Survey data on psychological wellbeing factors.

For this assignment, you will look at a real data file, condensed from a study that was conducted by a Graduate Diploma in Educational Psychology students. The study was designed to explore the factors that impact on respondents’ psychological adjustment and wellbeing. The survey contained a variety of validated scales measuring constructs that the extensive literature on stress and coping suggest influence people’s experience of stress. The scales measured self-esteem, optimism, perceptions of control, perceived stress, positive and negative affect, and life satisfaction. A scale was also included that measured people’s tendency to present themselves in a favorable or socially desirable manner. The survey was distributed to members of the general public in Melbourne, Australia and surrounding districts. The final sample size was 439, consisting of 42 per cent males and 58 per cent females.

Conduct the following analysis on the outdoor lifestyle data. Consider only the following 5 variables:

Total Optimism
Total Self-esteem,
Total Positive Affect,
Total Negative Affect,
Total Life Satisfaction
Total Perceived Stress
Total Social Desirability

Use 3 clusters in each of the following methods to answer the following questions:

Cluster the respondents based on the identified variables using hierarchical clustering. Use Ward’s method and squared Euclidean distances.
List the number of cases in each cluster
List the cases in each cluster
Interpret the clusters in terms of the values of the cluster means

Cluster the respondents based on the identified variables using the k-mean
List the number of cases in each cluster
List the cases in each cluster
Interpret the clusters in terms of the values of the cluster means

Cluster the respondents based on the identified variables using two step cluster
List the number of cases in each cluster
List the cases in each cluster
Interpret the clusters in terms of the values of the cluster means

Compare the results in parts a, b and c.

he survey data is based on a Graduate Diploma in Educational Psychology students of Melbourne, Australia and surrounding diatrict. The study was designed to explore the factors that influence on respondents’ psychological adjustment and wellbeing. In this study, there is a variety of validated scales measuring constructs. The scale included the measurement of self-esteem, optimism, perceptions of control, perceived stress, good and bad effect and satisfaction in lifespan. A “Likert” scale was also involved that measured tendency of people to present themselves in a favourable or socially desirable manner

Case Processing Summary^a
Cases
Valid		Missing		Total
N	Percent	N	Percent	N	Percent
426	97.0%	13	3.0%	439	100.0%
a. Squared Euclidean Distance used

