Statistical Analysis of Data Using SPSS

Introduction and dataset
The aim of this coursework is to investigate and predict the onset of diabetes based on
various diagnostic measurements.

The dataset was originally compiled by researcher at the Johns Hopkins University
School of Medicine, from a larger database owned by the National Institute of Diabetes
and Digestive and Kidney Diseases. All patients were females at least 21 years old of
Pima Indian heritage. Note that Pima Indians have one of the highest rates of diabetes
in the world.

This dataset includes 392 observations, taken at the individual level and available from
diabetes_dataset.xlsx file in Statistical Data Analysis Coursework folder on NOW.
The key indicator of diabetes (response variable), as defined by the World Health
Organization, is a plasma glucose concentration greater than 200 mg/dl two hours
following ingestion of a 75 gm carbohydrate solution (variable Glucose).

Glucose	Pregnancies	BloodPressure	SkinThickness	Insulin	BMI	DiabetesPedigreeFunction	Age	Outcome
56	2	56	28	45	24.2	0.332	22	0
68	2	62	13	15	20.1	0.257	23	0
68	2	70	32	66	25	0.187	25	0
68	10	106	23	49	35.5	0.285	47	0
71	1	48	18	76	20.4	0.323	22	0
71	1	78	50	45	33.2	0.422	21	0
74	0	52	10	36	27.8	0.269	22	0
74	3	68	28	45	29.7	0.293	23	0
74	8	70	40	49	35.3	0.705	39	0
75	2	64	24	55	29.7	0.37	33	0
77	1	56	30	56	33.3	1.251	24	0
77	5	82	41	42	35.8	0.156	35	0
78	3	50	32	88	31	0.248	26	1
78	0	88	29	40	36.9	0.434	21	0
79	1	80	25	37	25.4	0.583	22	0
79	1	60	42	48	43.5	0.678	23	0
80	1	74	11	60	30	0.527	22	0
80	3	82	31	70	34.2	1.292	27	1
81	1	72	18	40	26.6	0.283	24	0
81	3	86	16	66	27.5	0.306	22	0
81	2	72	15	76	30.1	0.547	25	0
81	1	74	41	57	46.3	1.096	32	0
81	7	78	40	48	46.7	0.261	42	0
82	1	64	13	95	21.2	0.415	23	0
82	2	52	22	115	28.5	1.699	25	0
83	7	78	26	71	29.3	0.767	36	0
83	2	66	23	50	32.2	0.497	22	0
83	3	58	31	18	34.3	0.336	25	0
83	2	65	28	66	36.8	0.629	24	0
84	2	50	23	76	30.4	0.968	21	0
84	3	68	30	106	31.9	0.591	25	0
84	0	64	22	66	35.8	0.545	21	0
84	1	64	23	115	36.9	0.471	28	0
84	0	82	31	125	38.2	0.233	23	0
84	4	90	23	56	39.5	0.159	25	0
85	4	58	22	49	27.8	0.306	28	0
86	5	68	28	71	30.2	0.364	24	0
86	1	66	52	65	41.3	0.917	29	0
87	2	58	16	52	32.7	0.166	25	0
87	1	78	27	32	34.6	0.101	22	0
87	1	60	37	75	37.2	0.509	22	0
87	1	68	34	77	37.6	0.401	24	0
88	5	66	21	23	24.4	0.342	30	0
88	3	58	11	54	24.8	0.267	22	0
88	2	58	26	16	28.4	0.766	22	0
88	2	74	19	53	29	0.229	22	0
88	1	62	24	44	29.9	0.422	23	0
88	1	78	29	76	32	0.365	29	0
88	12	74	40	54	35.3	0.378	48	0
88	1	30	42	99	55	0.496	26	1
89	1	24	19	25	27.8	0.559	21	0
89	1	66	23	94	28.1	0.167	21	0
89	3	74	16	85	30.4	0.551	38	0
89	1	76	34	37	31.2	0.192	23	0
