Multiple Linear Regression - Estimated Regression Equation

Happiness[t] = + 16.2821 + 0.0178742Connected[t] + 0.0120349Separate[t] -0.39727Depression[t] + 0.113729Learning[t] + e[t]

Multiple Linear Regression - Ordinary Least Squares
Variable	Parameter	S.D.	T-STAT H0: parameter = 0	2-tail p-value	1-tail p-value
(Intercept)	16.2821	1.59164	10.23	7.50552e-21	3.75276e-21
Connected	0.0178742	0.037247	0.4799	0.631716	0.315858
Separate	0.0120349	0.0382479	0.3147	0.753277	0.376638
Depression	-0.39727	0.0371081	-10.71	2.19497e-22	1.09749e-22
Learning	0.113729	0.0535672	2.123	0.0346937	0.0173469

Multiple Linear Regression - Regression Statistics
Multiple R	0.595756
R-squared	0.354925
Adjusted R-squared	0.344962
F-TEST (value)	35.6259
F-TEST (DF numerator)	4
F-TEST (DF denominator)	259
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	2.02226
Sum Squared Residuals	1059.19

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	14	14.1835	-0.183531
2	18	14.814	3.18597
3	11	13.8386	-2.83864
4	12	14.1721	-2.17207
5	16	10.5847	5.41533
6	18	13.968	4.03203
7	14	10.7732	3.22679
8	14	14.6591	-0.659069
9	15	14.9663	0.0336759
10	15	13.9422	1.05778
11	17	15.1814	1.81861
12	19	15.9763	3.02371
13	10	13.2432	-3.24318
14	16	13.6944	2.30557
15	18	15.278	2.72204
16	14	13.3954	0.604594
17	14	13.4549	0.545132
18	17	15.3233	1.67672
19	14	15.511	-1.51097
20	16	13.8944	2.10563
21	18	15.2968	2.70315
22	11	13.4672	-2.46719
23	14	14.8302	-0.830154
24	12	13.6707	-1.67071
25	17	14.9278	2.07224
26	9	15.758	-6.75805
27	16	14.7965	1.20349
28	14	13.0641	0.935851
29	15	13.527	1.47299
30	11	13.7147	-2.7147
31	16	15.3398	0.660188
32	13	12.5555	0.444456
33	17	14.9361	2.06394
34	15	14.7848	0.215167
35	14	13.6786	0.321409
36	16	15.2104	0.789617
37	9	10.3654	-1.36545
38	15	14.1477	0.852286
39	17	15.0205	1.97948
40	13	15.1518	-2.15184
41	15	15.5728	-0.572821
42	16	13.3174	2.68257
43	16	16.4429	-0.44288
44	12	13.3353	-1.3353
45	15	14.5206	0.479442
46	11	13.4512	-2.4512
47	15	15.4475	-0.447482
48	15	14.6171	0.382875
49	17	13.2435	3.75646
50	13	14.5687	-1.5687
51	16	15.1584	0.841611
52	14	13.2456	0.754428
53	11	11.4651	-0.465139
54	12	13.6051	-1.60506
55	12	13.8928	-1.89281
56	15	13.1965	1.80352
57	16	14.0436	1.95644
58	15	15.4539	-0.453897
59	12	15.11	-3.10996
60	12	13.1775	-1.17752
61	8	10.5747	-2.57468
62	13	14.423	-1.42295
63	11	14.3635	-3.36349
64	14	13.2879	0.712127
65	15	13.9181	1.08192
66	10	14.9164	-4.91644
67	11	12.6403	-1.64035
68	12	14.4232	-2.42317
69	15	13.6609	1.33915
70	15	13.6109	1.3891
71	14	13.3674	0.632617
72	16	12.9267	3.07329
73	15	14.2418	0.758181
74	15	15.5292	-0.529196
75	13	14.6645	-1.66448
76	12	11.7255	0.274473
77	17	14.0439	2.95609
78	13	12.329	0.670998
79	15	13.4697	1.53035
80	13	15.5126	-2.51265
81	15	14.7549	0.245077
82	15	15.5972	-0.597247
83	16	14.2793	1.72068
84	15	14.202	0.798019
85	14	13.9002	0.0997913
86	15	13.8584	1.1416
87	14	14.3336	-0.333584
88	13	13.0462	-0.0462065
89	7	10.2351	-3.23512
90	17	13.4697	3.53028
91	13	13.2851	-0.285055
