Tutorial 8 - Structural learning

7/23/2022
35 minutes to read

In this tutorial we will build a model from data, adding both nodes and links, and then learning the parameters.

The following concepts will be covered:

Creating a Data Connection
Adding nodes from data
Re-ordering discrete variable states
Adding links from data (structural learning)
Learning parameters from data

NOTE

Bayes Server must be installed, before starting this tutorial. An evaluation version can be downloaded from the Downloads page

Companion video (No Audio)

Setting up a data connection

For convenience, we will use Microsoft Excel as the data source, however another database can be substituted.

Adding a data connection

NOTE

You can skip this step, and instead use the pre-installed Tutorial data connection (Walkthrough Data in earlier versions).

Select the data (including the header) in the data section and copy it to the clipboard (Ctrl+C).
Open Microsoft Excel and paste the data into a new Microsoft Excel spreadsheet (Ctrl+V).
Save the new spreadsheet.
In Bayes Server, click the Data Connections button on the Data tab, Data Sources group. This will launch the Data connection manager.
Click the New button on the toolbar. This will launch the Data connection editor.
In the list of data providers, select the appropriate Excel Driver for the version of Microsoft Excel you are using.
Next to the File Name text box, click the Ellipsis (...) button, and select the Microsoft Excel spreadsheet created in an earlier step.
Click the Test Connection button, to ensure the new data connection is working.
Click OK to add the new Data Connection.

Adding nodes from data

It is possible to add nodes manually, however in this tutorial we will add nodes automatically from data.

Launch Bayes Server, and click New on the File tab to create a new empty network.
In Bayes Server, click the Add Nodes button on the Data tab, Network group. This will launch the Data tables window.
In the Data Connection drop down, select the new Data Connection created in an earlier step, or the Tutorial data connection if you skipped that step. This should enable the Data drop down.
In the Data drop down, select the worksheet that contains the data. (If the data is on the first worksheet, select Sheet1$). If you are using the pre-installed Tutorial data connection, select Tutorial 8 - Structural.
Click the OK button. This will launch the Add nodes from data wizard.
Ensure that the Case database column is not checked. This is an identifier column, which we do not want to include as a node/variable.

The window should look like this:
Click Next, accepting the default options, until you reach the Run page.
Click Run to run the detection algorithm.
Click the Finish button in the Add nodes from data wizard. This will add the nodes to the empty network.
Re-position the new nodes as per the network shown below. This can be done by dragging each node, or setting x and y positions in the Properties window.
Select the node named Hair Length and then click the States button on the Network tab, Editing group. This will launch the States editor window.
Use the up and down arrows to change the order of the states to Short, Medium, Long. Then click the OK button.
Repeat this step for the node named Build, re-ordering the states to Slim, Average, Large.

The network should look like this:

Structural learning - pre links

Structural learning (adding links from data)

At this point we could manually add links between the nodes we added to the network in the previous step, however the purpose of this tutorial is to demonstrate learning the links from data, known as structural learning.

In Bayes Server, click the Structural learning button on the Data tab, Network group. This will launch the Data tables window.
In the Data Connection drop down, select the new Data Connection created in an earlier step, or the Tutorial data connection if you skipped that step. This should enable the Data drop down.
In the Data drop down, select the worksheet that contains the data. (If the data is on the first worksheet, select Sheet1$). If you are using the pre-installed Tutorial data connection, select Tutorial 8 - Structural.
Click the OK button. This will launch the Data map window.
In the Data map window, ensure that all variables have been mapped to columns of the same name.

The window should look like this:
Click the OK button. This will launch the Structural learning wizard.
Click Next in the wizard, accepting all the default settings, until you reach the Run page. Click the Run button to start learning.
When learning has completed, click the Finish button on the wizard. This will launch the Candidate networks window. Click OK to update the existing network.

Links have now been added to the new network which should look like this:

Learning the distributions

We could now enter the distribution parameters for the nodes manually using the Distribution editor, however in this tutorial we will learn the parameter values from data.

Parameter learning

Click the Parameter Learning button, on the Data tab. This will launch the Data tables window.
In the Data Connection drop down, select the new Data Connection created in an earlier step, or the Tutorial data connection if you skipped that step. This should enable the Data drop down.
In the Data drop down, select the worksheet that contains the data. (If the data is on the first worksheet, select Sheet1$). If you are using the pre-installed Tutorial data connection, select Tutorial 8 - Structural.
Click the OK button. This will launch the Data map window.
In the Data map window, ensure that all variables have been mapped to columns of the same name.

The window should look like this:
Click the OK button. This will launch the Parameter learning wizard.
Click Next in the wizard, accepting all the default settings, until you reach the Run page. Click the Run button to start learning.
When learning has completed, click the Finish button on the wizard. This will launch the Candidate Networks window.
Click the OK button in the Candidate Networks window.
The network distributions have now been learned.

Summary

The network has now been fully specified from data. To see the network in action, click the All button on the network viewer toolbar, or use the keyboard shortcut F6.

