Multiple Linear Regression - Estimated Regression Equation

Happiness[t] = + 14.889 + 0.0329849Connected[t] + 0.0188242Separate[t] -0.55981Month[t] + 0.178135Learning[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)	14.889	2.97392	5.007	1.02548e-06	5.12742e-07
Connected	0.0329849	0.0443524	0.7437	0.457732	0.228866
Separate	0.0188242	0.0452612	0.4159	0.677827	0.338914
Month	-0.55981	0.199722	-2.803	0.00544671	0.00272335
Learning	0.178135	0.0649188	2.744	0.00649454	0.00324727

Multiple Linear Regression - Regression Statistics
Multiple R	0.311224
R-squared	0.0968607
Adjusted R-squared	0.0829126
F-TEST (value)	6.94436
F-TEST (DF numerator)	4
F-TEST (DF denominator)	259
p-value	2.52331e-05
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	2.39282
Sum Squared Residuals	1482.92

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	14	14.2342	-0.234184
2	18	14.5897	3.41033
3	11	14.8837	-3.88369
4	12	14.1665	-2.16648
5	16	14.1626	1.8374
6	18	13.8669	4.13314
7	14	15.1053	-1.10525
8	14	14.3219	-0.321911
9	15	14.1909	0.809078
10	15	14.4585	0.541486
11	17	14.5379	2.46214
12	19	14.5284	4.47163
13	10	14.6132	-4.61316
14	16	14.7026	1.29738
15	18	14.664	3.33598
16	14	14.1995	-0.199469
17	14	14.3126	-0.312584
18	17	15.3822	1.61783
19	14	15.0589	-1.05889
20	16	14.3588	1.64122
21	18	14.3776	3.6224
22	11	14.307	-3.30697
23	14	15.237	-1.23702
24	12	14.6555	-2.65547
25	17	14.7678	2.23219
26	9	14.8338	-5.83378
27	16	14.5472	1.45281
28	14	14.3078	-0.30775
29	15	14.4106	0.589411
30	11	14.0873	-3.0873
31	16	14.1288	1.87116
32	13	13.4813	-0.481316
33	17	14.1486	2.85139
34	15	14.5189	0.48113
35	14	14.0308	-0.0308314
36	16	13.3088	2.69121
37	9	13.1722	-4.17219
38	15	14.1533	0.846726
39	17	14.241	2.759
40	13	14.4766	-1.47656
41	15	14.5237	0.476296
42	16	14.0873	1.9127
43	16	15.2692	0.730772
44	12	14.1203	-2.12029
45	15	14.1251	0.874877
46	11	13.6895	-2.6895
47	15	14.3322	0.667812
48	15	14.2513	0.748722
49	17	14.6037	2.39634
50	13	14.2004	-1.20042
51	16	14.4717	1.52828
52	14	13.9649	0.0351384
53	11	13.6651	-2.66506
54	12	14.5377	-2.53769
55	12	13.1118	-1.11184
56	15	14.2239	0.776093
57	16	14.6273	1.37268
58	15	14.2975	0.702527
59	12	14.4209	-2.42087
60	12	14.4954	-2.49538
61	8	13.505	-5.50497
62	13	14.5943	-1.59434
63	11	14.4812	-3.48122
64	14	14.026	-0.0259976
65	15	14.4059	0.594075
66	10	14.1702	-4.17018
67	11	14.3437	-3.34365
68	12	13.9951	-1.99515
69	15	13.4679	1.53208
70	15	13.992	1.00795
71	14	13.0034	0.996633
72	16	13.5227	2.47734
73	15	14.353	0.647021
74	15	14.5226	0.477433
75	13	13.7708	-0.770819
76	12	14.1704	-2.17035
77	17	14.058	2.94198
78	13	13.8461	-0.846116
79	15	13.1138	1.8862
80	13	13.8698	-0.869774
81	15	13.9073	1.09275
82	15	13.992	1.00795
83	16	13.8046	2.19542
84	15	13.6585	1.34152
85	14	13.8131	0.186869
86	15	13.7724	1.22762
87	14	13.8696	0.130397
88	13	13.7	-0.700015
89	7	13.6726	-6.67264
90	17	13.1287	3.87126
91	13	14.109	-1.10904
92	15	14.0673	0.932658
93	14	13.5455	0.454461
94	13	13.128	-0.127963