Agglomeration Schedule
Stage	Cluster Combined		Coefficients	Stage Cluster First Appears		Next Stage
Stage	Cluster 1	Cluster 2	Coefficients	Cluster 1	Cluster 2	Next Stage
1	105	133	.003	0	0	161
2	154	160	.008	0	0	278
3	341	402	.015	0	0	110
4	298	312	.021	0	0	41
5	247	373	.027	0	0	190
6	145	197	.035	0	0	283
7	424	426	.043	0	0	83
8	152	292	.052	0	0	137
9	225	236	.061	0	0	226
10	211	264	.070	0	0	47
11	162	226	.080	0	0	153
12	127	161	.090	0	0	254
13	86	108	.101	0	0	100
14	55	91	.112	0	0	172
15	396	415	.124	0	0	140
16	358	422	.135	0	0	158
17	301	368	.147	0	0	64
18	260	291	.158	0	0	193
19	241	249	.170	0	0	161
20	70	117	.182	0	0	254
21	114	173	.194	0	0	195
22	289	300	.206	0	0	132
23	231	333	.218	0	0	127
24	360	420	.230	0	0	150
25	248	315	.242	0	0	176
26	314	339	.255	0	0	70
27	394	423	.268	0	0	138
28	153	198	.281	0	0	212
29	336	356	.295	0	0	185
30	253	267	.308	0	0	117
31	224	283	.322	0	0	103
32	166	178	.336	0	0	189
33	407	425	.350	0	0	143
34	332	355	.364	0	0	164
35	240	242	.378	0	0	189
36	295	395	.392	0	0	245
37	217	270	.407	0	0	170
38	54	84	.421	0	0	293
39	257	351	.436	0	0	98
40	131	216	.450	0	0	182
41	230	298	.465	0	4	135
42	232	388	.481	0	0	165
43	282	331	.497	0	0	94
44	293	361	.512	0	0	110
45	320	390	.528	0	0	210
46	271	352	.544	0	0	175
47	211	228	.560	10	0	152
48	318	340	.576	0	0	58
49	168	201	.592	0	0	160
50	41	112	.608	0	0	97
51	357	387	.624	0	0	171
52	71	90	.641	0	0	333
53	78	169	.657	0	0	154
54	122	155	.673	0	0	248
55	404	408	.690	0	0	180
56	251	400	.707	0	0	78
57	279	286	.724	0	0	124
58	188	318	.741	0	48	186
59	410	421	.759	0	0	164
60	92	100	.776	0	0	307
61	144	174	.794	0	0	173
62	93	342	.812	0	0	236
63	191	370	.830	0	0	156
64	172	301	.847	0	17	230
65	120	147	.865	0	0	123
66	268	350	.883	0	0	82
67	89	187	.901	0	0	218
68	209	354	.920	0	0	89
69	43	135	.938	0	0	272
70	314	366	.957	26	0	113
71	200	398	.975	0	0	106
72	254	280	.994	0	0	116
73	184	206	1.013	0	0	217
74	266	353	1.032	0	0	227
75	196	199	1.052	0	0	253
76	284	345	1.071	0	0	150
77	302	371	1.091	0	0	158
78	251	307	1.110	56	0	309
79	81	148	1.130	0	0	214
80	202	222	1.150	0	0	282
81	391	401	1.170	0	0	163
82	192	268	1.190	0	66	179
83	375	424	1.210	0	7	151
84	313	323	1.230	0	0	147
85	269	329	1.251	0	0	195
86	364	392	1.271	0	0	162
87	179	372	1.292	0	0	178
88	156	259	1.313	0	0	222
89	209	325	1.334	68	0	125
90	101	159	1.356	0	0	276
91	413	414	1.377	0	0	198
92	235	297	1.398	0	0	216
93	326	389	1.420	0	0	243
94	282	287	1.442	43	0	237
95	204	263	1.464	0	0	269
96	26	99	1.486	0	0	209
97	41	67	1.508	50	0	284
98	257	321	1.530	39	0	272
99	116	243	1.553	0	0	215
100	33	86	1.575	0	13	177
101	139	376	1.598	0	0	190
102	111	233	1.620	0	0	115
103	224	365	1.643	31	0	285
104	195	239	1.666	0	0	221
105	163	310	1.689	0	0	251
106	200	244	1.712	71	0	218
107	37	61	1.736	0	0	321
108	214	285	1.759	0	0	239
109	15	29	1.783	0	0	262
110	293	341	1.807	44	3	187
111	124	337	1.830	0	0	224
112	319	347	1.854	0	0	290
113	299	314	1.878	0	70	293
114	303	379	1.903	0	0	225
115	111	277	1.927	102	0	296
116	223	254	1.952	0	72	230
117	208	253	1.977	0	30	217
118	290	308	2.002	0	0	198
119	203	218	2.027	0	0	191
120	219	272	2.053	0	0	133
121	369	412	2.078	0	0	192
122	250	418	2.104	0	0	276
123	120	129	2.131	65	0	277
124	276	279	2.158	0	57	156
125	209	338	2.184	89	0	258
126	363	382	2.212	0	0	256
127	231	322	2.239	23	0	211
128	46	56	2.267	0	0	375
129	374	393	2.295	0	0	274
130	215	348	2.322	0	0	251
131	359	419	2.351	0	0	336
132	289	330	2.379	22	0	280
133	219	237	2.408	120	0	248
134	103	121	2.437	0	0	255
135	230	275	2.466	41	0	232
136	80	110	2.495	0	0	252
137	152	288	2.524	8	0	298
138	182	394	2.554	0	27	231
139	150	296	2.583	0	0	213
140	346	396	2.614	0	15	168
141	186	317	2.645	0	0	259
142	256	344	2.676	0	0	264
143	213	407	2.706	0	33	243
144	142	234	2.738	0	0	294
145	36	278	2.769	0	0	314
146	324	380	2.801	0	0	244
147	313	378	2.833	84	0	188
148	238	417	2.865	0	0	260
149	83	220	2.898	0	0	240
150	284	360	2.930	76	24	300
151	274	375	2.963	0	83	240
152	69	211	2.996	0	47	184
153	162	309	3.029	11	0	256
154	39	78	3.062	0	53	228
155	34	113	3.095	0	0	274
156	191	276	3.129	63	124	364
157	349	377	3.163	0	0	226
158	302	358	3.198	77	16	186
159	35	132	3.233	0	0	347
160	164	168	3.268	0	49	253
161	105	241	3.303	1	19	277
162	335	364	3.338	0	86	220
163	343	391	3.374	0	81	168
164	332	410	3.409	34	59	318
165	229	232	3.445	0	42	329
166	123	180	3.481	0	0	270
167	265	311	3.517	0	0	234
168	343	346	3.555	163	140	278
169	126	183	3.592	0	0	292
170	217	328	3.630	37	0	258
171	304	357	3.668	0	51	232
172	55	95	3.707	14	0	284
173	144	175	3.745	61	0	237
174	102	367	3.784	0	0	312
175	128	271	3.823	0	46	200
176	248	383	3.862	25	0	280
177	33	98	3.901	100	0	361
178	179	207	3.940	87	0	299
179	176	192	3.980	0	82	247
180	384	404	4.020	0	55	310
181	205	306	4.060	0	0	311
182	131	134	4.101	40	0	330
183	60	115	4.142	0	0	233
184	69	165	4.184	152	0	340
185	336	406	4.226	29	0	249
186	188	302	4.269	58	158	287
187	181	293	4.311	0	110	326
188	193	313	4.355	0	147	242
189	166	240	4.398	32	35	292
190	139	247	4.442	101	5	331
191	104	203	4.486	0	119	332
192	221	369	4.530	0	121	204
193	260	381	4.575	18	0	212
194	7	9	4.620	0	0	317
195	114	269	4.667	21	85	311
196	87	261	4.713	0	0	299
197	72	177	4.759	0	0	255
198	290	413	4.806	118	91	231
199	16	82	4.853	0	0	348
200	62	128	4.900	0	175	302
201	119	190	4.948	0	0	221
202	149	212	4.996	0	0	290
203	14	47	5.044	0	0	266
204	88	221	5.093	0	192	294
205	252	397	5.142	0	0	265
206	57	281	5.192	0	0	279
207	51	59	5.242	0	0	339
208	49	65	5.293	0	0	303
209	26	305	5.344	96	0	316
210	320	403	5.396	45	0	326
211	96	231	5.449	0	127	320
212	153	260	5.502	28	193	345
213	150	167	5.555	139	0	344
214	66	81	5.610	0	79	295
215	18	116	5.664	0	99	300
216	235	385	5.719	92	0	249
217	184	208	5.774	73	117	316
218	89	200	5.830	67	106	302
219	107	334	5.886	0	0	275
220	118	335	5.942	0	162	335
221	119	195	5.999	201	104	387
222	151	156	6.056	0	88	281
