Multiple Linear Regression - Estimated Regression Equation

Happiness[t] = + 12.6547460959361 + 0.0137609572325931Connected[t] + 0.0739108725388224Separate[t] + 0.0661953497728065Learning[t] -0.0462160812507193Software[t] -0.351184559016834Depression[t] + 0.0585099208420599Belonging[t] -0.0393031134505445Belonging_Final[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)	12.6547460959361	2.579722	4.9055	2e-06	1e-06
Connected	0.0137609572325931	0.050298	0.2736	0.784768	0.392384
Separate	0.0739108725388224	0.046838	1.578	0.116612	0.058306
Learning	0.0661953497728065	0.084678	0.7817	0.435576	0.217788
Software	-0.0462160812507193	0.085884	-0.5381	0.591271	0.295635
Depression	-0.351184559016834	0.052485	-6.6912	0	0
Belonging	0.0585099208420599	0.046748	1.2516	0.212611	0.106305
Belonging_Final	-0.0393031134505445	0.067414	-0.583	0.560736	0.280368

Multiple Linear Regression - Regression Statistics
Multiple R	0.579316084592813
R-squared	0.335607125867947
Adjusted R-squared	0.305407449771035
F-TEST (value)	11.1129379265849
F-TEST (DF numerator)	7
F-TEST (DF denominator)	154
p-value	2.443512059358e-11
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	1.94822277716126
Sum Squared Residuals	584.518086375289

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	14	13.9626165369954	0.0373834630046497
2	18	15.2716843091108	2.7283156908892
3	11	13.5132659631127	-2.51326596311267
4	12	14.3305506597591	-2.33055065975914
5	16	11.4471817922587	4.55281820774132
6	18	14.1804864225451	3.81951357745487
7	14	10.1065294559741	3.89347054402585
8	14	15.0212261214269	-1.02122612142689
9	15	15.1584114638485	-0.158411463848536
10	15	14.7222568137072	0.277743186292752
11	17	15.2504499006136	1.74955009938639
12	19	15.2206993534543	3.77930064654567
13	10	13.2707411772324	-3.27074117723238
14	16	13.4967344424571	2.50326555754289
15	18	15.7710922061371	2.22890779386291
16	14	13.0345722911279	0.965427708872069
17	14	13.749078043281	0.250921956718962
18	17	15.9190644062841	1.08093559371587
19	14	15.3045376788863	-1.30453767888631
20	16	13.3195314065367	2.68046859346331
21	18	15.876839434753	2.12316056524695
22	11	13.2098592394067	-2.20985923940674
23	14	14.3052574473078	-0.305257447307763
24	12	13.5029307884127	-1.50293078841269
25	17	15.3910087079345	1.6089912920655
26	9	15.7814914576308	-6.78149145763084
27	16	15.227675835464	0.772324164536037
28	14	13.2295442386558	0.770455761344155
29	15	13.9309989939196	1.06900100608037
30	11	13.6516799573128	-2.65167995731277
31	16	15.1834575499536	0.816542450046365
32	13	12.4108200060772	0.589179993922839
33	17	14.8720375578022	2.12796244219781
34	15	15.2912886223555	-0.291288622355473
35	14	13.8256908499904	0.17430915000963
36	16	15.2894013166425	0.710598683357498
37	9	10.9379265496515	-1.93792654965154
38	15	14.2112970651121	0.788702934887867
39	17	15.0689808633457	1.93101913665428
40	13	15.0470113597267	-2.04701135972668
41	15	15.5264472245285	-0.526447224528547
42	16	13.676142602531	2.32385739746903
43	16	15.2265326781809	0.773467321819061
44	12	12.9475480177547	-0.947548017754705
45	12	14.2351646101679	-2.2351646101679
46	11	13.7654887369126	-2.76548873691257
47	15	15.3385622855577	-0.338562285557675
48	15	14.8236513990101	0.176348600989858
49	17	13.9207374075288	3.0792625924712
50	13	14.6715261225225	-1.67152612252248