Data

Case	Build	Gender	Hair Length	Height	Weight
0	Slim	Male	Short	174	45.1
1	Average	Male	Long	162	65.6
2	Large	Female	Medium	154	63.4
3	Large	Male	Short	177	106
4	Average	Male	Short	182	72.3
5	Large	Male	Short	175	116
6	Large	Male	Short	162	86.3
7	Average	Female	Long	156	49
8	Large	Male	Long	169	93.6
9	Large	Female	Long	165	84.1
10	Average	Female	Long	167	52.8
11	Large	Male	Short	181	120
12	Large	Male	Short	178	114
13	Large	Male	Short	165	92.2
14	Large	Male	Short	187	116
15	Slim	Male	Short	175	43.2
16	Large	Female	Long	166	84
17	Large	Female	Medium	154	67
18	Large	Male	Medium	179	117
19	Large	Female	Long	157	69.8
20	Average	Female	Long	150	36.5
21	Large	Male	Medium	178	110
22	Large	Male	Medium	181	104
23	Average	Male	Medium	173	72.8
24	Large	Female	Medium	173	88.4
25	Average	Male	Short	169	67.6
26	Slim	Female	Long	163	27.3
27	Average	Male	Short	182	79.7
28	Slim	Male	Short	180	48.3
29	Large	Female	Long	173	93.8
30	Large	Female	Long	167	82.5
31	Large	Male	Short	178	113
32	Large	Male	Medium	172	102
33	Large	Male	Long	171	100
34	Large	Female	Medium	177	102
35	Average	Male	Short	176	78.5
36	Large	Female	Short	168	89.8
37	Average	Male	Short	184	72.2
38	Average	Male	Short	161	61.4
39	Large	Male	Short	180	108
40	Average	Female	Medium	162	57.3
41	Slim	Male	Medium	192	52.8
42	Average	Male	Short	170	60.3
43	Slim	Female	Long	172	34.8
44	Large	Male	Short	173	113
45	Average	Female	Long	164	56.3
46	Average	Female	Medium	162	53.6
47	Large	Female	Long	156	76.8
48	Slim	Female	Short	174	32
49	Slim	Female	Medium	157	25.5
50	Large	Male	Short	165	93.1
51	Large	Male	Short	172	110
52	Large	Male	Medium	169	96
53	Large	Male	Short	181	119
54	Average	Male	Short	167	61.7
55	Large	Male	Short	188	120
56	Average	Male	Short	169	61
57	Large	Female	Medium	167	93.2
58	Large	Male	Short	180	113
59	Slim	Male	Short	167	42.4
60	Average	Female	Medium	162	45.9
61	Large	Male	Short	170	100
62	Slim	Male	Medium	171	47.8
63	Large	Male	Short	175	94.8
64	Slim	Female	Medium	170	34.1
65	Average	Female	Medium	147	34.2
66	Large	Male	Medium	172	104
67	Large	Female	Long	145	57.1
68	Average	Female	Long	153	45.1
69	Slim	Female	Short	170	34.4
70	Slim	Male	Short	184	47.7
71	Large	Female	Medium	166	90.7
72	Large	Female	Long	161	72.4
73	Large	Female	Long	172	89.8
74	Average	Female	Medium	173	63.1
75	Large	Female	Long	165	96.8
76	Slim	Female	Medium	163	28.5
77	Large	Female	Long	176	95.9
78	Large	Female	Long	162	76.7
79	Large	Female	Short	156	72.8
80	Slim	Female	Medium	157	28.1
81	Large	Female	Long	163	83.3
82	Slim	Male	Short	176	41.5
83	Average	Male	Short	184	64.9
84	Average	Male	Short	196	87.4
85	Large	Male	Short	178	114
86	Large	Male	Short	177	104
87	Average	Male	Short	175	73.1
88	Average	Male	Short	178	70.8
89	Large	Female	Medium	172	97.6
90	Large	Male	Short	165	98.5
91	Average	Male	Medium	186	72.9
92	Large	Female	Long	161	83.4
93	Large	Female	Short	171	86.3
94	Large	Male	Short	176	110
95	Large	Female	Long	168	83.7
96	Average	Female	Short	171	60.9
97	Large	Female	Long	172	89.5
98	Large	Female	Long	170	82.7
99	Large	Female	Long	170	83.1
100	Large	Female	Long	163	92.2
101	Average	Female	Short	165	45.8
102	Slim	Female	Long	162	32.1
103	Slim	Male	Short	170	46.6
104	Large	Male	Medium	179	114
105	Large	Female	Long	173	97
106	Average	Female	Medium	151	35
107	Large	Female	Long	149	66.2
108	Slim	Female	Medium	148	26
109	Large	Female	Long	155	69.6
110	Large	Male	Short	177	109
111	Large	Female	Long	153	65.6
112	Large	Male	Short	179	113
113	Large	Male	Medium	176	109
114	Average	Male	Short	178	74.3
115	Slim	Female	Long	181	34.9
116	Large	Male	Medium	173	105
117	Large	Female	Medium	171	89.6
118	Large	Female	Long	161	74
119	Average	Female	Medium	149	43.1
120	Average	Male	Short	171	63
121	Average	Female	Long	164	50.3
122	Average	Female	Long	160	51.6
123	Average	Female	Long	164	54.2
124	Large	Female	Long	168	79.3
125	Average	Female	Medium	165	52.2
126	Large	Female	Long	151	61.8
127	Slim	Male	Short	172	39.9
128	Large	Female	Long	157	70.7
129	Slim	Female	Long	157	25.7
130	Large	Female	Short	166	82.7
131	Slim	Male	Short	178	47.8
132	Average	Male	Short	179	75.2
133	Average	Male	Short	180	77.1
134	Large	Female	Long	146	49.4
135	Large	Female	Long	167	79.1
136	Slim	Male	Short	172	46.8
137	Slim	Male	Short	174	42.1
138	Slim	Female	Long	177	35
139	Large	Female	Medium	175	105
140	Average	Male	Short	173	69.9
141	Average	Male	Short	175	68
142	Average	Male	Medium	173	67.7
143	Large	Male	Short	170	90.3
144	Large	Male	Medium	181	115