90	2	80	14	55	24.4	0.249	24	0
90	1	62	18	59	25.1	1.268	25	0
90	1	62	12	43	27.2	0.58	24	0
90	4	88	47	54	37.7	0.362	29	0
91	1	54	25	100	25.2	0.234	23	0
91	4	70	32	88	33.1	0.446	22	0
91	0	68	32	210	39.9	0.381	25	0
92	1	62	25	41	19.5	0.482	25	0
92	12	62	7	258	27.6	0.926	44	1
92	6	62	32	126	32	0.085	46	0
93	0	60	25	92	28.7	0.532	22	0
93	6	50	30	64	28.7	0.356	23	0
93	2	64	32	160	38	0.674	23	1
93	0	100	39	72	43.4	1.021	35	0
94	2	68	18	76	26	0.561	21	0
94	2	76	18	66	31.6	0.649	23	0
94	7	64	25	79	33.3	0.738	41	0
94	0	70	27	115	43.5	0.347	21	0
95	1	66	13	38	19.6	0.334	25	0
95	1	60	18	58	23.9	0.26	22	0
95	1	74	21	73	25.9	0.673	36	0
95	2	54	14	88	26.1	0.748	22	0
95	1	82	25	180	35	0.233	43	1
95	0	80	45	92	36.5	0.33	26	0
95	0	85	25	36	37.4	0.247	24	1
95	0	64	39	105	44.6	0.366	22	0
96	4	56	17	49	20.8	0.34	26	0
96	2	68	13	49	21.1	0.647	26	0
96	3	56	34	115	24.7	0.944	39	0
96	1	64	27	87	33.2	0.289	21	0
96	5	74	18	67	33.6	0.997	43	0
97	1	64	19	82	18.2	0.299	21	0
97	1	66	15	140	23.2	0.487	22	0
97	0	64	36	100	36.8	0.6	25	0
97	7	76	32	91	40.9	0.871	32	1
98	0	82	15	84	25.2	0.299	22	0
98	6	58	33	190	34	0.43	43	0
98	2	60	17	120	34.7	0.198	22	0
99	3	80	11	64	19.3	0.284	30	0
99	2	70	16	44	20.4	0.235	27	0
99	3	62	19	74	21.8	0.279	26	0
99	4	76	15	51	23.2	0.223	21	0
99	2	52	15	94	24.6	0.637	21	0
99	3	54	19	86	25.6	0.154	24	0
99	6	60	19	54	26.9	0.497	32	0
99	5	54	28	83	34	0.499	30	0
99	2	60	17	160	36.6	0.453	21	0
99	1	72	30	18	38.6	0.412	21	0
100	1	74	12	46	19.5	0.149	28	0
100	1	66	15	56	23.6	0.666	26	0
100	1	72	12	70	25.3	0.658	28	0
100	12	84	33	105	30	0.488	46	0
100	0	70	26	50	30.8	0.597	21	0
100	3	68	23	81	31.6	0.949	28	0
100	1	66	29	196	32	0.444	42	0
100	2	66	20	90	32.9	0.867	28	1
100	14	78	25	184	36.6	0.412	46	1
100	2	54	28	105	37.8	0.498	24	0
100	2	68	25	71	38.5	0.324	26	0
100	8	74	40	215	39.4	0.661	43	1
100	2	70	52	57	40.5	0.677	25	0
100	0	88	60	110	46.8	0.962	31	0
101	2	58	35	90	21.8	0.155	22	0
101	2	58	17	265	24.2	0.614	23	0
101	1	50	15	36	24.2	0.526	26	0
101	10	76	48	180	32.9	0.171	63	0
102	0	86	17	105	29.3	0.695	27	0
102	3	44	20	94	30.8	0.4	26	0
102	0	78	40	90	34.5	0.238	24	0
102	7	74	40	105	37.2	0.204	45	0
102	0	64	46	78	40.6	0.496	21	0
102	2	86	36	120	45.5	0.127	23	1
103	1	80	11	82	19.4	0.491	22	0
103	4	60	33	192	24	0.966	33	0
103	3	72	30	152	27.6	0.73	27	0
103	6	72	32	190	37.7	0.324	55	0
103	1	30	38	83	43.3	0.183	33	0
104	0	64	23	116	27.8	0.454	23	0
104	6	74	18	156	29.9	0.722	41	1
104	0	64	37	64	33.6	0.51	22	1
105	6	70	32	68	30.8	0.122	37	0
105	2	80	45	191	33.7	0.711	29	1
105	2	58	40	94	34.9	0.225	25	0
105	5	72	29	325	36.9	0.159	28	0
105	0	64	41	142	41.5	0.173	22	0
106	2	56	27	165	29	0.426	22	0
106	2	64	35	119	30.5	1.4	34	0
