Multiple Linear Regression - Estimated Regression Equation

Belonging[t] = + 65.5915982474038 + 0.889722068030321Happiness[t] -0.570504968361378Depression[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)	65.5915982474038	8.598315	7.6284	0	0
Happiness	0.889722068030321	0.411034	2.1646	0.031911	0.015955
Depression	-0.570504968361378	0.303472	-1.8799	0.061947	0.030974

Multiple Linear Regression - Regression Statistics
Multiple R	0.318675284277338
R-squared	0.101553936809242
Adjusted R-squared	0.0902527284672199
F-TEST (value)	8.98611314257667
F-TEST (DF numerator)	2
F-TEST (DF denominator)	159
p-value	0.000200731161597245
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	10.2279857720870
Sum Squared Residuals	16633.2591796883

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	53	71.2016475794921	-18.2016475794921
2	86	75.3310408199744	10.6689591800256
3	66	67.391471438678	-1.39147143867804
4	67	69.4222034434311	-2.42220344343110
5	76	67.8465470003	8.15345299970001
6	78	74.760535851613	3.23946414838697
7	53	65.496597895878	-12.4965978958780
8	80	71.7721525478531	8.22784745214688
9	74	73.2323795842448	0.767620415755177
10	76	71.5208646791607	4.47913532083931
11	79	75.0118237203055	3.98817627969454
12	54	77.9322777930889	-23.9322777930889
13	67	65.9312444022863	1.06875559771367
14	54	71.8400817788296	-17.8400817788296
15	87	75.9015457883358	11.0984542116642
16	58	70.060637642769	-12.060637642769
17	75	70.060637642769	4.93936235723101
18	88	74.4413187519441	13.5586812480559
19	64	72.3426575162145	-8.3426575162145
20	57	72.410586747191	-15.410586747191
21	66	77.6130606934199	-11.6130606934199
22	68	67.391471438678	0.608528561321973
23	54	71.2016475794917	-17.2016475794917
24	56	68.2811935067083	-12.2811935067083
25	86	74.4413187519441	11.5586812480559
26	80	68.4645521444243	11.5354478555757
27	76	73.5515966839138	2.44840331608623
28	69	69.4901326744076	-0.490132674407613
29	78	70.9503597107993	7.04964028920069
30	67	67.9619764070394	-0.961976407039405
31	80	74.6926066206365	5.30739337936348
32	54	68.6004106063773	-14.6004106063773
33	71	75.0118237203055	-4.01182372030546
34	84	72.6618746158834	11.3381253841166
35	74	70.6311426111304	3.36885738886963
36	71	75.2631115889979	-4.2631115889979
37	63	62.1889974924491	0.811002507550883
38	71	72.091369647522	-1.09136964752207
39	76	75.0118237203055	0.988176279694535
40	69	71.4529354481842	-2.45293544818418
41	74	73.8028845526062	0.197115447393799
42	75	71.8400817788296	3.15991822117037
43	54	75.2631115889979	-21.2631115889979
44	52	68.2811935067083	-16.2811935067083
45	69	69.9927084117925	-0.992708411792482
46	68	67.9619764070394	0.038023592960595
47	65	73.8028845526062	-8.8028845526062
48	75	72.6618746158834	2.33812538411655
49	74	72.1592988784986	1.84070112150142
50	75	70.8824304798228	4.1175695201772
51	72	74.1221016522751	-2.12210165227514
52	67	70.060637642769	-3.06063764276899
53	63	65.1094515652325	-2.10945156523252
54	62	68.2811935067083	-6.28119350670835
55	63	69.9927084117925	-6.99270841179248
56	76	72.091369647522	3.90863035247793
57	74	72.410586747191	1.58941325280899
58	67	73.8028845526062	-6.8028845526062
59	73	70.5632133801539	2.43678661984614
60	70	67.710688538347	2.28931146165303
61	53	61.2992754244188	-8.2992754244188
62	77	70.3119255114614	6.68807448853858
63	77	68.5324813754008	8.46751862459922
64	52	70.060637642769	-18.060637642769
65	54	71.5208646791607	-17.5208646791607
66	80	68.2132642757318	11.7867357242682
67	66	65.6799565335939	0.320043466406106
68	73	69.4222034434311	3.57779655656890
69	63	71.5208646791607	-8.52086467916069
70	69	70.9503597107993	-1.95035971079931
71	67	70.6311426111304	-3.63114261113037
72	54	71.2695768104683	-17.2695768104683
73	81	71.5208646791607	9.4791353208393
74	69	73.2323795842448	-4.23237958424482
75	84	70.8824304798228	13.1175695201772
76	80	65.4286686649015	14.5713313350985
77	70	73.3003088152213	-3.30030881522133
78	69	67.4594006696545	1.54059933034546
79	77	71.5208646791607	5.47913532083931
80	54	72.0234404165456	-18.0234404165456
81	79	72.6618746158834	6.33812538411655