145	Large	Female	Medium	158	70.4
146	Slim	Female	Long	166	23.2
147	Large	Male	Medium	171	99.2
148	Large	Female	Medium	165	86.6
149	Average	Female	Long	166	49.2
150	Large	Male	Short	163	83.6
151	Large	Female	Medium	167	83.9
152	Slim	Male	Short	177	41.2
153	Large	Female	Long	163	76.5
154	Large	Female	Medium	166	82
155	Average	Male	Short	181	80.1
156	Large	Female	Long	156	78.3
157	Large	Female	Medium	161	71.5
158	Average	Female	Medium	165	49
159	Average	Female	Long	153	44.5
160	Slim	Female	Medium	156	30.4
161	Slim	Female	Long	164	28.1
162	Large	Female	Long	160	68.8
163	Large	Male	Short	182	114
164	Large	Female	Medium	164	80.8
165	Average	Male	Short	170	54.9
166	Average	Male	Short	176	74
167	Large	Male	Short	179	113
168	Average	Female	Medium	158	48.7
169	Average	Female	Long	167	45.5
170	Average	Male	Short	172	66.8
171	Average	Male	Short	172	68.5
172	Average	Male	Short	173	70.6
173	Large	Female	Long	173	94.1
174	Large	Female	Short	163	73.9
175	Average	Male	Short	186	71.1
176	Average	Male	Short	174	66.5
177	Large	Male	Short	183	119
178	Slim	Female	Medium	168	34.1
179	Slim	Female	Medium	154	29.8
180	Slim	Male	Short	173	47
181	Large	Male	Short	184	112
182	Average	Female	Long	172	62.4
183	Average	Female	Short	152	45.8
184	Average	Male	Medium	183	82.5
185	Large	Female	Medium	162	83
186	Average	Female	Short	173	59
187	Slim	Male	Short	181	44
188	Large	Male	Short	166	99.4
189	Large	Female	Medium	162	81.4
190	Large	Female	Long	165	79.3
191	Large	Female	Long	155	71.7
192	Average	Male	Short	182	76.6
193	Large	Female	Medium	175	95.3
194	Average	Female	Medium	163	52.4
195	Large	Female	Medium	155	77.3
196	Average	Male	Short	180	70.1
197	Average	Male	Short	169	61.9
198	Slim	Female	Medium	164	29.3
199	Large	Female	Medium	167	81.2
200	Average	Female	Long	156	44.4
201	Slim	Female	Long	159	25.5
202	Slim	Female	Medium	166	27.1
203	Large	Female	Long	163	80.9
204	Large	Male	Short	177	105
205	Average	Male	Short	172	65
206	Large	Female	Long	171	92
207	Large	Female	Long	170	81
208	Large	Male	Short	174	105
209	Average	Male	Long	182	69.9
210	Large	Female	Long	165	83.5
211	Average	Male	Long	179	69
212	Large	Male	Short	191	122
213	Large	Female	Long	160	74.1
214	Large	Male	Long	172	108
215	Large	Female	Long	164	84.7
216	Large	Male	Short	173	109
217	Slim	Male	Short	187	48.4
218	Large	Female	Medium	156	74.8
219	Slim	Female	Short	160	30.5
220	Large	Male	Short	177	104
221	Large	Male	Short	179	113
222	Large	Female	Short	166	89.8
223	Large	Male	Medium	185	125
224	Slim	Male	Medium	188	43.9
225	Average	Female	Short	156	40.8
226	Average	Male	Medium	177	71
227	Large	Female	Medium	158	68.7
228	Average	Male	Short	168	64.9
229	Average	Female	Long	161	51.6
230	Large	Female	Medium	157	69.1
231	Average	Male	Short	169	69.6
232	Large	Male	Short	166	88
233	Average	Male	Short	196	87.1
234	Slim	Female	Long	156	28.8
235	Average	Male	Medium	172	66.4
236	Average	Female	Short	160	46.7
237	Slim	Female	Long	157	35.3
238	Large	Female	Medium	169	87.5
239	Large	Female	Long	165	73.8
240	Slim	Male	Medium	178	48.3
241	Slim	Male	Short	177	50.7
242	Slim	Male	Short	176	45.5
243	Average	Male	Short	169	66.3
244	Slim	Female	Long	138	17.3
245	Large	Male	Short	168	92.6
246	Average	Male	Medium	180	69.8
247	Large	Male	Long	189	111
248	Slim	Female	Long	156	24.3
249	Slim	Male	Short	173	39.3
250	Large	Female	Medium	152	73
251	Slim	Male	Medium	183	41.9
252	Large	Female	Long	159	77.9
253	Large	Female	Medium	162	74.6
254	Large	Male	Short	180	119
255	Average	Male	Short	181	68.6
256	Average	Male	Short	174	69.7
257	Large	Female	Medium	166	88.6
258	Slim	Female	Medium	155	21.3
259	Slim	Male	Short	178	48.5
260	Large	Female	Long	166	86.2
261	Large	Male	Short	172	101
262	Slim	Female	Long	161	26.3
263	Slim	Male	Short	189	52.9
264	Large	Female	Medium	169	82.5
265	Large	Female	Long	165	77.9
266	Large	Female	Medium	164	73.8
267	Large	Male	Short	182	123
268	Average	Female	Medium	165	53.2
269	Average	Male	Short	170	71.2
270	Average	Female	Long	160	49.6
271	Average	Female	Medium	160	49.3
272	Large	Female	Long	157	78.6
273	Large	Female	Long	167	96.8
274	Large	Male	Short	168	94.9
275	Large	Male	Short	182	113
276	Large	Male	Short	185	114
277	Large	Male	Medium	177	99.8
278	Average	Male	Short	169	57.4
279	Large	Male	Short	168	95
280	Slim	Male	Short	191	51.6
281	Large	Female	Medium	163	79.3
282	Large	Male	Short	174	108
283	Large	Female	Long	175	99.3
284	Average	Female	Medium	169	57
285	Large	Female	Medium	160	80.2
286	Large	Female	Long	154	79.4
287	Slim	Female	Medium	162	30.4