106	3	54	21	158	30.9	0.292	24	0
106	1	70	28	135	34.2	0.142	22	0
106	0	70	37	148	39.4	0.605	22	0
107	3	62	13	48	22.9	0.678	23	1
107	1	72	30	82	30.8	0.821	24	0
107	2	74	30	100	33.6	0.404	23	0
107	0	62	30	74	36.6	0.757	25	1
108	6	44	20	130	24	0.813	35	0
108	2	62	32	56	25.2	0.128	21	0
108	2	62	10	278	25.3	0.881	22	0
108	2	52	26	63	32.5	0.318	22	0
108	1	60	46	178	35.5	0.415	24	0
108	5	72	43	75	36.1	0.263	33	0
109	1	38	18	120	23.1	0.407	26	0
109	1	56	21	135	25.2	0.833	23	0
109	1	60	8	182	25.4	0.947	21	0
109	8	76	39	114	27.9	0.64	31	1
109	1	58	18	116	28.5	0.219	22	0
109	4	64	44	99	34.8	0.905	26	1
109	5	62	41	129	35.8	0.514	25	1
110	4	76	20	100	28.4	0.118	27	0
110	2	74	29	125	32.4	0.698	27	0
111	1	62	13	182	24	0.138	23	0
111	3	90	12	78	28.4	0.495	29	0
111	3	58	31	44	29.5	0.43	22	0
111	4	72	47	207	37.1	1.39	56	1
112	2	68	22	94	34.1	0.315	26	0
112	9	82	32	175	34.2	0.26	36	1
112	1	72	30	176	34.4	0.528	25	0
112	1	80	45	132	34.8	0.217	24	0
112	2	86	42	160	38.4	0.246	28	0
112	2	78	50	140	39.4	0.175	24	0
113	3	50	10	85	29.5	0.626	25	0
114	7	76	17	110	23.8	0.466	31	0
114	1	66	36	200	38.1	0.289	21	0
114	0	80	34	285	44.2	0.167	27	0
115	1	70	30	96	34.6	0.529	32	1
115	3	66	39	140	38.1	0.15	28	0
116	4	72	12	87	22.1	0.463	37	0
116	3	74	15	105	26.3	0.107	24	0
116	1	78	29	180	36.1	0.496	25	0
117	2	90	19	71	25.2	0.313	21	0
117	0	66	31	188	30.8	0.493	22	0
117	4	64	27	120	33.2	0.23	24	0
117	1	60	23	106	33.8	0.466	27	0
117	1	88	24	145	34.5	0.403	40	1
117	5	86	30	105	39.1	0.251	42	0
117	0	80	31	53	45.2	0.089	24	0
118	1	58	36	94	33.3	0.261	23	0
118	0	84	47	230	45.8	0.551	31	1
119	1	54	13	50	22.3	0.205	24	0
119	6	50	22	176	27.1	1.318	33	1
119	0	64	18	92	34.9	0.725	23	0
119	1	44	47	63	35.5	0.28	25	0
119	1	88	41	170	45.3	0.507	26	0
119	1	86	39	220	45.6	0.808	29	1
120	9	72	22	56	20.8	0.733	48	0
120	0	74	18	63	30.5	0.285	26	0
120	1	80	48	200	38.9	1.162	41	0
120	2	76	37	105	39.7	0.215	29	0
120	11	80	37	150	42.3	0.785	48	1
120	3	70	30	135	42.9	0.452	30	0
121	5	72	23	112	26.2	0.245	30	0
121	0	66	30	165	34.3	0.203	33	1
121	1	78	39	74	39	0.261	28	0
121	2	70	32	95	39.1	0.886	23	0
122	2	60	18	106	29.8	0.717	22	0
122	1	64	32	156	35.1	0.692	30	1
122	2	76	27	200	35.9	0.483	26	0
122	2	52	43	158	36.2	0.816	28	0
122	1	90	51	220	49.7	0.325	31	1
123	4	80	15	176	32	0.443	34	0
123	9	70	44	94	33.1	0.374	40	0
123	6	72	45	230	33.6	0.733	34	0
123	5	74	40	77	34.1	0.269	28	0
123	2	48	32	165	42.1	0.52	26	0
123	3	100	35	240	57.3	0.88	22	0
124	0	56	13	105	21.8	0.452	21	0
124	7	70	33	215	25.5	0.161	37	0
124	8	76	24	600	28.7	0.687	52	1
124	2	68	28	205	32.9	0.875	30	1
124	3	80	33	130	33.2	0.305	26	0
124	9	70	33	402	35.4	0.282	34	0
125	1	70	24	110	24.3	0.221	25	0