95	16	14.1052	1.89484
96	12	14.0204	-2.02037
97	14	13.8791	0.120899
98	17	14.0015	2.99846
99	15	13.518	1.482
100	17	14.0722	2.92782
101	12	14.0204	-2.02037
102	16	14.7376	1.26243
103	11	13.5455	-2.54554
104	15	13.9637	1.03628
105	9	13.5284	-4.52844
106	16	14.2315	1.76851
107	15	14.2276	0.772397
108	10	13.9874	-3.98738
109	10	13.6375	-3.63751
110	15	13.7706	1.22935
111	11	13.7848	-2.78481
112	13	14.1465	-1.14652
113	14	13.2834	0.71661
114	18	13.289	4.711
115	16	14.3202	1.67984
116	14	13.6263	0.373721
117	14	13.6593	0.340736
118	14	13.354	0.645977
119	14	14.0722	-0.072176
120	12	13.3917	-1.39167
121	14	13.6719	0.328136
122	15	13.5942	1.40576
123	15	14.0768	0.92316
124	15	13.734	1.26605
125	13	13.7848	-0.784809
126	17	13.8517	3.14827
127	17	14.5047	2.49531
128	19	13.7291	5.27088
129	15	13.2042	1.79579
130	13	13.8178	-0.817794
131	9	12.5982	-3.59822
132	15	14.157	0.84303
133	15	12.8839	2.11614
134	15	13.7206	1.27943
135	16	13.5644	2.43564
136	11	12.9444	-1.94438
137	14	13.7433	0.256723
138	11	12.8988	-1.8988
139	15	13.223	1.77697
140	13	12.9318	0.0682164
141	15	13.8366	1.16338
142	16	13.649	2.35101
143	14	13.9676	0.0323924
144	15	13.5966	1.40343
145	16	12.9752	3.02478
146	16	14.0611	1.93888
147	11	13.4718	-2.4718
148	12	13.7801	-1.78015
149	9	13.3635	-4.36352
150	16	13.0598	2.94016
151	13	14.0448	-1.0448
152	16	13.9779	2.02212
153	12	14.0297	-2.02969
154	9	14.2381	-5.23807
155	13	12.7443	0.255678
156	13	14.109	-1.10904
157	14	13.3587	0.641314
158	19	13.7291	5.27088
159	13	13.8649	-0.86494
160	12	13.1994	-1.19938
161	13	13.4058	-0.405832
162	10	12.4269	-2.42689
163	14	12.3807	1.61931
164	16	13.634	2.36597
165	10	13.2588	-3.25876
166	11	11.8688	-0.868824
167	14	12.8357	1.16425
168	12	12.0188	-0.0188078
169	9	12.8837	-3.88367
170	9	13.1684	-4.16836
171	11	12.6727	-1.67272
172	16	13.4652	2.53478
173	9	12.88	-3.87996
174	13	11.7615	1.23851
175	16	12.5833	3.41674
176	13	13.1175	-0.117498
177	9	12.7104	-3.71037
178	12	12.423	-0.423003
179	16	12.8311	3.16892
180	11	12.8187	-1.81865
181	14	13.4464	0.553603
182	13	12.4098	0.590207
183	15	13.8159	1.18412
184	14	13.2589	0.741065
185	16	11.4089	4.59106
186	13	13.3145	-0.314457
187	14	13.5869	0.413117
188	15	12.7387	2.26131
189	13	12.1413	0.85875
190	11	12.4238	-1.42378
191	11	12.9582	-1.95819
192	14	13.5877	0.412337
193	15	12.5454	2.45455
194	11	13.4322	-2.43224
195	15	12.7048	2.29524
196	12	13.3389	-1.3389
197	14	13.2863	0.713694
198	14	13.3663	0.633734
199	8	12.9347	-4.9347
200	13	13.0413	-0.0412511
201	9	13.1355	-4.13554
202	15	12.5814	2.41864
203	17	12.3956	4.60437
204	13	12.5926	0.407409
205	15	13.1317	1.86834
206	15	13.2023	1.79771
207	14	13.4322	0.567764
208	16	13.4134	2.58659
209	13	12.4993	0.50075
210	16	13.1458	2.85418
211	9	12.6114	-3.61142
212	16	13.0494	2.95062
213	11	13.1928	-2.19279
214	10	12.9951	-2.99506
215	11	13.3946	-2.39459
216	15	12.6192	2.38082
217	17	13.5068	3.49325
218	14	13.1514	0.848567
219	8	12.8932	-4.89317
220	15	13.3247	1.67527