223	185	245	6.114	0	0	298
224	106	124	6.172	0	111	318
225	170	303	6.230	0	114	287
226	225	349	6.288	9	157	344
227	140	266	6.346	0	74	337
228	25	39	6.405	0	154	346
229	194	255	6.464	0	0	267
230	172	223	6.523	64	116	309
231	182	290	6.583	138	198	291
232	230	304	6.643	135	171	368
233	60	130	6.704	183	0	306
234	265	409	6.766	167	0	324
235	262	405	6.828	0	0	310
236	48	93	6.890	0	62	273
237	144	282	6.953	173	94	338
238	136	210	7.016	0	0	324
239	12	214	7.079	0	108	289
240	83	274	7.143	149	151	331
241	4	23	7.208	0	0	315
242	171	193	7.273	0	188	334
243	213	326	7.338	143	93	366
244	324	362	7.403	146	0	332
245	85	295	7.469	0	36	322
246	294	327	7.536	0	0	271
247	146	176	7.602	0	179	369
248	122	219	7.669	54	133	312
249	235	336	7.738	216	185	329
250	189	258	7.806	0	0	285
251	163	215	7.876	105	130	308
252	52	80	7.946	0	136	350
253	164	196	8.017	160	75	333
254	70	127	8.088	20	12	340
255	72	103	8.161	197	134	307
256	162	363	8.234	153	126	355
257	42	273	8.308	0	0	362
258	209	217	8.382	125	170	349
259	125	186	8.456	0	141	351
260	138	238	8.531	0	148	353
261	24	27	8.606	0	0	342
262	15	77	8.681	109	0	321
263	64	158	8.758	0	0	286
264	74	256	8.834	0	142	354
265	252	411	8.914	205	0	365
266	14	19	8.994	203	0	348
267	75	194	9.076	0	229	336
268	28	157	9.158	0	0	288
269	204	227	9.241	95	0	314
270	45	123	9.325	0	166	306
271	294	386	9.410	246	0	354
272	43	257	9.496	69	98	322
273	44	48	9.582	0	236	338
274	34	374	9.669	155	129	341
275	97	107	9.756	0	219	327
276	101	250	9.844	90	122	305
277	105	120	9.934	161	123	343
278	154	343	10.024	2	168	372
279	57	68	10.114	206	0	320
280	248	289	10.206	176	132	341
281	151	316	10.299	222	0	379
282	143	202	10.392	0	80	313
283	21	145	10.485	0	6	362
284	41	55	10.579	97	172	345
285	189	224	10.674	250	103	366
286	31	64	10.772	0	263	327
287	170	188	10.870	225	186	325
288	11	28	10.968	0	268	370
289	12	399	11.068	239	0	296
290	149	319	11.169	202	112	323
291	182	416	11.271	231	0	391
292	126	166	11.376	169	189	350
293	54	299	11.484	38	113	367
294	88	142	11.593	204	144	357
295	2	66	11.703	0	214	346
296	12	111	11.813	289	115	390
297	13	30	11.925	0	0	328
298	152	185	12.037	137	223	339
299	87	179	12.151	196	178	353
300	18	284	12.266	215	150	369
301	17	22	12.382	0	0	376
302	62	89	12.498	200	218	343
303	32	49	12.614	0	208	352
304	3	38	12.731	0	0	380
305	94	101	12.849	0	276	357
306	45	60	12.967	270	233	403
307	72	92	13.084	255	60	388
308	141	163	13.204	0	251	356
309	172	251	13.326	230	78	389
310	262	384	13.449	235	180	373
311	114	205	13.573	195	181	335
312	102	122	13.698	174	248	361
313	137	143	13.824	0	282	351
314	36	204	13.951	145	269	395
315	1	4	14.078	0	241	370
316	26	184	14.206	209	217	349
317	7	10	14.338	194	0	352
318	106	332	14.471	224	164	379
319	50	79	14.604	0	0	377
320	57	96	14.738	279	211	355
321	15	37	14.874	262	107	347
322	43	85	15.011	272	245	373
323	40	149	15.148	0	290	363
324	136	265	15.287	238	234	385
325	58	170	15.432	0	287	374
326	181	320	15.578	187	210	360
327	31	97	15.725	286	275	383
328	13	53	15.875	297	0	371
329	229	235	16.025	165	249	389
330	73	131	16.177	0	182	356
331	83	139	16.328	240	190	360
332	104	324	16.480	191	244	375
333	71	164	16.633	52	253	365
334	171	246	16.787	242	0	394
335	114	118	16.948	311	220	386
336	75	359	17.112	267	131	394
337	109	140	17.280	0	227	364
338	44	144	17.449	273	237	400
339	51	152	17.619	207	298	368
340	69	70	17.791	184	254	367
341	34	248	17.967	274	280	374
342	24	63	18.148	261	0	359
343	62	105	18.337	302	277	384
344	150	225	18.527	213	226	397
345	41	153	18.720	284	212	398
346	2	25	18.914	295	228	393
347	15	35	19.111	321	159	380
348	14	16	19.309	266	199	388
349	26	209	19.511	316	258	396
350	52	126	19.718	252	292	382
351	125	137	19.926	259	313	381
352	7	32	20.138	317	303	376
353	87	138	20.357	299	260	386
354	74	294	20.575	264	271	392
355	57	162	20.799	320	256	384
356	73	141	21.024	330	308	401
357	88	94	21.250	294	305	402
358	5	6	21.478	0	0	371
359	20	24	21.710	0	342	378
360	83	181	21.946	331	326	385
361	33	102	22.183	177	312	398
362	21	42	22.425	283	257	377
363	40	76	22.676	323	0	399
364	109	191	22.928	337	156	396
365	71	252	23.183	333	265	408
366	189	213	23.446	285	243	372
367	54	69	23.709	293	340	382
368	51	230	23.983	339	232	387
369	18	146	24.269	300	247	381
370	1	11	24.555	315	288	393
371	5	13	24.845	358	328	414
372	154	189	25.139	278	366	390
373	43	262	25.433	322	310	392
374	34	58	25.734	341	325	400
375	46	104	26.038	128	332	383
376	7	17	26.347	352	301	413
377	21	50	26.664	362	319	410
378	8	20	26.990	0	359	404
379	106	151	27.323	318	281	391
380	3	15	27.658	304	347	406
381	18	125	28.003	369	351	399
382	52	54	28.352	350	367	412
383	31	46	28.720	327	375	404
384	57	62	29.097	355	343	395
385	83	136	29.478	360	324	407
386	87	114	29.868	353	335	397
387	51	119	30.261	368	221	411
388	14	72	30.655	348	307	401
389	172	229	31.062	309	329	405
390	12	154	31.473	296	372	407
391	106	182	31.958	379	291	403
392	43	74	32.474	373	354	414
393	1	2	33.039	370	346	402
394	75	171	33.649	336	334	406
395	36	57	34.263	314	384	409
396	26	109	34.885	349	364	405
397	87	150	35.517	386	344	411
398	33	41	36.155	361	345	409
399	18	40	36.823	381	363	416
400	34	44	37.521	374	338	415
401	14	73	38.288	388	356	410
402	1	88	39.086	393	357	416
403	45	106	39.886	306	391	408
404	8	31	40.778	378	383	418
405	26	172	41.687	396	389	417
406	3	75	42.667	380	394	415
407	12	83	43.704	390	385	412
408	45	71	44.756	403	365	420
409	33	36	45.931	398	395	421
410	14	21	47.120	401	377	413
411	51	87	48.477	387	397	419
412	12	52	49.836	407	382	417
413	7	14	51.425	376	410	424
414	5	43	53.163	371	392	420
415	3	34	55.073	406	400	419
416	1	18	57.064	402	399	418
417	12	26	59.068	412	405	421
418	1	8	61.626	416	404	422
419	3	51	64.379	415	411	423
420	5	45	67.820	414	408	422
421	12	33	72.644	417	409	423
422	1	5	78.126	418	420	424
423	3	12	86.907	419	421	425
424	1	7	96.042	422	413	425
425	1	3	134.134	424	423	0

