Multiple Linear Regression - Estimated Regression Equation

Happiness[t] = + 15.3447 + 0.115391Learning[t] -0.377668Depression[t] + 0.023582Sport1[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)	15.3447	1.4058	10.92	4.40589e-23	2.20294e-23
Learning	0.115391	0.0519332	2.222	0.0271497	0.0135748
Depression	-0.377668	0.0385335	-9.801	1.66972e-19	8.3486e-20
Sport1	0.023582	0.0126432	1.865	0.0632817	0.0316408

Multiple Linear Regression - Regression Statistics
Multiple R	0.601717
R-squared	0.362064
Adjusted R-squared	0.354703
F-TEST (value)	49.188
F-TEST (DF numerator)	3
F-TEST (DF denominator)	260
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	2.00717
Sum Squared Residuals	1047.47

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	14	13.5626	0.437426
2	18	14.9939	3.00612
3	11	13.8062	-2.80615
4	12	14.1235	-2.12351
5	16	10.8213	5.17866
6	18	14.1521	3.84788
7	14	10.4782	3.52175
8	14	14.8077	-0.807739
9	15	14.9285	0.0714765
10	15	13.9581	1.04192
11	17	15.2772	1.72278
12	19	15.443	3.557
13	10	13.1059	-3.10589
14	16	13.177	2.823
15	18	15.5813	2.41874
16	14	13.1559	0.844068
17	14	13.5568	0.443174
18	17	15.5734	1.42665
19	14	15.1543	-1.15427
20	16	13.6254	2.37459
21	18	15.1595	2.84052
22	11	13.5071	-2.50714
23	14	14.2785	-0.278505
24	12	13.2242	-1.22416
25	17	15.18	1.81999
26	9	15.7939	-6.79386
27	16	14.8288	1.1712
28	14	13.0377	0.962334
29	15	13.743	1.25704
30	11	13.6304	-2.63045
31	16	15.5631	0.436925
32	13	12.3378	0.662239
33	17	14.8578	2.14222
34	15	15.0175	-0.0174587
35	14	13.7955	0.20448
36	16	15.1515	0.848453
37	9	10.4309	-1.43088
38	15	14.1024	0.897558
39	17	15.2065	1.79353
40	13	15.0414	-2.0414
41	15	15.537	-0.536974
42	16	13.4414	2.55857
43	16	15.9046	0.0954323
44	12	12.899	-0.899048
45	15	14.4329	0.567054
46	11	13.3079	-2.30785
47	15	15.094	-0.0939532
48	15	14.6898	0.310171
49	17	13.271	3.72903
50	13	14.5744	-1.57444
51	16	15.1121	0.887858
52	14	13.2528	0.747222
53	11	11.417	-0.416996
54	12	13.3657	-1.36565
55	12	13.7145	-1.7145
56	15	13.2762	1.72382
57	16	14.0263	1.9737
58	15	15.3719	-0.3719
59	12	15.0203	-3.02033
60	12	13.1766	-1.17664
61	8	10.4258	-2.42584
62	13	14.4747	-1.47472
63	11	14.5455	-3.54546
64	14	12.899	1.10095
65	15	13.5547	1.44534
66	10	15.0385	-5.03852
67	11	12.5578	-1.55776
68	12	14.6112	-2.61117
69	15	13.3053	1.69466
70	15	13.5307	1.46927
71	14	13.1689	0.83112
72	16	12.5685	3.43146
73	15	14.4222	0.57784
74	15	15.2722	-0.272179
75	13	15.0175	-2.01746
76	12	12.0172	-0.0171799
77	17	13.932	3.06802
78	13	12.3977	0.602278
79	15	13.7509	1.24913
80	13	15.0653	-2.06533
81	15	14.8995	0.100451
82	15	15.4662	-0.466228
83	16	14.265	1.735
84	15	14.2414	0.758585
85	14	14.097	-0.0970491
86	15	13.8191	1.1809
87	14	14.2861	-0.286061
88	13	12.7993	0.200673
89	7	10.4176	-3.41757
90	17	13.5412	3.45884
91	13	12.9147	0.0852812
92	15	14.097	0.902951
93	14	13.3442	0.655768
94	13	14.0105	-1.01045
95	16	14.9231	1.07687
96	12	12.7754	-0.77539
97	14	14.876	-0.875967
98	17	14.9467	2.05329