51	16	15.2873420613452	0.71265793865477
52	14	13.2084533200165	0.791546679983543
53	11	11.6844944965019	-0.684494496501931
54	12	13.2926363856721	-1.29263638567211
55	12	14.2331051699681	-2.23310516996811
56	15	14.5637807877183	0.436219212281659
57	16	14.2046204855026	1.7953795144974
58	15	15.1800890437012	-0.180089043701222
59	12	15.3785910307025	-3.37859103070251
60	12	13.3842062445729	-1.38420624457285
61	8	10.4275458663947	-2.42754586639468
62	13	14.717573849813	-1.71757384981302
63	11	14.64400873092	-3.64400873092004
64	14	12.9941098526513	1.00589014734874
65	15	13.2155220262885	1.78447797371149
66	10	15.2875047319946	-5.28750473199463
67	11	12.5222987609356	-1.52229876093564
68	12	14.1918896354108	-2.19188963541079
69	15	14.0148169865355	0.985183013464535
70	15	13.8454844513132	1.1545155486868
71	14	13.7561071672698	0.243892832730181
72	16	12.9030715260339	3.09692847396608
73	15	14.8369887046207	0.163011295379289
74	15	15.7057138131789	-0.705713813178867
75	13	14.7093923507694	-1.70939235076943
76	12	12.2005603060215	-0.200560306021458
77	17	14.197181650936	2.80281834906399
78	13	12.3023144361468	0.6976855638532
79	15	13.7298548246343	1.27014517536572
80	13	14.3658996438983	-1.36589964389833
81	15	15.2254920959781	-0.225492095978114
82	16	14.9852807255583	1.0147192744417
83	15	15.6005177477299	-0.600517747729854
84	16	14.4082732138017	1.59172678619835
85	15	14.3617823471356	0.638217652864376
86	14	14.0896778226171	-0.0896778226171078
87	15	14.6251813560127	0.374818643987272
88	14	14.2985990372652	-0.298599037265213
89	13	12.5182589946307	0.481741005369304
90	7	10.6658540321768	-3.66585403217676
91	17	14.0184083830878	2.98159161691217
92	13	12.5421328012795	0.457867198720504
93	15	14.8031794134196	0.196820586580376
94	14	13.2464341082199	0.75356589178011
95	13	14.8987883489047	-1.89878834890474
96	16	15.4196968092666	0.580303190733374
97	12	12.9372963079658	-0.937296307965809
98	14	14.9635979706593	-0.963597970659285
99	17	15.1711277946139	1.82887220538613
100	15	15.347427398192	-0.347427398191999
101	17	15.4168226295808	1.58317737041916
102	12	13.1851619269344	-1.1851619269344
103	16	15.230875280886	0.769124719113958
104	11	13.9970483727683	-2.99704837276825
105	15	13.6982148863106	1.30178511368941
106	9	11.5710192229879	-2.57101922298795
107	16	15.0717484833983	0.928251516601661
108	15	13.4512195499863	1.54878045001369
109	10	12.882534394126	-2.88253439412603
110	10	9.90548907090124	0.0945109290987561
111	15	14.0404542243267	0.959545775673266
112	11	13.2651237880185	-2.26512378801847
113	13	15.8665581989868	-2.8665581989868
114	14	12.4095925332386	1.59040746676138
115	18	14.3943475082475	3.6056524917525
116	16	15.5566992638055	0.443300736194469
117	14	13.3371675820921	0.662832417907851
118	14	14.4370179901121	-0.437017990112142
119	14	15.2736936187868	-1.27369361878684
120	14	14.1794397542815	-0.179439754281502
121	12	12.7904872181875	-0.79048721818748
122	14	13.2574728078361	0.742527192163875
123	15	15.5881177512554	-0.588117751255369
124	15	16.1746463085585	-1.17464630855847
125	15	14.4317698906587	0.56823010934134
126	13	14.7982862066938	-1.79828620669376
127	17	16.3820859472053	0.617914052794726
128	17	15.8482478558843	1.15175214411575
129	19	15.1398430374878	3.86015696251223
