812	0	0	0	1	183
497	1	0	1227	0	1	0	0	0
498	1	3	2052	0	0	0	1	200
499	1	2	2746	1	0	1	1	182
500	0	1	2236	0	0	0	0	0
501	1	1	216	0	1	0	0	0
502	1	0	1451	0	0	0	0	0
503	0	0	3353	1	1	0	0	0
504	1	1	206	0	0	0	0	0
505	1	2	2962	1	1	0	1	95
506	1	1	3655	0	1	0	0	0
507	0	0	3107	0	0	0	0	0
508	1	1	3549	1	1	0	1	229
509	1	0	1710	0	1	0	0	0
510	1	1	196	0	1	0	0	0
511	1	1	3020	1	0	0	1	129
512	1	0	3747	0	1	0	0	0
513	1	0	2767	1	1	0	0	0
514	0	0	3747	1	0	0	0	0
515	1	0	2730	0	0	0	0	0
516	1	3	1592	1	1	1	1	30
517	1	1	681	1	0	1	0	0
518	1	2	3718	0	0	0	1	98
519	1	2	1379	0	0	1	1	63
520	1	3	148	0	1	1	1	214
521	1	0	3353	1	1	0	0	0
522	0	1	206	1	0	0	1	264
523	1	0	2781	0	0	0	0	0
524	1	1	216	1	0	0	0	0
525	0	0	3159	0	1	1	0	0
526	1	1	1792	1	0	0	1	167
527	1	1	2845	0	1	0	1	120
528	1	1	2607	1	0	0	1	6
529	1	1	118	0	0	0	0	0
530	1	2	1498	0	1	1	0	0
531	0	0	3489	0	1	0	0	0
532	1	1	1008	0	0	0	0	0
533	0	1	17	1	0	0	1	94
534	1	2	491	1	1	1	1	139
535	1	1	2941	1	1	0	0	0
536	1	1	1536	0	0	0	0	0
537	0	2	3513	1	1	0	1	219
538	1	1	1184	0	1	0	1	44
539	0	2	3636	1	1	0	1	128
540	1	0	3745	1	0	0	0	0
541	0	2	1995	1	0	1	1	243
542	0	1	2102	1	1	0	1	171
543	1	1	1851	1	1	0	1	30
544	1	1	3684	0	1	0	0	0
545	1	1	3027	1	0	0	1	96
546	0	0	3747	1	0	0	0	0
547	1	3	2957	0	1	0	1	130
548	1	1	2918	1	1	0	0	0
549	1	0	3401	1	0	0	0	0
550	1	1	2355	0	0	0	0	0
551	0	1	2220	0	1	0	1	171
552	0	0	3746	0	1	0	0	0
553	0	5	519	1	0	0	1	585
554	1	0	2740	0	1	0	0	0
555	0	2	2142	0	0	1	1	174
556	1	1	597	1	0	0	1	240
557	0	0	3394	1	1	0	0	0
558	1	1	1618	1	0	1	0	0
559	1	1	1168	1	0	0	1	40
560	1	0	3694	1	0	0	0	0
561	1	5	1374	0	1	0	1	369
562	1	2	1995	1	0	1	1	117
563	1	0	3507	0	0	0	0	0
564	1	1	1415	0	0	1	0	0
565	1	1	204	0	1	0	0	0
566	1	1	3201	1	1	0	1	129
567	1	3	2872	1	0	0	1	122
568	1	1	1795	0	0	0	1	230
569	1	1	581	1	0	0	1	331
570	1	0	3680	0	1	0	0	0
571	0	2	2459	1	1	0	1	153
572	1	2	1842	0	0	1	0	0
573	1	0	3747	0	1	0	0	0
574	1	5	216	1	1	1	1	123
575	0	2	2831	1	1	0	1	170
576	1	1	2417	1	1	0	1	130
577	1	1	3944	1	1	0	1	128
578	1	2	1646	1	0	1	1	130
579	1	1	2564	0	0	0	1	130
580	1	2	3374	1	0	1	1	128
581	1	2	3759	0	1	0	0	0
582	1	3	1134	1	0	0	1	406
583	1	1	1680	1	1	0	1	116
584	1	0	1870	0	1	0	0	0
585	1	3	465	0	1	0	1	133
586	1	2	3642	0	0	0	1	129
587	0	3	260	0	0	1	1	135
588	1	2	3914	0	0	1	1	581
589	0	2	3521	0	0	0	1	53
590	1	2	1850	0	0	0	1	35
591	1	0	181	1	0	0	0	0
592	1	1	2257	1	0	0	1	91
593	1	1	2809	0	1	0	0	0
594	1	2	1842	1	0	1	0	0
595	1	1	2878	0	0	0	0	0
596	1	2	2199	1	1	0	1	81
597	1	1	2445	1	0	1	1	35
598	1	1	3208	0	0	0	0	0
599	1	1	2481	1	1	0	1	153
600	1	1	216	1	0	1	0	0
601	1	7	216	1	1	1	1	150
602	1	1	3199	1	0	0	1	159
603	1	1	2781	1	0	0	1	130
604	1	1	2229	0	1	0	0	0
605	0	0	238	1	1	1	0	0
606	1	0	3398	0	1	0	0	0
607	1	2	2326	1	1	0	1	161
608	1	1	3630	0	1	0	0	0
609	1	1	2751	1	1	0	0	0
610	1	1	532	0	0	1	0	0
611	1	1	3548	0	0	0	0	0
612	0	1	2962	0	0	0	1	136
613	1	1	90	1	0	1	0	0
614	1	1	2863	0	1	0	0	0
615	1	2	162	1	1	0	1	1162
616	0	0	2257	0	1	0	0	0
617	1	0	2877	0	0	0	0	0
618	1	12	520	1	0	0	1	1195
619	0	1	2878	0	1	0	0	0
620	1	0	3522	0	1	0	0	0
621	0	1	1491	0	0	0	1	57
622	1	2	1837	1	0	1	0	0
623	1	1	717	1	0	0	1	30
624	1	3	3740	0	0	0	1	98
625	1	2	2957	0	1	0	1	129
626	1	0	3745	0	1	0	0	0
627	1	2	3213	1	0	1	1	34
628	1	1	1554	0	0	0	1	277
629	1	0	1598	0	0	0	0	0
630	1	1	554	1	0	0	0	0
631	1	1	3791	1	0	0	0	0
632	1	0	1709	0	0	0	0	0
633	1	1	1885	0	1	0	0	0
634	1	1	4065	1	1	0	1	128
635	1	2	850	1	1	0	1	210
636	1	5	15	0	1	0	1	142
637	1	1	3390	1	1	0	0	0
638	1	1	2361	0	1	0	0	0
639	0	1	2704	0	1	0	0	0
640	1	0	3680	0	0	0	0	0
641	1	1	120	0	1	0	1	149
642	1	1	3478	0	0	0	0	0
643	1	1	582	0	1	0	1	69
644	1	1	2704	1	1	0	1	8
645	1	7	1128	1	1	1	1	236
646	1	2	3944	0	1	1	1	362
647	0	0	3094	0	1	1	0	0
648	0	2	114	1	1	0	0	0
649	1	2	3381	1	0	0	1	98
650	1	1	3158	0	0	0	1	34
651	1	1	2759	0	1	0	1	35
652	1	2	1752	0	1	1	0	0
653	1	3	792	0	1	0	1	331
654	1	0	3394	0	1	0	0	0
655	1	0	4096	0	1	0	0	0
656	1	1	3327	1	1	1	1	98
657	1	1	2848	0	0	0	0	0
658	1	1	331	1	1	0	0	0
659	0	1	2662	0	0	0	0	0
660	1	1	1032	1	1	0	0	0
661	0	1	2466	0	1	0	0	0
662	1	0	3171	0	1	1	0	0
663	1	0	2891	1	0	0	0	0
664	0	2	3157	1	1	0	1	162
665	1	2	490	1	0	0	1	276
666	1	2	2012	1	1	1	1	160
667	0	1	2487	1	0	0	1	163
668	1	1	3342	0	1	0	1	98
669	1	1	2787	1	0	0	0	0
670	1	0	1164	0	1	0	0	0
671	1	1	2872	0	1	0	0	0
672	0	1	1091	1	1	0	0	0
673	1	0	4157	1	0	0	0	0
674	1	3	2829	0	1	0	1	163
675	1	2	1346	0	1	1	0	0
676	0	1	1017	0	0	0	1	197
677	1	1	3024	0	1	0	0	0
678	1	1	581	0	1	1	1	203
679	1	0	2221	0	1	0	0	0
680	1	1	3397	1	1	0	0	0
681	1	4	2807	1	0	1	1	239
682	1	1	3041	1	0	0	1	30
683	1	0	3423	1	1	0	0	0
684	1	2	1582	0	1	1	0	0
685	1	3	441	0	1	0	0	0
686	1	1	3397	0	0	0	0	0
687	1	2	2723	0	0	0	1	161
688	1	1	3397	1	0	0	0	0
689	0	1	2878	1	1	0	0	0
690	1	1	2402	0	1	0	1	85
691	1	1	709	1	0	0	1	160
692	1	1	1962	0	0	1	0	0
693	1	1	1673	1	0	0	1	129
694	1	3	804	1	0	1	0	0
695	1	1	2379	0	1	0	1	207
696	1	3	1248	0	0	1	1	202
697	1	1	3883	1	0	0	1	97
698	1	3	1809	1	1	1	1	58
699	1	0	3852	0	1	0	0	0
700	1	0	136	0	1	0	0	0
701	1	1	994	0	1	0	0	0
702	1	5	549	1	1	1	1	484
703	1	1	2941	0	0	0	1	285
704	1	1	609	0	1	0	1	162
705	1	3	2158	1	1	0	1	64
706	0	0	2768	0	1	0	0	0
707	0	1	1052	0	1	0	1	170
708	1	2	2466	1	0	0	1	188
709	1	0	3558	0	0	0	0	0
710	1	2	1882	0	0	1	0	0
711	1	1	2897	1	0	0	0	1
712	1	2	1563	0	0	0	1	160
713	1	1	3166	1	0	1	0	0
714	1	0	1072	0	0	0	0	0
715	1	1	3650	0	0	0	0	0
716	1	2	465	1	0	1	1	260
717	1	1	3496	0	1	0	1	40
718	0	1	3597	0	1	0	0	0
719	1	0	3507	0	0	0	0	0
720	1	2	841	0	1	1	0	0
721	1	4	1128	0	1	0	1	620
722	1	2	3382	1	1	0	1	132
723	1	1	1058	0	0	1	0	0
724	1	1	582	1	1	0	1	89
725	1	2	1582	1	0	1	0	0
726	1	1	2313	0	1	0	1	140
727	0	1	1437	0	1	0	0	0
728	1	2	1879	0	1	1	0	0
729	1	1	4036	0	0	0	1	65
730	0	1	770	0	1	0	1	43
731	1	1	869	1	1	0	0	0
732	0	1	1521	0	0	0	0	0
733	1	2	1120	1	0	0	1	193
734	1	2	1498	1	0	1	1	344
735	0	1	2634	0	1	0	1	116
736	1	2	1120	0	1	0	1	124
737	1	1	2452	1	1	0	1	100
738	1	2	3769	0	0	0	0	0
739	0	3	1436	1	0	1	1	192
740	1	2	1625	0	0	0	1	169
741	1	1	608	0	1	0	0	0
742	1	0	1112	0	0	0	0	0
743	1	2	3054	0	1	1	1	99
744	1	3	1130	0	0	0	1	274
745	1	3	3583	0	0	0	1	100
746	1	2	3695	0	1	0	1	129
747	1	1	1968	0	0	0	0	0
748	1	1	1233	0	1	0	0	0
749	1	1	2158	1	0	0	0	0
750	1	4	567	1	0	1	1	410
751	1	0	104	0	0	0	0	0
752	1	2	3660	0	1	0	0	0
753	1	1	2947	0	1	0	1	230
754	1	1	4157	1	0	0	1	33
755	1	2	3436	0	0	0	1	98
756	0	2	1801	0	0	1	0	0
757	0	0	3107	1	1	0	0	0
758	1	0	3201	0	1	1	0	0
759	1	1	198	1	0	0	0	0
760	1	0	3746	0	0	0	0	0
761	1	3	3570	1	0	0	1	98
762	1	2	3670	1	1	0	1	19
763	1	1	1240	0	1	0	0	0
764	1	0	3311	0	1	0	0	0
765	0	3	1442	0	0	1	1	79
766	1	0	71	0	0	0	0	0
767	0	0	653	0	0	0	0	0
768	1	1	1605	1	1	0	1	85
769	1	3	1164	1	1	0	1	349
770	1	1	829	0	1	0	0	0
771	1	1	2905	0	0	0	0	0
772	1	1	216	0	1	1	0	0
773	1	0	2773	1	1	0	0	0
774	1	0	2735	0	1	0	0	0
775	1	1	1991	0	0	0	1	103
776	1	1	3264	0	1	0	1	39
777	0	2	822	1	0	0	1	71
778	1	1	1752	0	1	0	1	54
779	1	2	479	1	1	0	1	204
780	1	3	2564	0	1	0	1	73
781	1	1	2058	0	1	1	0	0
782	1	0	1274	0	1	0	0	0
783	1	2	1710	0	0	1	1	167
784	0	2	1463	0	1	1	0	0
785	0	0	3694	0	0	0	0	0
786	1	1	2828	0	1	0	1	130
787	1	2	1043	0	1	0	1	335
788	1	2	2080	1	1	0	1	130
789	0	0	3747	1	0	0	0	0
790	1	0	3746	1	0	0	0	0
791	1	0	744	0	1	0	0	0
792	1	2	2656	0	1	0	1	85
793	1	1	1154	1	1	1	1	44
794	1	1	2815	0	0	0	0	0
795	1	2	1758	0	0	1	0	0
796	1	0	3159	0	0	0	0	0
797	1	0	3423	0	1	0	0	0
798	0	1	1319	1	1	0	0	0
799	1	3	3374	0	1	1	1	163
800	1	2	744	0	1	1	0	0
801	1	2	1710	1	1	1	0	0
802	1	2	539	1	1	0	1	131
803	1	1	2333	0	1	0	1	161
804	1	1	2626	1	1	0	1	25
805	1	1	2375	1	1	0	1	145