92	15	14.0563	0.943694
93	14	12.938	1.06204
94	13	13.6741	-0.674126
95	16	14.8622	1.13783
96	12	12.828	-0.828035
97	14	14.7305	-0.730497
98	17	14.8024	2.19765
99	15	14.9069	0.0931379
100	17	15.2416	1.75844
101	12	12.828	-0.828035
102	16	14.8782	1.12177
103	11	14.527	-3.52704
104	15	12.8047	2.19532
105	9	11.3126	-2.31256
106	16	14.946	1.05401
107	15	12.9477	2.05233
108	10	13.2074	-3.20743
109	10	9.38645	0.613551
110	15	13.4854	1.51458
111	11	13.094	-2.09399
112	13	14.911	-1.91095
113	14	12.7707	1.22932
114	18	13.9502	4.04983
115	16	15.403	0.596992
116	14	13.3838	0.616205
117	14	13.7989	0.20106
118	14	15.1962	-1.19624
119	14	13.2552	0.744786
120	12	12.8367	-0.836692
121	14	13.4191	0.580949
122	15	14.5392	0.460787
123	15	16.0423	-1.0423
124	15	14.6346	0.365357
125	13	14.6831	-1.68307
126	17	15.8921	1.10789
127	17	15.4986	1.50136
128	19	14.6412	4.35881
129	15	13.5051	1.49489
130	13	14.7009	-1.70094
131	9	10.3596	-1.35961
132	15	15.2893	-0.289348
133	15	12.5315	2.46853
134	15	14.2258	0.774237
135	16	13.3473	2.65273
136	11	9.38864	1.61136
137	14	13.4552	0.544776
138	11	12.1343	-1.13427
139	15	14.3117	0.688312
140	13	13.7412	-0.741227
141	15	15.1102	-0.11025
142	16	13.4078	2.5922
143	14	14.4057	-0.405724
144	15	14.1655	0.834549
145	16	14.1375	1.8625
146	16	14.4589	1.54108
147	11	13.6728	-2.67282
148	12	14.6769	-2.67687
149	9	11.2232	-2.22319
150	16	13.8008	2.19924
151	13	12.4305	0.569523
152	16	15.5914	0.408592
153	12	14.4295	-2.42951
154	9	11.4146	-2.41461
155	13	11.2315	1.76851
156	13	13.2851	-0.285055
157	14	13.2161	0.783912
158	19	14.6412	4.35881
159	13	15.5192	-2.5192
160	12	11.5253	0.474686
161	13	12.4453	0.554739
162	10	9.02163	0.978368
163	14	12.9521	1.0479
164	16	11.3465	4.65351
165	10	11.9143	-1.91428
166	11	9.07223	1.92777
167	14	14.0405	-0.0404688
168	12	12.737	-0.736967
169	9	12.4693	-3.46933
170	9	11.8788	-2.87882
171	11	10.7359	0.2641
172	16	14.4233	1.57669
173	9	14.0337	-5.0337
174	13	11.3713	1.62868
175	16	13.4628	2.53719
176	13	15.4058	-2.40583
177	9	12.3491	-3.34905
178	12	11.3933	0.606714
179	16	14.8288	1.17119
180	11	13.2096	-2.2096
181	14	14.8085	-0.808546
182	13	14.9444	-1.94436
183	15	15.0604	-0.0603608
184	14	15.0797	-1.0797
185	16	13.5522	2.4478
186	13	11.5589	1.44111
187	14	13.7064	0.293605
188	15	13.9498	1.05019
189	13	12.8088	0.19118
190	11	10.1957	0.804295
191	11	13.7151	-2.71505
192	14	15.2897	-1.2897
193	15	12.6569	2.34305
194	11	12.8164	-1.81636
195	15	13.1559	1.84409
196	12	14.3395	-2.33949
197	14	11.5345	2.46554
198	14	13.1779	0.822122
199	8	11.3132	-3.3132
200	13	13.7871	-0.787124
201	9	12.2455	-3.24547
202	15	13.8971	1.10288
203	17	14.144	2.85602
204	13	13.0779	-0.0779333
205	15	14.6171	0.382875
206	15	13.8645	1.13547
207	14	14.4054	-0.405437
208	16	13.2016	2.79841
209	13	13.012	-0.0119881
210	16	14.2257	1.77431
211	9	11.8982	-2.89816
212	16	14.5393	1.46072
213	11	11.8785	-0.878534
214	10	13.7449	-3.74489
215	11	12.395	-1.39502
216	15	13.5112	1.48883
217	17	14.8566	2.14338
218	14	14.2134	-0.213372