221	11	12.8225	-1.82253
222	16	13.1561	2.8439
223	10	13.094	-3.09401
224	15	12.4936	2.50636
225	9	12.846	-3.84602
226	16	11.8894	4.11062
227	19	12.8499	6.15009
228	12	12.9535	-0.953524
229	8	12.4333	-4.43328
230	11	12.6491	-1.64906
231	14	12.7331	1.26692
232	9	12.3163	-3.31628
233	15	13.2768	1.72319
234	13	13.9111	-0.911118
235	16	12.7707	3.22927
236	11	12.4616	-1.4616
237	12	11.2288	0.771181
238	13	12.7426	0.257425
239	10	13.1214	-3.12138
240	11	12.2976	-1.29763
241	12	12.3617	-0.361697
242	8	12.682	-4.68205
243	12	11.9631	0.0368847
244	12	12.8225	-0.822535
245	15	13.2071	1.79287
246	11	12.4841	-1.48414
247	13	12.9394	0.0606366
248	14	12.3023	1.69771
249	10	11.8908	-1.89075
250	12	11.9379	0.0621027
251	15	12.3531	2.64685
252	13	12.2033	0.796664
253	13	12.6962	0.303791
254	13	13.2721	-0.272145
255	12	12.7104	-0.71037
256	12	12.9677	-0.967685
257	9	13.4322	-4.43224
258	9	12.8499	-3.84991
259	15	12.9073	2.09267
260	10	11.1628	-1.16285
261	14	12.8585	1.14155
262	15	12.5274	2.4726
263	7	12.6877	-5.68766
264	14	12.7839	1.21606

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
8	0.604274	0.791452	0.395726
9	0.437482	0.874964	0.562518
10	0.331563	0.663126	0.668437
11	0.231105	0.462209	0.768895
12	0.498421	0.996841	0.501579
13	0.777555	0.44489	0.222445
14	0.752898	0.494204	0.247102
15	0.887027	0.225945	0.112973
16	0.846895	0.30621	0.153105
17	0.814721	0.370557	0.185279
18	0.815237	0.369526	0.184763
19	0.771097	0.457806	0.228903
20	0.728238	0.543523	0.271762
21	0.763192	0.473617	0.236808
22	0.824855	0.35029	0.175145
23	0.784073	0.431853	0.215927
24	0.785834	0.428332	0.214166
25	0.748758	0.502484	0.251242
26	0.936123	0.127754	0.0638768
27	0.920348	0.159303	0.0796517
28	0.897302	0.205395	0.102698
29	0.868803	0.262394	0.131197
30	0.902468	0.195064	0.0975322
31	0.884058	0.231884	0.115942
32	0.863959	0.272082	0.136041
33	0.85301	0.29398	0.14699
34	0.821542	0.356915	0.178458
35	0.789336	0.421328	0.210664
36	0.763055	0.47389	0.236945
37	0.870417	0.259166	0.129583
38	0.842265	0.315471	0.157735
39	0.849027	0.301946	0.150973
40	0.831905	0.33619	0.168095
41	0.798876	0.402248	0.201124
42	0.778317	0.443366	0.221683
43	0.742631	0.514738	0.257369
44	0.741469	0.517062	0.258531
45	0.702633	0.594735	0.297367
46	0.715318	0.569363	0.284682
47	0.680116	0.639768	0.319884
48	0.64029	0.719419	0.35971
49	0.642903	0.714195	0.357097
50	0.614083	0.771833	0.385917
51	0.587208	0.825585	0.412792
52	0.542876	0.914248	0.457124
53	0.553233	0.893533	0.446767
54	0.555049	0.889903	0.444951
55	0.516601	0.966798	0.483399
56	0.477286	0.954572	0.522714
57	0.444901	0.889803	0.555099
58	0.405105	0.810209	0.594895
59	0.403913	0.807827	0.596087
60	0.410358	0.820716	0.589642
61	0.583241	0.833519	0.416759
62	0.562242	0.875516	0.437758
63	0.606957	0.786086	0.393043
64	0.566896	0.866208	0.433104
65	0.527154	0.945692	0.472846
66	0.516672	0.966656	0.483328
67	0.497083	0.994165	0.502917
68	0.472871	0.945742	0.527129
69	0.533025	0.93395	0.466975