806	1	0	2779	1	1	0	0	0
807	1	2	2887	0	1	1	1	159
808	1	2	834	1	1	1	0	0
809	1	1	2796	0	0	0	0	0
810	0	1	1464	0	1	0	0	0
811	0	0	3369	1	0	0	0	0
812	0	1	2590	1	1	0	1	163
813	1	1	905	0	1	0	1	81
814	0	2	1379	1	0	1	0	0
815	1	0	3394	0	0	0	0	0
816	0	2	2571	0	0	0	1	174
817	1	2	841	0	0	1	0	0
818	1	0	3401	1	0	0	0	0
819	1	1	3502	0	1	0	0	0
820	1	1	2417	1	1	0	1	270
821	1	1	3158	0	1	0	1	34
822	1	1	2387	0	1	1	0	0
823	0	1	155	0	1	0	1	164
824	1	0	3507	0	1	0	0	0
825	1	0	3746	0	1	0	0	0
826	1	2	807	1	0	0	1	114
827	1	0	1890	0	0	0	0	0
828	1	1	3251	1	1	0	1	15
829	1	1	3269	0	1	0	1	31
830	1	4	218	1	0	0	1	581
831	1	1	930	0	1	1	0	0
832	1	1	890	1	1	0	0	0
833	1	2	1710	1	1	1	0	0
834	1	1	2786	0	1	0	0	0
835	0	11	918	0	1	0	1	1441
836	0	1	920	1	1	0	0	0
837	1	4	1240	0	1	0	1	232
838	1	0	3694	0	1	0	0	0
839	1	2	4005	0	1	0	1	141
840	1	2	1618	1	0	1	1	40
841	1	2	1882	0	0	1	0	0
842	1	1	1646	0	1	1	0	0
843	1	3	3573	0	0	0	1	440
844	1	2	1962	0	0	1	0	0
845	0	1	1589	1	0	0	0	0
846	1	1	1277	1	0	0	1	164
847	1	0	3852	0	1	0	0	0
848	1	1	3024	0	0	0	0	0
849	1	0	3107	0	0	0	0	0
850	0	1	3944	1	1	0	1	49
851	1	4	801	1	1	0	1	253
852	1	3	1759	1	1	1	1	130
853	1	1	2999	1	1	0	1	160
854	0	4	1794	1	1	0	1	525
855	1	2	2975	0	0	0	1	160
856	1	4	610	0	0	1	1	317
857	1	1	3446	0	1	0	0	0
858	1	1	862	0	1	0	0	0
859	1	1	3397	1	0	0	0	0
860	1	1	869	0	1	0	0	0
861	1	1	1261	1	0	1	0	0
862	1	1	1752	0	1	0	1	160
863	1	1	3822	1	0	0	1	65
864	1	1	3047	1	1	1	0	0
865	1	2	744	0	1	1	0	0
866	1	1	1827	1	1	0	0	0
867	1	2	3536	0	1	0	1	128
868	1	3	1121	1	1	0	1	247
869	1	1	3852	1	1	0	1	128
870	1	1	608	0	1	0	0	0
871	1	2	2018	0	1	0	1	161
872	1	0	2744	0	0	0	0	0
873	1	2	1240	1	1	0	1	54
874	1	2	834	0	0	1	0	0
875	1	3	2438	1	0	1	1	227
876	0	1	2487	0	0	0	0	0
877	1	1	2117	0	1	0	1	161
878	1	1	2138	1	0	1	0	0
879	1	3	3522	0	0	0	0	0
880	1	2	2009	0	1	0	1	230
881	1	0	3694	0	1	0	0	0
882	0	2	2418	0	0	0	1	263
883	1	1	1095	1	0	1	0	0
884	1	0	3747	0	1	0	0	0
885	1	0	3158	0	0	0	0	0
886	1	0	162	0	0	0	0	0
887	1	2	1780	1	0	1	1	130
888	1	3	2893	0	1	0	1	160
889	1	0	3680	1	0	0	0	0
890	1	2	1646	0	0	1	0	0
891	1	0	2901	0	0	0	0	0
892	1	1	2863	0	1	1	0	0
893	1	4	332	1	1	0	1	410
894	1	2	1465	0	0	0	1	228
895	1	3	822	0	0	0	1	421
896	1	2	216	1	0	0	1	43
897	1	2	834	1	0	1	0	0
898	1	1	2544	1	0	0	1	130
899	1	1	2912	1	1	0	1	96
900	0	1	17	0	1	0	0	0
901	1	2	1752	1	0	1	0	0
902	1	1	2508	0	0	0	1	9
903	1	1	868	1	1	0	0	0
904	1	0	2900	1	0	0	0	0
905	1	8	1030	1	0	0	1	819
906	0	1	3578	1	0	1	1	130
907	1	1	891	1	1	0	1	163
908	1	0	2968	1	1	0	0	0
909	1	1	2962	0	0	0	1	68
910	1	0	2728	0	0	0	0	0
911	1	0	1232	0	1	0	0	0
912	1	1	3171	0	1	0	1	260
913	0	1	1107	0	0	0	0	0
914	1	1	3454	0	0	0	0	0
915	1	2	2527	0	0	0	1	10
916	1	2	3201	0	0	0	0	0
917	1	1	3822	0	1	0	1	128
918	1	3	1794	1	1	0	1	107
919	1	13	281	1	0	0	1	1443
920	1	0	3944	1	1	0	0	0
921	1	0	2742	0	0	0	0	0
922	1	1	3641	0	1	0	0	0
923	1	3	2814	0	0	0	1	162
924	1	1	2107	1	0	0	1	130
925	0	1	3425	1	1	0	0	0
926	1	1	1218	1	1	0	1	44
927	1	3	400	1	1	0	1	522
928	1	0	3746	0	0	0	0	0
929	1	7	2842	1	0	0	1	1393
930	1	3	486	0	1	1	1	266
931	1	2	3445	0	0	0	0	0
932	1	0	3680	0	0	0	0	0
933	0	1	1190	0	1	0	1	205
934	1	5	1011	0	1	1	1	471
935	1	0	55	0	0	0	0	0
936	1	0	3747	0	0	0	0	0
937	0	1	2053	0	0	0	1	345
938	0	0	2765	0	0	0	0	0
939	1	0	3354	1	1	0	0	0
940	0	0	4036	0	0	0	0	0
941	1	1	3356	0	1	0	0	0
942	1	1	3249	0	1	0	0	0
943	1	0	3522	1	1	0	0	0
944	1	0	2742	0	0	0	0	0
945	1	1	3678	1	1	0	0	0
946	1	1	2530	0	0	0	1	136
947	1	0	2900	0	1	0	0	0
948	1	1	4096	0	0	1	1	97
949	1	1	1638	1	1	0	1	30
950	1	3	2962	1	0	0	1	162
951	1	0	3339	0	1	0	0	0
952	1	1	4096	1	0	0	1	128
953	1	0	3237	0	0	0	0	0
954	1	1	1288	1	0	1	1	30
955	1	7	1502	0	0	1	1	347
956	1	0	3206	0	1	0	0	0
957	0	1	3548	1	1	0	0	0
958	1	2	2072	0	1	0	1	105
959	1	3	91	1	0	0	1	1370
960	1	1	2533	1	1	0	1	9
961	1	0	3680	0	1	0	0	0
962	1	3	2284	1	0	0	1	271
963	1	0	2735	0	1	0	0	0
964	1	3	2799	1	0	0	1	104
965	1	3	744	0	1	1	1	128
966	1	1	3791	0	1	0	0	0
967	0	1	216	1	0	0	1	8
968	0	1	1556	1	1	0	1	46
969	1	1	2404	0	0	0	1	114
970	1	2	2143	0	1	1	0	0
971	1	1	2100	0	0	0	0	0
972	1	1	2382	0	1	0	0	0
973	0	1	659	1	1	0	1	58
974	1	1	2849	1	1	0	0	0
975	1	4	871	0	1	0	1	496
976	1	1	2677	0	1	0	0	0
977	0	3	1137	0	1	0	1	292
978	1	2	1752	0	0	1	0	0
979	0	1	3222	0	0	0	1	33
980	1	11	220	0	0	0	1	1227
981	1	4	701	1	1	0	1	290
982	1	1	2487	1	1	0	0	0
983	1	2	3791	0	1	1	1	98
984	0	1	427	0	1	0	1	56
985	1	0	3394	0	1	0	0	0
986	0	1	919	0	1	0	0	0
987	1	3	715	1	1	1	1	129
988	1	0	3746	0	1	0	0	0
989	1	3	3521	1	1	0	1	331
990	1	1	3278	0	0	0	0	0
991	1	0	3746	1	1	0	0	0
992	1	1	3229	1	1	0	1	279
993	0	1	2648	0	0	0	1	46
994	1	1	868	1	0	0	1	43
995	1	1	3684	0	1	0	0	0
996	1	4	442	1	0	0	1	350
997	1	0	2768	0	1	0	0	0
998	1	8	1130	1	0	1	1	559
999	1	1	2828	1	1	0	1	100
1000	1	0	3522	0	0	0	0	0
1001	1	0	3403	1	1	0	0	0
1002	1	1	3242	0	0	0	0	0
1003	1	3	2200	0	1	1	1	161
1004	1	1	3024	0	1	0	0	0
1005	1	1	1010	1	0	0	0	0
1006	1	3	1242	0	0	1	1	165
1007	1	2	834	0	0	1	0	0
1008	0	2	469	0	0	0	1	338
1009	1	1	2016	0	1	0	1	54
1010	0	3	1379	0	1	0	1	143
1011	1	2	2361	1	1	1	0	0
1012	1	1	427	0	1	0	0	0
1013	1	0	2773	1	1	0	0	0
1014	1	1	791	1	1	0	1	68
1015	1	1	3433	0	1	0	0	0
1016	0	1	3548	0	0	0	0	0
1017	1	2	1801	1	1	1	0	0
1018	1	2	1710	0	1	1	1	311
1019	1	1	198	0	0	0	0	0
1020	1	3	1879	0	1	1	1	164
1021	1	1	2438	1	1	0	1	104
1022	1	0	2024	1	1	0	0	0
1023	0	1	1095	0	1	1	0	0
1024	1	1	1836	1	1	0	1	130
1025	1	2	549	0	0	0	1	215
1026	1	4	2052	1	0	0	1	355
1027	1	2	3706	0	1	0	1	228
1028	1	1	3360	1	0	0	1	128
1029	1	4	2240	0	1	1	1	189
1030	1	1	2802	0	0	0	0	0
1031	1	1	1577	0	1	0	0	0
1032	1	1	1052	1	1	0	1	40
1033	1	6	1122	0	0	1	1	425
1034	1	0	3680	1	1	0	0	0
1035	1	5	534	0	0	0	1	361
1036	1	1	1	1	1	0	1	109
1037	1	2	492	0	1	0	1	43
1038	1	1	2285	1	0	0	0	0
1039	0	0	2781	0	1	0	0	0
1040	1	2	472	1	1	0	1	229
1041	1	1	2768	0	1	0	0	0
1042	1	2	2464	1	1	0	1	86
1043	1	0	3403	0	1	0	0	0
1044	1	1	2977	1	1	0	1	160
1045	0	2	469	1	1	0	1	377
1046	1	2	3566	1	1	0	1	229
1047	1	3	2389	0	1	0	1	385
1048	0	1	2249	1	1	0	1	146
1049	1	1	4096	1	1	0	1	229
1050	1	0	2977	0	1	0	0	0
1051	0	1	2794	1	0	0	0	0
1052	1	2	1618	0	0	1	0	0
1053	1	1	3067	0	0	0	1	229
1054	1	1	3822	1	0	0	0	0
1055	1	1	513	1	1	0	1	119
1056	1	2	442	0	0	0	1	138
1057	1	6	471	0	1	1	1	623
1058	1	2	1962	1	0	1	0	0
1059	0	1	1800	0	0	1	0	0
1060	0	5	1340	1	0	0	1	262
1061	1	0	1451	0	0	0	0	0
1062	0	1	912	0	0	0	1	551
1063	1	1	2752	0	1	1	1	35
1064	1	2	1379	1	0	1	1	63
1065	1	2	1415	0	0	1	0	0
1066	1	6	380	1	1	0	1	450
1067	1	2	3791	0	0	0	0	0
1068	1	1	1261	1	0	1	1	44
1069	1	2	1379	0	0	1	1	193
1070	1	1	2072	0	1	0	0	0
1071	1	0	3500	0	1	0	0	0
1072	1	12	220	0	1	0	1	1446
1073	1	1	3339	1	0	0	1	38
1074	0	1	604	1	0	0	0	0
1075	0	2	1521	1	0	1	0	0
1076	1	2	3444	0	1	0	1	71
1077	0	2	1582	0	1	0	0	0
1078	1	0	2905	0	0	0	0	0
1079	1	1	967	1	0	0	0	0
1080	1	2	2571	1	1	0	1	161
1081	1	1	2857	0	0	0	0	0
1082	1	2	1882	0	0	1	0	0
1083	0	0	3502	0	1	0	0	0
1084	1	2	2257	1	0	0	1	264
1085	0	1	2961	0	1	1	0	0
1086	1	2	1882	1	0	1	1	4
1087	1	2	3608	1	0	0	1	22
1088	0	3	486	0	1	0	1	321
1089	1	2	490	0	0	0	1	204
1090	0	1	3040	1	1	0	0	0
1091	0	1	1318	1	1	0	0	0
1092	0	2	1920	1	1	0	1	138
1093	1	2	1882	0	1	1	0	0
1094	1	0	3694	1	1	0	0	0
1095	0	1	2978	1	0	0	0	0
1096	1	2	1882	0	1	1	0	0
1097	1	1	1010	1	0	0	0	0
1098	0	7	700	1	0	1	1	438
1099	1	6	239	1	0	0	1	1161
1100	1	1	486	1	1	0	1	159
1101	1	2	1882	1	1	1	0	0
1102	1	1	3009	1	1	0	1	184
1103	1	1	3311	1	1	0	0	0
1104	1	2	2460	1	1	0	1	162
1105	1	3	455	0	0	1	0	0
1106	1	2	1021	0	1	1	1	285
1107	1	3	1109	0	0	1	1	173
1108	1	1	1350	1	1	0	0	0
1109	1	1	2327	0	0	1	1	158