219	8	10.0854	-2.08535
220	15	13.5391	1.46089
221	11	14.0161	-3.01611
222	16	14.2196	1.78043
223	10	12.2094	-2.20943
224	15	15.0107	-0.0106613
225	9	10.4589	-1.45891
226	16	14.2245	1.77551
227	19	14.4436	4.55642
228	12	14.1061	-2.10613
229	8	9.40081	-1.40081
230	11	13.5113	-2.51131
231	14	13.9621	0.0378676
232	9	12.1103	-3.11027
233	15	15.5075	-0.50752
234	13	12.7056	0.294351
235	16	15.178	0.821987
236	11	12.9879	-1.98792
237	12	11.0058	0.994153
238	13	13.5645	-0.564506
239	10	14.6233	-4.62325
240	11	13.6746	-2.67457
241	12	14.5419	-2.54189
242	8	11.1456	-3.14556
243	12	11.9006	0.099449
244	12	12.427	-0.427031
245	15	13.4607	1.53929
246	11	10.641	0.358954
247	13	12.9085	0.0915234
248	14	9.31079	4.68921
249	10	10.2938	-0.293815
250	12	11.9066	0.0933906
251	15	12.9347	2.06535
252	13	11.6408	1.35921
253	13	14.3296	-1.32956
254	13	13.9122	-0.912244
255	12	11.9518	0.0482195
256	12	12.9202	-0.920155
257	9	10.83	-1.83001
258	9	11.6627	-2.66269
259	15	12.8721	2.12792
260	10	14.5455	-4.54553
261	14	14.0645	-0.06447
262	15	13.831	1.16905
263	7	9.94143	-2.94143
264	14	14.0106	-0.0105596

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
8	0.754202	0.491595	0.245798
9	0.613195	0.77361	0.386805
10	0.52514	0.94972	0.47486
11	0.427237	0.854474	0.572763
12	0.723775	0.55245	0.276225
13	0.929879	0.140243	0.0701213
14	0.924147	0.151705	0.0758527
15	0.968924	0.0621529	0.0310765
16	0.952515	0.0949697	0.0474849
17	0.937852	0.124295	0.0621477
18	0.926592	0.146817	0.0734083
19	0.919547	0.160906	0.0804531
20	0.901332	0.197335	0.0986675
21	0.904277	0.191445	0.0957225
22	0.939742	0.120516	0.0602582
23	0.923549	0.152902	0.0764511
24	0.919663	0.160675	0.0803374
25	0.897805	0.20439	0.102195
26	0.997026	0.00594864	0.00297432
27	0.995754	0.00849178	0.00424589
28	0.993685	0.0126302	0.00631508
29	0.991087	0.0178257	0.00891286
30	0.995313	0.00937443	0.00468722
31	0.99321	0.0135794	0.00678972
32	0.990893	0.0182145	0.00910723
33	0.988995	0.0220104	0.0110052
34	0.98459	0.0308198	0.0154099
35	0.979564	0.0408719	0.0204359
36	0.972459	0.0550827	0.0275414
37	0.978657	0.0426867	0.0213433
38	0.971664	0.0566727	0.0283364
39	0.968894	0.0622121	0.0311061
40	0.97079	0.0584204	0.0292102
41	0.962969	0.0740619	0.037031
42	0.962705	0.0745906	0.0372953
43	0.952084	0.0958324	0.0479162
44	0.949803	0.100395	0.0501973
45	0.936673	0.126655	0.0633273
46	0.94645	0.107099	0.0535495
47	0.932723	0.134554	0.0672769
48	0.916553	0.166895	0.0834474
49	0.94039	0.119221	0.0596103
50	0.935279	0.129442	0.0647209
51	0.921584	0.156832	0.0784161
52	0.90459	0.190821	0.0954103
53	0.89146	0.217079	0.10854
54	0.889181	0.221638	0.110819
55	0.883186	0.233627	0.116814
56	0.87333	0.25334	0.12667
57	0.865059	0.269883	0.134941
58	0.841646	0.316708	0.158354
59	0.868833	0.262334	0.131167
60	0.860906	0.278188	0.139094
61	0.889448	0.221103	0.110552
62	0.88072	0.238561	0.11928
63	0.913214	0.173572	0.0867859
64	0.897329	0.205342	0.102671
65	0.881485	0.237031	0.118515
66	0.949642	0.100716	0.050358