99	15	14.9757	0.0243125
100	17	15.2065	1.79353
101	12	12.8697	-0.869718
102	16	15.1249	0.875061
103	11	14.4776	-3.47759
104	15	13.0112	1.98879
105	9	11.2726	-2.27263
106	16	14.9442	1.05581
107	15	12.8226	2.17745
108	10	12.7993	-2.79933
109	10	8.7501	1.2499
110	15	13.908	1.09196
111	11	13.271	-2.27097
112	13	15.2272	-2.22718
113	14	12.0758	1.92416
114	18	13.9896	4.01043
115	16	15.6731	0.326927
116	14	12.9462	1.05379
117	14	13.6304	0.369554
118	14	15.0729	-1.07289
119	14	13.6483	0.35172
120	12	12.4532	-0.453153
121	14	13.6958	0.304201
122	15	14.7892	0.210806
123	15	15.9618	-0.961806
124	15	14.6427	0.357335
125	13	14.8995	-1.89955
126	17	16.1766	0.823437
127	17	15.2747	1.7253
128	19	14.8313	4.16868
129	15	13.5176	1.48243
130	13	14.7109	-1.71089
131	9	10.5016	-1.50162
132	15	15.2301	-0.230052
133	15	12.5972	2.40284
134	15	14.1732	0.826812
135	16	13.7926	2.20735
136	11	9.43181	1.56819
137	14	13.2738	0.726158
138	11	11.8447	-0.844702
139	15	14.0843	0.915747
140	13	13.7091	-0.709103
141	15	14.6877	0.312334
142	16	13.7691	2.23094
143	14	14.8023	-0.802346
144	15	14.4747	0.525283
145	16	14.443	1.55698
146	16	14.6819	1.31808
147	11	13.35	-2.34998
148	12	14.8052	-2.80522
149	9	11.3905	-2.39054
150	16	13.971	2.02898
151	13	12.5182	0.481849
152	16	15.4662	0.533772
153	12	14.3568	-2.35681
154	9	11.4116	-2.4116
155	13	11.5399	1.46006
156	13	12.9147	0.0852812
157	14	13.1846	0.815449
158	19	14.8313	4.16868
159	13	15.7728	-2.77279
160	12	11.9122	0.0877816
161	13	12.4292	0.570785
162	10	9.33713	0.662873
163	14	13.3521	0.647856
164	16	11.6867	4.31332
165	10	11.9754	-1.97541
166	11	9.08564	1.91436
167	14	14.2675	-0.267516
168	12	13.0717	-1.07168
169	9	12.7358	-3.73578
170	9	12.1144	-3.11438
171	11	10.473	0.526995
172	16	14.3568	1.64319
173	9	14.0367	-5.03673
174	13	11.3542	1.64584
175	16	13.5176	2.48243
176	13	15.5159	-2.51591
177	9	12.2902	-3.29024
178	12	11.5585	0.441512
179	16	14.7634	1.23655
180	11	13.1871	-2.18707
181	14	14.31	-0.309998
182	13	14.7949	-1.79494
183	15	15.0335	-0.033485
184	14	15.1854	-1.18541
185	16	14.2122	1.78776
186	13	11.8075	1.19254
187	14	13.764	0.235973
188	15	14.249	0.751029
189	13	12.6	0.399962
190	11	10.1214	0.878563
191	11	12.9466	-1.94657
192	14	15.1829	-1.18289
193	15	12.6915	2.30851
194	11	12.6103	-1.61032
195	15	13.2553	1.7447
196	12	14.1943	-2.19425
197	14	11.8782	2.12179
198	14	13.5775	0.422466
199	8	11.2465	-3.24653
200	13	14.097	-1.09705
201	9	12.3977	-3.39772
202	15	14.0553	0.944722
203	17	14.2283	2.77174
204	13	12.7154	0.284571
205	15	14.6191	0.380917
206	15	13.9109	1.08909
207	14	14.6634	-0.663373
208	16	12.7522	3.24784
209	13	12.9773	0.0226501
210	16	14.5244	1.4756
211	9	11.8182	-2.81825
212	16	14.5559	1.44411
213	11	12.3291	-1.32914
214	10	14.0288	-4.02882
215	11	12.3506	-1.35056
216	15	13.5833	1.41672
217	17	15.1564	1.84357
218	14	14.3854	-0.385426
219	8	9.97455	-1.97455
220	15	13.7219	1.2781
221	11	14.105	-3.10496
222	16	13.7959	2.20412
223	10	12.3531	-2.35308