125	4	70	18	122	28.9	1.144	45	1
125	6	68	30	120	30	0.464	32	0
125	10	70	26	115	31.1	0.205	41	1
125	1	50	40	167	33.3	0.962	28	1
125	2	60	20	140	33.8	0.088	31	0
126	8	74	38	75	25.9	0.162	39	0
126	0	86	27	120	27.4	0.515	21	0
126	1	56	29	152	28.7	0.801	21	0
126	5	78	27	22	29.6	0.439	40	0
126	0	84	29	215	30.7	0.52	24	0
126	8	88	36	108	38.5	0.349	49	0
126	3	88	41	235	39.3	0.704	27	0
127	2	58	24	275	27.7	1.6	25	0
127	2	46	21	335	34.4	0.176	22	0
127	4	88	11	155	34.5	0.598	28	0
127	0	80	37	210	36.3	0.804	23	0
128	1	82	17	183	27.5	0.115	22	0
128	0	68	19	180	30.5	1.391	25	1
128	1	98	41	58	32	1.321	33	1
128	3	72	25	190	32.4	0.549	27	1
128	1	88	39	110	36.5	1.057	37	1
128	1	48	45	194	40.5	0.613	24	1
128	2	78	37	182	43.3	1.224	31	1
129	6	90	7	326	19.6	0.582	60	0
129	3	64	29	115	26.4	0.219	28	1
129	4	60	12	231	27.5	0.527	31	0
129	2	74	26	205	33.2	0.591	25	0
129	4	86	20	270	35.1	0.231	23	0
129	10	76	28	122	35.9	0.28	39	0
129	3	92	49	155	36.4	0.968	32	1
129	7	68	49	125	38.5	0.439	43	1
129	0	110	46	130	67.1	0.319	26	1
130	1	70	13	105	25.9	0.472	22	0
130	3	78	23	79	28.4	0.323	34	1
130	1	60	23	170	28.6	0.692	21	0
131	1	64	14	415	23.7	0.389	21	0
131	4	68	21	166	33.1	0.16	28	0
133	7	88	15	155	32.4	0.262	37	0
133	1	102	28	140	32.8	0.234	45	1
134	9	74	33	60	25.9	0.46	81	0
134	0	58	20	291	26.4	0.352	21	0
134	6	70	23	130	35.4	0.542	29	1
134	6	80	37	370	46.2	0.238	46	1
135	0	94	46	145	40.6	0.284	26	0
135	0	68	42	250	42.3	0.365	24	1
136	7	74	26	135	26	0.647	51	0
136	11	84	35	130	28.3	0.26	42	1
136	5	84	41	88	35	0.286	35	1
136	15	70	32	110	37.1	0.153	43	1
136	1	74	50	204	37.4	0.399	24	0
137	0	68	14	148	24.8	0.143	21	0
137	0	40	35	168	43.1	2.288	33	1
138	0	60	35	167	34.6	0.534	21	1
138	11	74	26	144	36.1	0.557	50	1
139	0	62	17	210	22.1	0.207	21	0
139	5	64	35	140	28.6	0.411	26	0
139	1	46	19	83	28.7	0.654	22	0
139	5	80	35	160	31.6	0.361	25	1
139	1	62	41	480	40.7	0.536	21	0
140	1	74	26	180	24.1	0.828	23	0
140	12	82	43	325	39.2	0.528	58	1
140	0	65	26	130	42.6	0.431	24	1
141	2	58	34	128	25.4	0.699	24	0
142	2	82	18	64	24.7	0.761	21	0
142	7	60	33	190	28.8	0.687	61	0
142	7	90	24	480	30.4	0.128	43	1
143	1	74	22	61	26.2	0.256	21	0
143	1	86	30	330	30.1	0.892	23	0
143	11	94	33	146	36.6	0.254	51	1
143	1	84	23	310	42.4	1.076	22	0
144	4	58	28	140	29.5	0.287	37	0
144	2	58	33	135	31.6	0.422	25	1
144	5	82	26	285	32	0.452	58	1
144	6	72	27	228	33.9	0.255	40	0
144	1	82	46	180	46.1	0.335	46	1
145	13	82	19	110	22.2	0.245	57	0
145	9	88	34	165	30.3	0.771	53	1
145	9	80	46	130	37.9	0.637	40	1
146	2	70	38	360	28	0.337	29	1
146	4	85	27	100	28.9	0.189	27	0
146	2	76	35	194	38.2	0.329	29	0
147	4	74	25	293	34.9	0.385	30	0
148	4	60	27	318	30.9	0.15	29	1
148	10	84	48	237	37.6	1.001	51	1