288	Large	Male	Medium	174	98.7
289	Slim	Female	Medium	164	33.2
290	Average	Male	Short	174	66.9
291	Large	Male	Medium	184	119
292	Large	Male	Short	162	93.5
293	Large	Male	Short	175	104
294	Large	Female	Long	153	65.2
295	Average	Female	Long	162	49.5
296	Average	Female	Medium	160	45.2
297	Average	Male	Short	177	69.5
298	Average	Male	Short	184	74.6
299	Slim	Female	Medium	161	32.1
300	Large	Female	Short	158	76.9
301	Average	Male	Short	186	79.1
302	Average	Female	Medium	149	44.6
303	Large	Male	Short	173	109
304	Average	Female	Medium	165	56.7
305	Large	Male	Short	184	113
306	Slim	Male	Short	174	46.7
307	Average	Female	Long	167	54.6
308	Average	Female	Long	162	55.6
309	Large	Male	Short	188	133
310	Large	Female	Long	155	73.5
311	Average	Male	Short	183	72.9
312	Large	Male	Short	186	110
313	Large	Male	Short	177	109
314	Large	Female	Long	148	63.6
315	Slim	Female	Short	152	28.8
316	Slim	Female	Long	161	25.1
317	Average	Female	Medium	160	50.2
318	Average	Female	Long	167	49.6
319	Slim	Male	Short	169	47.4
320	Slim	Female	Long	166	27
321	Slim	Male	Short	172	42.5
322	Large	Female	Medium	166	83.7
323	Slim	Female	Long	166	30.7
324	Average	Female	Long	162	48.4
325	Large	Female	Medium	156	74.1
326	Average	Male	Short	174	66.9
327	Slim	Male	Short	170	46.7
328	Large	Female	Long	164	87
329	Large	Female	Long	172	91.8
330	Large	Female	Medium	163	79.3
331	Large	Male	Short	167	86.5
332	Average	Female	Long	170	63.6
333	Average	Male	Short	179	65.5
334	Large	Female	Long	168	88.5
335	Large	Female	Long	175	102
336	Large	Male	Short	185	120
337	Large	Female	Medium	159	78.8
338	Large	Male	Short	165	92.8
339	Large	Female	Long	151	62.6
340	Slim	Male	Short	188	46.8
341	Large	Female	Long	152	60
342	Large	Female	Long	161	81.8
343	Large	Female	Long	163	76.9
344	Slim	Female	Long	153	25.2
345	Average	Female	Short	163	47.4
346	Slim	Female	Long	159	30.7
347	Large	Male	Short	183	116
348	Average	Female	Long	163	52.3
349	Average	Female	Long	154	46.3
350	Average	Female	Long	167	55.1
351	Slim	Male	Short	173	40.9
352	Large	Female	Medium	164	80.9
353	Large	Male	Short	181	121
354	Average	Male	Medium	177	64.4
355	Large	Male	Short	165	101
356	Large	Female	Medium	169	88.8
357	Large	Male	Short	177	101
358	Slim	Female	Long	158	29.7
359	Large	Male	Short	181	118
360	Large	Female	Short	147	61
361	Large	Male	Short	171	104
362	Average	Female	Medium	161	47.1
363	Large	Female	Medium	163	78.6
364	Average	Male	Short	177	65
365	Average	Female	Medium	154	36.2
366	Average	Female	Long	177	60
367	Large	Female	Medium	170	94.9
368	Slim	Female	Long	158	29.1
369	Average	Male	Short	174	67.3
370	Large	Male	Medium	173	108
371	Large	Male	Short	173	100
372	Average	Male	Short	174	66.2
373	Slim	Female	Long	158	30.4
374	Large	Female	Long	173	95.3
375	Slim	Male	Medium	178	41.8
376	Large	Male	Short	180	112
377	Slim	Male	Short	164	40.8
378	Average	Male	Long	170	67.4
379	Large	Female	Long	158	79.3
380	Large	Male	Medium	171	106
381	Large	Male	Short	178	113
382	Average	Male	Medium	179	74.7
383	Large	Female	Long	159	75.8
384	Average	Male	Short	178	70.9
385	Slim	Female	Medium	163	32.4
386	Large	Male	Short	170	99.2
387	Large	Male	Short	173	106
388	Average	Male	Short	172	68
389	Large	Female	Long	152	59.3
390	Large	Female	Medium	151	59.9
391	Average	Female	Medium	174	66
392	Large	Male	Short	186	115
393	Average	Male	Short	180	68.1
394	Large	Female	Long	165	88.3
395	Average	Female	Long	158	42.2
396	Large	Male	Long	173	103
397	Large	Female	Long	161	77.9
398	Large	Female	Long	158	65.7
399	Large	Female	Long	166	87.6
400	Average	Male	Short	169	64.1
401	Large	Female	Long	160	71.8
402	Slim	Female	Short	161	29.4
403	Large	Male	Short	166	98.6
404	Large	Male	Short	177	114
405	Slim	Female	Medium	167	36.2
406	Large	Female	Long	169	84.2
407	Average	Female	Long	168	54.9
408	Average	Female	Medium	163	53.7
409	Slim	Male	Short	169	42.5
410	Large	Male	Short	172	102
411	Large	Female	Medium	165	81.1
412	Large	Male	Short	179	117
413	Large	Female	Long	159	75.3
414	Slim	Male	Short	183	47.9
415	Slim	Female	Medium	157	26
416	Large	Male	Short	171	101
417	Average	Female	Long	156	48.9
418	Large	Male	Medium	174	106
419	Slim	Female	Long	165	25.8
420	Average	Female	Medium	152	42.9
421	Slim	Female	Medium	170	29.4
422	Large	Female	Long	159	74.1
423	Large	Female	Short	151	68.6
424	Large	Female	Short	176	97.1
425	Average	Female	Medium	142	35.8
426	Large	Male	Short	169	103
427	Large	Female	Medium	169	88.6
428	Slim	Female	Long	162	26.9
429	Large	Female	Medium	150	71.4
430	Large	Male	Medium	180	115