224	15	15.0282	-0.0282443
225	9	9.80983	-0.809834
226	16	14.3305	1.6695
227	19	14.0792	4.92078
228	12	13.9138	-1.91379
229	8	9.48401	-1.48401
230	11	13.4704	-2.47041
231	14	13.9871	0.0129496
232	9	12.0359	-3.03588
233	15	15.1597	-0.159662
234	13	12.6993	0.300749
235	16	15.1436	0.856364
236	11	12.9773	-1.97735
237	12	11.1781	0.821902
238	13	13.1142	-0.11416
239	10	14.7345	-4.73447
240	11	13.6645	-2.66446
241	12	15.0279	-3.02789
242	8	10.8035	-2.80351
243	12	11.8236	0.176361
244	12	12.3585	-0.358469
245	15	13.7219	1.2781
246	11	10.8032	0.196847
247	13	12.8987	0.101307
248	14	8.84982	5.15018
249	10	10.4966	-0.496587
250	12	11.9365	0.0634883
251	15	12.9773	2.02265
252	13	11.9176	1.08239
253	13	14.2493	-1.24933
254	13	13.9791	-0.979139
255	12	11.9126	0.087426
256	12	12.8751	-0.875111
257	9	11.0285	-2.02854
258	9	11.6242	-2.6242
259	15	12.7597	2.24028
260	10	14.7422	-4.74218
261	14	14.0528	-0.0527593
262	15	13.6855	1.31448
263	7	9.76735	-2.76735
264	14	14.126	-0.126024

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
7	0.841623	0.316753	0.158377
8	0.797831	0.404338	0.202169
9	0.688783	0.622433	0.311217
10	0.573966	0.852068	0.426034
11	0.577792	0.844416	0.422208
12	0.922947	0.154106	0.0770528
13	0.977937	0.0441264	0.0220632
14	0.973503	0.0529943	0.0264972
15	0.972612	0.0547768	0.0273884
16	0.958647	0.0827061	0.041353
17	0.944368	0.111263	0.0556316
18	0.927319	0.145362	0.072681
19	0.90716	0.185679	0.0928395
20	0.895087	0.209826	0.104913
21	0.900546	0.198909	0.0994544
22	0.943198	0.113605	0.0568023
23	0.922562	0.154876	0.0774378
24	0.918107	0.163786	0.0818932
25	0.897769	0.204462	0.102231
26	0.995228	0.00954457	0.00477228
27	0.993184	0.0136327	0.00681637
28	0.990257	0.0194852	0.0097426
29	0.986283	0.0274338	0.0137169
30	0.992305	0.0153906	0.00769531
31	0.988981	0.0220383	0.0110191
32	0.985018	0.0299641	0.014982
33	0.983166	0.0336675	0.0168337
34	0.977345	0.0453095	0.0226547
35	0.970625	0.0587507	0.0293753
36	0.961234	0.0775315	0.0387657
37	0.972073	0.0558546	0.0279273
38	0.963592	0.0728159	0.0364079
39	0.958205	0.0835907	0.0417954
40	0.959141	0.0817173	0.0408587
41	0.94858	0.10284	0.0514201
42	0.945947	0.108106	0.0540528
43	0.93274	0.134521	0.0672603
44	0.921878	0.156244	0.078122
45	0.903669	0.192661	0.0963307
46	0.917483	0.165033	0.0825167
47	0.89842	0.203159	0.10158
48	0.87671	0.24658	0.12329
49	0.901385	0.197229	0.0986147
50	0.897554	0.204892	0.102446
51	0.878983	0.242034	0.121017
52	0.856113	0.287773	0.143887
53	0.838043	0.323914	0.161957
54	0.829408	0.341184	0.170592
55	0.815376	0.369248	0.184624
56	0.795736	0.408528	0.204264
57	0.781441	0.437118	0.218559
58	0.74911	0.50178	0.25089
59	0.792059	0.415883	0.207941
60	0.785296	0.429407	0.214704
61	0.808351	0.383298	0.191649
62	0.804132	0.391736	0.195868
63	0.87124	0.257521	0.12876
64	0.85646	0.28708	0.14354
65	0.844143	0.311713	0.155857
66	0.94053	0.11894	0.0594701
67	0.939384	0.121232	0.0606159
68	0.94704	0.105921	0.0529604
69	0.94274	0.11452	0.0572602
