Multiple Linear Regression - Estimated Regression Equation

Belonging_Final[t] = -4.15016520024616 -0.0138900563993642Connected[t] + 0.0563768650883617Separate[t] -0.0825593641025312Learning[t] -0.0101629601067501Software[t] -0.0560342490511005Happiness[t] + 0.102192401128386Depression[t] + 0.658887864782968Belonging[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)	-4.15016520024616	3.29525	-1.2594	0.209777	0.104889
Connected	-0.0138900563993642	0.060061	-0.2313	0.817417	0.408708
Separate	0.0563768650883617	0.056192	1.0033	0.317298	0.158649
Learning	-0.0825593641025312	0.10109	-0.8167	0.415366	0.207683
Software	-0.0101629601067501	0.102641	-0.099	0.921255	0.460628
Happiness	-0.0560342490511005	0.096111	-0.583	0.560736	0.280368
Depression	0.102192401128386	0.070719	1.445	0.150479	0.075239
Belonging	0.658887864782968	0.018119	36.3643	0	0

Multiple Linear Regression - Regression Statistics
Multiple R	0.950126542673743
R-squared	0.902740447093159
Adjusted R-squared	0.898319558324666
F-TEST (value)	204.198860085986
F-TEST (DF numerator)	7
F-TEST (DF denominator)	154
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	2.32622606183604
Sum Squared Residuals	833.344464377844

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	32	31.5903222664463	0.4096777335537
2	51	52.4592961970192	-1.45929619701917
3	42	39.9861670182274	2.01383298177257
4	41	40.6796961424973	0.320303857502687
5	46	47.5005374740057	-1.50053747400573
6	47	47.4346563626305	-0.434656362630515
7	37	31.7500321502951	5.24996784970485
8	49	49.0771342306583	-0.077134230658302
9	45	44.98430869821	0.0156913017900486
10	47	46.7423205665647	0.257679433435267
11	49	47.7685991428789	1.23140085712114
12	33	31.156534010796	1.84346598920401
13	42	40.9703280546228	1.02967194537719
14	33	32.1317914159817	0.868208584018294
15	53	53.2580051199822	-0.258005119982212
16	36	34.7671538465653	1.2328461534347
17	45	45.8766363774034	-0.876636377403445
18	54	53.8448570060489	0.155142993951137
19	41	38.258850229195	2.74114977080501
20	36	33.7550688533609	2.24493114663915
21	41	39.0263765567302	1.97362344326983
22	44	41.3427122036684	2.6572877963316
23	33	31.771471099306	1.22852890069396
24	37	33.7578611196391	3.24213888036087
25	52	52.4530970021812	-0.453097002181235
26	47	48.6752270504097	-1.67522705040973
27	43	46.2034497718616	-3.20344977186161
28	44	42.3084042440469	1.69159575595308
29	45	47.7924274726717	-2.79242747267168
30	44	40.8381601471542	3.16183985284576
31	49	48.371662099004	0.628337900995968
32	33	32.591232387256	0.408767612744029
33	43	42.6765050092195	0.323494990780465
34	54	51.6507948619384	2.34920513806159
35	42	45.0928159380031	-3.09281593800313
36	44	43.3187628972254	0.681237102774623
37	37	39.3576098426805	-2.35760984268049
38	43	43.0992761759411	-0.099276175941094
39	46	45.9169460561242	0.0830539438757718
40	42	41.5582813906284	0.441718609371611
41	45	44.5543028374256	0.445697162574446
42	44	45.9109583010774	-1.91095830107737
43	33	30.8233765782435	2.17662342175654
44	31	30.9871102710876	0.0128897289123697
45	42	41.558072274373	0.441927725626963
46	40	41.7954837450099	-1.79548374500993
47	43	39.1396899014828	3.86031009851718
48	46	45.6582858642353	0.341714135764745
49	42	45.3973770329165	-3.39737703291645
50	45	45.6605467541597	-0.660546754159693
51	44	43.6497448920369	0.350255107963107