67	0.948591	0.102818	0.0514092
68	0.952794	0.0944126	0.0472063
69	0.945716	0.108569	0.0542843
70	0.938467	0.123066	0.061533
71	0.926061	0.147878	0.073939
72	0.937857	0.124286	0.0621429
73	0.926106	0.147788	0.0738942
74	0.912603	0.174794	0.0873969
75	0.904475	0.191051	0.0955253
76	0.887075	0.22585	0.112925
77	0.901096	0.197808	0.0989039
78	0.884325	0.231349	0.115675
79	0.875539	0.248922	0.124461
80	0.877545	0.24491	0.122455
81	0.85716	0.285679	0.14284
82	0.83615	0.327701	0.16385
83	0.828532	0.342936	0.171468
84	0.806716	0.386569	0.193284
85	0.779657	0.440686	0.220343
86	0.756093	0.487814	0.243907
87	0.726385	0.547229	0.273615
88	0.694335	0.611329	0.305665
89	0.763787	0.472427	0.236213
90	0.80662	0.38676	0.19338
91	0.780444	0.439112	0.219556
92	0.756131	0.487738	0.243869
93	0.735723	0.528554	0.264277
94	0.708014	0.583972	0.291986
95	0.684325	0.63135	0.315675
96	0.659257	0.681485	0.340743
97	0.628178	0.743644	0.371822
98	0.633551	0.732898	0.366449
99	0.598821	0.802357	0.401179
100	0.587949	0.824102	0.412051
101	0.560838	0.878324	0.439162
102	0.536008	0.927985	0.463992
103	0.59618	0.807641	0.40382
104	0.594103	0.811794	0.405897
105	0.611368	0.777264	0.388632
106	0.585376	0.829247	0.414624
107	0.578853	0.842295	0.421147
108	0.637167	0.725665	0.362833
109	0.610446	0.779109	0.389554
110	0.594106	0.811789	0.405894
111	0.596948	0.806104	0.403052
112	0.603784	0.792432	0.396216
113	0.580675	0.83865	0.419325
114	0.673444	0.653113	0.326556
115	0.645049	0.709903	0.354951
116	0.616348	0.767303	0.383652
117	0.585566	0.828867	0.414434
118	0.565028	0.869944	0.434972
119	0.534303	0.931395	0.465697
120	0.508682	0.982636	0.491318
121	0.479182	0.958364	0.520818
122	0.447307	0.894614	0.552693
123	0.422584	0.845168	0.577416
124	0.389361	0.778721	0.610639
125	0.376965	0.753931	0.623035
126	0.353532	0.707064	0.646468
127	0.33917	0.678341	0.66083
128	0.467174	0.934349	0.532826
129	0.449994	0.899987	0.550006
130	0.437157	0.874314	0.562843
131	0.420801	0.841603	0.579199
132	0.388861	0.777722	0.611139
133	0.406067	0.812133	0.593933
134	0.379271	0.758541	0.620729
135	0.406895	0.813789	0.593105
136	0.392361	0.784721	0.607639
137	0.362025	0.724051	0.637975
138	0.343169	0.686337	0.656831
139	0.315256	0.630513	0.684744
140	0.289864	0.579729	0.710136
141	0.260265	0.520531	0.739735
142	0.283116	0.566232	0.716884
143	0.254483	0.508966	0.745517
144	0.232977	0.465953	0.767023
145	0.227198	0.454397	0.772802
146	0.219275	0.438549	0.780725
147	0.23947	0.478941	0.76053
148	0.256354	0.512707	0.743646
149	0.264785	0.52957	0.735215
150	0.275149	0.550299	0.724851
151	0.251117	0.502233	0.748883
152	0.227278	0.454556	0.772722
153	0.23401	0.46802	0.76599
154	0.245922	0.491843	0.754078
155	0.237325	0.47465	0.762675
156	0.210674	0.421349	0.789326
157	0.191473	0.382947	0.808527
158	0.307245	0.61449	0.692755
159	0.319599	0.639198	0.680401
160	0.294195	0.58839	0.705805
161	0.268985	0.53797	0.731015
162	0.243491	0.486982	0.756509
163	0.220746	0.441492	0.779254
164	0.360181	0.720362	0.639819