Cluster Membership
Case	3 Clusters
1:Case 1	1
2:Case 2	1
3:Case 3	2
4:Case 4	1
5:Case 5	1
6:Case 6	1
7:Case 7	3
8:Case 8	1
9:Case 9	3
10:Case 10	3
11:Case 11	1
12:Case 12	2
13:Case 13	1
14:Case 14	3
15:Case 15	2
16:Case 16	3
17:Case 17	3
18:Case 18	1
19:Case 19	3
20:Case 20	1
21:Case 21	3
22:Case 22	3
23:Case 23	1
24:Case 24	1
25:Case 25	1
26:Case 26	2
27:Case 27	1
28:Case 28	1
29:Case 29	2
30:Case 30	1
31:Case 31	1
32:Case 32	3
33:Case 33	2
34:Case 34	2
35:Case 35	2
36:Case 36	2
37:Case 37	2
38:Case 38	2
39:Case 39	1
40:Case 41	1
41:Case 42	2
42:Case 43	3
43:Case 44	1
44:Case 45	2
45:Case 46	1
46:Case 47	1
47:Case 48	3
48:Case 49	2
49:Case 50	3
50:Case 51	3
51:Case 52	2
52:Case 53	2
53:Case 54	1
54:Case 55	2
55:Case 56	2
56:Case 57	1
57:Case 59	2
58:Case 60	2
59:Case 61	2
60:Case 62	1
61:Case 63	2
62:Case 64	2
63:Case 65	1
64:Case 66	1
65:Case 67	3
66:Case 68	1
67:Case 69	2
68:Case 70	2
69:Case 71	2
70:Case 72	2
71:Case 73	1
72:Case 74	3
73:Case 75	3
74:Case 76	1
75:Case 77	2
76:Case 78	1
77:Case 79	2
78:Case 80	1
79:Case 81	3
80:Case 82	2
81:Case 83	1
82:Case 84	3
83:Case 85	2
84:Case 86	2
85:Case 87	1
86:Case 88	2
87:Case 89	2
88:Case 90	1
89:Case 91	2
90:Case 92	1
91:Case 93	2
92:Case 94	3
93:Case 95	2
94:Case 96	1
95:Case 97	2
96:Case 98	2
97:Case 99	1
98:Case 100	2
99:Case 101	2
100:Case 102	3
101:Case 103	1
102:Case 104	2
103:Case 105	3
104:Case 106	1
105:Case 107	2
106:Case 108	1
107:Case 109	1
108:Case 110	2
109:Case 111	2
110:Case 112	2
111:Case 113	2
112:Case 114	2
113:Case 115	2
114:Case 116	2
115:Case 117	1
116:Case 118	1
117:Case 119	2
118:Case 120	2
119:Case 121	2
120:Case 122	2
121:Case 123	3
122:Case 124	2
123:Case 125	1
124:Case 126	1
125:Case 127	1
126:Case 128	2
127:Case 129	2
128:Case 130	2
129:Case 131	2
130:Case 132	1
131:Case 133	3
132:Case 134	2
133:Case 135	2
134:Case 136	3
135:Case 137	1
136:Case 138	2
137:Case 139	1
138:Case 140	2
139:Case 141	2
140:Case 142	2
141:Case 143	3
142:Case 144	1
143:Case 145	1
144:Case 146	2
145:Case 147	3
146:Case 148	1
147:Case 149	2
148:Case 150	1
149:Case 151	1
150:Case 152	2
151:Case 153	1
152:Case 154	2
153:Case 155	2
154:Case 156	2
155:Case 157	2
156:Case 158	1
157:Case 159	1
158:Case 160	1
159:Case 161	1
160:Case 162	2
161:Case 163	2
162:Case 164	2
163:Case 165	3
164:Case 166	1
165:Case 167	2
166:Case 168	2
167:Case 169	2
168:Case 170	1
169:Case 171	1
170:Case 172	2
171:Case 173	2
172:Case 174	2
173:Case 175	2
174:Case 177	2
175:Case 178	2
176:Case 179	1
177:Case 180	3
178:Case 181	2
179:Case 182	2
180:Case 183	1
181:Case 184	2
182:Case 185	1
183:Case 186	2
184:Case 187	2
185:Case 188	2
186:Case 189	1
187:Case 190	2
188:Case 191	2
189:Case 192	2
190:Case 193	2
191:Case 194	2
192:Case 195	1
193:Case 196	2
194:Case 197	2
195:Case 198	2
196:Case 199	1
197:Case 200	3
198:Case 201	2
199:Case 202	1
200:Case 203	2
201:Case 204	1
202:Case 205	1
203:Case 206	1
204:Case 207	2
205:Case 208	2
206:Case 209	2
207:Case 210	2
208:Case 211	2
209:Case 212	2
210:Case 213	2
211:Case 214	2
212:Case 215	1
213:Case 216	2
214:Case 217	2
215:Case 218	3
216:Case 219	3
217:Case 220	2
218:Case 221	1
219:Case 222	2
220:Case 223	2
221:Case 224	1
222:Case 225	1
223:Case 226	2
224:Case 227	2
225:Case 228	2
226:Case 229	2
227:Case 230	2
228:Case 231	2
229:Case 232	2
230:Case 233	2
231:Case 234	2
232:Case 235	2
233:Case 236	2
234:Case 237	1
235:Case 238	2
236:Case 239	2
237:Case 240	2
238:Case 241	2
239:Case 242	2
240:Case 243	2
241:Case 244	2
242:Case 245	2
243:Case 246	1
244:Case 247	2
245:Case 248	2
246:Case 249	2
247:Case 250	2
248:Case 251	2
249:Case 252	2
250:Case 253	1
251:Case 254	2
252:Case 255	1
253:Case 256	2
254:Case 257	2
255:Case 258	2
256:Case 259	1
257:Case 260	1
258:Case 261	2
259:Case 262	1
260:Case 263	2
261:Case 264	2
262:Case 265	1
263:Case 266	2
264:Case 267	2
265:Case 268	2
266:Case 269	2
267:Case 270	2
268:Case 271	1
269:Case 272	2
270:Case 273	2
271:Case 274	2
272:Case 275	2
273:Case 276	3
274:Case 277	2
275:Case 279	2
276:Case 280	2
277:Case 281	2
278:Case 282	2
279:Case 283	2
280:Case 284	2
281:Case 285	2
282:Case 286	2
283:Case 287	2
284:Case 288	1
285:Case 289	2
286:Case 290	2
287:Case 291	2
288:Case 292	2
289:Case 293	2
290:Case 294	1
291:Case 295	2
292:Case 296	2
293:Case 297	2
294:Case 299	1
295:Case 300	1
296:Case 301	2
297:Case 302	2
298:Case 303	2
299:Case 304	2
300:Case 305	2
301:Case 306	2
302:Case 307	2
303:Case 308	2
304:Case 309	2
305:Case 310	2
306:Case 311	2
307:Case 312	2
308:Case 313	1
309:Case 314	2
310:Case 315	3
311:Case 316	2
312:Case 317	2
313:Case 318	2
314:Case 319	2
315:Case 320	2
316:Case 321	1
317:Case 322	1
318:Case 323	2
319:Case 324	1
320:Case 325	2
321:Case 326	1
322:Case 327	2
323:Case 328	2
324:Case 329	1
325:Case 330	2
326:Case 331	2
327:Case 332	1
328:Case 333	2
329:Case 334	2
330:Case 335	2
331:Case 336	2
332:Case 337	1
333:Case 338	2
334:Case 339	1
335:Case 340	2
336:Case 341	2
337:Case 342	1
338:Case 343	2
339:Case 344	2
340:Case 345	2
341:Case 346	2
342:Case 347	2
343:Case 348	2
344:Case 349	1
345:Case 350	1
346:Case 351	2
347:Case 352	1
348:Case 353	3
349:Case 354	2
350:Case 355	1
351:Case 356	1
352:Case 357	2
353:Case 358	2
354:Case 359	2
355:Case 360	1
356:Case 361	2
357:Case 362	2
358:Case 363	2
359:Case 364	2
360:Case 365	1
361:Case 366	2
362:Case 367	1
363:Case 368	2
364:Case 369	2
365:Case 370	2
366:Case 371	2
367:Case 372	2
368:Case 373	2
369:Case 374	1
370:Case 375	2
371:Case 376	2
372:Case 377	2
373:Case 378	2
374:Case 379	2
375:Case 380	2
376:Case 381	2
377:Case 382	2
378:Case 383	2
379:Case 384	2
380:Case 385	1
381:Case 386	2
382:Case 387	2
383:Case 388	2
384:Case 389	1
385:Case 390	2
386:Case 391	1
387:Case 392	2
388:Case 394	2
389:Case 395	2
390:Case 396	2
391:Case 397	2
392:Case 398	2
393:Case 399	2
394:Case 400	1
395:Case 401	1
396:Case 402	2
397:Case 403	1
398:Case 404	2
399:Case 405	2
400:Case 406	2
401:Case 407	2
402:Case 408	2
403:Case 409	2
404:Case 410	1
405:Case 411	1
406:Case 412	2
407:Case 413	2
408:Case 414	1
409:Case 415	2
410:Case 416	1
411:Case 417	1
412:Case 418	1
413:Case 419	1
414:Case 420	1
415:Case 421	2
416:Case 422	1
417:Case 423	2
418:Case 424	1
419:Case 425	2
420:Case 426	1
421:Case 427	1
422:Case 428	2
423:Case 429	1
424:Case 430	2
425:Case 431	2
426:Case 432	2

