Multiple Linear Regression - Estimated Regression Equation

Belonging[t] = + 62.5511357635815 + 0.925603289655825Happiness[t] -0.635347076551754Depression[t] + 0.0414054045932947t + 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)	62.5511357635815	8.56179	7.3058	0	0
Happiness	0.925603289655825	0.405143	2.2846	0.023665	0.011833
Depression	-0.635347076551754	0.300117	-2.117	0.035826	0.017913
t	0.0414054045932947	0.017081	2.4241	0.016474	0.008237

Multiple Linear Regression - Regression Statistics
Multiple R	0.365747082062413
R-squared	0.133770928037170
Adjusted R-squared	0.117323540594837
F-TEST (value)	8.13326301859167
F-TEST (DF numerator)	3
F-TEST (DF denominator)	158
p-value	4.53014548817965e-05
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	10.0746625058079
Sum Squared Residuals	16036.8142877371

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	53	67.9268223047357	-14.9268223047357
2	86	72.3059879445037	13.6940120554963
3	66	63.962129091851	2.03787090814907
4	67	66.1998319392035	0.800168060796447
5	76	64.2255268134544	11.7744731865457
6	78	71.8362624863251	6.16373751367492
7	53	61.8217839667775	-8.82178396677753
8	80	68.8520072134401	11.1479927865599
9	74	70.454362984241	3.545637015759
10	76	68.589727159179	7.41027284082097
11	79	72.3883803727392	6.61161962726076
12	54	75.5516865097477	-21.5516865097477
13	67	62.8152327715763	4.18476722842372
14	54	69.0456049906563	-15.0456049906563
15	87	73.4796052807682	13.5203947192318
16	58	67.2772092205312	-9.27720922053122
17	75	67.3186146251245	7.68138537487549
18	88	72.0428711283406	15.9571288716595
19	64	69.9428137405181	-5.94281374051812
20	57	69.9293844947678	-12.9293844947678
21	66	75.6340789379833	-9.63407893798327
22	68	64.7488317791235	3.25116822087649
23	54	68.8377412057878	-14.8377412057878
24	56	65.7572458779659	-9.75724587796593
25	86	72.3327089604936	13.6672910395064
26	80	66.2399822009438	13.7600177990562
27	76	71.4899164800244	4.51008351997563
28	69	67.138726999099	1.86127300090100
29	78	68.7410827698999	9.25891723010012
30	67	65.7154220924216	1.28457790757837
31	80	72.9262322515011	7.07376774849894
32	54	66.3787453278164	-12.3787453278164
33	71	73.2992992737917	-2.29929927379172
34	84	70.8541510225216	13.1458489774784
35	74	68.6992589843556	5.30074101564443
36	71	73.7686063510193	-2.76860635101929
37	63	59.7066238094008	3.29337619059924
38	71	70.384425564343	0.615574435656963
39	76	73.5477317013515	2.45226829864851
40	69	69.8867239473215	-0.886723947321485
41	74	72.4146830077782	1.58531699222182
42	75	70.2049563192685	4.79504368073147
43	54	74.0584441831724	-20.0584441831724
44	52	66.5853539698318	-14.5853539698318
45	69	68.5328006040804	0.467199395919621
46	68	66.3779085659143	1.62209143408566
47	65	72.663115435338	-7.66311543533795
48	75	71.4338266868277	3.56617331317226
49	74	70.7850503645257	3.21494963547433
50	75	69.6654309167027	5.33456908329732
51	72	73.1189932668152	-1.11899326681520
52	67	68.7678037858898	-1.76780378588983
53	63	63.4910110153086	-0.491011015308632
54	62	66.9994080157648	-4.99940801576477
55	63	68.9468546500133	-5.94685465001333
56	76	71.1297228470223	4.87027715297766
57	74	71.4613844647197	2.53861553528029
58	67	73.1185748858642	-6.11857488586419
59	73	69.7478233449383	3.25217665506174
60	70	66.6124933667728	3.38750663322722
61	53	59.774750229984	-6.774750229984
62	77	69.5269486952705	7.47305130472954
63	77	67.7171475205521	9.2828524794479
64	52	69.2646686410094	-17.2646686410094
65	54	70.8670244118102	-16.8670244118102
66	80	67.5511075212279	12.4488924787721
67	66	64.7060337561665	1.29396624383349
68	73	68.8497778331744	4.1502221668256
69	63	71.0326460301834	-8.03264603018342
70	69	70.438704358225	-1.43870435822496
71	67	70.1898535497142	-3.18985354971418
72	54	70.8117713805156	-16.8117713805156
73	81	71.1982676485566	9.8017323514434
74	69	73.1457142828052	-4.14571428280516
75	84	70.700566031535	13.2994339684650
76	80	64.7335915340585	15.2664084659415
77	70	73.2150958462414	-3.21509584624143
78	69	67.0126997860044	1.98730021399560