82	30	74.1221016522751	-44.1221016522751
83	71	73.8028845526062	-2.8028845526062
84	73	72.9810917155524	0.0189082844476121
85	72	72.091369647522	-0.0913696475220673
86	77	70.6311426111304	6.36885738886963
87	75	71.5208646791607	3.47913532083931
88	69	71.2016475794917	-2.20164757949175
89	54	68.6004106063773	-14.6004106063773
90	70	59.2685434196657	10.7314565803343
91	73	73.3003088152213	-0.300308815221332
92	54	68.6004106063773	-14.6004106063773
93	77	71.5208646791607	5.47913532083931
94	82	69.4901326744076	12.5098673255924
95	80	71.4529354481842	8.54706455181582
96	80	73.5515966839138	6.44840331608623
97	69	67.1401835699856	1.85981643001441
98	78	71.7721525478531	6.22784745214688
99	81	74.4413187519441	6.55868124805591
100	76	73.2323795842448	2.76762041575518
101	76	75.0118237203055	0.988176279694535
102	73	67.1401835699856	5.8598164300144
103	85	72.9810917155524	12.0189082844476
104	66	69.1029863437622	-3.10298634376216
105	79	69.8093497740766	9.19065022592344
106	68	62.7595024608105	5.2404975391895
107	76	73.5515966839138	2.44840331608623
108	71	69.8093497740766	1.19065022592344
109	54	65.9312444022863	-11.9312444022863
110	46	60.7966996870339	-14.7966996870339
111	82	70.9503597107993	11.0496402892007
112	74	66.8209664703166	7.17903352968335
113	88	70.8824304798228	17.1175695201772
114	38	69.4901326744076	-31.4901326744076
115	76	74.760535851613	1.23946414838697
116	86	74.1221016522751	11.8778983477249
117	54	70.060637642769	-16.060637642769
118	70	70.6311426111304	-0.631142611130368
119	69	72.9131624845759	-3.91316248457588
120	90	69.4901326744076	20.5098673255924
121	54	67.710688538347	-13.7106885383470
122	76	70.060637642769	5.93936235723101
123	89	72.6618746158834	16.3381253841166
124	76	74.3733895209676	1.62661047903242
125	73	72.6618746158834	0.338125384116555
126	79	70.8824304798228	8.1175695201772
127	90	76.1528336570282	13.8471663429718
128	74	75.0118237203055	-1.01182372030547
129	81	76.2207628880047	4.77923711199527
130	72	71.5208646791607	0.47913532083931
131	71	70.8824304798228	0.117569520177197
132	66	62.1889974924491	3.81100250755088
133	77	73.2323795842448	3.76762041575518
134	65	70.379854742438	-5.37985474243793
135	74	72.091369647522	1.90863035247793
136	82	71.8400817788296	10.1599182211704
137	54	62.2569267234256	-8.25692672342563
138	63	70.060637642769	-7.06063764276899
139	54	66.2504615019553	-12.2504615019553
140	64	72.6618746158834	-8.66187461588345
141	69	70.3119255114614	-1.31192551146142
142	54	73.2323795842448	-19.2323795842448
143	84	71.8400817788296	12.1599182211704
144	86	71.2016475794917	14.7983524205083
145	77	72.091369647522	4.90863035247793
146	89	73.5515966839138	15.4484033160862
147	76	72.9810917155524	3.01890828444761
148	60	67.9619764070394	-7.9619764070394
149	75	69.9927084117925	5.00729158820752
150	73	62.7595024608105	10.2404975391895
151	85	72.9810917155524	12.0189082844476
152	79	67.4594006696545	11.5405993303455
153	71	74.6926066206365	-3.69260662063652
154	72	69.4222034434311	2.57779655656890
155	69	62.7595024608105	6.2404975391895
156	78	66.8888957012932	11.1111042987068
157	54	68.6004106063773	-14.6004106063773
158	69	70.060637642769	-1.06063764276899
159	81	76.2207628880047	4.77923711199527
160	84	72.0234404165456	11.9765595834544
161	84	65.9991736332628	18.0008263667372
162	69	68.0299056380159	0.970094361984086

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
6	0.627800612163592	0.744398775672816	0.372199387836408
7	0.666406205155663	0.667187589688674	0.333593794844337
8	0.635918433089962	0.728163133820075	0.364081566910038
9	0.51073579479163	0.97852841041674	0.48926420520837
10	0.407148068765248	0.814296137530497	0.592851931234752
11	0.303865075601501	0.607730151203003	0.696134924398499
12	0.814769629789204	0.370460740421592	0.185230370210796
13	0.749315088564422	0.501369822871156	0.250684911435578
14	0.819358258646258	0.361283482707484	0.180641741353742
15	0.84051997586439	0.318960048271218	0.159480024135609
16	0.831991329649691	0.336017340700617	0.168008670350309