70	0.935703	0.128594	0.0642968
71	0.923914	0.152171	0.0760857
72	0.942354	0.115293	0.0576464
73	0.930845	0.13831	0.0691549
74	0.916994	0.166011	0.0830057
75	0.916365	0.16727	0.0836348
76	0.901462	0.197077	0.0985385
77	0.918312	0.163376	0.0816881
78	0.903524	0.192952	0.0964758
79	0.891315	0.217369	0.108685
80	0.88933	0.221339	0.11067
81	0.870252	0.259497	0.129748
82	0.849689	0.300622	0.150311
83	0.841943	0.316115	0.158057
84	0.820763	0.358474	0.179237
85	0.795409	0.409183	0.204591
86	0.774814	0.450372	0.225186
87	0.746425	0.50715	0.253575
88	0.715817	0.568366	0.284183
89	0.794058	0.411883	0.205942
90	0.832654	0.334693	0.167346
91	0.808428	0.383144	0.191572
92	0.786638	0.426724	0.213362
93	0.760574	0.478852	0.239426
94	0.741829	0.516343	0.258171
95	0.71947	0.561061	0.28053
96	0.694258	0.611484	0.305742
97	0.667937	0.664126	0.332063
98	0.667671	0.664658	0.332329
99	0.633986	0.732028	0.366014
100	0.62639	0.747219	0.37361
101	0.600043	0.799915	0.399957
102	0.572377	0.855245	0.427623
103	0.641884	0.716232	0.358116
104	0.636572	0.726857	0.363428
105	0.654769	0.690462	0.345231
106	0.630345	0.73931	0.369655
107	0.633306	0.733388	0.366694
108	0.66224	0.67552	0.33776
109	0.638845	0.72231	0.361155
110	0.613337	0.773327	0.386663
111	0.625518	0.748964	0.374482
112	0.634395	0.73121	0.365605
113	0.630144	0.739711	0.369856
114	0.714381	0.571238	0.285619
115	0.684506	0.630988	0.315494
116	0.660525	0.678949	0.339475
117	0.628384	0.743232	0.371616
118	0.605616	0.788768	0.394384
119	0.572015	0.85597	0.427985
120	0.539915	0.920171	0.460085
121	0.505431	0.989139	0.494569
122	0.470701	0.941403	0.529299
123	0.442492	0.884983	0.557508
124	0.40885	0.817699	0.59115
125	0.404806	0.809612	0.595194
126	0.376355	0.752711	0.623645
127	0.370039	0.740079	0.629961
128	0.483039	0.966078	0.516961
129	0.464083	0.928166	0.535917
130	0.452637	0.905274	0.547363
131	0.447407	0.894814	0.552593
132	0.413199	0.826398	0.586801
133	0.423396	0.846793	0.576604
134	0.394969	0.789938	0.605031
135	0.401539	0.803079	0.598461
136	0.384619	0.769238	0.615381
137	0.356224	0.712448	0.643776
138	0.332468	0.664935	0.667532
139	0.307055	0.614111	0.692945
140	0.282643	0.565287	0.717357
141	0.255138	0.510277	0.744862
142	0.262375	0.524749	0.737625
143	0.23846	0.476921	0.76154
144	0.214868	0.429737	0.785132
145	0.203307	0.406614	0.796693
146	0.193409	0.386819	0.806591
147	0.203359	0.406718	0.796641
148	0.223711	0.447422	0.776289
149	0.239556	0.479113	0.760444
150	0.239147	0.478294	0.760853
151	0.215116	0.430233	0.784884
152	0.193158	0.386315	0.806842
153	0.19901	0.39802	0.80099
154	0.211437	0.422874	0.788563
155	0.19888	0.397761	0.80112
156	0.174969	0.349938	0.825031
157	0.15674	0.31348	0.84326
158	0.248447	0.496894	0.751553
159	0.266845	0.53369	0.733155
160	0.240612	0.481225	0.759388
161	0.216306	0.432611	0.783694
162	0.193847	0.387694	0.806153
163	0.174644	0.349287	0.825356
164	0.295849	0.591697	0.704151
165	0.290787	0.581573	0.709213
166	0.286865	0.57373	0.713135