149	1	68	29	127	29.3	0.349	42	1
150	7	66	42	342	34.7	0.718	42	0
150	7	78	29	126	35.2	0.692	54	1
151	6	62	31	120	35.5	0.692	28	0
151	12	70	40	271	41.8	0.742	38	1
151	8	78	32	210	42.9	0.516	36	1
152	13	90	33	29	26.8	0.731	43	1
152	9	78	34	171	34.2	0.893	33	1
152	0	82	39	272	41.5	0.27	27	0
153	1	82	42	485	40.6	0.687	23	0
153	13	88	37	140	40.6	1.174	39	0
154	6	74	32	193	29.3	0.839	39	0
154	9	78	30	100	30.9	0.164	45	0
154	4	72	29	126	31.3	0.338	37	0
154	4	62	31	284	32.8	0.237	23	0
154	6	78	41	140	46.1	0.571	27	0
155	2	74	17	96	26.6	0.433	27	1
155	11	76	28	150	33.3	1.353	51	1
155	8	62	26	495	34	0.543	46	1
155	2	52	27	540	38.7	0.24	25	1
155	5	84	44	545	38.7	0.619	34	0
156	9	86	28	155	34.3	1.189	42	1
157	1	72	21	168	25.6	0.123	24	0
157	2	74	35	440	39.4	0.134	30	0
158	3	64	13	387	31.2	0.295	24	0
158	3	76	36	245	31.6	0.851	28	1
158	3	70	30	328	35.5	0.344	35	1
158	5	84	41	210	39.4	0.395	29	1
160	7	54	32	175	30.5	0.588	39	1
161	10	68	23	132	25.5	0.326	47	1
162	0	76	56	100	53.2	0.759	25	1
163	3	70	18	105	31.6	0.268	28	1
163	17	72	41	114	40.9	0.817	47	1
164	1	82	43	67	32.8	0.341	50	0
165	6	68	26	168	33.6	0.631	49	0
165	0	76	43	255	47.9	0.259	26	0
165	0	90	33	680	52.3	0.427	23	0
166	5	72	19	175	25.8	0.587	51	1
167	1	74	17	144	23.4	0.447	33	1
167	8	106	46	231	37.6	0.165	43	1
168	7	88	42	321	38.2	0.787	40	1
169	3	74	19	125	29.9	0.268	31	1
170	3	64	37	225	34.5	0.356	30	1
171	3	72	33	135	33.3	0.199	24	1
171	9	110	24	240	45.4	0.721	54	1
172	1	68	49	579	42.4	0.702	28	1
173	4	70	14	168	29.7	0.361	33	1
173	3	78	39	185	33.8	0.97	31	1
173	3	84	33	474	35.7	0.258	22	1
173	3	82	48	465	38.4	2.137	25	1
173	0	78	32	265	46.5	1.159	58	0
174	3	58	22	194	32.9	0.593	36	1
174	2	88	37	120	44.5	0.646	24	1
176	3	86	27	156	33.3	1.154	52	1
176	8	90	34	300	33.7	0.467	58	1
177	0	60	29	478	34.6	1.072	21	1
179	8	72	42	130	32.7	0.719	36	1
179	0	50	36	159	37.8	0.455	22	1
180	3	64	25	70	34	0.271	26	0
180	0	90	26	90	36.5	0.314	35	1
180	0	78	63	14	59.4	2.42	25	1
181	8	68	36	495	30.1	0.615	60	1
181	1	64	30	180	34.1	0.328	38	1
181	7	84	21	192	35.9	0.586	51	1
181	1	78	42	293	40	1.258	22	1
181	0	88	44	510	43.3	0.222	26	1
184	4	78	39	277	37	0.264	31	1
186	8	90	35	225	34.5	0.423	37	1
187	7	50	33	392	33.9	0.826	34	1
187	3	70	22	200	36.4	0.408	36	1
187	7	68	39	304	37.7	0.254	41	1
187	5	76	27	207	43.6	1.034	53	1
188	0	82	14	185	32	0.682	22	1
189	1	60	23	846	30.1	0.398	59	1
189	5	64	33	325	31.2	0.583	29	1
191	3	68	15	130	30.9	0.299	34	0
193	1	50	16	375	25.9	0.655	24	0
195	7	70	33	145	25.1	0.163	55	1
196	1	76	36	249	36.5	0.875	29	1
196	8	76	29	280	37.5	0.605	57	1
197	2	70	45	543	30.5	0.158	53	1
197	4	70	39	744	36.7	2.329	31	0
198	0	66	32	274	41.3	0.502	28	1