1110	1	1	724	1	1	0	1	43
1111	1	4	1856	1	0	1	0	0
1112	1	0	3694	0	1	0	0	0
1113	0	1	828	0	0	0	0	0
1114	1	1	2506	0	0	0	0	0
1115	1	2	2960	0	1	1	1	160
1116	0	1	372	0	0	0	1	149
1117	1	2	1962	0	0	0	0	0
1118	1	1	556	1	0	0	1	174
1119	0	0	3124	0	1	0	0	0
1120	1	1	2662	1	1	0	0	0
1121	0	1	3548	1	0	0	0	0
1122	1	1	2404	0	0	0	0	0
1123	1	2	1521	0	1	0	0	0
1124	1	0	3747	1	1	0	0	0
1125	1	1	23	1	1	0	0	0
1126	1	1	658	0	1	0	1	56
1127	0	1	1402	1	0	0	0	0
1128	1	1	3400	0	0	0	0	0
1129	1	1	3458	0	0	0	0	0
1130	1	1	1879	0	0	1	0	0
1131	1	1	2856	0	0	0	0	0
1132	1	1	2872	0	0	0	0	0
1133	0	1	829	0	1	0	1	89
1134	1	1	1779	0	0	0	0	0
1135	1	0	1036	1	1	0	0	0
1136	1	7	360	1	0	0	1	1305
1137	1	1	995	0	1	1	0	0
1138	1	0	3694	1	1	0	0	0
1139	0	3	835	1	0	0	1	241
1140	1	1	890	1	0	0	0	0
1141	1	0	3159	1	0	0	0	0
1142	1	1	3292	0	0	0	1	128
1143	1	1	2467	1	1	0	1	130
1144	1	1	1619	1	0	0	1	20
1145	0	1	1079	1	1	0	0	0
1146	1	1	2739	0	0	0	1	8
1147	1	4	1877	0	0	0	1	255
1148	1	0	2877	0	0	0	0	0
1149	1	1	3286	1	0	0	1	128
1150	1	0	2786	0	1	0	0	0
1151	1	0	2900	0	0	0	0	0
1152	0	0	3747	1	1	0	0	0
1153	1	1	3822	0	1	0	1	97
1154	1	1	23	1	1	0	0	0
1155	1	1	27	0	1	0	0	0
1156	1	1	868	0	1	0	0	0
1157	1	1	456	1	0	1	1	306
1158	1	2	3201	0	1	0	0	0
1159	1	1	134	0	0	0	1	163
1160	1	1	4157	1	1	0	1	254
1161	1	1	204	0	1	0	0	0
1162	0	1	1617	1	1	0	1	170
1163	1	0	1583	0	0	0	0	0
1164	1	1	2863	0	0	0	0	0
1165	1	3	499	1	1	0	1	237
1166	1	1	829	1	1	0	1	202
1167	1	1	220	0	0	0	0	0
1168	1	0	3403	0	1	0	0	0
1169	1	3	835	0	0	1	1	56
1170	1	0	3745	0	0	0	0	0
1171	0	1	437	0	0	0	1	114
1172	1	1	2996	0	1	0	0	0
1173	1	2	2809	0	0	0	1	191
1174	1	0	3746	0	1	0	0	0
1175	1	1	4065	0	1	1	1	99
1176	1	0	3619	0	1	0	0	0
1177	1	2	3641	1	0	0	0	0
1178	1	0	2376	1	0	0	0	0
1179	0	3	743	1	1	1	1	47
1180	1	2	804	1	0	0	1	303
1181	1	0	2786	0	1	0	0	0
1182	0	0	2859	0	1	0	0	0
1183	1	2	1710	0	0	1	0	0
1184	1	2	583	1	1	0	1	149
1185	0	0	2767	0	1	0	0	0
1186	1	0	3914	0	1	0	0	0
1187	1	3	471	1	1	0	1	249
1188	1	5	542	0	0	0	1	578
1189	1	3	463	0	0	0	1	412
1190	1	1	925	1	1	0	1	104
1191	1	1	2863	1	1	0	0	0
1192	0	0	3522	0	1	0	0	0
1193	1	1	3587	1	1	0	1	33
1194	1	1	854	0	1	0	0	0
1195	1	1	2963	1	1	0	1	165
1196	0	0	3507	1	1	0	0	0
1197	1	1	4096	1	0	0	0	0
1198	0	1	1010	0	1	0	0	0
1199	1	0	3747	1	0	0	0	0
1200	0	0	2891	0	1	0	0	0
1201	1	1	3125	1	0	0	1	103
1202	1	2	2899	1	1	0	1	320
1203	1	2	744	0	1	1	0	0
1204	0	1	2564	0	0	0	0	0
1205	1	0	3747	0	1	0	0	0
1206	0	2	3474	1	1	0	1	45
1207	1	1	1646	0	1	1	0	0
1208	1	0	3680	0	0	0	0	0
1209	1	5	525	0	1	0	1	490
1210	1	0	3353	0	0	0	0	0
1211	0	0	2765	1	0	0	0	0
1212	1	0	3114	0	0	0	0	0
1213	1	1	2558	1	1	0	0	0
1214	1	1	2634	0	1	0	0	0
1215	0	4	1018	1	0	0	1	405
1216	1	2	869	0	1	0	1	117
1217	1	1	689	1	0	0	0	0
1218	1	2	2856	0	0	0	1	78
1219	0	0	2632	0	0	0	0	0
1220	1	1	2943	1	1	0	1	183
1221	1	1	2851	0	1	0	0	0
1222	1	1	2522	0	1	1	0	0
1223	1	1	3772	0	1	0	0	0
1224	1	4	37	0	0	1	1	624
1225	1	0	3401	0	0	0	0	0
1226	1	2	2318	1	0	0	1	161
1227	1	2	2165	1	1	0	1	157
1228	1	1	2838	1	0	0	1	35
1229	1	0	2730	0	0	0	0	0
1230	1	0	1451	1	1	0	0	0
1231	1	6	408	1	0	0	1	197
1232	1	1	3180	0	0	0	0	0
1233	0	1	532	0	0	0	0	0
1234	1	2	2817	1	0	0	1	163
1235	1	1	3613	0	1	0	0	0
1236	1	3	1877	1	1	0	1	212
1237	1	1	3270	0	1	0	1	38
1238	1	1	3143	0	1	0	1	229
1239	0	2	511	0	0	1	1	173
1240	1	0	2009	0	1	0	0	0
1241	1	3	1017	1	1	0	1	254
1242	1	1	2744	1	1	0	1	230
1243	1	2	1521	1	0	1	1	40
1244	1	1	784	1	1	1	0	0
1245	0	3	1121	1	1	0	1	288
1246	1	1	2787	1	1	0	0	0
1247	1	1	2255	0	1	0	1	161
1248	0	2	1618	0	1	1	0	0
1249	1	2	1436	0	1	1	0	0
1250	1	2	1275	1	1	1	1	140
1251	0	1	3548	0	0	0	0	0
1252	0	3	1241	1	0	1	1	255
1253	1	1	3215	0	0	0	1	230
1254	1	1	1962	0	0	1	0	0
1255	1	0	3403	1	1	0	0	0
1256	1	2	3564	1	0	1	1	128
1257	1	4	463	0	1	0	1	517
1258	1	0	2569	1	0	0	0	0
1259	1	1	1221	1	1	1	1	164
1260	1	3	1430	0	1	1	1	65
1261	1	1	364	0	1	0	1	149
1262	1	0	3694	0	1	0	0	0
1263	1	4	463	0	0	1	1	406
1264	1	1	3304	0	0	0	1	129
1265	0	0	4096	0	0	0	0	0
1266	1	1	2977	0	0	1	0	0
1267	1	0	3852	1	0	1	0	0
1268	1	0	3354	0	1	0	0	0
1269	0	1	2274	0	0	0	1	46
1270	1	1	1221	1	1	1	1	44
1271	1	1	3464	1	1	0	0	0
1272	1	1	3269	1	0	0	0	0
1273	1	2	3426	1	0	0	1	198
1274	1	2	3243	1	0	1	1	7
1275	1	1	3883	1	0	1	1	128
1276	1	1	3353	1	0	0	1	213
1277	1	1	1147	1	1	0	1	201
1278	1	0	3852	0	0	1	0	0
1279	1	1	2527	1	0	0	1	161
1280	1	2	1758	0	0	0	1	230
1281	1	1	216	0	0	1	0	0
1282	1	1	792	1	1	1	0	0
1283	1	1	3717	0	1	0	0	0
1284	1	1	3755	0	1	0	0	0
1285	1	1	4188	1	0	0	0	0
1286	1	1	666	0	0	0	1	265
1287	1	2	3605	0	0	0	1	246
1288	1	0	3536	0	1	0	0	0
1289	0	2	255	1	1	0	1	318
1290	0	0	2915	0	1	1	0	0
1291	1	0	3401	0	0	0	0	0
1292	1	5	1857	0	1	0	1	240
1293	1	1	890	1	1	0	0	0
1294	1	1	2807	1	0	0	1	54
1295	1	0	167	0	0	1	0	0
1296	1	1	1897	0	0	0	1	165
1297	1	1	2618	0	0	0	0	0
1298	0	3	1969	1	0	1	1	171
1299	1	2	3709	1	1	0	1	98
1300	1	1	217	1	1	0	1	40
1301	1	0	2773	1	0	0	0	0
1302	1	0	3430	0	0	0	0	0
1303	1	5	295	1	1	1	1	531
1304	1	0	3944	0	1	0	0	0
1305	1	1	2914	1	1	0	1	85
1306	1	0	3680	1	0	0	0	0
1307	0	1	3328	0	1	0	0	0
1308	1	2	1521	1	1	1	0	0
1309	0	2	1752	0	0	1	0	0
1310	1	0	3746	1	0	0	0	0
1311	1	4	2850	1	1	1	1	129
1312	1	2	1752	1	1	1	0	0
1313	1	5	72	1	1	0	1	229
1314	1	2	744	0	1	1	0	0
1315	1	1	2128	0	0	0	0	0
1316	1	9	1128	1	1	0	1	1289
1317	1	0	3680	0	1	0	0	0
1318	1	0	3104	0	1	1	0	0
1319	1	1	2310	0	1	0	1	100
1320	1	1	897	1	0	0	0	0
1321	1	3	2235	1	0	0	1	390
1322	1	1	1878	1	1	0	1	35
1323	1	1	3020	0	1	0	1	129
1324	1	2	1592	1	0	1	1	40
1325	1	4	14	1	0	1	1	303
1326	1	0	3747	0	1	0	0	0
1327	1	0	462	0	1	0	0	0
1328	1	1	2696	0	0	0	1	230
1329	1	1	3066	0	1	1	0	0
1330	0	1	2101	0	1	0	1	146
1331	1	6	1581	0	1	0	1	158
1332	1	3	1168	0	1	1	1	40
1333	1	2	1882	0	1	1	0	0
1334	1	1	2383	0	0	0	1	161
1335	0	2	2548	1	1	0	1	236
1336	1	1	2912	0	1	0	1	161
1337	1	3	1021	1	0	0	1	182
1338	1	0	4157	1	0	0	0	0
1339	0	2	1701	0	1	0	1	192
1340	0	0	3401	1	0	0	0	0
1341	1	10	289	0	1	0	1	1214
1342	0	0	3401	0	0	0	0	0
1343	1	2	3374	1	0	0	1	130
1344	1	1	1491	0	1	0	0	0
1345	1	1	2719	1	0	0	1	105
1346	0	1	1228	0	1	0	0	0
1347	1	0	3694	1	1	0	0	0
1348	1	1	647	1	0	0	0	0
1349	1	1	2982	0	1	0	0	0
1350	1	3	995	1	1	0	1	236
1351	1	1	178	0	1	0	0	0
1352	1	2	1780	0	1	1	0	0
1353	1	1	653	0	0	0	1	263
1354	1	3	1995	0	1	1	1	220
1355	1	0	3394	1	0	0	0	0
1356	1	0	3680	0	1	0	0	0
1357	0	1	2268	1	1	0	0	0
1358	1	0	2725	1	1	0	0	0
1359	1	1	2400	0	1	0	1	161
1360	1	1	1512	1	0	0	0	0
1361	1	3	3620	1	0	0	1	72
1362	1	2	429	0	1	0	1	303
1363	1	1	2318	0	0	0	1	85
1364	0	0	3489	0	1	0	0	0
1365	0	1	1058	1	0	1	0	0
1366	0	1	28	0	0	0	1	255
1367	1	0	2173	0	0	0	0	0
1368	1	3	1879	1	1	1	1	258
1369	0	0	2982	0	1	0	0	0
1370	1	2	2891	1	1	0	1	153
1371	1	2	1920	1	1	1	1	130
1372	1	2	1646	0	1	1	0	0
1373	0	3	822	0	0	0	1	429
1374	0	2	1962	0	0	1	0	0
1375	1	1	1100	1	0	0	1	164
1376	0	2	2863	0	1	0	0	0
1377	0	3	2333	0	1	0	1	175
1378	1	1	3660	1	1	0	0	0
1379	1	0	3159	0	0	0	0	0
1380	1	1	2962	1	1	0	1	128
1381	1	0	3122	0	0	0	0	0
1382	1	1	608	1	1	0	0	0
1383	1	0	2901	0	1	0	0	0
1384	1	1	3157	1	1	0	1	220
1385	1	1	890	0	1	0	0	0
1386	1	1	2400	1	1	0	1	13
1387	1	1	644	0	1	0	0	0
1388	1	1	2677	0	0	0	1	161
1389	1	3	772	0	0	0	1	551
1390	1	3	2887	0	1	0	1	162
1391	1	1	1261	1	0	1	1	45
1392	1	2	1346	0	0	0	0	0
1393	1	0	2765	0	1	0	0	0
1394	1	0	2900	1	0	0	0	0
1395	1	0	2508	0	0	1	0	0
1396	1	0	2018	0	0	0	0	0
1397	1	2	1801	0	0	1	0	0
1398	0	1	255	1	0	0	1	244
1399	1	2	217	1	1	1	1	81
1400	0	1	658	0	1	1	1	203
1401	1	1	2723	0	1	0	0	0
1402	1	1	2464	0	0	0	1	35
1403	1	2	1842	0	1	1	0	0
1404	1	1	2960	0	0	1	1	160
1405	1	0	3694	0	0	0	0	0
1406	1	2	1498	0	1	1	0	0