17	0.800394352943246	0.399211294113509	0.199605647056754
18	0.833794712434333	0.332410575131334	0.166205287565667
19	0.805310040192938	0.389379919614124	0.194689959807062
20	0.837464631818143	0.325070736363713	0.162535368181857
21	0.830734479059394	0.338531041881211	0.169265520940606
22	0.788102453041817	0.423795093916366	0.211897546958183
23	0.827677853654329	0.344644292691342	0.172322146345671
24	0.816192037779036	0.367615924441928	0.183807962220964
25	0.83923902489764	0.32152195020472	0.16076097510236
26	0.867914437217962	0.264171125564076	0.132085562782038
27	0.83743945200007	0.325121095999861	0.162560547999930
28	0.7983471115103	0.403305776979399	0.201652888489699
29	0.783726758206316	0.432546483587367	0.216273241793684
30	0.737653016187678	0.524693967624643	0.262346983812322
31	0.70449972850464	0.59100054299072	0.29550027149536
32	0.728732450632513	0.542535098734975	0.271267549367487
33	0.683946989855047	0.632106020289906	0.316053010144953
34	0.70217763920379	0.595644721592421	0.297822360796210
35	0.661851164593846	0.676297670812307	0.338148835406154
36	0.617977197553547	0.764045604892906	0.382022802446453
37	0.569773357558837	0.860453284882325	0.430226642441163
38	0.515630976494514	0.968738047010971	0.484369023505486
39	0.462971167878528	0.925942335757055	0.537028832121472
40	0.41154263506721	0.82308527013442	0.58845736493279
41	0.360383889808767	0.720767779617535	0.639616110191233
42	0.320745395501026	0.641490791002052	0.679254604498974
43	0.474263410250183	0.948526820500367	0.525736589749817
44	0.53221509496057	0.93556981007886	0.46778490503943
45	0.481757117469672	0.963514234939345	0.518242882530328
46	0.432805365436511	0.865610730873023	0.567194634563489
47	0.411468021853911	0.822936043707822	0.588531978146089
48	0.369624922794451	0.739249845588901	0.630375077205549
49	0.327049645253696	0.654099290507393	0.672950354746304
50	0.295883893221119	0.591767786442238	0.704116106778881
51	0.255334754198501	0.510669508397001	0.744665245801499
52	0.218838000290221	0.437676000580441	0.781161999709779
53	0.184581028920836	0.369162057841671	0.815418971079164
54	0.161398716811213	0.322797433622425	0.838601283188787
55	0.142525596777764	0.285051193555527	0.857474403222236
56	0.1232516073354	0.2465032146708	0.8767483926646
57	0.101703894346751	0.203407788693503	0.898296105653249
58	0.088627345786843	0.177254691573686	0.911372654213157
59	0.0736964787297675	0.147392957459535	0.926303521270232
60	0.0602264629547096	0.120452925909419	0.93977353704529
61	0.0532024111407584	0.106404822281517	0.946797588859242
62	0.0486711827312047	0.0973423654624093	0.951328817268795
63	0.0478397849988057	0.0956795699976114	0.952160215001194
64	0.0759886154750654	0.151977230950131	0.924011384524935
65	0.110489256037214	0.220978512074427	0.889510743962787
66	0.122196739698059	0.244393479396118	0.877803260301941
67	0.100957523460073	0.201915046920146	0.899042476539927
68	0.0849760179899104	0.169952035979821	0.91502398201009
69	0.0780555393948009	0.156111078789602	0.921944460605199
70	0.0631398161898766	0.126279632379753	0.936860183810123
71	0.0512637817561778	0.102527563512356	0.948736218243822
72	0.0748950920272416	0.149790184054483	0.925104907972758
73	0.0769169815143366	0.153833963028673	0.923083018485663
74	0.0639524887871246	0.127904977574249	0.936047511212875
75	0.076697727788887	0.153395455577774	0.923302272211113
76	0.102674342631075	0.205348685262150	0.897325657368925
77	0.0863785970789504	0.172757194157901	0.91362140292105
78	0.0708020733893181	0.141604146778636	0.929197926610682
79	0.0616022785692453	0.123204557138491	0.938397721430755
80	0.0965738871988602	0.193147774397720	0.90342611280114
81	0.0863781429385428	0.172756285877086	0.913621857061457
82	0.757527697650848	0.484944604698304	0.242472302349152
83	0.727970867532501	0.544058264934998	0.272029132467499
84	0.692699116078577	0.614601767842846	0.307300883921423
85	0.654649709293039	0.690700581413923	0.345350290706961
86	0.62878836020055	0.7424232795989	0.37121163979945
87	0.59138770822902	0.81722458354196	0.40861229177098