431	Large	Male	Medium	184	115
432	Average	Male	Medium	165	63.5
433	Average	Female	Medium	170	59.4
434	Average	Male	Medium	176	67.3
435	Average	Female	Short	163	54.1
436	Average	Male	Short	183	76.8
437	Average	Male	Short	176	68.4
438	Large	Female	Long	160	76.3
439	Average	Female	Medium	153	44.7
440	Large	Male	Medium	165	102
441	Average	Female	Short	162	49.3
442	Average	Female	Long	166	54.7
443	Large	Female	Medium	164	82.2
444	Average	Male	Short	180	67.1
445	Average	Male	Medium	175	63.9
446	Large	Male	Short	174	109
447	Large	Female	Medium	171	96.4
448	Large	Female	Long	151	70.2
449	Large	Female	Long	156	67.2
450	Large	Female	Medium	151	59.6
451	Average	Female	Long	157	44.5
452	Average	Male	Medium	176	62.1
453	Large	Female	Long	155	74.2
454	Large	Female	Short	149	62
455	Large	Male	Short	175	108
456	Slim	Male	Short	188	46.8
457	Large	Male	Medium	181	108
458	Average	Male	Short	163	62.7
459	Slim	Male	Short	179	49.6
460	Large	Female	Long	165	83.7
461	Slim	Male	Short	190	55.4
462	Slim	Female	Medium	156	30.6
463	Large	Female	Long	160	84.3
464	Average	Female	Long	164	54
465	Large	Male	Short	172	100
466	Average	Male	Short	190	80
467	Large	Female	Long	166	81.4
468	Average	Male	Short	172	60.9
469	Large	Female	Medium	167	86.5
470	Average	Female	Medium	169	58.7
471	Average	Female	Long	162	50.2
472	Average	Female	Long	174	61.3
473	Large	Male	Long	169	98.1
474	Average	Male	Short	185	65.2
475	Large	Female	Long	170	91.8
476	Average	Female	Medium	164	49.4
477	Large	Female	Short	173	91.2
478	Large	Male	Short	163	90.2
479	Average	Female	Medium	161	53.2
480	Large	Female	Long	167	77
481	Large	Female	Medium	169	76.5
482	Average	Male	Short	189	76.8
483	Average	Female	Long	163	55.8
484	Large	Female	Medium	155	76.7
485	Large	Female	Medium	157	77.9
486	Average	Male	Short	179	75.9
487	Slim	Female	Medium	159	28.5
488	Average	Female	Long	162	50.5
489	Average	Male	Short	180	74.4
490	Large	Female	Medium	157	69.2
491	Slim	Male	Medium	171	38.8
492	Average	Female	Long	157	44.9
493	Average	Male	Medium	175	66
494	Large	Female	Medium	162	80.8
495	Average	Male	Short	175	66.9
496	Average	Female	Long	156	41.4
497	Large	Female	Short	175	102
498	Average	Female	Medium	153	42.4
499	Average	Male	Short	177	72.6
500	Slim	Male	Short	176	43.3
501	Large	Female	Short	177	102
502	Slim	Male	Short	166	42.2
503	Large	Female	Short	166	90.1
504	Average	Male	Short	176	76.4
505	Average	Female	Medium	160	46.8
506	Average	Male	Short	188	81.6
507	Large	Female	Long	169	81.8
508	Large	Female	Medium	160	72.6
509	Slim	Female	Medium	166	28.9
510	Large	Male	Medium	176	110
511	Slim	Female	Short	167	34.1
512	Large	Female	Medium	172	86.9
513	Average	Male	Short	181	76
514	Average	Female	Long	154	36.1
515	Large	Female	Medium	173	87.2
516	Large	Female	Long	162	79.9
517	Slim	Female	Long	162	29.7
518	Average	Female	Medium	167	55.8
519	Average	Female	Long	160	49.7
520	Large	Female	Long	165	77.9
521	Slim	Male	Medium	175	46.5
522	Large	Female	Medium	165	84.5
523	Slim	Female	Medium	159	28.5
524	Slim	Female	Medium	179	38.4
525	Slim	Male	Short	181	42.7
526	Large	Male	Medium	173	113
527	Large	Female	Long	165	87.8
528	Average	Female	Long	146	36.2
529	Average	Male	Short	179	73.9
530	Average	Male	Short	186	73
531	Average	Male	Long	172	63.5
532	Average	Male	Short	178	73
533	Large	Female	Long	158	76.7
534	Large	Male	Short	184	111
535	Slim	Male	Short	187	50.4
536	Large	Female	Long	180	112
537	Large	Male	Short	173	110
538	Slim	Female	Long	163	33.4
539	Large	Female	Long	166	87.7
540	Large	Male	Short	180	115
541	Large	Male	Short	193	129
542	Slim	Female	Medium	161	29
543	Average	Female	Long	159	48.9
544	Large	Female	Long	161	73.9
545	Average	Female	Medium	159	58
546	Average	Female	Medium	164	49.8
547	Average	Male	Short	183	63.4
548	Average	Male	Short	170	61.8
549	Slim	Male	Short	165	42.6
550	Average	Male	Short	173	58.9
551	Large	Female	Medium	152	70.3
552	Large	Male	Medium	177	112
553	Average	Male	Short	178	64.2
554	Large	Female	Short	158	76.3
555	Large	Male	Long	177	114
556	Slim	Female	Long	149	24.3
557	Large	Female	Medium	163	82.3
558	Average	Male	Short	172	67.7
559	Slim	Male	Long	179	47.8
560	Slim	Male	Short	181	47.5
561	Large	Male	Short	190	124
562	Large	Female	Medium	168	87.2
563	Average	Female	Long	165	49.9
564	Large	Male	Short	175	111
565	Large	Male	Short	166	86.9
566	Average	Male	Short	171	68.6
567	Large	Male	Short	178	115
568	Slim	Female	Long	158	24.3
569	Large	Male	Short	176	95.6
570	Large	Female	Long	176	99.3
571	Large	Male	Long	180	115