1407	1	0	1242	0	0	0	0	0
1408	1	1	3249	0	0	0	0	0
1409	0	1	2880	1	1	0	0	0
1410	1	0	2960	0	1	0	0	0
1411	0	1	2282	0	0	1	0	0
1412	1	2	1346	0	1	1	0	0
1413	1	1	1968	1	0	0	0	0
1414	1	0	3522	1	0	0	0	0
1415	1	1	3125	1	0	0	0	0
1416	0	1	687	0	1	1	0	0
1417	0	1	3458	0	1	0	0	0
1418	0	0	2728	0	0	0	0	0
1419	1	1	889	1	0	0	0	0
1420	1	3	3433	1	1	0	1	99
1421	1	1	192	0	0	0	0	0
1422	1	0	2779	1	1	0	0	0
1423	0	0	3528	0	0	0	0	0
1424	1	2	3390	0	0	1	1	98
1425	1	0	3061	0	0	1	0	0
1426	1	2	2142	0	1	0	1	68
1427	1	1	2873	1	1	1	1	128
1428	1	0	553	0	0	0	0	0
1429	1	1	2848	0	0	0	0	0
1430	1	2	1995	1	0	1	1	117
1431	1	1	3461	1	1	0	1	198
1432	1	0	3536	1	0	0	0	0
1433	1	5	1240	0	1	0	1	271
1434	1	0	3747	0	1	0	0	0
1435	1	1	2324	0	0	0	0	0
1436	1	0	1044	0	1	1	0	0
1437	0	3	1498	0	1	1	1	162
1438	1	1	3465	0	0	0	0	0
1439	1	0	204	0	1	0	0	0
1440	1	1	2955	1	0	1	1	184
1441	1	0	3619	0	1	0	0	0
1442	1	1	3430	0	1	0	0	0
1443	0	2	1865	1	0	1	0	0
1444	1	1	751	0	1	0	1	43
1445	1	2	3391	0	1	0	0	0
1446	1	1	3683	0	1	1	0	0
1447	1	1	2481	1	1	0	1	130
1448	1	2	3791	0	0	0	1	198
1449	1	1	120	1	1	0	0	0
1450	0	1	2599	1	0	0	1	149
1451	1	2	1135	1	1	0	1	281
1452	0	0	3747	0	0	0	0	0
1453	0	1	4036	0	1	1	1	129
1454	1	0	2186	0	0	0	0	0
1455	1	5	520	0	0	0	1	456
1456	0	2	3552	1	1	0	1	45
1457	0	1	1091	1	0	0	0	0
1458	1	1	567	1	1	1	1	139
1459	1	1	167	1	0	0	1	43
1460	0	0	2803	0	0	0	0	0
1461	1	0	3401	0	1	0	0	0
1462	1	0	3745	0	1	0	0	0
1463	0	1	2697	1	1	0	0	0
1464	1	2	619	1	1	1	1	43
1465	0	1	717	1	1	0	1	40
1466	1	1	3311	0	0	0	0	0
1467	1	1	27	1	0	0	0	0
1468	1	0	2837	0	0	0	0	0
1469	1	2	1149	1	0	0	1	411
1470	1	1	2213	0	0	0	1	65
1471	0	0	2879	0	1	0	0	0
1472	1	2	3405	1	1	0	1	229
1473	1	1	2900	0	1	0	0	0
1474	1	1	1647	1	1	0	1	267
1475	1	2	3374	1	1	0	1	34
1476	1	1	2305	0	0	0	1	161
1477	1	1	2856	1	1	0	1	130
1478	1	1	3600	0	0	1	1	167
1479	1	4	519	0	1	0	1	422
1480	1	2	1752	0	0	1	0	0
1481	1	0	3694	1	1	0	0	0
1482	0	1	2961	0	1	0	0	0
1483	1	1	3464	0	1	0	0	0
1484	1	0	616	0	1	0	0	0
1485	1	1	3052	1	0	0	1	49
1486	1	2	2456	1	0	0	1	266
1487	1	1	1968	0	0	0	0	0
1488	1	2	3615	0	0	0	1	270
1489	0	0	3746	1	1	0	0	0
1490	1	0	1224	0	1	0	0	0
1491	1	1	1008	1	1	0	0	0
1492	1	1	3166	0	1	0	0	0
1493	0	1	976	1	0	0	1	54
1494	1	1	469	0	0	1	1	163
1495	1	0	3914	0	0	0	0	0
1496	1	3	3405	0	0	0	1	131
1497	1	1	2710	0	0	1	0	0
1498	1	0	3694	0	0	0	0	0
1499	1	2	757	0	1	0	1	163
1500	1	6	79	0	0	0	1	415
1501	1	1	861	1	1	0	1	65
1502	0	1	3552	1	1	0	1	100
1503	1	0	2542	0	0	0	0	0
1504	1	1	1112	1	1	0	0	0
1505	1	0	2905	0	0	0	0	0
1506	1	1	1836	1	1	0	1	40
1507	1	1	3615	1	0	0	1	43
1508	1	1	2886	1	0	0	0	0
1509	0	1	2872	0	0	0	0	0
1510	1	2	1780	0	1	1	0	0
1511	1	0	3094	0	0	0	0	0
1512	1	1	923	1	0	0	0	0
1513	1	1	1456	0	1	0	0	0
1514	1	1	3306	0	1	0	0	0
1515	1	1	2298	1	1	0	0	0
1516	0	1	3304	0	0	0	1	140
1517	1	3	3387	1	1	0	1	203
1518	1	0	2885	0	0	0	0	0
1519	0	1	2551	0	1	0	1	282
1520	1	1	2681	1	1	0	1	130
1521	1	1	2996	1	0	0	1	34
1522	1	3	1031	1	0	1	1	214
1523	1	1	2530	0	1	0	1	130
1524	1	1	2690	0	0	0	0	0
1525	1	3	2934	0	0	0	1	160
1526	1	2	3768	1	0	0	1	198
1527	1	1	574	1	1	0	1	495
1528	0	4	1521	1	1	1	1	20
1529	1	5	463	1	1	0	1	402
1530	1	2	1882	1	0	1	0	0
1531	1	3	2348	1	0	0	1	207
1532	0	1	115	0	0	0	1	164
1533	0	2	1197	1	0	0	1	213
1534	0	2	987	0	1	1	1	58
1535	1	1	868	1	1	0	0	0
1536	1	0	3694	0	0	0	0	0
1537	0	1	2891	1	1	1	1	273
1538	1	3	3724	1	0	0	1	38
1539	1	1	3024	1	1	0	1	129
1540	1	1	2982	0	1	0	0	0
1541	1	1	2912	1	1	0	1	161
1542	0	2	3642	1	1	0	1	125
1543	1	2	1240	1	0	0	1	371
1544	0	1	973	1	0	1	1	243
1545	1	3	216	1	1	0	1	360
1546	1	1	2583	0	1	0	1	55
1547	1	0	2373	0	1	0	0	0
1548	1	3	463	1	0	1	1	302
1549	1	3	3376	0	0	1	1	132
1550	1	1	2289	1	0	0	1	230
1551	1	1	3464	1	0	0	1	38
1552	1	2	981	0	1	0	0	0
1553	1	2	2831	0	0	0	1	100
1554	0	1	822	1	1	0	1	56
1555	0	1	1232	0	0	0	0	0
1556	1	1	2831	1	1	0	1	160
1557	1	1	701	0	1	0	0	0
1558	1	1	366	0	0	0	0	0
1559	1	1	2578	1	0	0	1	161
1560	1	3	1206	0	1	0	1	195
1561	1	2	835	1	1	0	1	99
1562	0	2	2233	0	0	0	1	189
1563	1	2	3709	1	1	0	1	198
1564	1	2	3704	1	1	0	1	326
1565	1	1	1267	1	0	0	0	0
1566	1	1	3241	1	0	0	1	48
1567	1	0	2728	0	1	0	0	0
1568	1	1	3243	0	1	0	1	183
1569	1	0	2618	1	0	0	0	0
1570	1	0	2900	0	0	0	0	0
1571	1	1	673	0	1	1	0	0
1572	1	1	2278	0	0	0	1	54
1573	1	0	3944	0	1	0	0	0
1574	1	3	1836	0	0	0	1	179
1575	1	1	2331	0	1	0	0	0
1576	1	1	2074	0	1	0	1	130
1577	1	1	3009	1	0	0	0	0
1578	0	1	640	1	1	0	1	58
1579	1	2	1235	0	0	1	0	0
1580	0	3	1646	0	0	1	1	98
1581	1	0	899	0	1	0	0	0
1582	0	2	2803	1	1	0	0	0
1583	1	2	1868	1	0	0	1	49
1584	1	1	2467	1	0	0	1	136
1585	0	3	1722	0	0	1	1	439
1586	1	0	3680	0	1	0	0	0
1587	1	1	3265	0	1	0	1	98
1588	1	2	3684	1	1	0	1	69
1589	1	1	2618	0	0	0	1	130
1590	1	0	4127	0	1	0	0	0
1591	1	2	1226	0	0	1	1	40
1592	1	2	1582	0	1	0	0	0
1593	1	1	1240	1	1	0	0	0
1594	1	2	2375	0	1	1	1	318
1595	1	5	90	0	0	0	1	399
1596	1	2	1436	0	0	1	0	0
1597	1	1	3311	0	0	0	1	68
1598	1	1	2962	1	1	0	1	181
1599	1	1	2310	1	0	0	1	136
1600	1	4	245	1	0	0	1	655
1601	0	1	1322	0	1	0	0	0
1602	1	4	77	0	0	1	1	407
1603	1	1	2192	1	0	0	0	0
1604	1	1	2690	1	0	0	1	163
1605	1	1	2829	0	0	1	1	185
1606	1	1	253	0	1	1	0	0
1607	1	1	3339	0	0	0	0	0
1608	1	1	2499	1	0	0	1	85
1609	0	0	2009	1	0	0	0	0
1610	1	2	1863	1	0	0	1	136
1611	1	1	2005	0	1	0	0	0
1612	0	1	1164	0	0	0	0	0
1613	1	0	3975	0	1	0	0	0
1614	1	0	3185	0	1	0	0	0
1615	1	3	1400	1	0	1	1	63
1616	1	1	3611	0	0	0	1	173
1617	1	0	2901	0	0	0	0	0
1618	1	1	4036	1	1	1	1	97
1619	0	5	1143	1	0	0	1	1123
1620	1	2	1920	0	1	1	0	0
1621	1	1	2807	0	0	1	1	60
1622	1	0	843	0	1	0	0	0
1623	1	1	3125	1	0	0	0	0
1624	1	1	1584	0	1	0	1	140
1625	0	1	1087	1	1	0	1	263
1626	1	1	723	0	1	1	0	0
1627	1	1	197	0	1	0	0	0
1628	1	4	1856	0	1	0	1	141
1629	0	0	3500	1	0	0	0	0
1630	0	0	3401	1	1	0	0	0
1631	0	1	2996	0	0	0	1	150
1632	1	1	4188	0	0	0	1	127
1633	1	2	1582	1	0	1	0	0
1634	1	2	1646	0	0	1	1	167
1635	1	0	2728	0	0	0	0	0
1636	1	0	2009	0	0	0	0	0
1637	1	2	1582	0	1	1	0	0
1638	0	1	3390	1	0	0	0	0
1639	0	0	3528	0	1	0	0	0
1640	0	3	2682	0	1	0	1	429
1641	1	1	1968	0	0	0	0	0
1642	1	0	3852	1	1	0	0	0
1643	1	1	3262	0	0	0	0	0
1644	1	5	2045	1	1	1	1	187
1645	1	1	2150	1	1	1	0	0
1646	1	0	3131	0	0	0	0	0
1647	1	0	2996	0	1	0	0	0
1648	0	1	71	1	1	0	1	55
1649	1	1	164	0	0	0	1	135
1650	0	1	2670	0	1	0	0	0
1651	1	0	2735	0	0	0	0	0
1652	0	1	3325	1	1	0	0	0
1653	1	0	2732	0	0	0	0	0
1654	1	2	1823	0	1	0	1	75
1655	1	2	2080	1	1	1	1	161
1656	0	1	2466	0	0	0	1	274
1657	1	1	160	1	0	0	0	0
1658	1	0	3747	0	0	0	0	0
1659	0	2	1275	0	0	1	0	0
1660	0	1	2878	0	1	0	0	0
1661	1	3	1976	1	0	0	1	67
1662	1	0	3746	0	0	0	0	0
1663	1	0	2900	1	1	0	0	0
1664	1	2	3419	1	1	0	0	0
1665	1	1	2128	1	0	0	1	80
1666	1	1	1128	0	1	0	1	153
1667	1	0	3401	0	0	0	0	0
1668	1	2	1563	0	0	0	1	463
1669	1	1	2415	1	0	0	0	0
1670	1	0	3747	0	1	0	0	0
1671	1	1	2936	1	0	0	1	66
1672	1	1	4005	1	1	0	1	68
1673	0	1	1416	0	0	0	0	0
1674	0	1	1528	0	1	0	0	0
1675	1	2	1382	1	1	0	1	159
1676	1	2	1856	0	1	1	0	0
1677	1	1	260	0	0	0	1	148
1678	1	1	526	1	0	0	1	280
1679	1	1	3360	0	0	1	1	247
1680	1	0	3507	1	0	0	0	0
1681	1	1	2291	1	0	0	0	0
1682	1	1	1240	1	1	0	0	0
1683	1	0	1835	0	0	0	0	0
1684	1	1	2317	1	1	1	0	0
1685	1	2	1879	0	0	1	0	0
1686	1	1	2327	1	1	0	1	418
1687	0	2	1856	0	0	1	0	0
1688	1	2	1115	1	0	0	1	390
1689	1	1	2408	0	1	0	1	130
1690	1	1	1128	0	0	1	1	44
1691	1	0	2766	0	1	0	0	0
1692	1	2	1123	1	0	0	1	399
1693	1	2	1823	0	0	0	1	230
1694	1	0	3353	0	0	0	0	0
1695	1	2	1801	0	1	1	0	0
1696	0	1	617	0	1	0	1	178
1697	1	1	416	1	1	0	1	40
1698	1	0	3403	0	1	0	0	0
1699	1	0	3401	0	0	0	0	0
1700	1	2	434	1	0	0	1	184
1701	1	1	3306	0	1	0	1	68
1702	1	1	3125	1	1	0	1	134
1703	1	3	556	0	1	1	0	0