88	0.551995014934709	0.896009970130582	0.448004985065291
89	0.60781242499266	0.78437515001468	0.39218757500734
90	0.622023426018375	0.75595314796325	0.377976573981625
91	0.584570938660633	0.830858122678735	0.415429061339367
92	0.641947263951387	0.716105472097227	0.358052736048613
93	0.610379099423635	0.77924180115273	0.389620900576365
94	0.628904586405482	0.742190827189035	0.371095413594518
95	0.612801048033695	0.774397903932609	0.387198951966305
96	0.583820613512308	0.832358772975384	0.416179386487692
97	0.539224295575337	0.921551408849325	0.460775704424662
98	0.507399863084537	0.985200273830926	0.492600136915463
99	0.477205741940656	0.954411483881312	0.522794258059344
100	0.434631743721534	0.869263487443067	0.565368256278466
101	0.394580308626363	0.789160617252726	0.605419691373637
102	0.363333897406754	0.726667794813509	0.636666102593246
103	0.368773492021713	0.737546984043427	0.631226507978287
104	0.330243739638688	0.660487479277375	0.669756260361312
105	0.316260278130850	0.632520556261701	0.68373972186915
106	0.289629082827581	0.579258165655162	0.710370917172419
107	0.252792866856312	0.505585733712625	0.747207133143688
108	0.216444948959499	0.432889897918997	0.783555051040501
109	0.22848789405831	0.45697578811662	0.77151210594169
110	0.262238811293822	0.524477622587643	0.737761188706178
111	0.258936887093362	0.517873774186725	0.741063112906638
112	0.236355402922266	0.472710805844532	0.763644597077734
113	0.295899498478121	0.591798996956243	0.704100501521879
114	0.743663450566094	0.512673098867812	0.256336549433906
115	0.708429011561247	0.583141976877505	0.291570988438753
116	0.707576014000258	0.584847971999484	0.292423985999742
117	0.802072530137226	0.395854939725549	0.197927469862774
118	0.767446325598247	0.465107348803507	0.232553674401753
119	0.736281084015391	0.527437831969218	0.263718915984609
120	0.829114702466917	0.341770595066165	0.170885297533083
121	0.873135100551238	0.253729798897523	0.126864899448762
122	0.847607023857486	0.304785952285029	0.152392976142514
123	0.881370807740652	0.237258384518696	0.118629192259348
124	0.851475799137123	0.297048401725755	0.148524200862877
125	0.818223122279291	0.363553755441417	0.181776877720709
126	0.79937732332971	0.401245353340582	0.200622676670291
127	0.819255127500834	0.361489744998332	0.180744872499166
128	0.78350666334914	0.432986673301721	0.216493336650860
129	0.740406027193141	0.519187945613718	0.259593972806859
130	0.692728306493556	0.614543387012888	0.307271693506444
131	0.638197880108284	0.723604239783431	0.361802119891716
132	0.584110825185605	0.83177834962879	0.415889174814395
133	0.527298596544129	0.945402806911742	0.472701403455871
134	0.512895801636292	0.974208396727415	0.487104198363708
135	0.451170060837366	0.902340121674732	0.548829939162634
136	0.414031621613112	0.828063243226224	0.585968378386888
137	0.490195631290096	0.980391262580192	0.509804368709904
138	0.49610177787343	0.99220355574686	0.50389822212657
139	0.595258782468067	0.809482435063865	0.404741217531933
140	0.604284720412977	0.791430559174046	0.395715279587023
141	0.541017721379169	0.917964557241663	0.458982278620831
142	0.80318420373978	0.39363159252044	0.19681579626022
143	0.766340437161036	0.467319125677928	0.233659562838964
144	0.784646265615082	0.430707468769835	0.215353734384918
145	0.72071630213408	0.55856739573184	0.27928369786592
146	0.759592003433977	0.480815993132046	0.240407996566023
147	0.686325897205368	0.627348205589264	0.313674102794632
148	0.717161466476863	0.565677067046274	0.282838533523137
149	0.634130638729912	0.731738722540176	0.365869361270088
150	0.54964136094937	0.90071727810126	0.45035863905063
151	0.526993414896247	0.946013170207507	0.473006585103753
152	0.459251806228762	0.918503612457523	0.540748193771238
153	0.371811214674754	0.743622429349509	0.628188785325246
154	0.264106604552904	0.528213209105807	0.735893395447096
155	0.167449889236602	0.334899778473204	0.832550110763398
156	0.115286820959986	0.230573641919971	0.884713179040014

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	2	0.0132450331125828	OK