167	0.257898	0.515796	0.742102
168	0.237946	0.475892	0.762054
169	0.302132	0.604265	0.697868
170	0.336951	0.673903	0.663049
171	0.306651	0.613303	0.693349
172	0.301156	0.602313	0.698844
173	0.476483	0.952967	0.523517
174	0.464465	0.928929	0.535535
175	0.490375	0.98075	0.509625
176	0.505344	0.989311	0.494656
177	0.561576	0.876848	0.438424
178	0.528794	0.942413	0.471206
179	0.506797	0.986407	0.493203
180	0.508438	0.983123	0.491562
181	0.470965	0.94193	0.529035
182	0.463523	0.927046	0.536477
183	0.425636	0.851272	0.574364
184	0.398197	0.796395	0.601803
185	0.397863	0.795727	0.602137
186	0.384325	0.76865	0.615675
187	0.350116	0.700233	0.649884
188	0.325968	0.651936	0.674032
189	0.292345	0.584691	0.707655
190	0.27152	0.54304	0.72848
191	0.284808	0.569617	0.715192
192	0.261738	0.523476	0.738262
193	0.280664	0.561329	0.719336
194	0.266677	0.533355	0.733323
195	0.265976	0.531953	0.734024
196	0.270315	0.54063	0.729685
197	0.309281	0.618562	0.690719
198	0.292226	0.584451	0.707774
199	0.332751	0.665502	0.667249
200	0.30147	0.60294	0.69853
201	0.350991	0.701982	0.649009
202	0.320991	0.641983	0.679009
203	0.371062	0.742124	0.628938
204	0.331779	0.663558	0.668221
205	0.295804	0.591607	0.704196
206	0.276581	0.553162	0.723419
207	0.243342	0.486685	0.756658
208	0.281642	0.563283	0.718358
209	0.248191	0.496381	0.751809
210	0.255441	0.510882	0.744559
211	0.27582	0.55164	0.72418
212	0.287491	0.574981	0.712509
213	0.256849	0.513697	0.743151
214	0.32386	0.647721	0.67614
215	0.294159	0.588318	0.705841
216	0.276339	0.552678	0.723661
217	0.311393	0.622786	0.688607
218	0.278589	0.557179	0.721411
219	0.265116	0.530232	0.734884
220	0.28996	0.57992	0.71004
221	0.303067	0.606134	0.696933
222	0.303025	0.60605	0.696975
223	0.286779	0.573558	0.713221
224	0.248746	0.497491	0.751254
225	0.247182	0.494364	0.752818
226	0.283433	0.566866	0.716567
227	0.509196	0.981608	0.490804
228	0.484216	0.968432	0.515784
229	0.459351	0.918703	0.540649
230	0.447531	0.895061	0.552469
231	0.404428	0.808855	0.595572
232	0.446956	0.893912	0.553044
233	0.393341	0.786682	0.606659
234	0.351453	0.702906	0.648547
235	0.361524	0.723048	0.638476
236	0.329187	0.658374	0.670813
237	0.298517	0.597034	0.701483
238	0.248161	0.496321	0.751839
239	0.400691	0.801383	0.599309
240	0.386214	0.772428	0.613786
241	0.358362	0.716723	0.641638
242	0.494661	0.989323	0.505339
243	0.425785	0.85157	0.574215
244	0.358916	0.717832	0.641084
245	0.417288	0.834576	0.582712
246	0.354519	0.709038	0.645481
247	0.28688	0.57376	0.71312
248	0.510485	0.97903	0.489515
249	0.423778	0.847556	0.576222
250	0.337806	0.675611	0.662194
251	0.423591	0.847181	0.576409
252	0.645664	0.708673	0.354336
253	0.551899	0.896202	0.448101
254	0.473719	0.947439	0.526281
255	0.429245	0.85849	0.570755
256	0.308332	0.616664	0.691668
257	0.1879	0.375801	0.8121

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	1	0.00398406	OK
5% type I error level	10	0.0398406	OK
10% type I error level	19	0.0756972	OK