1704	1	7	1710	1	0	1	1	213
1705	0	0	3852	1	1	0	0	0
1706	1	1	2746	1	1	0	1	411
1707	0	2	3579	1	1	0	1	107
1708	1	1	3397	0	0	0	0	0
1709	1	2	3646	0	1	0	1	128
1710	1	0	3747	0	1	0	0	0
1711	0	1	1850	1	0	0	1	136
1712	0	1	3458	1	1	0	0	0
1713	1	1	3177	0	1	0	1	10
1714	1	5	1577	1	0	1	1	588
1715	1	0	3694	1	1	0	0	0
1716	1	1	2380	1	0	0	0	0
1717	1	1	2787	0	0	0	1	4
1718	1	0	1710	0	0	0	0	0
1719	1	1	709	1	1	1	0	0
1720	1	1	920	0	1	1	1	141
1721	1	1	2417	0	0	0	1	85
1722	1	2	1962	0	0	1	0	0
1723	0	1	1774	1	0	1	0	0
1724	1	2	2284	0	1	1	1	251
1725	1	1	539	1	0	0	0	0
1726	1	1	3583	1	0	0	1	43
1727	1	9	216	1	0	1	1	378
1728	1	2	1856	0	1	1	0	0
1729	1	0	1352	0	0	0	0	0
1730	1	2	962	1	1	0	1	206
1731	1	0	3171	0	1	1	0	0
1732	1	1	198	0	0	0	0	0
1733	0	0	3164	0	0	1	0	0
1734	1	1	2446	0	0	1	1	100
1735	1	1	1877	1	1	0	1	56
1736	1	0	2900	0	0	0	0	0
1737	1	0	2004	0	0	0	0	0
1738	1	1	192	1	0	0	0	0
1739	1	1	532	0	1	1	0	0
1740	1	1	3222	1	1	0	1	34
1741	0	0	2669	0	1	0	0	0
1742	1	2	1618	0	1	1	1	3
1743	0	0	470	0	1	0	0	0
1744	1	1	3243	1	0	0	1	252
1745	1	0	3694	0	1	0	0	0
1746	0	1	3453	1	0	0	0	0
1747	0	1	1036	0	1	0	0	0
1748	1	15	192	0	0	0	1	1133
1749	0	2	1752	0	0	1	0	0
1750	1	1	2311	1	1	0	0	0
1751	1	1	2998	0	1	0	1	410
1752	1	1	1261	1	1	0	1	44
1753	1	1	2634	1	0	0	1	74
1754	1	1	1514	0	1	0	0	0
1755	1	1	3229	0	0	0	1	136
1756	1	0	3746	1	1	0	0	0
1757	1	1	702	1	1	0	0	0
1758	1	4	227	1	1	1	1	508
1759	0	2	3496	0	0	0	1	3
1760	0	5	644	1	0	1	1	260
1761	1	3	1878	0	1	0	1	182
1762	1	1	1968	1	0	0	0	0
1763	1	7	1130	1	1	0	1	1055
1764	0	1	3311	0	1	0	0	0
1765	1	2	360	0	1	0	1	279
1766	1	8	91	0	0	0	1	1326
1767	1	1	2905	1	1	0	0	0
1768	1	4	875	0	1	1	1	197
1769	1	0	896	0	0	0	0	0
1770	1	1	862	0	0	0	0	0
1771	1	1	2243	1	0	0	0	0
1772	1	0	2859	0	1	0	0	0
1773	0	1	2744	0	1	0	0	0
1774	1	1	2787	0	1	0	0	0
1775	1	1	3523	1	0	1	1	98
1776	1	1	3229	1	1	0	1	68
1777	1	2	2971	1	1	0	1	316
1778	1	0	3487	0	1	0	0	0
1779	0	1	2850	0	1	0	0	0
1780	0	1	1018	0	0	0	0	0
1781	1	1	1948	1	1	0	1	54
1782	1	1	3416	1	1	0	1	10
1783	0	0	2844	1	0	0	0	0
1784	1	1	604	0	1	0	0	0
1785	0	1	4127	0	0	0	1	35
1786	1	2	1983	1	1	0	1	190
1787	1	0	3041	0	1	0	0	0
1788	1	1	3249	0	0	0	0	0
1789	0	1	2880	0	1	0	0	0
1790	1	0	3401	0	1	0	0	0
1791	1	1	3177	1	0	1	0	0
1792	1	2	2366	1	1	0	1	288
1793	0	2	982	0	1	1	0	0
1794	1	2	2831	0	1	1	1	161
1795	1	1	192	1	0	0	0	0
1796	1	2	3703	0	1	0	0	0
1797	1	1	723	0	0	1	0	0
1798	1	0	2997	1	1	0	0	0
1799	1	0	2425	0	0	0	0	0
1800	1	2	2326	1	1	0	1	343
1801	1	1	2796	1	0	0	0	0
1802	1	2	470	1	0	1	1	242
1803	0	1	967	0	0	1	0	0
1804	0	0	2950	1	0	0	0	0
1805	1	3	1658	1	1	1	1	184
1806	1	1	2324	0	0	0	0	0
1807	1	1	945	0	1	0	0	0
1808	1	2	721	1	0	0	1	83
1809	1	2	3354	1	0	0	1	345
1810	1	2	2456	0	1	0	1	220
1811	1	1	3069	0	1	1	0	0
1812	1	1	1095	1	0	0	0	0
1813	1	3	2836	1	1	0	1	506
1814	0	1	2955	1	1	1	1	173
1815	0	1	3342	0	1	0	1	110
1816	1	1	974	0	0	0	0	0
1817	1	0	1653	0	0	0	0	0
1818	0	2	3276	1	0	0	1	140
1819	0	1	2975	1	0	0	0	0
1820	0	0	3494	0	1	0	0	0
1821	0	2	1962	1	0	1	1	138
1822	1	1	1346	1	0	1	0	0
1823	1	1	2752	0	0	0	0	0
1824	1	2	2759	0	1	0	1	136
1825	1	1	512	0	0	1	0	0
1826	1	0	3120	0	0	0	0	0
1827	1	2	744	0	0	1	1	163
1828	1	1	1646	1	0	1	0	0
1829	1	1	4005	1	0	0	1	43
1830	1	1	2656	1	1	0	1	130
1831	1	1	2415	0	0	0	0	0
1832	1	1	2158	1	0	0	1	10
1833	1	1	2107	1	1	0	1	161
1834	1	1	304	0	1	0	0	0
1835	0	1	2918	0	0	0	0	0
1836	1	1	960	0	1	0	1	81
1837	1	2	2080	0	0	1	0	0
1838	1	1	3398	0	1	0	1	10
1839	1	1	2257	1	0	0	1	130
1840	1	1	3517	1	0	0	0	0
1841	1	1	2418	1	1	1	1	161
1842	1	0	3522	0	1	0	0	0
1843	1	1	3436	1	1	0	0	0
1844	0	0	2984	1	0	0	0	0
1845	1	1	3590	1	1	0	1	228
1846	1	1	3513	1	1	0	0	0
1847	1	1	608	0	0	0	0	0
1848	1	2	841	0	1	1	0	0
1849	1	9	216	0	1	0	1	1176
1850	1	0	3159	0	1	1	0	0
1851	1	1	868	0	0	0	0	0
1852	1	1	2102	0	1	0	1	54
1853	1	3	3662	1	0	0	1	128
1854	1	2	3662	0	0	0	0	0
1855	1	2	1123	0	1	0	1	42
1856	1	2	3548	1	1	1	1	131
1857	0	0	3694	0	1	0	0	0
1858	1	2	1710	0	0	1	0	0
1859	1	0	2172	0	1	0	0	0
1860	1	1	896	0	1	0	0	0
1861	0	1	1073	1	0	0	1	105
1862	1	1	3587	1	1	0	1	43
1863	1	0	3507	1	1	0	0	0
1864	1	1	2775	0	1	0	1	33
1865	1	3	2143	1	0	1	1	242
1866	1	0	3680	0	0	0	0	0
1867	0	5	1170	1	0	0	1	598
1868	1	3	1842	0	1	1	0	0
1869	1	2	239	1	1	0	1	1200
1870	1	0	2765	0	0	0	0	0
1871	1	0	3747	0	0	0	0	0
1872	1	2	1392	1	1	0	1	303
1873	1	1	532	1	1	1	0	0
1874	1	0	1962	1	0	0	0	0
1875	1	2	3340	0	0	0	1	199
1876	1	1	3019	1	1	0	1	184
1877	0	1	2767	1	0	0	0	0
1878	1	0	3500	1	1	0	0	0
1879	0	1	1052	1	1	1	0	0
1880	1	0	2422	1	1	0	0	0
1881	1	2	1646	0	0	1	1	130
1882	1	0	3522	0	1	0	0	0
1883	1	3	1739	0	0	1	1	58
1884	1	1	15	0	1	0	0	0
1885	1	2	458	0	0	0	1	142
1886	1	1	2128	0	0	0	0	0
1887	1	1	2509	0	1	0	0	0
1888	1	1	3312	0	0	0	1	132
1889	0	1	1052	0	0	0	0	0
1890	1	0	77	0	0	0	0	0
1891	0	0	2492	0	1	1	0	0
1892	0	1	2859	0	0	0	0	0
1893	1	2	1226	0	0	1	1	104
1894	1	1	668	1	1	0	1	84
1895	1	0	1673	0	1	0	0	0
1896	1	1	3047	0	1	1	0	0
1897	1	1	2744	0	0	0	0	0
1898	1	2	3276	0	0	0	1	128
1899	0	0	3507	0	0	0	0	0
1900	1	3	3215	0	1	0	1	122
1901	1	3	834	0	1	1	1	160
1902	0	4	1135	0	0	0	1	272
1903	1	0	2766	0	0	0	0	0
1904	1	0	3747	0	1	0	0	0
1905	1	0	3522	0	1	0	0	0
1906	1	2	1123	0	0	1	1	217
1907	1	3	598	0	1	1	1	6
1908	1	2	2380	1	1	0	1	88
1909	1	1	532	0	0	1	0	0
1910	1	1	4036	1	0	0	1	30
1911	1	4	841	0	0	1	1	44
1912	1	1	1561	1	1	0	0	0
1913	0	3	1261	1	0	0	0	0
1914	1	1	192	1	1	0	0	0
1915	1	5	465	1	1	0	1	297
1916	0	1	1003	1	1	1	0	0
1917	0	2	1752	0	0	1	0	0
1918	0	0	3394	0	1	0	0	0
1919	1	1	2746	0	1	0	0	0
1920	0	3	2296	1	0	0	1	514
1921	1	1	216	0	1	0	0	0
1922	1	2	3660	0	1	0	1	33
1923	1	2	3222	1	1	0	1	130
1924	1	1	2681	1	1	0	0	0
1925	1	1	2404	1	1	0	0	0
1926	1	1	714	0	1	0	1	163
1927	0	1	2583	0	0	0	0	0
1928	1	2	2296	0	1	0	1	318
1929	0	5	1639	1	0	0	1	563
1930	1	1	2960	0	1	1	1	160
1931	1	0	3746	0	1	0	0	0
1932	1	1	359	0	0	0	1	43
1933	1	0	3619	1	1	0	0	0
1934	1	1	2848	0	1	1	0	0
1935	0	2	519	0	0	0	1	154
1936	1	1	2705	0	1	1	0	0
1937	1	2	3716	0	1	0	0	0
1938	1	1	3655	1	1	0	0	0
1939	1	1	216	0	0	1	0	0
1940	1	1	3914	1	1	0	1	139
1941	1	2	1570	1	1	0	1	203
1942	1	1	3384	0	0	0	0	0
1943	1	0	280	1	1	0	0	0
1944	1	2	1710	0	0	1	0	0
1945	1	0	3522	1	1	0	0	0
1946	1	2	1073	0	1	0	1	57
1947	1	1	3032	0	1	0	0	0
1948	1	0	3369	0	1	0	0	0
1949	1	1	1564	1	1	0	1	91
1950	1	1	3243	0	1	0	1	135
1951	1	2	1000	0	0	0	1	80
1952	0	1	2809	0	0	0	0	0
1953	1	0	2186	0	1	0	0	0
1954	1	2	1899	1	0	0	1	248
1955	1	1	1766	0	1	0	1	142
1956	1	1	3604	0	1	0	0	0
1957	1	1	1288	0	1	0	1	95
1958	1	2	491	1	0	1	1	259
1959	1	2	2012	0	0	1	1	35
1960	1	1	2607	1	1	1	0	0
1961	1	2	1288	1	1	0	1	508
1962	1	1	962	0	1	0	1	263
1963	1	1	1464	1	1	0	0	0
1964	1	1	1919	1	1	0	1	150
1965	1	1	3157	0	0	1	0	0
1966	0	1	2165	1	0	0	1	138
1967	0	1	216	0	1	1	0	0
1968	1	1	3453	1	0	0	0	0
1969	1	3	2837	0	0	1	1	160
1970	1	2	1233	0	1	0	1	81
1971	1	0	3159	0	1	0	0	0
1972	1	2	3541	1	0	1	1	101
1973	1	3	939	0	0	0	1	320
1974	1	2	1135	1	1	0	1	287
1975	0	1	1708	0	0	0	1	98
1976	1	6	778	0	1	0	1	577
1977	1	2	3791	1	0	1	1	98
1978	1	2	3678	0	1	0	0	0
1979	1	1	3020	1	1	0	0	0
1980	0	2	1710	0	0	1	0	0
1981	1	1	3340	1	1	0	1	98
1982	1	2	3381	1	0	0	0	0
1983	0	1	2620	1	0	0	0	0
1984	1	0	3772	0	1	0	0	0
1985	1	2	2044	0	0	1	0	0
1986	1	1	659	1	1	0	1	188
1987	1	4	1710	0	0	1	1	145
1988	0	1	695	1	0	0	1	58
1989	1	1	3299	1	1	0	1	69
1990	0	1	3436	0	1	0	1	1030
1991	1	3	1415	1	1	1	1	130
1992	1	1	2807	0	1	0	1	55
1993	1	2	2466	0	1	0	1	133
1994	1	0	3746	1	0	0	0	0
1995	1	2	1136	0	1	0	1	184
1996	1	1	1701	1	0	0	1	30
1997	1	1	2633	1	1	0	1	10
1998	1	0	3394	0	0	0	0	0
1999	1	1	253	0	1	1	0	0
2000	1	1	1261	0	0	0	0	0