130	15	13.7793837379593	1.22061626204067
131	13	14.7715637706962	-1.77156377069619
132	9	10.8246164808787	-1.82461648087872
133	15	15.8147587114807	-0.814758711480679
134	15	12.4928373523562	2.50716264764379
135	15	14.6522328072134	0.347767192786616
136	16	13.4750139725228	2.52498602747718
137	11	8.89597503430895	2.10402496569105
138	14	13.3128629554285	0.687137044571486
139	11	12.0854171971992	-1.08541719719924
140	15	14.3834450593497	0.616554940650326
141	13	13.9933765543591	-0.9933765543591
142	15	14.6481507314932	0.351849268506834
143	16	14.1513207330891	1.84867926691088
144	14	14.8211085504859	-0.821108550485934
145	15	13.815140519058	1.184859480942
146	16	14.9713278476439	1.02867215235611
147	16	14.0666904691975	1.93330953080255
148	11	13.568556211929	-2.56855621192902
149	12	14.6081370926832	-2.60813709268317
150	9	11.7368967175347	-2.73689671753472
151	16	15.074690979256	0.925309020743982
152	13	13.1644296850352	-0.164429685035201
153	16	15.9565283605904	0.0434716394095803
154	12	15.0698953375539	-3.06989533755392
155	9	11.8809995506193	-2.88099955061928
156	13	11.9303125584374	1.06968744156258
157	13	12.5421328012795	0.457867198720504
158	14	13.8436089043508	0.156391095649228
159	19	15.1398430374878	3.86015696251223
160	13	15.7882287992974	-2.78822879929738
161	12	12.7349484294086	-0.734948429408634
162	13	12.8845093253904	0.115490674609604

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
11	0.0594429281729405	0.118885856345881	0.940557071827059
12	0.885682392212383	0.228635215575234	0.114317607787617
13	0.983884498012487	0.0322310039750251	0.0161155019875126
14	0.974540933051691	0.0509181338966187	0.0254590669483094
15	0.98564854135685	0.0287029172862997	0.0143514586431498
16	0.974701768666339	0.0505964626673218	0.0252982313336609
17	0.975723155924303	0.0485536881513937	0.0242768440756968
18	0.961481547751962	0.0770369044960753	0.0385184522480376
19	0.942060397416027	0.115879205167946	0.0579396025839729
20	0.942892938112098	0.114214123775803	0.0571070618879016
21	0.94980952782001	0.10038094435998	0.0501904721799902
22	0.951748822563112	0.0965023548737754	0.0482511774368877
23	0.947337630769471	0.105324738461059	0.0526623692305294
24	0.926497968801876	0.147004062396249	0.0735020311981243
25	0.904056604351282	0.191886791297436	0.095943395648718
26	0.999687546123821	0.000624907752357735	0.000312453876178867
27	0.999458972102793	0.00108205579441393	0.000541027897206964
28	0.999095078050605	0.00180984389878959	0.000904921949394795
29	0.998558495610971	0.00288300877805786	0.00144150438902893
30	0.999001381342803	0.00199723731439448	0.00099861865719724
31	0.998425463352968	0.00314907329406367	0.00157453664703184
32	0.997667886505786	0.00466422698842829	0.00233211349421414
33	0.99729374187836	0.00541251624327969	0.00270625812163985
34	0.995891207292579	0.0082175854148411	0.00410879270742055
35	0.994719464480102	0.0105610710397959	0.00528053551989793
36	0.992280590259752	0.0154388194804963	0.00771940974024813
37	0.995011997015261	0.00997600596947713	0.00498800298473856
38	0.992817213272817	0.0143655734543661	0.00718278672718307
39	0.992078549977432	0.0158429000451358	0.00792145002256792
40	0.992226596776893	0.0155468064462144	0.00777340322310719
41	0.989204381844496	0.0215912363110073	0.0107956181555036