572	Average	Male	Short	182	70.4
573	Average	Female	Long	167	56.7
574	Slim	Male	Short	179	47.4
575	Average	Female	Short	182	69.5
576	Average	Female	Long	160	51.7
577	Average	Male	Short	171	60.6
578	Large	Male	Long	182	114
579	Average	Male	Short	178	65.5
580	Average	Male	Short	191	78
581	Large	Female	Short	156	74.8
582	Large	Male	Short	171	95.3
583	Slim	Male	Short	185	50.6
584	Large	Female	Medium	156	73.3
585	Large	Female	Long	156	76.8
586	Large	Female	Medium	170	94.7
587	Large	Female	Medium	169	90.4
588	Large	Female	Long	170	83.2
589	Large	Male	Short	175	118
590	Large	Female	Long	167	85.1
591	Large	Female	Medium	165	74.4
592	Average	Male	Short	179	67.5
593	Average	Male	Medium	175	65.7
594	Average	Male	Short	173	68.3
595	Slim	Female	Medium	185	36.9
596	Large	Male	Short	176	101
597	Average	Female	Medium	161	47.7
598	Slim	Female	Long	161	30.8
599	Large	Male	Medium	176	109
600	Average	Male	Short	170	69.7
601	Large	Male	Short	180	117
602	Large	Female	Long	175	92.8
603	Large	Male	Short	164	86.1
604	Large	Female	Long	161	77.9
605	Large	Male	Short	175	104
606	Average	Female	Long	169	52.3
607	Average	Female	Short	166	52.5
608	Slim	Male	Short	175	43.9
609	Average	Male	Short	178	68.5
610	Average	Male	Short	179	69.1
611	Large	Female	Medium	151	66.3
612	Large	Female	Medium	161	81
613	Slim	Female	Long	170	33.7
614	Large	Female	Short	170	94.1
615	Slim	Male	Short	177	46.2
616	Average	Male	Short	171	66
617	Large	Female	Medium	171	84.9
618	Large	Female	Long	170	92.8
619	Large	Male	Short	190	119
620	Large	Female	Medium	165	83.3
621	Large	Female	Long	154	71.6
622	Large	Male	Short	179	112
623	Slim	Female	Long	165	28.7
624	Large	Male	Short	166	99.5
625	Large	Female	Long	166	78.2
626	Slim	Female	Long	166	34.3
627	Average	Male	Short	175	67.8
628	Average	Male	Short	178	68.7
629	Large	Female	Long	147	62.2
630	Large	Male	Short	178	115
631	Large	Male	Short	183	114
632	Large	Male	Medium	178	118
633	Large	Male	Short	176	108
634	Average	Male	Short	171	68.3
635	Large	Female	Long	156	70.3
636	Average	Male	Short	173	66.7
637	Large	Female	Medium	156	71.6
638	Large	Male	Medium	179	106
639	Large	Female	Medium	178	94.7
640	Large	Female	Medium	157	79.9
641	Average	Male	Short	187	74.1
642	Large	Female	Long	162	69.8
643	Large	Male	Medium	173	109
644	Large	Female	Medium	158	75.5
645	Large	Male	Short	180	117
646	Large	Male	Short	172	96.5
647	Slim	Male	Short	178	44.7
648	Large	Male	Short	182	117
649	Large	Male	Short	179	112
650	Large	Male	Short	175	111
651	Average	Male	Medium	196	85.5
652	Large	Male	Medium	180	115
653	Average	Female	Long	157	43.3
654	Average	Male	Short	178	75.8
655	Large	Female	Long	162	76.3
656	Average	Male	Medium	178	67.9
657	Slim	Male	Short	162	37.2
658	Slim	Female	Medium	161	28.1
659	Slim	Male	Short	173	45.9
660	Large	Female	Medium	159	85.7
661	Large	Male	Short	171	96.8
662	Average	Male	Short	177	71.9
663	Slim	Female	Long	163	35.5
664	Slim	Male	Medium	175	42.6
665	Large	Female	Medium	151	69.1
666	Average	Female	Medium	159	49.4
667	Slim	Male	Short	174	38.6
668	Slim	Female	Long	166	27.7
669	Average	Female	Long	154	42.5
670	Slim	Male	Short	180	48.5
671	Average	Female	Long	161	47.5
672	Large	Female	Short	169	95
673	Large	Female	Medium	159	73.6
674	Average	Male	Short	168	58.2
675	Large	Female	Medium	163	84.1
676	Average	Female	Medium	167	54.5
677	Average	Male	Short	183	81.1
678	Large	Male	Short	181	107
679	Slim	Female	Long	160	24.1
680	Average	Male	Short	176	67.2
681	Large	Female	Medium	163	74.6
682	Average	Female	Medium	168	60.2
683	Slim	Female	Long	164	30.7
684	Average	Female	Short	150	46.7
685	Large	Male	Short	161	96.8
686	Large	Female	Long	169	87.9
687	Large	Female	Long	172	94.8
688	Large	Female	Medium	175	91.5
689	Large	Female	Long	162	67.7
690	Average	Male	Short	173	61.9
691	Large	Male	Short	175	110
692	Large	Female	Long	167	85.9
693	Large	Male	Short	179	115
694	Slim	Male	Short	168	41.1
695	Average	Female	Long	165	54.4
696	Large	Female	Long	153	68.2
697	Average	Female	Short	161	49
698	Slim	Male	Short	178	47.6
699	Average	Female	Medium	159	57.7
700	Large	Male	Short	179	113
701	Large	Male	Short	165	87.9
702	Average	Female	Long	160	58.7
703	Average	Female	Long	169	57.9
704	Large	Female	Medium	168	94.3
705	Average	Male	Short	184	77.5
706	Average	Female	Long	169	51.7
707	Large	Male	Short	166	88.7
708	Large	Female	Long	166	85.3
709	Large	Female	Medium	158	73.9
710	Large	Female	Short	166	77.3
711	Average	Female	Medium	162	48.1
712	Slim	Male	Short	178	42
713	Average	Male	Short	178	70.3