NA

Select variables for regression


selected.var <- c("Spending","Address_US","Freq","last_update","Web","Gender",
                  "Address_RES")

Partition data


set.seed(1)  # set seed for reproducing the partition
train.index <- sample(c(1:dim(Tayko.df)[1]), dim(Tayko.df)[1]*0.7)  
train.df <- Tayko.df[train.index, selected.var]
valid.df <- Tayko.df[-train.index, selected.var]

Building the model for Spending


Tayko.lm <- lm(Spending ~ ., data = train.df)
options(scipen = 999)
summary(Tayko.lm)


Call:
lm(formula = Spending ~ ., data = train.df)

Residuals:
    Min      1Q  Median      3Q     Max
-419.79  -78.81   -5.26   33.16 1328.95

Coefficients:
              Estimate Std. Error t value             Pr(>|t|)    
(Intercept)  15.282719  13.521836   1.130              0.25858    
Address_US   -9.557749   9.521419  -1.004              0.31564    
Freq         91.015349   2.850089  31.934 < 0.0000000000000002 ***
last_update  -0.010032   0.003403  -2.948              0.00325 **
Web          13.261350   7.260800   1.826              0.06800 .  
Gender       -1.299859   7.153707  -0.182              0.85584    
Address_RES -82.835233   8.914574  -9.292 < 0.0000000000000002 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 133.5 on 1393 degrees of freedom
Multiple R-squared:  0.4719,    Adjusted R-squared:  0.4697
F-statistic: 207.5 on 6 and 1393 DF,  p-value: < 0.00000000000000022

What does it mean?

Call: is the formula of the predictor variable “Spending”
Residuals: are the difference between the actual observed response and the response the values the model predicted, in this case I will plot the residuals to look for symmetry. Another way to think of it is how far the true value is from the predicted value.

plot(Tayko.lm$residuals)

TKLM <- resid(Tayko.lm)

qqnorm(TKLM)
qqline(TKLM)

NA
NA

This plot will suggest that the data is not normally distrubed

Another way to see distrubution is with the Shapiro-Wilk Test

shapiro.test(TKLM)


    Shapiro-Wilk normality test

data:  TKLM
W = 0.73318, p-value < 0.00000000000000022

In this case it is not normal distrubted as the p-value is not closes to 1.00

Coefficients

the coefficients are two unknown constants that represent the intercept and slope terms in the linear model. In our case how much the consumer is spending. Ultimately, the analyst wants to find an intercept and a slope such that the resulting fitted line is as close as possible ## Coefficient - Estimate The intercept, in our example, is essentially the expected value of “SPending”

Coefficient - Standard Error

The coefficient Standard Error measures the average amount that the coefficient estimates vary from the actual average value of our response variable. We’d ideally want a lower number relative to its coefficients.

Coefficient - t value

The coefficient t-value is a measure of how many standard deviations our coefficient estimate is far away from 0. We want it to be far away from zero as this would indicate we could reject the null hypothesis

Coefficient - Pr(>t)

The Pr(>t) acronym found in the model output relates to the probability of observing any value equal or larger than t. A small p-value indicates that it is unlikely we will observe a relationship between the predictor and response variables due to chance.

Signif. codes:

These help us build a better model. IF we use only the predictors with three stars to build a model we should see a better result

Multiple R-squared, Adjusted R-squared

The R-squared (R2) statistic provides a measure of how well the model is fitting the actual data. It takes the form of a proportion of variance. R2 is a measure of the linear relationship between our predictor variable and our response / target variable. A side note: In multiple regression settings, the R2 will always increase as more variables are included in the model. That’s why the adjusted R2 is the preferred measure as it adjusts for the number of variables considered.

F-Statistic

F-statistic is a good indicator of whether there is a relationship between our predictor and the response variables. The further the F-statistic is from 1 the better it is. However, how much larger the F-statistic needs to be depends on both the number of data points and the number of predictors. Generally, when the number of data points is large, an F-statistic that is only a little bit larger than 1 is already sufficient to reject the null hypothesis (H0 : There is no relationship between the two variables

Note that the model we ran above was just an example to illustrate how a linear model output looks like in R and how we can start to interpret its components. Obviously the model is not optimised. One way we could start to improve is by transforming our response variable

Prediction

library(forecast)
Tayko.lm.pred <- predict(Tayko.lm, valid.df)
accuracy(Tayko.lm.pred, valid.df$Spending)

               ME    RMSE      MAE MPE MAPE
Test set 4.040333 123.228 78.73779 NaN  Inf

Varible selection with stepwose regression


null=lm(Spending~1, data=train.df)    
forward_model<-step(null, scope=list(lower=null, upper=Tayko.lm), direction="forward")

Start:  AIC=14593.15
Spending ~ 1

              Df Sum of Sq      RSS   AIC
+ Freq         1  20491505 26547018 13794
+ last_update  1   3324525 43713998 14492
+ Web          1    553981 46484542 14579
<none>                     47038523 14593
+ Gender       1     10046 47028476 14595
+ Address_RES  1      1757 47036765 14595
+ Address_US   1       926 47037597 14595

Step:  AIC=13794.28
Spending ~ Freq

              Df Sum of Sq      RSS   AIC
+ Address_RES  1   1471612 25075405 13716
+ Web          1     85416 26461602 13792
+ last_update  1     47115 26499903 13794
<none>                     26547018 13794
+ Address_US   1     35793 26511224 13794
+ Gender       1       710 26546307 13796

Step:  AIC=13716.44
Spending ~ Freq + Address_RES

              Df Sum of Sq      RSS   AIC
+ last_update  1    157875 24917530 13710
+ Web          1     58515 25016890 13715
<none>                     25075405 13716
+ Address_US   1     22117 25053289 13717
+ Gender       1       770 25074636 13718

Step:  AIC=13709.6
Spending ~ Freq + Address_RES + last_update

             Df Sum of Sq      RSS   AIC
+ Web         1     59507 24858023 13708
<none>                    24917530 13710
+ Address_US  1     18232 24899298 13711
+ Gender      1       728 24916802 13712

Step:  AIC=13708.25
Spending ~ Freq + Address_RES + last_update + Web

             Df Sum of Sq      RSS   AIC
<none>                    24858023 13708
+ Address_US  1   18160.9 24839862 13709
+ Gender      1     781.8 24857241 13710

stepwise_model<-step(null, scope=list(lower=null, upper=Tayko.lm), direction="both")

Start:  AIC=14593.15
Spending ~ 1

              Df Sum of Sq      RSS   AIC
+ Freq         1  20491505 26547018 13794
+ last_update  1   3324525 43713998 14492
+ Web          1    553981 46484542 14579
<none>                     47038523 14593
+ Gender       1     10046 47028476 14595
+ Address_RES  1      1757 47036765 14595
+ Address_US   1       926 47037597 14595

Step:  AIC=13794.28
Spending ~ Freq

              Df Sum of Sq      RSS   AIC
+ Address_RES  1   1471612 25075405 13716
+ Web          1     85416 26461602 13792
+ last_update  1     47115 26499903 13794
<none>                     26547018 13794
+ Address_US   1     35793 26511224 13794
+ Gender       1       710 26546307 13796
- Freq         1  20491505 47038523 14593

Step:  AIC=13716.44
Spending ~ Freq + Address_RES

              Df Sum of Sq      RSS   AIC
+ last_update  1    157875 24917530 13710
+ Web          1     58515 25016890 13715
<none>                     25075405 13716
+ Address_US   1     22117 25053289 13717
+ Gender       1       770 25074636 13718
- Address_RES  1   1471612 26547018 13794
- Freq         1  21961360 47036765 14595

Step:  AIC=13709.6
Spending ~ Freq + Address_RES + last_update

              Df Sum of Sq      RSS   AIC
+ Web          1     59507 24858023 13708
<none>                     24917530 13710
+ Address_US   1     18232 24899298 13711
+ Gender       1       728 24916802 13712
- last_update  1    157875 25075405 13716
- Address_RES  1   1582373 26499903 13794
- Freq         1  18588777 43506308 14488