79	77	71.4467000761164	5.55329992388364
80	54	72.178287207605	-18.1782872076050
81	79	72.8002050384065	6.19979496159354
82	30	74.4025608092073	-44.4025608092073
83	71	74.1537100006966	-3.15371000069656
84	73	73.2146774652904	-0.214677465290417
85	72	72.3304795802279	-0.330479580227887
86	77	70.8109346186136	6.1890653813864
87	75	71.7779433128627	3.22205668713728
88	69	71.529092504352	-2.52909250435195
89	54	68.7388533896342	-14.7388533896342
90	70	58.7792095204302	11.2207904795698
91	73	73.7947715105475	-0.794771510547551
92	54	68.863069603414	-14.8630696034140
93	77	72.0263757404225	4.97362425957751
94	82	69.8714837022565	12.1285162977435
95	80	72.1640211999527	7.8359788000473
96	80	74.3468893969617	5.65311060303829
97	69	67.509146260173	1.49085373982707
98	78	72.5784936268366	5.42150637316335
99	81	75.3967089003974	5.60329109960258
100	76	74.2222548022308	1.77774519776918
101	76	76.1148667861358	-0.114866786135760
102	73	67.7161732831394	5.2838267168606
103	85	74.001380152563	10.9986198474370
104	66	70.0501161854289	-4.05011618542894
105	79	70.6171993658868	8.38280063411324
106	68	63.1989438028898	4.80105619711015
107	76	74.802348847488	1.19765115251205
108	71	70.7414155796667	0.258584420333352
109	54	66.7901516125326	-12.7901516125326
110	46	61.11343332816	-15.1134333281601
111	82	72.13632594655	9.86367405344996
112	74	67.8399711159683	6.16002888403172
113	88	72.2739714060802	15.7260285939198
114	38	70.6995917941223	-32.6995917941223
115	76	76.3494515869942	-0.349451586994203
116	86	75.8103445653794	10.1896554346206
117	54	71.459155084454	-17.459155084454
118	70	72.135907565599	-2.13590756559903
119	69	74.7187012763993	-5.71870127639934
120	90	70.9480242216821	19.0519757783179
121	54	69.1382230469638	-15.1382230469638
122	76	71.6661821074205	4.33381789257954
123	89	74.5392320313248	14.4607679686752
124	76	76.4866786655734	-0.486678665573397
125	73	74.6220428405114	-1.62204284051143
126	79	72.812241665793	6.18775833420693
127	90	78.462101458665	11.5378985413351
128	74	77.2328127101547	-3.23281271015472
129	81	78.490077617508	2.50992238249209
130	72	73.5583757103744	-1.55837571037439
131	71	73.0192686887596	-2.01926868875955
132	66	63.6401372457638	2.35986275423625
133	77	75.5886331538095	1.41136684619046
134	65	72.453303175644	-7.45330317564406
135	74	74.4007498098926	-0.400749809892622
136	82	74.0970643510382	7.90293564896177
137	54	63.7923296183866	-9.79232961838661
138	63	72.3286685809132	-9.32866858091317
139	54	68.3225699634355	-14.3225699634355
140	64	75.2431239094109	-11.2431239094108
141	69	72.7979756581407	-3.79797565814074
142	54	75.9612817951492	-21.9612817951492
143	84	74.3869021831913	9.6130978168087
144	86	73.8477951615764	12.1522048384236
145	77	74.8148038558256	2.18519614417443
146	89	76.4171596266264	12.5828403733736
147	76	75.823217954668	0.176782045332018
148	60	70.6012598344304	-10.6012598344304
149	75	72.838962681783	2.16103731821697
150	73	65.0207816049948	7.97921839500519
151	85	75.9888395730412	9.01116042695884
152	79	70.0766997259082	8.9233002740918
153	71	77.977691611883	-6.97769161188301
154	72	72.4106426281977	-0.410642628197746
155	69	65.2278086279613	3.77219137203871
156	78	69.6069742677296	8.39302573227036
157	54	71.5544209019782	-17.5544209019782
158	69	73.156776672779	-4.15677667277907
159	81	79.7322397553068	1.26776024469325
160	84	75.4907195750686	8.5092804249314
161	84	68.8883980010403	15.1116019989597
162	69	71.1261008483929	-2.12610084839291

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
7	0.802443379726021	0.395113240547958	0.197556620273979
8	0.703300751647251	0.593398496705498	0.296699248352749
9	0.613489915357881	0.773020169284238	0.386510084642119
10	0.488229015945317	0.976458031890635	0.511770984054682
11	0.397035394802989	0.794070789605977	0.602964605197011
12	0.880822588199103	0.238354823601794	0.119177411800897
13	0.833481791093288	0.333036417813425	0.166518208906712
14	0.858227372422462	0.283545255155075	0.141772627577538
15	0.897165556435136	0.205668887129729	0.102834443564864