Ward Method
		Frequency	Percent	Valid Percent	Cumulative Percent
Valid	1	128	29.2	30.0	30.0
	2	263	59.9	61.7	91.8
	3	35	8.0	8.2	100.0
	Total	426	97.0	100.0
Missing	System	13	3.0
Total		439	100.0

Cluster 1	Cluster 2	Cluster 3
1:Case 1	102:Case 104	10:Case 10
101:Case 103	105:Case 107	100:Case 102
104:Case 106	108:Case 110	103:Case 105
106:Case 108	109:Case 111	121:Case 123
107:Case 109	110:Case 112	131:Case 133
11:Case 11	111:Case 113	134:Case 136
115:Case 117	112:Case 114	14:Case 14
116:Case 118	113:Case 115	141:Case 143
123:Case 125	114:Case 116	145:Case 147
124:Case 126	117:Case 119	16:Case 16
125:Case 127	118:Case 120	163:Case 165
13:Case 13	119:Case 121	17:Case 17
130:Case 132	12:Case 12	177:Case 180
135:Case 137	120:Case 122	19:Case 19
137:Case 139	122:Case 124	197:Case 200
142:Case 144	126:Case 128	21:Case 21
143:Case 145	127:Case 129	215:Case 218
146:Case 148	128:Case 130	216:Case 219
148:Case 150	129:Case 131	22:Case 22
149:Case 151	132:Case 134	273:Case 276
151:Case 153	133:Case 135	310:Case 315
156:Case 158	136:Case 138	32:Case 32
157:Case 159	138:Case 140	348:Case 353
158:Case 160	139:Case 141	42:Case 43
159:Case 161	140:Case 142	47:Case 48
164:Case 166	144:Case 146	49:Case 50
168:Case 170	147:Case 149	50:Case 51
169:Case 171	15:Case 15	65:Case 67
176:Case 179	150:Case 152	7:Case 7
18:Case 18	152:Case 154	72:Case 74
180:Case 183	153:Case 155	73:Case 75
182:Case 185	154:Case 156	79:Case 81
186:Case 189	155:Case 157	82:Case 84
192:Case 195	160:Case 162	9:Case 9
196:Case 199	161:Case 163	92:Case 94
199:Case 202	162:Case 164
2:Case 2	165:Case 167
20:Case 20	166:Case 168
201:Case 204	167:Case 169
202:Case 205	170:Case 172
203:Case 206	171:Case 173
212:Case 215	172:Case 174
218:Case 221	173:Case 175
221:Case 224	174:Case 177
222:Case 225	175:Case 178
23:Case 23	178:Case 181
234:Case 237	179:Case 182
24:Case 24	181:Case 184
243:Case 246	183:Case 186
25:Case 25	184:Case 187
250:Case 253	185:Case 188
252:Case 255	187:Case 190
256:Case 259	188:Case 191
257:Case 260	189:Case 192
259:Case 262	190:Case 193
262:Case 265	191:Case 194
268:Case 271	193:Case 196
27:Case 27	194:Case 197
28:Case 28	195:Case 198
284:Case 288	198:Case 201
290:Case 294	200:Case 203
294:Case 299	204:Case 207
295:Case 300	205:Case 208
30:Case 30	206:Case 209
308:Case 313	207:Case 210
31:Case 31	208:Case 211
316:Case 321	209:Case 212
317:Case 322	210:Case 213
319:Case 324	211:Case 214
321:Case 326	213:Case 216
324:Case 329	214:Case 217
327:Case 332	217:Case 220
332:Case 337	219:Case 222
334:Case 339	220:Case 223
337:Case 342	223:Case 226
344:Case 349	224:Case 227
345:Case 350	225:Case 228
347:Case 352	226:Case 229
350:Case 355	227:Case 230
351:Case 356	228:Case 231
355:Case 360	229:Case 232
360:Case 365	230:Case 233
362:Case 367	231:Case 234
369:Case 374	232:Case 235
380:Case 385	233:Case 236
384:Case 389	235:Case 238
386:Case 391	236:Case 239
39:Case 39	237:Case 240
394:Case 400	238:Case 241
395:Case 401	239:Case 242
397:Case 403	240:Case 243
4:Case 4	241:Case 244
40:Case 41	242:Case 245
404:Case 410	244:Case 247
405:Case 411	245:Case 248
408:Case 414	246:Case 249
410:Case 416	247:Case 250
411:Case 417	248:Case 251
412:Case 418	249:Case 252
413:Case 419	251:Case 254
414:Case 420	253:Case 256
416:Case 422	254:Case 257
418:Case 424	255:Case 258
420:Case 426	258:Case 261
421:Case 427	26:Case 26
423:Case 429	260:Case 263
43:Case 44	261:Case 264
45:Case 46	263:Case 266
46:Case 47	264:Case 267
5:Case 5	265:Case 268
53:Case 54	266:Case 269
56:Case 57	267:Case 270
6:Case 6	269:Case 272
60:Case 62	270:Case 273
63:Case 65	271:Case 274
64:Case 66	272:Case 275
66:Case 68	274:Case 277
71:Case 73	275:Case 279
74:Case 76	276:Case 280
76:Case 78	277:Case 281
78:Case 80	278:Case 282
8:Case 8	279:Case 283
81:Case 83	280:Case 284
85:Case 87	281:Case 285
88:Case 90	282:Case 286
90:Case 92	283:Case 287
94:Case 96	285:Case 289
97:Case 99	286:Case 290