Step:  AIC=13708.25
Spending ~ Freq + Address_RES + last_update + Web

              Df Sum of Sq      RSS   AIC
<none>                     24858023 13708
+ Address_US   1     18161 24839862 13709
- Web          1     59507 24917530 13710
+ Gender       1       782 24857241 13710
- last_update  1    158867 25016890 13715
- Address_RES  1   1555037 26413060 13791
- Freq         1  18174345 43032368 14474

backward_model<-step(Tayko.lm, direction="backward")

Start:  AIC=13711.19
Spending ~ Address_US + Freq + last_update + Web + Gender + Address_RES

              Df Sum of Sq      RSS   AIC
- Gender       1       589 24839862 13709
- Address_US   1     17968 24857241 13710
<none>                     24839273 13711
- Web          1     59483 24898757 13712
- last_update  1    154958 24994231 13718
- Address_RES  1   1539631 26378905 13793
- Freq         1  18184451 43023724 14478

Step:  AIC=13709.23
Spending ~ Address_US + Freq + last_update + Web + Address_RES

              Df Sum of Sq      RSS   AIC
- Address_US   1     18161 24858023 13708
<none>                     24839862 13709
- Web          1     59436 24899298 13711
- last_update  1    154976 24994838 13716
- Address_RES  1   1540033 26379895 13791
- Freq         1  18192258 43032120 14476

Step:  AIC=13708.25
Spending ~ Freq + last_update + Web + Address_RES

              Df Sum of Sq      RSS   AIC
<none>                     24858023 13708
- Web          1     59507 24917530 13710
- last_update  1    158867 25016890 13715
- Address_RES  1   1555037 26413060 13791
- Freq         1  18174345 43032368 14474

summary(backward_model)


Call:
lm(formula = Spending ~ Freq + last_update + Web + Address_RES,
    data = train.df)

Residuals:
    Min      1Q  Median      3Q     Max
-421.55  -77.25   -5.18   31.86 1326.62

Coefficients:
             Estimate Std. Error t value             Pr(>|t|)    
(Intercept)   7.13180   10.70556   0.666              0.50541    
Freq         90.92205    2.84699  31.936 < 0.0000000000000002 ***
last_update  -0.01015    0.00340  -2.986              0.00288 **
Web          13.26390    7.25827   1.827              0.06785 .  
Address_RES -83.10448    8.89611  -9.342 < 0.0000000000000002 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 133.5 on 1395 degrees of freedom
Multiple R-squared:  0.4715,    Adjusted R-squared:   0.47
F-statistic: 311.2 on 4 and 1395 DF,  p-value: < 0.00000000000000022

summary(forward_model)


Call:
lm(formula = Spending ~ Freq + Address_RES + last_update + Web,
    data = train.df)

Residuals:
    Min      1Q  Median      3Q     Max
-421.55  -77.25   -5.18   31.86 1326.62

Coefficients:
             Estimate Std. Error t value             Pr(>|t|)    
(Intercept)   7.13180   10.70556   0.666              0.50541    
Freq         90.92205    2.84699  31.936 < 0.0000000000000002 ***
Address_RES -83.10448    8.89611  -9.342 < 0.0000000000000002 ***
last_update  -0.01015    0.00340  -2.986              0.00288 **
Web          13.26390    7.25827   1.827              0.06785 .  
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 133.5 on 1395 degrees of freedom
Multiple R-squared:  0.4715,    Adjusted R-squared:   0.47
F-statistic: 311.2 on 4 and 1395 DF,  p-value: < 0.00000000000000022

summary(stepwise_model)


Call:
lm(formula = Spending ~ Freq + Address_RES + last_update + Web,
    data = train.df)

Residuals:
    Min      1Q  Median      3Q     Max
-421.55  -77.25   -5.18   31.86 1326.62

Coefficients:
             Estimate Std. Error t value             Pr(>|t|)    
(Intercept)   7.13180   10.70556   0.666              0.50541    
Freq         90.92205    2.84699  31.936 < 0.0000000000000002 ***
Address_RES -83.10448    8.89611  -9.342 < 0.0000000000000002 ***
last_update  -0.01015    0.00340  -2.986              0.00288 **
Web          13.26390    7.25827   1.827              0.06785 .  
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 133.5 on 1395 degrees of freedom
Multiple R-squared:  0.4715,    Adjusted R-squared:   0.47
F-statistic: 311.2 on 4 and 1395 DF,  p-value: < 0.00000000000000022

Choseing the right variables now

As you can see Freq, last_update, address_RES are the key predictors so lets make a new formula with those.

Better_Model <- lm(formula = Spending ~ Freq + Address_RES + last_update + Web,
    data = valid.df)

summary(Better_Model)


Call:
lm(formula = Spending ~ Freq + Address_RES + last_update + Web,
    data = valid.df)

Residuals:
    Min      1Q  Median      3Q     Max
-445.94  -74.97    6.52   32.23  999.64

Coefficients:
              Estimate Std. Error t value             Pr(>|t|)    
(Intercept) -21.320770  14.648338  -1.456                0.146    
Freq        101.344111   3.624125  27.964 < 0.0000000000000002 ***
Address_RES -85.897719  12.729987  -6.748      0.0000000000357 ***
last_update  -0.002733   0.004657  -0.587                0.557    
Web          19.650706  10.263894   1.915                0.056 .  
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 122.6 on 595 degrees of freedom
Multiple R-squared:  0.6057,    Adjusted R-squared:  0.603
F-statistic: 228.5 on 4 and 595 DF,  p-value: < 0.00000000000000022

#Conclusion we can now validate that the factor most involved with Spending habits of the customers are Freq and Address. Which is to say that the spending habits of the consumer are american and they have bought before.

Logistic Regression

select variables for logistic regression

Business Problem Will they purchase yes or no?


selected.var <- c("Purchase","Address_US","Freq","last_update","Web","Gender",
                  "Address_RES")

partition data


set.seed(5)  # set seed for reproducing the partition
train.index <- sample(c(1:dim(Tayko.df)[1]), dim(Tayko.df)[1]*0.7)  
train.df <- Tayko.df[train.index, selected.var]
valid.df <- Tayko.df[-train.index, selected.var]

logistic regression model using glm()

In statistics, the generalized linear model (GLM) is a flexible generalization of ordinary linear regression that allows for response variables that have error distribution models other than a normal distribution. The glmnet() function has an alpha argument that determines what type of model is fit. If alpha = 0 then a ridge regression model is fit, and if alpha = 1 then a lasso model is fit.


library(caret)
library(glmnet)
logit.reg <- glm(Purchase ~ ., data = train.df, family = "binomial")
options(scipen=999) # remove scientific notation
summary(logit.reg)


Call:
glm(formula = Purchase ~ ., family = "binomial", data = train.df)

Deviance Residuals:
    Min       1Q   Median       3Q      Max  
-3.2384  -0.8908   0.0001   0.9792   2.0750  

Coefficients:
                Estimate   Std. Error z value             Pr(>|z|)    
(Intercept) -2.654978396  0.272584783  -9.740 < 0.0000000000000002 ***
Address_US   0.151198045  0.180471495   0.838                0.402    
Freq         2.066303697  0.129641932  15.939 < 0.0000000000000002 ***
last_update -0.000004276  0.000062811  -0.068                0.946    
Web          0.923794671  0.137531679   6.717    0.000000000018556 ***
Gender      -0.118614602  0.137017893  -0.866                0.387    
Address_RES -1.438979263  0.194460099  -7.400    0.000000000000136 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for binomial family taken to be 1)

    Null deviance: 1940.8  on 1399  degrees of freedom
Residual deviance: 1297.2  on 1393  degrees of freedom
AIC: 1311.2

Number of Fisher Scoring iterations: 6

Prediction

logit.reg.pred <- predict(logit.reg, valid.df, type = "response")

confusionMatrix(as.factor(ifelse(logit.reg.pred > 0.5, "Purchase", "No Purchase")),
                as.factor(ifelse(valid.df$Purchase==1,"Purchase","No Purchase")))

Confusion Matrix and Statistics

             Reference
Prediction    No Purchase Purchase
  No Purchase         222       71
  Purchase             82      225

               Accuracy : 0.745              
                 95% CI : (0.7081, 0.7794)   
    No Information Rate : 0.5067             
    P-Value [Acc > NIR] : <0.0000000000000002

                  Kappa : 0.4902             

 Mcnemar's Test P-Value : 0.4188             

            Sensitivity : 0.7303             
            Specificity : 0.7601             
         Pos Pred Value : 0.7577             
         Neg Pred Value : 0.7329             
             Prevalence : 0.5067             
         Detection Rate : 0.3700             
   Detection Prevalence : 0.4883             
      Balanced Accuracy : 0.7452             

       'Positive' Class : No Purchase

ctrl <- trainControl(method = "repeatedcv", number = 10, savePredictions = TRUE)
mod_fit <- train(Purchase ~ Address_US+Freq+last_update+Web+Gender+Address_RES,
                 data=Tayko.df, method="glm", family="binomial",
                 trControl = ctrl)

You are trying to do regression and your outcome only has two possible values Are you trying to do classification? If so, use a 2 level factor as your outcome column.

summary(mod_fit)


Call:
NULL

Deviance Residuals:
    Min       1Q   Median       3Q      Max  
-3.1998  -0.9101  -0.0895   0.8005   2.1205  

Coefficients:
               Estimate  Std. Error z value            Pr(>|z|)    
(Intercept) -2.69016918  0.23192505 -11.599 <0.0000000000000002 ***
Address_US   0.08887531  0.14967875   0.594               0.553    
Freq         2.02725297  0.10620432  19.088 <0.0000000000000002 ***
last_update  0.00002795  0.00005356   0.522               0.602    
Web          0.96667886  0.11519835   8.391 <0.0000000000000002 ***
Gender      -0.07942773  0.11428352  -0.695               0.487    
Address_RES -1.41279307  0.16147795  -8.749 <0.0000000000000002 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for binomial family taken to be 1)

    Null deviance: 2772.6  on 1999  degrees of freedom
Residual deviance: 1862.1  on 1993  degrees of freedom
AIC: 1876.1

Number of Fisher Scoring iterations: 6

# select variables for regression
selected.var <- c("Spending","Address_US","Freq","last_update","Web","Gender",
                  "Address_RES")

partition data


set.seed(6)  # set seed for reproducing the partition
train.index <- sample(c(1:dim(Tayko.df)[1]), dim(Tayko.df)[1]*0.7)  
train.df <- Tayko.df[train.index, selected.var]
valid.df <- Tayko.df[-train.index, selected.var]

#glmnet

Ridge regression with glmnet# The glmnet package provides the functionality for ridge regression via glmnet(). Important things to know:

Rather than accepting a formula and data frame, it requires a vector input and matrix of predictors. You must specify alpha = 0 for ridge regression. Ridge regression involves tuning a hyperparameter, lambda. glmnet() will generate default values for you. Alternatively, it is common practice to define your own with the lambda argument (which we’ll do).

x <- as.matrix(train.df[,c("Address_US","Freq","last_update","Web","Gender",
                           "Address_RES")])
y <- train.df$Spending

CvRidgeMod <- cv.glmnet(x, y, alpha=0, nlambda=100, lambda.min.ratio=0.0001)


best.lambda <- CvRidgeMod$lambda.min
best.lambda

[1] 13.26638

coef(CvRidgeMod, s = "lambda.min")

7 x 1 sparse Matrix of class "dgCMatrix"
                       1
(Intercept)  14.43623446
Address_US   -2.85562995
Freq         85.24201532
last_update  -0.01026718
Web          15.20347802
Gender       -2.49455878
Address_RES -68.61384598

x_pred <- as.matrix(valid.df[,c("Address_US","Freq","last_update","Web","Gender",
                                "Address_RES")])
Ridge.pred <- predict(CvRidgeMod, s = best.lambda, newx = x_pred)
accuracy(as.vector(Ridge.pred), valid.df$Spending)

               ME     RMSE      MAE MPE MAPE
Test set 6.258279 148.1573 85.76817 NaN  Inf

plot(CvRidgeMod)

The lowest point in the curve indicates the optimal lambda: the log value of lambda that best minimised the error in cross-validation. We can extract this values as:

opt_lambda <- CvRidgeMod$lambda.min
opt_lambda

[1] 13.26638

Lasso

Least Absolute Shrinkage and Selection Operator

Lasso regression is a parsimonious model that performs L1 regularization. The L1 regularization adds a penalty equivalent to the absolute magnitude of regression coefficients and tries to minimize them. The equation of lasso is similar to ridge regression and looks like as given below. Lasso regression analysis is also used for variable selection as the model imposes coefficients of some variables to shrink towards zero.

The two models, lasso and ridge regression, are almost similar to each other. However, in lasso, the coefficients which are responsible for large variance are converted to zero. On the other hand, coefficients are only shrunk but are never made zero in ridge regression.