52	40	40.630899318663	-0.630899318662964
53	37	38.8861436144546	-1.88614361445458
54	46	37.6761556922332	8.32384430776682
55	36	38.3772045054713	-2.37720450547126
56	47	46.3844263390087	0.615573660991289
57	45	44.9716858900525	0.0283141099475099
58	42	40.1456360451029	1.85436395489709
59	43	44.4636139852735	-1.4636139852735
60	43	42.8405423751927	0.159457624807253
61	32	32.4664631039256	-0.466463103925641
62	45	47.0281498868257	-2.02814988682568
63	45	47.2318295554002	-2.2318295554002
64	31	31.0331927686529	-0.0331927686528642
65	33	31.750282530176	1.24971746982404
66	49	49.1888022674534	-0.188802267453393
67	42	40.3021262074257	1.69787379257432
68	41	44.010159304223	-3.01015930422297
69	38	38.4484522734312	-0.448452273431234
70	42	42.0601640371797	-0.0601640371796765
71	44	41.1341911462922	2.86580885370781
72	33	32.5102229965101	0.489777003489934
73	48	49.8058251516044	-1.80582515160443
74	40	41.6497870754029	-1.64978707540293
75	50	51.199094709157	-1.19909470915699
76	49	49.4847265375893	-0.484726537589288
77	43	42.4668479298266	0.53315207017342
78	44	42.164601564643	1.83539843535702
79	47	47.235721850888	-0.235721850888011
80	33	31.1864037942131	1.81359620578692
81	46	48.3138687293346	-2.31386872933457
82	0	15.5970927529588	-15.5970927529588
83	45	42.8669777611037	2.13302223889631
84	43	44.264568235954	-1.26456823595403
85	44	43.7977047274141	0.202295272585901
86	47	46.9949536458482	0.00504635415180158
87	45	46.177989994253	-1.17798999425304
88	42	41.7704630015077	0.229536998492351
89	33	32.1925629776201	0.807437022379885
90	43	43.8696971199463	-0.869697119946347
91	46	44.8413642943204	1.15863570567957
92	33	31.9822843384018	1.01771566159822
93	46	47.4545820146685	-1.45458201466848
94	48	50.4007706770431	-2.40077067704312
95	47	48.9476098184662	-1.94760981846623
96	47	48.8537079268838	-1.85370792688375
97	43	42.2819547835075	0.718045216492453
98	46	47.4318395556824	-1.43183955568241
99	48	49.3512620050241	-1.35126200502413
100	46	46.4343474386752	-0.434347438675208
101	45	46.0331680335448	-1.03316803354476
102	45	44.9378321628529	0.0621678371470785
103	52	51.9673344292696	0.0326655707304391
104	42	39.6280609432621	2.37193905673786
105	47	49.0041242903483	-2.00412429034833
106	41	42.1447871572142	-1.1447871572142
107	47	46.0727843747469	0.927215625253149
108	43	43.6117379607829	-0.611737960782922
109	33	32.4427288853497	0.557271114650296
110	30	28.7596545349015	1.24034546509847
111	49	50.52602596609	-1.52602596609
112	44	45.4906596034578	-1.49065960345782
113	55	54.5793059883289	0.42069401167112
114	11	21.8668706403461	-10.8668706403461
115	47	46.4535442098102	0.546455790189806
116	53	52.3115077583731	0.688492241626854
117	33	32.5847467906484	0.415253209351624
118	44	43.0616849701819	0.938315029818128
119	42	41.7781037156252	0.221896284374802
120	55	55.956988813515	-0.956988813515041
121	33	32.7327623789299	0.267237621070089
122	46	46.2100419543186	-0.210041954318644
123	54	55.2501057827401	-1.25010578274011
124	47	46.0674955159663	0.932504484033725
125	45	44.1510536191907	0.848946380809268
126	47	48.2540978646502	-1.25409786465016
127	55	54.9370270260263	0.0629729739737349
128	44	44.7491120770654	-0.749112077065439
129	53	49.5205557071189	3.47944429288111
130	44	44.0495281865636	-0.0495281865636252
131	42	43.0199196905208	-1.0199196905208
132	40	41.3537255579834	-1.35372555798337