ANOVA
		Sum of Squares	df	Mean Square	F	Sig.
Total Optimism	Between Groups	2219.527	2	1109.763	75.561	.000
	Within Groups	6212.576	423	14.687
	Total	8432.103	425
Total positive affect	Between Groups	4177.210	2	2088.605	49.427	.000
	Within Groups	17874.276	423	42.256
	Total	22051.486	425
Total negative affect	Between Groups	10522.060	2	5261.030	204.051	.000
	Within Groups	10906.184	423	25.783
	Total	21428.244	425
Total life satisfaction	Between Groups	4763.542	2	2381.771	67.450	.000
	Within Groups	14936.787	423	35.312
	Total	19700.329	425
Total perceived stress	Between Groups	7224.305	2	3612.153	204.774	.000
	Within Groups	7461.601	423	17.640
	Total	14685.906	425
Total Self esteem	Between Groups	7034.253	2	3517.127	286.143	.000
	Within Groups	5199.308	423	12.292
	Total	12233.561	425
Total social desirability	Between Groups	155.207	2	77.604	20.487	.000
	Within Groups	1602.279	423	3.788
	Total	1757.486	425

a) According to the hierarchical clustering, in dissimilarity matrix, we calculated the one-to-one distances between the 426 samples among 439 samples.

The number of cases in Cluster 1 is 128 (29.2%), Cluster 2 is 263 (59.9%) and Cluster 3 is 35 (8.0%).

b) We have considered three clusters and calculated the Ward linkage. Here also the total number of cases is 426. The Ward linkage dendogram is also executed in the analysis.

The cases in each cluster have been provided in a new table.

c) The Ward linkage is single hierarchical linkage. This kind of agglomerative hierarchical clustering created the dendogram diagram. Most of the samples are located in cluster 2.

There are statistically significant differences between the variables used to study outdoor lifestyle and the cluster means at 0.05 level of significance (p-value < 0.000).