714	Average	Male	Short	184	80.8
715	Slim	Male	Medium	168	44
716	Average	Male	Short	174	71
717	Large	Female	Medium	160	75.1
718	Large	Male	Medium	167	108
719	Large	Male	Long	176	104
720	Large	Male	Short	176	100
721	Large	Male	Short	170	98.8
722	Average	Male	Short	182	74.6
723	Large	Female	Long	166	78.4
724	Large	Female	Long	150	55
725	Slim	Female	Long	154	33.4
726	Average	Male	Medium	160	62.7
727	Large	Male	Short	177	108
728	Large	Male	Short	192	133
729	Slim	Male	Medium	173	43.5
730	Large	Male	Short	170	104
731	Average	Male	Short	190	75.6
732	Large	Male	Medium	172	100
733	Large	Male	Short	180	108
734	Large	Female	Long	162	73.5
735	Average	Female	Long	157	43
736	Average	Female	Medium	161	52.3
737	Large	Female	Long	172	98.9
738	Average	Male	Short	170	72.5
739	Average	Female	Medium	167	53.9
740	Large	Female	Long	154	68.4
741	Large	Female	Medium	163	81
742	Large	Male	Short	180	116
743	Average	Male	Short	189	80
744	Large	Female	Medium	175	97.2
745	Large	Female	Long	162	81.9
746	Large	Male	Short	167	99.4
747	Large	Female	Medium	164	84.2
748	Large	Male	Short	174	115
749	Slim	Male	Short	174	44.5
750	Average	Male	Medium	175	75.2
751	Slim	Female	Long	167	31.7
752	Average	Male	Short	181	68.1
753	Large	Female	Long	167	80.6
754	Large	Female	Medium	160	75.2
755	Slim	Female	Long	166	26.6
756	Large	Male	Short	170	104
757	Large	Male	Short	184	121
758	Large	Male	Short	163	96.6
759	Large	Male	Short	166	90.8
760	Average	Male	Short	169	59.2
761	Large	Male	Short	168	97.8
762	Large	Male	Short	184	115
763	Average	Male	Short	169	63.8
764	Average	Male	Medium	182	82.7
765	Large	Female	Medium	152	65
766	Average	Male	Long	193	81
767	Slim	Male	Short	177	42.9
768	Average	Female	Short	161	51.4
769	Large	Male	Short	171	102
770	Large	Male	Short	172	98.8
771	Average	Male	Short	178	69.8
772	Average	Female	Long	176	59.6
773	Average	Male	Short	178	67.1
774	Large	Male	Short	178	107
775	Slim	Female	Long	164	29.3
776	Large	Female	Long	173	94.6
777	Slim	Male	Medium	180	48.4
778	Large	Female	Long	164	79.1
779	Large	Female	Long	158	72.3
780	Average	Male	Short	174	72.2
781	Average	Male	Medium	176	69
782	Average	Male	Medium	186	78.5
783	Average	Female	Long	162	55.1
784	Large	Female	Long	166	83.1
785	Large	Female	Medium	150	58.3
786	Slim	Male	Medium	174	43.8
787	Average	Female	Long	156	47.9
788	Large	Male	Short	168	99.5
789	Large	Female	Medium	171	90.5
790	Large	Female	Long	156	80.1
791	Large	Female	Long	163	91
792	Large	Male	Short	172	100
793	Average	Male	Short	171	62.3
794	Large	Female	Long	156	63.2
795	Average	Female	Long	161	53.3
796	Large	Male	Short	180	110
797	Large	Male	Short	175	101
798	Large	Male	Short	193	135
799	Large	Male	Short	177	109
800	Large	Female	Long	159	70
801	Average	Male	Short	175	70.6
802	Large	Female	Long	164	84.3
803	Large	Male	Medium	177	113
804	Large	Male	Medium	182	123
805	Large	Female	Medium	167	85.9
806	Large	Female	Medium	155	65.6
807	Large	Female	Long	152	72.7
808	Large	Female	Medium	170	91.9
809	Slim	Male	Short	168	43
810	Average	Male	Short	183	76.4
811	Large	Female	Long	160	87.7
812	Large	Male	Long	157	91.7
813	Average	Female	Long	177	59.9
814	Average	Male	Medium	194	76.9
815	Average	Male	Short	166	57.8
816	Large	Male	Short	178	114
817	Average	Female	Long	164	58.1
818	Slim	Male	Short	182	52.2
819	Slim	Male	Short	172	46.3
820	Large	Female	Long	151	70.8
821	Large	Female	Long	169	79.4
822	Large	Female	Medium	153	63.6
823	Large	Male	Short	178	119
824	Average	Male	Short	174	67.5
825	Slim	Female	Long	162	25.9
826	Average	Male	Medium	184	76.3
827	Large	Female	Medium	148	64.7
828	Average	Female	Long	149	35.7
829	Average	Female	Long	177	65.5
830	Average	Female	Long	167	54.1
831	Average	Male	Short	180	72.2
832	Average	Male	Short	177	71.3
833	Average	Female	Medium	159	47.3
834	Large	Male	Short	183	116
835	Large	Male	Medium	176	106
836	Large	Female	Long	157	75.4
837	Average	Female	Short	154	41.3
838	Slim	Female	Long	165	29.5
839	Average	Female	Medium	157	47.7
840	Large	Female	Long	171	96.3
841	Large	Female	Long	155	69.9
842	Slim	Male	Short	170	42.1
843	Average	Male	Short	184	75.2
844	Large	Female	Long	156	80
845	Average	Male	Short	178	70.4
846	Large	Male	Short	179	119
847	Large	Female	Long	160	88
848	Average	Female	Long	152	44.3
849	Average	Male	Short	181	70.1
850	Slim	Female	Short	153	25.1
851	Large	Male	Short	161	81.7
852	Large	Male	Short	171	102
853	Slim	Female	Long	169	39.3
854	Average	Male	Short	181	71.2
855	Large	Male	Short	191	126
856	Slim	Male	Short	174	44
857	Average	Male	Short	168	56.4