16	0.876303742946226	0.247392514107548	0.123696257053774
17	0.8631081762873	0.273783647425400	0.136891823712700
18	0.89328710544078	0.213425789118441	0.106712894559221
19	0.871297096797706	0.257405806404588	0.128702903202294
20	0.88360021360424	0.232799572791519	0.116399786395760
21	0.866136571640335	0.267726856719331	0.133863428359665
22	0.838372368942621	0.323255262114757	0.161627631057379
23	0.846249237192924	0.307501525614152	0.153750762807076
24	0.815191232105391	0.369617535789217	0.184808767894609
25	0.873013765161725	0.25397246967655	0.126986234838275
26	0.906389483120741	0.187221033758518	0.0936105168792588
27	0.885255925071109	0.229488149857782	0.114744074928891
28	0.8546233434018	0.290753313196400	0.145376656598200
29	0.845662894871325	0.30867421025735	0.154337105128675
30	0.807498901887399	0.385002196225203	0.192501098112601
31	0.779315465609514	0.441369068780973	0.220684534390486
32	0.796964791172118	0.406070417655764	0.203035208827882
33	0.755783449322146	0.488433101355708	0.244216550677854
34	0.777659330278803	0.444681339442393	0.222340669721197
35	0.742800214991739	0.514399570016522	0.257199785008261
36	0.704009505656441	0.591980988687118	0.295990494343559
37	0.659056943749676	0.681886112500647	0.340943056250324
38	0.607866142796160	0.784267714407679	0.392133857203839
39	0.556753610992037	0.886492778015926	0.443246389007963
40	0.505416077328899	0.989167845342201	0.494583922671101
41	0.452943371212964	0.905886742425928	0.547056628787036
42	0.410483639364009	0.820967278728018	0.589516360635991
43	0.564491011422897	0.871017977154206	0.435508988577103
44	0.605283827663962	0.789432344672076	0.394716172336038
45	0.556041401517654	0.887917196964691	0.443958598482345
46	0.508406211867466	0.983187576265068	0.491593788132534
47	0.476642296500898	0.953284593001795	0.523357703499102
48	0.438308468579777	0.876616937159553	0.561691531420223
49	0.397831585755551	0.795663171511101	0.602168414244449
50	0.368260085303106	0.736520170606212	0.631739914696894
51	0.321953924516178	0.643907849032357	0.678046075483822
52	0.278826894014355	0.55765378802871	0.721173105985645
53	0.238570576119791	0.477141152239581	0.761429423880209
54	0.207413598313484	0.414827196626967	0.792586401686516
55	0.180860922119265	0.36172184423853	0.819139077880735
56	0.161264987455246	0.322529974910493	0.838735012544754
57	0.136388794701791	0.272777589403583	0.863611205298209
58	0.117135404225341	0.234270808450682	0.88286459577466
59	0.0993682712233182	0.198736542446636	0.900631728776682
60	0.0831379128828646	0.166275825765729	0.916862087117135
61	0.0718160995208143	0.143632199041629	0.928183900479186
62	0.0676221523892136	0.135244304778427	0.932377847610786
63	0.0682834137153751	0.136566827430750	0.931716586284625
64	0.0991352182298016	0.198270436459603	0.900864781770198
65	0.129567482454544	0.259134964909089	0.870432517545455
66	0.150853262217674	0.301706524435349	0.849146737782326
67	0.126828131566806	0.253656263133611	0.873171868433194
68	0.110263498546817	0.220526997093634	0.889736501453183
69	0.0975708782463324	0.195141756492665	0.902429121753668
70	0.0791022008387203	0.158204401677441	0.92089779916128
71	0.0636430629475352	0.127286125895070	0.936356937052465
72	0.0822468297572893	0.164493659514579	0.91775317024271
73	0.0899420223774442	0.179884044754888	0.910057977622556
74	0.0736258022687788	0.147251604537558	0.926374197731221
75	0.0942219478890844	0.188443895778169	0.905778052110916
76	0.132331837051449	0.264663674102898	0.867668162948551
77	0.110201096923000	0.220402193846000	0.889798903077
78	0.0917854029164382	0.183570805832876	0.908214597083562
79	0.0817828846392938	0.163565769278588	0.918217115360706
80	0.117419068744822	0.234838137489643	0.882580931255178
81	0.107785792790294	0.215571585580589	0.892214207209706
82	0.760218898484937	0.479562203030127	0.239781101515063
83	0.72786124175285	0.544277516494301	0.272138758247151
84	0.692443086515934	0.615113826968132	0.307556913484066
85	0.653916295258584	0.692167409482832	0.346083704741416
86	0.632711389868369	0.734577220263262	0.367288610131631