165	0.351548	0.703096	0.648452
166	0.346791	0.693583	0.653209
167	0.313821	0.627641	0.686179
168	0.288168	0.576335	0.711832
169	0.34065	0.6813	0.65935
170	0.366313	0.732625	0.633687
171	0.33493	0.669859	0.66507
172	0.330155	0.66031	0.669845
173	0.500087	0.999827	0.499913
174	0.483803	0.967605	0.516197
175	0.50927	0.98146	0.49073
176	0.520022	0.959955	0.479978
177	0.575307	0.849386	0.424693
178	0.542937	0.914126	0.457063
179	0.519154	0.961692	0.480846
180	0.519786	0.960428	0.480214
181	0.485298	0.970597	0.514702
182	0.480688	0.961376	0.519312
183	0.44234	0.88468	0.55766
184	0.413311	0.826623	0.586689
185	0.433138	0.866276	0.566862
186	0.423939	0.847877	0.576061
187	0.387532	0.775065	0.612468
188	0.359911	0.719821	0.640089
189	0.325195	0.65039	0.674805
190	0.305084	0.610168	0.694916
191	0.322763	0.645527	0.677237
192	0.300389	0.600779	0.699611
193	0.321602	0.643205	0.678398
194	0.308206	0.616413	0.691794
195	0.308142	0.616285	0.691858
196	0.318053	0.636107	0.681947
197	0.351303	0.702607	0.648697
198	0.323587	0.647174	0.676413
199	0.363585	0.72717	0.636415
200	0.328225	0.656451	0.671775
201	0.371295	0.742591	0.628705
202	0.348841	0.697682	0.651159
203	0.396035	0.792069	0.603965
204	0.356418	0.712837	0.643582
205	0.319238	0.638476	0.680762
206	0.296156	0.592311	0.703844
207	0.26047	0.520941	0.73953
208	0.302438	0.604876	0.697562
209	0.266569	0.533138	0.733431
210	0.265481	0.530962	0.734519
211	0.284827	0.569654	0.715173
212	0.278115	0.556229	0.721885
213	0.243204	0.486408	0.756796
214	0.311277	0.622554	0.688723
215	0.283133	0.566265	0.716867
216	0.269728	0.539456	0.730272
217	0.285618	0.571235	0.714382
218	0.247342	0.494683	0.752658
219	0.237527	0.475054	0.762473
220	0.233649	0.467298	0.766351
221	0.25514	0.51028	0.74486
222	0.264072	0.528145	0.735928
223	0.256118	0.512235	0.743882
224	0.220775	0.441549	0.779225
225	0.195422	0.390843	0.804578
226	0.225681	0.451362	0.774319
227	0.507624	0.984752	0.492376
228	0.473945	0.94789	0.526055
229	0.45312	0.90624	0.54688
230	0.434888	0.869776	0.565112
231	0.386876	0.773752	0.613124
232	0.41395	0.8279	0.58605
233	0.367939	0.735879	0.632061
234	0.317738	0.635476	0.682262
235	0.328828	0.657655	0.671172
236	0.297949	0.595898	0.702051
237	0.258834	0.517668	0.741166
238	0.213047	0.426094	0.786953
239	0.330541	0.661083	0.669459
240	0.316675	0.633349	0.683325
241	0.301199	0.602399	0.698801
242	0.384877	0.769754	0.615123
243	0.319284	0.638568	0.680716
244	0.258184	0.516369	0.741816
245	0.258803	0.517605	0.741197
246	0.208772	0.417545	0.791228
247	0.156103	0.312206	0.843897
248	0.522048	0.955904	0.477952
249	0.432048	0.864096	0.567952
250	0.377262	0.754524	0.622738
251	0.398519	0.797039	0.601481
252	0.687533	0.624933	0.312467
253	0.696881	0.606239	0.303119
254	0.877143	0.245714	0.122857
255	0.835929	0.328141	0.164071
256	0.840024	0.319953	0.159976

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	3	0.0120482	NOK
5% type I error level	11	0.0441767	OK
10% type I error level	21	0.0843373	OK