133	46	46.8936989093601	-0.893698909360059
134	40	39.5836877912694	0.416312208730554
135	46	45.3439340393324	0.656065960667557
136	53	50.2428866429009	2.75711335709911
137	33	32.850459062893	0.149540937107007
138	42	38.1567297479649	3.84327025203511
139	35	32.9951871564426	2.00481284355742
140	40	38.6609062114517	1.33909378854828
141	41	42.6016180215863	-1.60161802158634
142	33	31.6812678752816	1.31873212471838
143	51	51.9008156910276	-0.900815691027617
144	53	52.9565554926818	0.0434445073182159
145	46	46.4033292276538	-0.403329227653794
146	55	55.003606432918	-0.00360643291798442
147	47	45.7145798693552	1.28542013064475
148	38	36.4295290200288	1.57047097997116
149	46	45.5784257483136	0.421574251686445
150	46	45.5391656434461	0.460834356553884
151	53	52.9592053685269	0.0407946314731348
152	47	49.0428543956969	-2.04285439569695
153	41	42.9116993138606	-1.91169931386056
154	44	44.1742770672423	-0.174277067242337
155	43	42.9439715104952	0.056028489504815
156	51	48.7365198701529	2.26348012984712
157	33	31.9822843384018	1.01771566159822
158	43	42.466524308377	0.533475691623035
159	53	49.5205557071189	3.47944429288111
160	51	51.2867571924488	-0.286757192448781
161	50	52.8201600964495	-2.82016009644954
162	46	42.6224604615842	3.37753953841576

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
11	0.151939582924481	0.303879165848961	0.848060417075519
12	0.0637378949448871	0.127475789889774	0.936262105055113
13	0.0278117125312881	0.0556234250625762	0.972188287468712
14	0.0146475037319504	0.0292950074639008	0.98535249626805
15	0.00634234646418108	0.0126846929283622	0.993657653535819
16	0.00221838239786551	0.00443676479573102	0.997781617602134
17	0.00175981880626474	0.00351963761252948	0.998240181193735
18	0.000749629657809503	0.00149925931561901	0.99925037034219
19	0.000413358563674328	0.000826717127348656	0.999586641436326
20	0.000152739030111491	0.000305478060222981	0.999847260969889
21	7.34448925026419e-05	0.000146889785005284	0.999926555107497
22	5.34034362223847e-05	0.000106806872444769	0.999946596563778
23	0.000113422195297719	0.000226844390595438	0.999886577804702
24	0.000207170074761082	0.000414340149522163	0.999792829925239
25	9.45852010826995e-05	0.000189170402165399	0.999905414798917
26	0.000137122254033244	0.000274244508066487	0.999862877745967
27	0.00146874641183077	0.00293749282366154	0.998531253588169
28	0.00110351387096553	0.00220702774193107	0.998896486129034
29	0.00344907209547184	0.00689814419094367	0.996550927904528
30	0.00629775886308181	0.0125955177261636	0.993702241136918
31	0.00392002259572329	0.00784004519144658	0.996079977404277
32	0.00316090626277991	0.00632181252555982	0.99683909373722
33	0.00185002430383225	0.0037000486076645	0.998149975696168
34	0.00445558012541197	0.00891116025082394	0.995544419874588
35	0.00870345056178676	0.0174069011235735	0.991296549438213
36	0.010018838529709	0.0200376770594179	0.989981161470291
37	0.0114319978868388	0.0228639957736775	0.988568002113161
38	0.00745407026390322	0.0149081405278064	0.992545929736097
39	0.00490919983448181	0.00981839966896362	0.995090800165518
40	0.00318478221020403	0.00636956442040807	0.996815217789796
41	0.00198393778995037	0.00396787557990074	0.99801606221005
42	0.00166514525068973	0.00333029050137945	0.99833485474931
43	0.00141844512034885	0.0028368902406977	0.998581554879651