From the tabulated figures:

(1) Generate two random numbers between 2 and 7 and provide SPSS output.
(1 mark)

(2) Using SPSS, erase columns corresponding to your generated numbers (e.g. if
one of the generated numbers is 5 then erase column C5, etc). Describe how you did
this and provide the sequence of actions (e.g. Calc->Descriptive Stats->….)
(2 mark)

(3) Using SPSS select a random sample of 300 observations (n = 300) from your
dataset. Provide the sequence of actions of how you did this.
(1 mark)
Your unique dataset will now consist of 300 rows and seven columns including
Glucose, Age and Outcome.
Investigating your unique dataset

(4) For your unique dataset summarise information about your observations and present
graphically the frequency distributions for all variables that are left in your unique
dataset including Glucose but excluding Outcome variables. Comment on unusual
observations and make your own decision, how to deal with them.
(6 marks)

(5) Using SPSS, define a new variable, Age_Group, by combining observations
for participants younger than 30 into group 1 and all others (of age 30 and older) into
group 2. Provide either a description or a screen shot of how you did this.
(3 marks)

(6) Investigate whether there is a significant difference in mean/median Glucose
concentration between age groups. Formulate the null and alternative hypotheses;
choose, justify and perform an appropriate statistical test using SPSS; provide all
SPSS outputs; write your conclusions.
(10 marks)

(7) Show whether the proportion of participants with Glucose concentration greater
than 100 mg/dl is different between age groups that you defined previously. Formulate
the null and alternative hypotheses; choose, justify and perform an appropriate
statistical test using SPSS; provide all SPSS outputs; write your conclusions.
(10 marks)

(8) Using SPSS, produce a table of correlation coefficients. Justify the choice of
correlation coefficient, investigate the resulting table and comment on most interesting
relationships between chosen variables. Do not use Glucose and Outcome variables in
this analysis.
(4 marks)

(9) Using simple linear regression, model Glucose concentration by one of the
variables of your choice that are available in your unique dataset. Comment on
significance of intercept and slope.
(4 marks)

(10) Fit a multiple regression model with Glucose being a response variable and other
five variables excluding Outcome as predictors. Treat variable Pregnancies as an
interval scale data. Identify insignificant predictors in the model and explain why they
are insignificant.
(4 marks)

(11) Cluster your 300 observation into 10 groups using one of the linkage method and
similarity measure from the corresponding drop-down menus. Give a brief (half a page)
description of the linkage method and similarity measure chosen. Show a dendrogram
with cases labelled by Outcome. Comment on the results obtained. Provide all
SPSS outputs.
(6 marks)

(12) It is known that the incidence of diabetes in the UK is 0.6. In a small northern
village of 100 people isolated from the mainland for six months per year the pharmacy
wants to know how many insulin shots to order. We want to know what is the
probability that between A and B people will develop the disease during this period. To
perform analysis, generate two random numbers between 0 and 100 using SPSS
and paste the outputs into your report. Denote by A the smallest number and by B the
largest number out of these two generated numbers. Calculate the probability that
between A and B people develop the disease and how many shots should be ordered.
(9 marks)