70	0.530728	0.938544	0.469272
71	0.510498	0.979005	0.489502
72	0.536661	0.926677	0.463339
73	0.502765	0.99447	0.497235
74	0.464353	0.928706	0.535647
75	0.426689	0.853379	0.573311
76	0.41053	0.82106	0.58947
77	0.433791	0.867582	0.566209
78	0.39785	0.7957	0.60215
79	0.392187	0.784375	0.607813
80	0.358141	0.716283	0.641859
81	0.329383	0.658765	0.670617
82	0.299391	0.598782	0.700609
83	0.29247	0.584939	0.70753
84	0.26844	0.536881	0.73156
85	0.237767	0.475535	0.762233
86	0.212267	0.424534	0.787733
87	0.185394	0.370788	0.814606
88	0.162861	0.325721	0.837139
89	0.372764	0.745528	0.627236
90	0.421943	0.843885	0.578057
91	0.392717	0.785434	0.607283
92	0.359456	0.718912	0.640544
93	0.328776	0.657552	0.671224
94	0.295864	0.591728	0.704136
95	0.279194	0.558388	0.720806
96	0.274243	0.548485	0.725757
97	0.244688	0.489375	0.755312
98	0.257612	0.515225	0.742388
99	0.236139	0.472278	0.763861
100	0.242377	0.484753	0.757623
101	0.239611	0.479222	0.760389
102	0.218007	0.436015	0.781993
103	0.219459	0.438919	0.780541
104	0.195939	0.391877	0.804061
105	0.27642	0.55284	0.72358
106	0.260115	0.520229	0.739885
107	0.232561	0.465123	0.767439
108	0.292478	0.584955	0.707522
109	0.351582	0.703163	0.648418
110	0.325256	0.650512	0.674744
111	0.339963	0.679926	0.660037
112	0.320296	0.640592	0.679704
113	0.291644	0.583287	0.708356
114	0.381391	0.762782	0.618609
115	0.364079	0.728158	0.635921
116	0.331572	0.663143	0.668428
117	0.300254	0.600507	0.699746
118	0.271163	0.542325	0.728837
119	0.242522	0.485045	0.757478
120	0.226635	0.45327	0.773365
121	0.202511	0.405022	0.797489
122	0.184275	0.36855	0.815725
123	0.163558	0.327115	0.836442
124	0.147794	0.295589	0.852206
125	0.130631	0.261262	0.869369
126	0.142087	0.284174	0.857913
127	0.139923	0.279845	0.860077
128	0.225738	0.451476	0.774262
129	0.212606	0.425211	0.787394
130	0.190573	0.381146	0.809427
131	0.223259	0.446518	0.776741
132	0.200424	0.400848	0.799576
133	0.195743	0.391486	0.804257
134	0.178511	0.357021	0.821489
135	0.179939	0.359877	0.820061
136	0.172753	0.345506	0.827247
137	0.151371	0.302742	0.848629
138	0.14432	0.28864	0.85568
139	0.134841	0.269681	0.865159
140	0.116587	0.233174	0.883413
141	0.104067	0.208133	0.895933
142	0.104982	0.209965	0.895018
143	0.0900363	0.180073	0.909964
144	0.0819092	0.163818	0.918091
145	0.0904639	0.180928	0.909536
146	0.088041	0.176082	0.911959
147	0.0878975	0.175795	0.912103
148	0.0801896	0.160379	0.91981
149	0.112937	0.225874	0.887063
150	0.125372	0.250744	0.874628
151	0.111748	0.223496	0.888252
152	0.11181	0.22362	0.88819
153	0.104995	0.209991	0.895005
154	0.171854	0.343708	0.828146
155	0.150301	0.300602	0.849699
156	0.140094	0.280188	0.859906
157	0.121117	0.242235	0.878883
158	0.1985	0.396999	0.8015
159	0.176574	0.353148	0.823426
160	0.158877	0.317754	0.841123
161	0.138712	0.277424	0.861288
162	0.145257	0.290513	0.854743
163	0.130829	0.261657	0.869171
164	0.126913	0.253827	0.873087
165	0.143722	0.287443	0.856278