44	0.00114632452897962	0.00229264905795924	0.99885367547102
45	0.000732203362477551	0.0014644067249551	0.999267796637522
46	0.000528717034106085	0.00105743406821217	0.999471282965894
47	0.00130688002428624	0.00261376004857248	0.998693119975714
48	0.000813306456942464	0.00162661291388493	0.999186693543058
49	0.00219815207432697	0.00439630414865393	0.997801847925673
50	0.00141931115671801	0.00283862231343602	0.998580688843282
51	0.000933904469455653	0.00186780893891131	0.999066095530544
52	0.000620007465708515	0.00124001493141703	0.999379992534291
53	0.000526286404954387	0.00105257280990877	0.999473713595046
54	0.0464446413983074	0.0928892827966148	0.953555358601693
55	0.0462265603568431	0.0924531207136863	0.953773439643157
56	0.0400998539930217	0.0801997079860434	0.959900146006978
57	0.030251114688342	0.060502229376684	0.969748885311658
58	0.0254313128123983	0.0508626256247966	0.974568687187602
59	0.0236957186582255	0.047391437316451	0.976304281341774
60	0.0176201859000567	0.0352403718001133	0.982379814099943
61	0.0131028700236556	0.0262057400473112	0.986897129976344
62	0.0123259592344123	0.0246519184688246	0.987674040765588
63	0.0131056317093337	0.0262112634186675	0.986894368290666
64	0.0119305891723186	0.0238611783446373	0.988069410827681
65	0.00999125588165816	0.0199825117633163	0.990008744118342
66	0.00721017028546614	0.0144203405709323	0.992789829714534
67	0.00624933946945264	0.0124986789389053	0.993750660530547
68	0.00956043350415862	0.0191208670083172	0.990439566495841
69	0.00730025541451442	0.0146005108290288	0.992699744585486
70	0.00544341912483904	0.0108868382496781	0.994556580875161
71	0.00883546033994942	0.0176709206798988	0.991164539660051
72	0.00755121892626332	0.0151024378525266	0.992448781073737
73	0.00688747757347195	0.0137749551469439	0.993112522426528
74	0.00864365054150334	0.0172873010830067	0.991356349458497
75	0.00676665992117047	0.0135333198423409	0.99323334007883
76	0.0050764305890325	0.010152861178065	0.994923569410967
77	0.00381722832339797	0.00763445664679595	0.996182771676602
78	0.00366701625836642	0.00733403251673284	0.996332983741634
79	0.00270069602391093	0.00540139204782186	0.997299303976089
80	0.00249993738987892	0.00499987477975784	0.997500062610121
81	0.00246570571390364	0.00493141142780729	0.997534294286096
82	0.997801248830097	0.00439750233980656	0.00219875116990328
83	0.997741965505319	0.00451606898936132	0.00225803449468066
84	0.997082890574811	0.00583421885037721	0.00291710942518861
85	0.995835286835839	0.00832942632832153	0.00416471316416076
86	0.994129595210178	0.0117408095796448	0.0058704047898224
87	0.992499011478401	0.0150019770431987	0.00750098852159934
88	0.989664517068153	0.0206709658636946	0.0103354829318473
89	0.986395036625493	0.0272099267490146	0.0136049633745073
90	0.98244025747592	0.0351194850481598	0.0175597425240799
91	0.978098786216481	0.0438024275670379	0.021901213783519
92	0.973445312023104	0.0531093759537917	0.0265546879768959
93	0.968012062217448	0.0639758755651044	0.0319879377825522
94	0.969135979454373	0.0617280410912545	0.0308640205456273
95	0.966355305894705	0.0672893882105904	0.0336446941052952
96	0.96392574866907	0.0721485026618606	0.0360742513309303
97	0.955078458024903	0.0898430839501939	0.044921541975097
98	0.950544491468727	0.0989110170625453	0.0494555085312727