858	Slim	Male	Short	165	40.3
859	Slim	Female	Long	161	24.8
860	Large	Male	Medium	174	101
861	Large	Male	Short	179	98.6
862	Average	Male	Short	173	73.1
863	Average	Female	Short	159	53.9
864	Average	Female	Long	156	42.2
865	Slim	Male	Short	182	49.7
866	Large	Female	Medium	161	89.4
867	Slim	Male	Short	179	45
868	Average	Female	Long	159	42.2
869	Large	Male	Short	183	117
870	Average	Male	Short	163	63.4
871	Slim	Female	Medium	165	29.1
872	Slim	Female	Medium	148	21.8
873	Average	Female	Long	154	44.9
874	Slim	Male	Short	181	48.8
875	Large	Female	Medium	169	82.9
876	Large	Male	Long	180	117
877	Large	Female	Medium	167	82.1
878	Average	Male	Medium	177	74.9
879	Average	Female	Long	164	48.1
880	Average	Female	Medium	159	49.3
881	Large	Male	Short	184	130
882	Large	Female	Long	161	77.3
883	Large	Female	Short	159	70.9
884	Large	Female	Long	163	82.8
885	Large	Female	Long	159	68.8
886	Large	Female	Long	151	53.6
887	Large	Female	Medium	164	77.5
888	Average	Male	Short	179	72.9
889	Large	Male	Short	174	107
890	Slim	Male	Short	180	42.2
891	Slim	Male	Short	179	47
892	Large	Female	Long	165	83.3
893	Average	Female	Medium	162	51.3
894	Large	Female	Long	157	66.3
895	Average	Male	Short	178	70.5
896	Average	Male	Medium	168	61.7
897	Average	Female	Long	163	52.6
898	Average	Female	Medium	152	45.6
899	Average	Female	Long	180	70.8
900	Average	Male	Medium	168	66.5
901	Slim	Male	Short	185	52.9
902	Average	Female	Long	153	37
903	Average	Female	Long	170	50.4
904	Slim	Female	Medium	159	27
905	Large	Male	Short	181	119
906	Slim	Male	Medium	175	45.9
907	Slim	Female	Long	159	25.4
908	Average	Female	Long	167	56.4
909	Average	Male	Medium	181	74.2
910	Large	Female	Medium	173	94.2
911	Large	Female	Long	157	70.9
912	Average	Female	Long	169	56.1
913	Average	Female	Long	160	50.8
914	Large	Male	Short	177	113
915	Large	Female	Long	169	89
916	Slim	Female	Long	161	27.2
917	Average	Female	Medium	159	44.6
918	Large	Male	Short	187	131
919	Average	Male	Short	182	74.7
920	Average	Female	Medium	160	53
921	Average	Female	Short	166	56.7
922	Average	Female	Long	162	48.1
923	Large	Female	Long	154	72
924	Large	Male	Short	177	108
925	Average	Female	Short	160	52.1
926	Large	Female	Medium	154	69.5
927	Slim	Female	Long	163	29.2
928	Slim	Female	Medium	168	32.1
929	Large	Male	Medium	181	117
930	Large	Male	Short	173	106
931	Large	Male	Short	169	92.3
932	Average	Male	Short	182	67
933	Large	Female	Long	162	80.5
934	Average	Male	Short	176	68.1
935	Average	Male	Short	167	59.4
936	Large	Female	Medium	165	81.7
937	Slim	Female	Medium	159	31
938	Slim	Male	Short	168	41
939	Average	Male	Medium	174	72.6
940	Large	Female	Medium	152	69.2
941	Large	Male	Short	194	133
942	Large	Female	Long	166	82.1
943	Average	Male	Short	170	61.5
944	Large	Male	Short	183	111
945	Large	Female	Medium	151	69.4
946	Average	Male	Short	164	56.4
947	Large	Male	Short	176	102
948	Large	Male	Medium	155	75.1
949	Large	Female	Medium	157	74.2
950	Slim	Female	Medium	161	30.1
951	Average	Male	Short	170	70
952	Large	Female	Medium	170	84.2
953	Large	Female	Medium	166	90.7
954	Large	Female	Medium	160	78.8
955	Large	Male	Medium	175	111
956	Slim	Female	Long	169	30.2
957	Average	Female	Medium	159	44.9
958	Slim	Female	Medium	161	27.4
959	Large	Female	Short	164	78.4
960	Average	Female	Long	159	50.2
961	Average	Female	Long	168	55.9
962	Average	Male	Short	190	81.4
963	Slim	Female	Long	167	31.8
964	Large	Female	Short	172	99.6
965	Large	Male	Short	174	106
966	Average	Male	Short	158	54.4
967	Large	Female	Long	155	64.8
968	Average	Male	Short	179	73.6
969	Slim	Female	Long	177	35.3
970	Large	Female	Long	163	78.6
971	Slim	Male	Short	178	46.4
972	Large	Male	Short	177	108
973	Average	Female	Long	169	57
974	Slim	Male	Short	165	44.3
975	Large	Male	Short	189	125
976	Average	Female	Long	158	46.9
977	Average	Male	Short	167	59.6
978	Large	Female	Long	153	68.4
979	Large	Male	Short	179	109
980	Large	Female	Long	150	58.1
981	Slim	Male	Short	179	46.4
982	Slim	Female	Long	151	27.5
983	Slim	Female	Long	156	26
984	Slim	Female	Long	164	27.8
985	Large	Female	Long	157	68
986	Average	Male	Medium	180	79.5
987	Average	Male	Medium	182	74.7
988	Large	Female	Long	159	70.8
989	Large	Male	Short	174	123
990	Large	Female	Long	169	86.9
991	Slim	Female	Long	149	25
992	Average	Female	Long	165	53.7
993	Large	Male	Short	166	94.3
994	Large	Female	Long	151	63.9
995	Large	Female	Long	167	91.8
996	Average	Male	Short	174	70.4
997	Large	Male	Short	183	118
998	Slim	Male	Short	181	38.6
999	Average	Male	Short	180	78.4