# Lasso
CvLassoMod <- cv.glmnet(x, y, alpha=1, nlambda=100, lambda.min.ratio=0.0001)

plot(CvLassoMod)


best.lambda <- CvLassoMod$lambda.min
best.lambda

[1] 0.3778312

coef(CvLassoMod, s = "lambda.min")

7 x 1 sparse Matrix of class "dgCMatrix"
                        1
(Intercept)   2.017827662
Address_US   -2.967548697
Freq         92.273465509
last_update  -0.008102858
Web          12.863715457
Gender       -1.524717302
Address_RES -76.238518400

Lasso.pred <- predict(CvLassoMod, s = best.lambda, newx = x_pred)
accuracy(as.vector(Lasso.pred), valid.df$Spending)

               ME     RMSE      MAE MPE MAPE
Test set 6.444591 147.2725 86.61665 NaN  Inf

# identifying best lamda
best.lambda

[1] 0.3778312

coef(CvLassoMod, s = "lambda.min")

7 x 1 sparse Matrix of class "dgCMatrix"
                        1
(Intercept)   2.017827662
Address_US   -2.967548697
Freq         92.273465509
last_update  -0.008102858
Web          12.863715457
Gender       -1.524717302
Address_RES -76.238518400


# TAYKO SOFTWARE 



### Business Problem
### Predicting Software Reselling Profits
### Tayko is a software catalog firm.  It sells games and educational software.  Initially it began as a software manufacturer and later it added third-party titles to its offerings.  It has recently put together a revised collection of items in a new catalog.  Tayko is preparing to roll out the catalog in a mailing.

### Tayko has joined a consortium of catalog firms that specialize in computer and software products.  Through this it gets to send its cataloges to a names drawn from a pooled list of customers.  It supplies a list of customers to the consortium and in return can get a list of new customers. Members can do predictive modeling on the available records in the pool to get a good set of names generating profits to the company.

### In this regard, Tayko has supplied 200000 names to the pool of 5000000 names.  It is entitled to draw 200000 names.  To draw the best names, it tests with 2000 names for its new catalog.  The work presented here uses Logistics Regression Model to help Tayko decide if the drawn list is good for its revenue generation.

### OBJECTIVE: From the dataset Tayko.csv, Purchase output variable is considered for the analysis and prediction.  The objective of the model is to classify records into 'PURCHASE' or "NO PURCHASE'.  

The following list explains the details for the independent variables in the dataset:

Variable Name            Description

US                       Is the address in US?

Freq                     Number of transactions in the last year 

last_update_days_ago     How many days ago last update was made

1st_update_days_ago      How many days ago first update was made

Web_Order                Customer placed at least one order via web

Gender                   Customer is male or not

Address_is_res           Address is a residence

Purchase                 Person made purchase in testing mailing or not


# Read in data 
```{r}
library(tibble)
library(kableExtra)
rm(list = ls())
Tayko.df <- read.csv("https://raw.githubusercontent.com/HenryBernreuter/test_data/main/CSV_Tayko.csv")


Tayko.df %>%
  kbl() %>%
  scroll_box(width = "750px", height = "500px")

```
# Select variables for regression
```{r}

selected.var <- c("Spending","Address_US","Freq","last_update","Web","Gender",
                  "Address_RES")
```
# Partition data
```{r}

set.seed(1)  # set seed for reproducing the partition
train.index <- sample(c(1:dim(Tayko.df)[1]), dim(Tayko.df)[1]*0.7)  
train.df <- Tayko.df[train.index, selected.var]
valid.df <- Tayko.df[-train.index, selected.var]
```
# Building the model for Spending
```{r}

Tayko.lm <- lm(Spending ~ ., data = train.df)
options(scipen = 999)
summary(Tayko.lm)

```
## What does it mean?
Call: is the formula of the predictor variable "Spending"  
Residuals: are the difference between the actual observed response and the response the values the model predicted, in this case I will plot the residuals to look for symmetry. Another way to think of it is how far the true value is from the predicted value.   

```{r}
plot(Tayko.lm$residuals)
```
```{r}
TKLM <- resid(Tayko.lm)

qqnorm(TKLM)
qqline(TKLM)


```
## This plot will suggest that the data is not normally distrubed 
# Another way to see distrubution is with the Shapiro-Wilk Test

```{r}
shapiro.test(TKLM)

```
In this case it is not normal distrubted as the p-value is not closes to 1.00

# Coefficients
the coefficients are two unknown constants that represent the intercept and slope terms in the linear model. In our case how much the consumer is spending. Ultimately, the analyst wants to find an intercept and a slope such that the resulting fitted line is as close as possible
## Coefficient - Estimate
The intercept, in our example, is essentially the expected value of "SPending"

## Coefficient - Standard Error
The coefficient Standard Error measures the average amount that the coefficient estimates vary from the actual average value of our response variable. We’d ideally want a lower number relative to its coefficients.

## Coefficient - t value
The coefficient t-value is a measure of how many standard deviations our coefficient estimate is far away from 0. We want it to be far away from zero as this would indicate we could reject the null hypothesis

## Coefficient - Pr(>t)
The Pr(>t) acronym found in the model output relates to the probability of observing any value equal or larger than t. A small p-value indicates that it is unlikely we will observe a relationship between the predictor and response variables due to chance. 

## Signif. codes:
These help us build a better model. IF we use only the predictors with three stars to build a model we should see a better result

## Multiple R-squared, Adjusted R-squared
The R-squared (R2) statistic provides a measure of how well the model is fitting the actual data. It takes the form of a proportion of variance. R2 is a measure of the linear relationship between our predictor variable and our response / target variable.
A side note: In multiple regression settings, the R2 will always increase as more variables are included in the model. That’s why the adjusted R2 is the preferred measure as it adjusts for the number of variables considered.

## F-Statistic
F-statistic is a good indicator of whether there is a relationship between our predictor and the response variables. The further the F-statistic is from 1 the better it is. However, how much larger the F-statistic needs to be depends on both the number of data points and the number of predictors. Generally, when the number of data points is large, an F-statistic that is only a little bit larger than 1 is already sufficient to reject the null hypothesis (H0 : There is no relationship between the two variables

Note that the model we ran above was just an example to illustrate how a linear model output looks like in R and how we can start to interpret its components. Obviously the model is not optimised. One way we could start to improve is by transforming our response variable


# Prediction

```{r}
library(forecast)
Tayko.lm.pred <- predict(Tayko.lm, valid.df)
accuracy(Tayko.lm.pred, valid.df$Spending)
```
# Varible selection with stepwose  regression

```{r}

null=lm(Spending~1, data=train.df)    
forward_model<-step(null, scope=list(lower=null, upper=Tayko.lm), direction="forward")
stepwise_model<-step(null, scope=list(lower=null, upper=Tayko.lm), direction="both")
backward_model<-step(Tayko.lm, direction="backward")



```

```{r}
summary(backward_model)
```

```{r}
summary(forward_model)
```

```{r}
summary(stepwise_model)
```
# Choseing the right variables now
As you can see Freq, last_update, address_RES are the key predictors so lets make a new formula with those. 

```{r}
Better_Model <- lm(formula = Spending ~ Freq + Address_RES + last_update + Web, 
    data = valid.df)

summary(Better_Model)

```

#Conclusion we can now validate that the factor most involved with Spending habits of the customers are Freq and Address. Which is to say that the spending habits of the consumer are american and they have bought before. 





# Logistic Regression
## select variables for logistic regression 
Business Problem Will they purchase yes or no?
```{r}

selected.var <- c("Purchase","Address_US","Freq","last_update","Web","Gender",
                  "Address_RES")

```

# partition data
```{r}

set.seed(5)  # set seed for reproducing the partition
train.index <- sample(c(1:dim(Tayko.df)[1]), dim(Tayko.df)[1]*0.7)  
train.df <- Tayko.df[train.index, selected.var]
valid.df <- Tayko.df[-train.index, selected.var]

```
# logistic regression model using glm()
In statistics, the generalized linear model (GLM) is a flexible generalization of ordinary linear regression that allows for response variables that have error distribution models other than a normal distribution.
The glmnet() function has an alpha argument that determines what type of model is fit. If alpha = 0 then a ridge regression model is fit, and if alpha = 1 then a lasso model is fit. 
```{r}

library(caret)
library(glmnet)
logit.reg <- glm(Purchase ~ ., data = train.df, family = "binomial") 
options(scipen=999) # remove scientific notation
summary(logit.reg)

```
# Prediction
```{r}
logit.reg.pred <- predict(logit.reg, valid.df, type = "response")

confusionMatrix(as.factor(ifelse(logit.reg.pred > 0.5, "Purchase", "No Purchase")), 
                as.factor(ifelse(valid.df$Purchase==1,"Purchase","No Purchase")))

ctrl <- trainControl(method = "repeatedcv", number = 10, savePredictions = TRUE)
mod_fit <- train(Purchase ~ Address_US+Freq+last_update+Web+Gender+Address_RES, 
                 data=Tayko.df, method="glm", family="binomial",
                 trControl = ctrl)
summary(mod_fit)
```

```{r}
# select variables for regression
selected.var <- c("Spending","Address_US","Freq","last_update","Web","Gender",
                  "Address_RES")



```
# partition data
```{r}

set.seed(6)  # set seed for reproducing the partition
train.index <- sample(c(1:dim(Tayko.df)[1]), dim(Tayko.df)[1]*0.7)  
train.df <- Tayko.df[train.index, selected.var]
valid.df <- Tayko.df[-train.index, selected.var]
```

#glmnet

Ridge regression with glmnet#
The glmnet package provides the functionality for ridge regression via glmnet(). Important things to know:

Rather than accepting a formula and data frame, it requires a vector input and matrix of predictors.
You must specify alpha = 0 for ridge regression.
Ridge regression involves tuning a hyperparameter, lambda. glmnet() will generate default values for you. Alternatively, it is common practice to define your own with the lambda argument (which we’ll do).
```{r}
x <- as.matrix(train.df[,c("Address_US","Freq","last_update","Web","Gender",
                           "Address_RES")])
y <- train.df$Spending

CvRidgeMod <- cv.glmnet(x, y, alpha=0, nlambda=100, lambda.min.ratio=0.0001)


best.lambda <- CvRidgeMod$lambda.min
best.lambda

coef(CvRidgeMod, s = "lambda.min")

x_pred <- as.matrix(valid.df[,c("Address_US","Freq","last_update","Web","Gender",
                                "Address_RES")])
Ridge.pred <- predict(CvRidgeMod, s = best.lambda, newx = x_pred)
accuracy(as.vector(Ridge.pred), valid.df$Spending)
```
```{r}
plot(CvRidgeMod)
```
The lowest point in the curve indicates the optimal lambda: the log value of lambda that best minimised the error in cross-validation. We can extract this values as:
```{r}
opt_lambda <- CvRidgeMod$lambda.min
opt_lambda
```

# Lasso
Least Absolute Shrinkage and Selection Operator

Lasso regression is a parsimonious model that performs L1 regularization. The L1 regularization adds a penalty equivalent to the absolute magnitude of regression coefficients and tries to minimize them. The equation of lasso is similar to ridge regression and looks like as given below.
Lasso regression analysis is also used for variable selection as the model imposes coefficients of some variables to shrink towards zero.

The two models, lasso and ridge regression, are almost similar to each other. However, in lasso, the coefficients which are responsible for large variance are converted to zero. On the other hand, coefficients are only shrunk but are never made zero in ridge regression.



```{r}
# Lasso
CvLassoMod <- cv.glmnet(x, y, alpha=1, nlambda=100, lambda.min.ratio=0.0001)

plot(CvLassoMod)

best.lambda <- CvLassoMod$lambda.min
best.lambda



Lasso.pred <- predict(CvLassoMod, s = best.lambda, newx = x_pred)
accuracy(as.vector(Lasso.pred), valid.df$Spending)

```

```{r}
# identifying best lamda
best.lambda
```

```{r}
coef(CvLassoMod, s = "lambda.min")
```






HenryBernreuter.com v1.0

Linear Regression Example

TAYKO SOFTWARE

Business Problem

Predicting Software Reselling Profits

OBJECTIVE: From the dataset Tayko.csv, Purchase output variable is considered for the analysis and prediction. The objective of the model is to classify records into ‘PURCHASE’ or "NO PURCHASE’.

Read in data

Select variables for regression

Partition data

Building the model for Spending

What does it mean?

This plot will suggest that the data is not normally distrubed

Another way to see distrubution is with the Shapiro-Wilk Test

Coefficients

Coefficient - Standard Error

Coefficient - t value

Coefficient - Pr(>t)

Signif. codes:

Multiple R-squared, Adjusted R-squared

F-Statistic

Prediction

Varible selection with stepwose regression

Choseing the right variables now

Logistic Regression

select variables for logistic regression

partition data

logistic regression model using glm()

Prediction

partition data

Lasso

Python in One Post

Linear Regression Example

TAYKO SOFTWARE

Business Problem

Predicting Software Reselling Profits

OBJECTIVE: From the dataset Tayko.csv, Purchase output variable is considered for the analysis and prediction. The objective of the model is to classify records into ‘PURCHASE’ or "NO PURCHASE’.

Read in data

Select variables for regression

Partition data

Building the model for Spending

What does it mean?

This plot will suggest that the data is not normally distrubed

Another way to see distrubution is with the Shapiro-Wilk Test

Coefficients

Coefficient - Standard Error

Coefficient - t value

Coefficient - Pr(>t)

Signif. codes:

Multiple R-squared, Adjusted R-squared

F-Statistic

Prediction

Varible selection with stepwose regression

Choseing the right variables now

Logistic Regression

select variables for logistic regression

partition data

logistic regression model using glm()

Prediction

partition data

Lasso

Python in One Post

Don't go yet!

How this site was built

Estimating COVID-19s transmission rates in Georgia

Like this page? Consider buying me a cup of coffee or sharing it?