99	0.942567191143798	0.114865617712404	0.0574328088562018
100	0.92790488189724	0.14419023620552	0.0720951181027602
101	0.912573769834756	0.174852460330489	0.0874262301652443
102	0.891025264085343	0.217949471829315	0.108974735914657
103	0.865878435096123	0.268243129807754	0.134121564903877
104	0.866826344042029	0.266347311915942	0.133173655957971
105	0.8654966146747	0.2690067706506	0.1345033853253
106	0.84121974006961	0.317560519860779	0.15878025993039
107	0.812697486744569	0.374605026510862	0.187302513255431
108	0.780567266154978	0.438865467690043	0.219432733845022
109	0.748328260491487	0.503343479017026	0.251671739508513
110	0.725939949128808	0.548120101742383	0.274060050871192
111	0.715232830225779	0.569534339548442	0.284767169774221
112	0.685609866842483	0.628780266315035	0.314390133157517
113	0.640992756837215	0.718014486325571	0.359007243162785
114	0.999984538367158	3.09232656839859e-05	1.54616328419929e-05
115	0.999974226587065	5.15468258689698e-05	2.57734129344849e-05
116	0.999955240884756	8.95182304875276e-05	4.47591152437638e-05
117	0.999931707675229	0.000136584649542376	6.82923247711882e-05
118	0.999879925531609	0.000240148936781333	0.000120074468390667
119	0.999784338738353	0.00043132252329327	0.000215661261646635
120	0.999633508605511	0.000732982788977019	0.000366491394488509
121	0.999411177177201	0.00117764564559828	0.000588822822799138
122	0.999037404533068	0.00192519093386404	0.000962595466932019
123	0.998521500312222	0.0029569993755556	0.0014784996877778
124	0.997788016886617	0.0044239662267651	0.00221198311338255
125	0.996445083563353	0.00710983287329346	0.00355491643664673
126	0.994755079856347	0.0104898402873063	0.00524492014365317
127	0.991717101440133	0.0165657971197348	0.0082828985598674
128	0.991149715228973	0.0177005695420549	0.00885028477102745
129	0.991702956702569	0.0165940865948629	0.00829704329743143
130	0.987968101704919	0.0240637965901614	0.0120318982950807
131	0.983426951253027	0.0331460974939454	0.0165730487469727
132	0.978591914143517	0.0428161717129656	0.0214080858564828
133	0.971583339664145	0.0568333206717097	0.0284166603358549
134	0.962187744384372	0.0756245112312558	0.0378122556156279
135	0.944174625660581	0.111650748678838	0.0558253743394191
136	0.946474717381828	0.107050565236344	0.053525282618172
137	0.94636233327339	0.10727533345322	0.0536376667266102
138	0.959656140699551	0.0806877186008976	0.0403438593004488
139	0.942070539976923	0.115858920046153	0.0579294600230767
140	0.913420566052899	0.173158867894201	0.0865794339471007
141	0.939705282517927	0.120589434964146	0.0602947174820731
142	0.914384976472867	0.171230047054266	0.0856150235271331
143	0.890165189861068	0.219669620277864	0.109834810138932
144	0.842272668205788	0.315454663588423	0.157727331794212
145	0.850318811613307	0.299362376773386	0.149681188386693
146	0.837080834157059	0.325838331685881	0.162919165842941
147	0.784076504626248	0.431846990747504	0.215923495373752
148	0.832725674217171	0.334548651565659	0.167274325782829
149	0.795107985131199	0.409784029737602	0.204892014868801
150	0.665635756850909	0.668728486298182	0.334364243149091
151	0.503432210776415	0.993135578447171	0.496567789223585

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	54	0.382978723404255	NOK
5% type I error level	92	0.652482269503546	NOK
10% type I error level	108	0.765957446808511	NOK