Initial Cluster Centers
	Cluster
	1	2	3
Total Optimism	26	9	19
Total Self esteem	40	23	31
Total positive affect	49	20	15
Total negative affect	36	39	14
Total life satisfaction	33	5	33
Total perceived stress	31	46	19
Total social desirability	3	2	8

Iteration History^a
Iteration	Change in Cluster Centers
Iteration	1	2	3
1	21.701	22.738	20.581
2	2.347	.725	3.255
3	.011	.009	.025
4	5.030E-005	.000	.000
5	2.329E-007	1.181E-006	1.552E-006
6	1.078E-009	1.389E-008	1.213E-008
7	5.000E-012	1.634E-010	9.475E-011
8	2.436E-014	1.921E-012	7.363E-013
9	.000	2.119E-014	1.020E-014
10	.000	.000	.000
a. Convergence achieved due to no or small change in cluster centers. The maximum absolute coordinate change for any center is .000. The current iteration is 10. The minimum distance between initial centers is 44.034.

Final Cluster Centers
	Cluster
	1	2	3
Total Optimism	24	19	21
Total Self esteem	36	28	34
Total positive affect	39	28	30
Total negative affect	17	28	16
Total life satisfaction	27	16	20
Total perceived stress	24	34	26
Total social desirability	5	5	6

Cluster Membership
Case Number	Cluster	Distance
1	1	23.688
2	1	18.579
3	3	20.534
4	1	22.973
5	3	23.389
6	3	23.150
7	2	24.854
8	2	23.251
9	2	22.970
10	2	23.080
11	1	16.504
12	1	12.799
13	2	20.732
14	2	19.281
15	3	14.206
16	2	14.403
17	2	17.638
18	2	13.826
19	2	16.501
20	2	17.938
21	2	12.194
22	2	18.507
23	1	17.226
24	2	14.168
25	2	16.685
26	1	11.956
27	2	14.660
28	2	20.688
29	3	11.743
30	2	20.198
31	2	18.507
32	2	16.310
33	3	11.705
34	3	11.979
35	3	13.405
36	1	14.153
37	3	12.281
38	3	19.107
39	2	16.057
40	.	.
41	2	24.166
42	1	17.872
43	2	20.039
44	2	11.920
45	1	17.454
46	1	17.057
47	1	19.714
48	2	10.909
49	3	13.721
50	2	14.916
51	2	15.740
52	3	8.763
53	1	15.801
54	2	14.348
55	3	14.056
56	1	16.455
57	1	17.735
58	.	.
59	1	13.765
60	3	11.296
61	3	13.324
62	1	16.705
63	3	10.544
64	1	12.829
65	2	12.219
66	2	15.102
67	2	16.245
68	2	14.080
69	1	18.580
70	1	11.859
71	1	11.105
72	1	10.674
73	3	12.870
74	2	10.068
75	2	10.990
76	3	14.578
77	1	15.539
78	2	15.417
79	3	9.689
80	2	12.845
81	2	13.601
82	1	16.690
83	1	12.676
84	2	11.172
85	1	9.267
86	1	11.351
87	3	12.271
88	3	11.799
89	1	16.616
90	2	17.628
91	1	8.449
92	1	12.467
93	1	15.755
94	2	8.652
95	1	14.356
96	1	15.195
97	1	16.270
98	1	10.369
99	2	10.184
100	3	14.446
101	1	7.253
102	2	8.307
103	1	8.984
104	3	14.478
105	2	6.680
106	2	13.651
107	1	11.842
108	3	10.834
109	2	12.101
110	3	10.982
111	1	18.247
112	1	15.334
113	1	7.807
114	1	15.917
115	3	11.844
116	3	9.787
117	1	11.650
118	2	10.276
119	1	11.394
120	3	12.661
121	2	16.156
122	1	10.862
123	2	7.734
124	3	14.497
125	1	16.247
126	3	11.562
127	2	14.143
128	1	12.101
129	1	13.023
130	1	9.722
131	1	12.680
132	1	13.396
133	2	5.934
134	3	14.340
135	1	10.870
136	2	7.350
137	3	10.294
138	1	13.803
139	2	15.897
140	1	14.323
141	1	9.254
142	1	8.236
143	2	9.020
144	1	13.854
145	2	12.415
146	1	8.635
147	2	8.401
148	2	12.934
149	1	10.718
150	1	12.430
151	1	13.680
152	3	13.311
153	2	9.576
154	3	7.739
155	1	14.158
156	3	9.239
157	1	13.788
158	2	11.023
159	1	12.313
160	2	11.933
161	1	8.683
162	3	10.275
163	1	11.570
164	1	8.941
165	2	8.067
166	3	13.157
167	1	9.458
168	1	9.606
169	3	11.925
170	3	7.944
171	2	11.137
172	3	8.508
173	3	9.764
174	3	8.509
175	3	9.084
176	.	.
177	1	10.415
178	1	11.557
179	2	8.204
180	2	7.644
181	1	11.314
182	1	12.539
183	1	11.382
184	1	6.490
185	1	9.792
186	1	14.839
187	1	8.445
188	3	9.823
189	2	9.981
190	1	8.755
191	3	7.505
192	1	12.476
193	2	10.873
194	1	8.247
195	2	10.753
196	3	8.710
197	1	12.411
198	2	11.592
199	3	10.716
200	2	9.589
201	1	13.682
202	3	10.850
203	1	8.449
204	3	8.198
205	2	15.231
206	2	13.912
207	1	10.478
208	3	12.425
209	1	8.832
210	3	16.353
211	1	6.609
212	1	5.799
213	1	12.710
214	1	8.504
215	1	16.032
216	1	6.614
217	1	10.197
218	2	9.572
219	2	5.210
220	1	8.124
221	2	12.563
222	1	14.060
223	1	9.982
224	3	12.354
225	2	13.632
226	3	10.329
227	1	8.069
228	3	12.248
229	1	8.414
230	1	13.318
231	1	9.540
232	3	6.484
233	3	7.948
234	1	6.759
235	3	5.987
236	1	9.067
237	1	15.726
238	3	9.034
239	3	11.088
240	1	13.505
241	1	8.149
242	2	12.077
243	1	13.629
244	1	8.473
245	1	11.066
246	2	5.747
247	1	9.579
248	3	12.578
249	2	15.070
250	1	6.070
251	3	7.439
252	1	9.460
253	3	9.682
254	3	7.542
255	3	16.823
256	1	8.192
257	3	7.945
258	1	8.856
259	2	13.636
260	2	9.586
261	1	12.589
262	2	10.669
263	1	10.020
264	3	13.026
265	1	11.171
266	1	8.479
267	1	9.821
268	1	7.674
269	1	10.620
270	1	6.436
271	2	6.619
272	3	10.060
273	1	8.079
274	1	7.807
275	1	9.769
276	2	15.182
277	1	8.333
278	.	.
279	3	8.820
280	1	8.229
281	1	7.976
282	1	10.624
283	1	7.661
284	3	6.768
285	1	11.673
286	1	9.671
287	1	7.455
288	3	9.272
289	1	10.910
290	1	6.566
291	1	6.725
292	3	8.147
293	3	6.927
294	3	9.971
295	1	9.297
296	3	6.389
297	1	6.592
298	.	.
299	2	14.008
300	3	11.246
301	3	15.036
302	3	5.954
303	3	6.158
304	1	9.151
305	1	8.593
306	3	5.103
307	3	3.411
308	3	7.183
309	3	11.922
310	1	9.129
311	3	11.211
312	3	10.954
313	1	9.325
314	1	7.854
315	2	6.536
316	1	8.322
317	3	5.325
318	3	8.593
319	1	9.722
320	3	8.135
321	2	11.197
322	2	10.680
323	3	7.668
324	2	12.975
325	1	7.183
326	3	9.111
327	1	4.987
328	3	9.096
329	1	13.838
330	1	5.964
331	1	4.302
332	2	9.479
333	1	10.972
334	3	7.906
335	3	6.738
336	1	9.185
337	1	12.424
338	1	5.171
339	2	14.046
340	3	13.986
341	3	4.016
342	3	9.596
343	1	6.362
344	1	7.420
345	3	5.192
346	1	4.756
347	1	10.089
348	1	8.420
349	2	15.759
350	2	9.820
351	3	9.016
352	2	13.549
353	2	9.748
354	3	13.116
355	2	8.778
356	3	9.679
357	1	6.246
358	3	12.127
359	1	7.041
360	3	13.387
361	3	4.928
362	3	7.654
363	3	5.600
364	1	10.597
365	3	7.777
366	1	6.869
367	3	12.294
368	1	9.423
369	3	11.187
370	1	6.716
371	1	7.182
372	1	13.535
373	3	5.749
374	1	12.082
375	1	7.410
376	3	6.206
377	3	12.957
378	1	4.756
379	3	8.129
380	1	5.588
381	1	6.979
382	3	8.684
383	3	11.451
384	3	6.001
385	2	14.869
386	1	11.058
387	1	9.634
388	1	7.030
389	3	6.745
390	3	7.441
391	2	16.220
392	3	8.196
393	.	.
394	3	6.217
395	1	3.481
396	1	8.190
397	1	7.931
398	3	8.397
399	1	7.759
400	1	7.997
401	3	8.567
402	1	8.017
403	3	12.229
404	1	7.668
405	1	12.894
406	3	5.771
407	1	4.758
408	1	5.506
409	3	6.446
410	3	5.775
411	1	12.606
412	3	9.684
413	1	3.954
414	3	10.555
415	1	10.348
416	3	8.945
417	2	13.605
418	1	10.898
419	1	9.283
420	3	9.646
421	1	7.803
422	3	14.389
423	3	9.174
424	1	8.572
425	1	9.539
426	3	6.906
427	2	10.174
428	3	7.191
429	1	9.118
430	1	4.713
431	1	7.114
432	1	6.311