166	0.127457	0.254913	0.872543
167	0.112771	0.225542	0.887229
168	0.0970008	0.194002	0.902999
169	0.122893	0.245785	0.877107
170	0.162789	0.325579	0.837211
171	0.151105	0.30221	0.848895
172	0.155592	0.311185	0.844408
173	0.188416	0.376831	0.811584
174	0.169302	0.338604	0.830698
175	0.190901	0.381801	0.809099
176	0.166472	0.332943	0.833528
177	0.197655	0.395309	0.802345
178	0.173744	0.347487	0.826256
179	0.189307	0.378615	0.810693
180	0.176746	0.353492	0.823254
181	0.155065	0.310129	0.844935
182	0.134413	0.268826	0.865587
183	0.1205	0.241	0.8795
184	0.104557	0.209114	0.895443
185	0.146488	0.292975	0.853512
186	0.125739	0.251479	0.874261
187	0.107542	0.215084	0.892458
188	0.104362	0.208725	0.895638
189	0.0892357	0.178471	0.910764
190	0.0792362	0.158472	0.920764
191	0.0737646	0.147529	0.926235
192	0.0616589	0.123318	0.938341
193	0.0612366	0.122473	0.938763
194	0.0598467	0.119693	0.940153
195	0.0582572	0.116514	0.941743
196	0.0500881	0.100176	0.949912
197	0.0415126	0.0830253	0.958487
198	0.0338996	0.0677991	0.9661
199	0.0613658	0.122732	0.938634
200	0.0499007	0.0998014	0.950099
201	0.0711805	0.142361	0.928819
202	0.0694393	0.138879	0.930561
203	0.111055	0.22211	0.888945
204	0.0931401	0.18628	0.90686
205	0.0859589	0.171918	0.914041
206	0.0789095	0.157819	0.921091
207	0.0653988	0.130798	0.934601
208	0.0683666	0.136733	0.931633
209	0.0561521	0.112304	0.943848
210	0.062521	0.125042	0.937479
211	0.0752096	0.150419	0.92479
212	0.0921982	0.184396	0.907802
213	0.0829673	0.165935	0.917033
214	0.0885682	0.177136	0.911432
215	0.0837091	0.167418	0.916291
216	0.0800804	0.160161	0.91992
217	0.103997	0.207995	0.896003
218	0.0899856	0.179971	0.910014
219	0.141241	0.282483	0.858759
220	0.135209	0.270418	0.864791
221	0.119312	0.238624	0.880688
222	0.141973	0.283947	0.858027
223	0.146878	0.293756	0.853122
224	0.151086	0.302173	0.848914
225	0.17707	0.354139	0.82293
226	0.267642	0.535284	0.732358
227	0.584857	0.830287	0.415143
228	0.53275	0.934499	0.46725
229	0.626679	0.746643	0.373321
230	0.583093	0.833814	0.416907
231	0.549047	0.901905	0.450953
232	0.566183	0.867634	0.433817
233	0.566203	0.867593	0.433797
234	0.507974	0.984052	0.492026
235	0.600992	0.798017	0.399008
236	0.551189	0.897622	0.448811
237	0.491283	0.982567	0.508717
238	0.437389	0.874779	0.562611
239	0.440235	0.88047	0.559765
240	0.38135	0.7627	0.61865
241	0.318404	0.636808	0.681596
242	0.448147	0.896295	0.551853
243	0.377478	0.754957	0.622522
244	0.311142	0.622284	0.688858
245	0.340262	0.680524	0.659738
246	0.337766	0.675531	0.662234
247	0.266639	0.533277	0.733361
248	0.275707	0.551414	0.724293
249	0.297991	0.595983	0.702009
250	0.241601	0.483201	0.758399
251	0.198354	0.396707	0.801646
252	0.14095	0.2819	0.85905
253	0.107479	0.214959	0.892521
254	0.0708274	0.141655	0.929173
255	0.0489902	0.0979804	0.95101
256	0.0250307	0.0500613	0.974969

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	0	0	OK
5% type I error level	0	0	OK
10% type I error level	5	0.0200803	OK