87	0.597121046488671	0.805757907022657	0.402878953511329
88	0.554989639972516	0.890020720054968	0.445010360027484
89	0.600547978639125	0.79890404272175	0.399452021360875
90	0.622196533422049	0.755606933155902	0.377803466577951
91	0.582995667899279	0.834008664201441	0.417004332100721
92	0.63138101823494	0.737237963530121	0.368618981765061
93	0.601838865459368	0.796322269081265	0.398161134540632
94	0.625180927277911	0.749638145444178	0.374819072722089
95	0.611994916005316	0.776010167989368	0.388005083994684
96	0.583444866647581	0.833110266704838	0.416555133352419
97	0.539575986017841	0.920848027964319	0.460424013982159
98	0.509216474933197	0.981567050133606	0.490783525066803
99	0.478066456474799	0.956132912949598	0.521933543525201
100	0.4338266804041	0.8676533608082	0.5661733195959
101	0.389621512840665	0.77924302568133	0.610378487159335
102	0.361863200810426	0.723726401620853	0.638136799189574
103	0.371273143164801	0.742546286329602	0.628726856835199
104	0.330596266643971	0.661192533287943	0.669403733356029
105	0.322108910359929	0.644217820719858	0.677891089640071
106	0.308424974712269	0.616849949424538	0.69157502528773
107	0.268834319694355	0.53766863938871	0.731165680305645
108	0.232282531397608	0.464565062795216	0.767717468602392
109	0.235233135017128	0.470466270034257	0.764766864982872
110	0.256640353118296	0.513280706236592	0.743359646881704
111	0.260012491452382	0.520024982904764	0.739987508547618
112	0.247500050932471	0.495000101864942	0.752499949067529
113	0.339470372429948	0.678940744859896	0.660529627570052
114	0.739703834777433	0.520592330445134	0.260296165222567
115	0.698468613722972	0.603062772554056	0.301531386277028
116	0.705734556814849	0.588530886370302	0.294265443185151
117	0.783550106542142	0.432899786915716	0.216449893457858
118	0.744329190183152	0.511341619633695	0.255670809816848
119	0.709169307176097	0.581661385647806	0.290830692823903
120	0.82107092746793	0.357858145064139	0.178929072532069
121	0.854305334381523	0.291389331236954	0.145694665618477
122	0.827493527387598	0.345012945224805	0.172506472612402
123	0.874150581261465	0.25169883747707	0.125849418738535
124	0.843381024426116	0.313237951147768	0.156618975573884
125	0.806650976482638	0.386698047034723	0.193349023517362
126	0.80226820245716	0.395463595085679	0.197731797542839
127	0.846370889234256	0.307258221531487	0.153629110765744
128	0.809140501793148	0.381718996413705	0.190859498206852
129	0.77187962263116	0.456240754737681	0.228120377368840
130	0.725317044232362	0.549365911535276	0.274682955767638
131	0.680659323058017	0.638681353883965	0.319340676941983
132	0.652659878106378	0.694680243787243	0.347340121893622
133	0.623994500528243	0.752010998943514	0.376005499471757
134	0.576969687909847	0.846060624180307	0.423030312090153
135	0.523330380213542	0.953339239572916	0.476669619786458
136	0.534751546861562	0.930496906276876	0.465248453138438
137	0.521925776082615	0.95614844783477	0.478074223917385
138	0.485089362584628	0.970178725169256	0.514910637415372
139	0.534892834556801	0.930214330886397	0.465107165443199
140	0.53471556888003	0.93056886223994	0.46528443111997
141	0.469114232457609	0.938228464915218	0.530885767542391
142	0.785315753988075	0.429368492023850	0.214684246011925
143	0.730829485579493	0.538341028841013	0.269170514420506
144	0.723829235251503	0.552341529496993	0.276170764748497
145	0.649701625352685	0.70059674929463	0.350298374647315
146	0.684516409036449	0.630967181927102	0.315483590963551
147	0.599299736610547	0.801400526778906	0.400700263389453
148	0.630294457573192	0.739411084853616	0.369705542426808
149	0.53419019901572	0.93161960196856	0.46580980098428
150	0.439403581149058	0.878807162298116	0.560596418850942
151	0.428253873406906	0.856507746813812	0.571746126593094
152	0.421411452383239	0.842822904766477	0.578588547616761
153	0.304519956781488	0.609039913562975	0.695480043218512
154	0.201887094425443	0.403774188850886	0.798112905574557
155	0.121299936006469	0.242599872012938	0.878700063993531

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	0	0	OK