Distances between Final Cluster Centers
Cluster	1	2	3
1		23.722	12.005
2	23.722		16.726
3	12.005	16.726

ANOVA
	Cluster		Error		F	Sig.
	Mean Square	df	Mean Square	df	F	Sig.
Total Optimism	1142.863	2	14.530	423	78.653	.000
Total Self esteem	2544.653	2	16.889	423	150.665	.000
Total positive affect	5603.862	2	25.635	423	218.599	.000
Total negative affect	4770.436	2	28.103	423	169.751	.000
Total life satisfaction	3954.891	2	27.874	423	141.886	.000
Total perceived stress	3267.305	2	19.270	423	169.552	.000
Total social desirability	26.178	2	4.031	423	6.494	.002
The F tests should be used only for descriptive purposes because the clusters have been chosen to maximize the differences among cases in different clusters. The observed significance levels are not corrected for this and thus cannot be interpreted as tests of the hypothesis that the cluster means are equal.

Number of Cases in each Cluster
Cluster	1	196.000
	2	98.000
	3	132.000
Valid		426.000
Missing		13.000

a) The k-means clustering for three different clusters indicate that most of the samples are located in cluster 1 (196) whereas the least number of samples are located in cluster 2 (98). The number of samples is 426 for k-mean clustering.
b) There are three clusters calculated for seven variables over 426 samples.

2.c) The Distances between cluster 1 and cluster 2 is maximum (23.722) and the distances between cluster 1 and cluster 3 is minimum (12.005).

The mean-square error is higher in case of positive effect and negative effect. The life satisfaction is higher than total optimism, total life satisfaction and total perceived stress in this case. The significant p-values all are less than 0.05 when F-test in handled. The F-test is used for descriptive purposes as the clusters have been chosen to optimize the differences among cases in different clusters. The hypothesis of equal cluster means is rejected at 95% confidence level.

a) In two-step cluster analysis, samples in cluster 2 (187, 43.9%) is highest followed by samples in cluster 1 (164, 38.5%). The Lowest number of samples in cluster 3 is 75 and 17.6% in percentage.

3.b) The sharing percentages of seven variables of 426 samples are clustered in the output table.

c) Both total perceived stress and total negative effect is highest in cluster 3 and lowest in cluster 1. Conversely, the total self-esteem, total optimism, total positive effect, total social desirability and total life satisfaction is highest in cluster 1 and lowest in cluster 3.
For k-means and two-step clustering, most of the samples lie in cluster 2. However, in hierarchical clustering, most of the samples lie in cluster 1. In all the clusters, the minimum numbers of samples lie in cluster 3. The clusters took into account the 426 samples in each case. All the clustering methods were incorporated with the division of three clusters.

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