42	0.988382275599893	0.0232354488002139	0.011617724400107
43	0.984213521933174	0.0315729561336527	0.0157864780668264
44	0.980728397116919	0.0385432057661621	0.019271602883081
45	0.983422318421542	0.033155363156915	0.0165776815784575
46	0.988278091644948	0.0234438167101038	0.0117219083550519
47	0.983840549979486	0.0323189000410284	0.0161594500205142
48	0.977953844188085	0.0440923116238295	0.0220461558119148
49	0.982388878799556	0.0352222424008869	0.0176111212004435
50	0.980849811912917	0.0383003761741656	0.0191501880870828
51	0.974723114042274	0.0505537719154511	0.0252768859577256
52	0.967179897492513	0.0656402050149749	0.0328201025074874
53	0.960569972274866	0.0788600554502677	0.0394300277251338
54	0.951921281975223	0.0961574360495548	0.0480787180247774
55	0.953627573243516	0.0927448535129687	0.0463724267564844
56	0.94146552203699	0.11706895592602	0.0585344779630101
57	0.936789707018614	0.126420585962772	0.0632102929813859
58	0.920462113327673	0.159075773344654	0.079537886672327
59	0.950225228511357	0.0995495429772861	0.049774771488643
60	0.945685218428519	0.108629563142961	0.0543147815714805
61	0.953632805682646	0.0927343886347074	0.0463671943173537
62	0.952681648219098	0.0946367035618044	0.0473183517809022
63	0.976490903139858	0.0470181937202849	0.0235090968601424
64	0.971104847989886	0.0577903040202279	0.0288951520101139
65	0.968863061710485	0.0622738765790307	0.0311369382895154
66	0.994985256176522	0.010029487646956	0.00501474382347799
67	0.994313830007102	0.0113723399857958	0.00568616999289789
68	0.995044717321435	0.00991056535712954	0.00495528267856477
69	0.993636950693661	0.0127260986126779	0.00636304930633895
70	0.992119023592853	0.0157619528142942	0.0078809764071471
71	0.989258929316778	0.0214821413664446	0.0107410706832223
72	0.993275060930097	0.0134498781398056	0.00672493906990278
73	0.990780762055191	0.0184384758896169	0.00921923794480845
74	0.987867171256718	0.0242656574865636	0.0121328287432818
75	0.987234447430019	0.0255311051399613	0.0127655525699806
76	0.982878394867972	0.034243210264055	0.0171216051320275
77	0.987756290934225	0.0244874181315504	0.0122437090657752
78	0.984248080152326	0.0315038396953487	0.0157519198476743
79	0.981319936107027	0.0373601277859455	0.0186800638929728
80	0.979386125161112	0.0412277496777766	0.0206138748388883
81	0.972845618712634	0.0543087625747317	0.0271543812873659
82	0.967216406597812	0.0655671868043756	0.0327835934021878
83	0.958616471354863	0.0827670572902734	0.0413835286451367
84	0.954537932513818	0.0909241349723647	0.0454620674861824
85	0.943526030600977	0.112947938798047	0.0564739693990233
86	0.928843091031019	0.142313817937963	0.0711569089689814
87	0.912035093864121	0.175929812271758	0.0879649061358788
88	0.891900928228822	0.216198143542356	0.108099071771178
89	0.871462647861765	0.257074704276471	0.128537352138235
90	0.920063150524097	0.159873698951805	0.0799368494759025
91	0.941525899612601	0.116948200774798	0.0584741003873988
92	0.927790556637472	0.144418886725056	0.072209443362528
93	0.911536500771415	0.176926998457171	0.0884634992285854
94	0.89361078412851	0.21277843174298	0.10638921587149
95	0.894028331275371	0.211943337449259	0.105971668724629
96	0.872006794742176	0.255986410515647	0.127993205257824
97	0.849937708667579	0.300124582664842	0.150062291332421
98	0.830668265446147	0.338663469107705	0.169331734553853
99	0.825323802809726	0.349352394380547	0.174676197190274
100	0.792912568438698	0.414174863122604	0.207087431561302
101	0.784077779041427	0.431844441917147	0.215922220958573
102	0.758859754812657	0.482280490374686	0.241140245187343
103	0.731816996524289	0.536366006951422	0.268183003475711
104	0.803979662856762	0.392040674286475	0.196020337143238
105	0.807707714227492	0.384584571545016	0.192292285772508
106	0.840290489322774	0.319419021354452	0.159709510677226
107	0.814811216696267	0.370377566607466	0.185188783303733
108	0.820437309973397	0.359125380053206	0.179562690026603
109	0.856567244031105	0.286865511937789	0.143432755968895
110	0.829846430517653	0.340307138964694	0.170153569482347
111	0.818943472299642	0.362113055400716	0.181056527700358
112	0.814793190089356	0.370413619821287	0.185206809910644
113	0.824749976127215	0.350500047745569	0.175250023872785
114	0.914186385233199	0.171627229533601	0.0858136147668006
115	0.954940388238225	0.0901192235235505	0.0450596117617752
116	0.940758946506667	0.118482106986666	0.0592410534933332
117	0.944949564387072	0.110100871225856	0.0550504356129282
118	0.927852427138641	0.144295145722719	0.0721475728613594
119	0.914305497787134	0.171389004425733	0.0856945022128664
120	0.890064947792531	0.219870104414939	0.109935052207469
121	0.864251642985154	0.271496714029693	0.135748357014846
122	0.832848327662023	0.334303344675955	0.167151672337977
123	0.794942879240181	0.410114241519637	0.205057120759819
124	0.764376005514871	0.471247988970259	0.235623994485129
125	0.717186231708518	0.565627536582965	0.282813768291482
126	0.694713329341688	0.610573341316624	0.305286670658312
127	0.64488394712647	0.71023210574706	0.35511605287353
128	0.674231127178221	0.651537745643559	0.325768872821779
129	0.735787497635217	0.528425004729566	0.264212502364783
130	0.708397030553039	0.583205938893922	0.291602969446961
131	0.681561078214077	0.636877843571846	0.318438921785923
132	0.654537088455096	0.690925823089808	0.345462911544904
133	0.595885209677065	0.808229580645871	0.404114790322935
134	0.607649669105862	0.784700661788276	0.392350330894138
135	0.559380080890226	0.881239838219548	0.440619919109774
136	0.524115105686694	0.951769788626611	0.475884894313306
137	0.55316810648028	0.893663787039439	0.44683189351972
138	0.482359417356462	0.964718834712925	0.517640582643538
139	0.410278512631143	0.820557025262285	0.589721487368857
140	0.344716428115109	0.689432856230219	0.655283571884891
141	0.276349172546872	0.552698345093744	0.723650827453128
142	0.234035294694127	0.468070589388255	0.765964705305873
143	0.243422575780464	0.486845151560928	0.756577424219536
144	0.203758896283672	0.407517792567344	0.796241103716328
145	0.194787957862502	0.389575915725004	0.805212042137498
146	0.192350875784387	0.384701751568775	0.807649124215613
147	0.321510159372848	0.643020318745696	0.678489840627152
148	0.768888886542934	0.462222226914131	0.231111113457066
149	0.820664829886079	0.358670340227842	0.179335170113921
150	0.704865831665592	0.590268336668817	0.295134168334408
151	0.578013306757231	0.843973386485537	0.421986693242769

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	11	0.0780141843971631	NOK
5% type I error level	44	0.312056737588652	NOK
10% type I error level	63	0.446808510638298	NOK