Multiple Linear Regression - Estimated Regression Equation

Happiness[t] = + 14.8142535198111 + 0.0562934670907469Learning[t] + 0.0478898476578772Connected[t] -0.341950967442765Depression[t] + 0.0264152274333828`Belonging `[t] -1.04946913607642M1[t] -0.72472249767663M2[t] + 0.00254117037458653M3[t] -1.16696732931539M4[t] -0.065593006997021M5[t] -1.20991410656088M6[t] + 0.0952095811044339M7[t] -0.92323399118414M8[t] + 0.306604585858594M9[t] -0.964929050551642M10[t] -1.11710048861157M11[t] -0.0018864249031574t + 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)	14.8142535198111	2.401578	6.1685	0	0
Learning	0.0562934670907469	0.073854	0.7622	0.447165	0.223582
Connected	0.0478898476578772	0.048585	0.9857	0.325925	0.162963
Depression	-0.341950967442765	0.055195	-6.1954	0	0
`Belonging `	0.0264152274333828	0.015697	1.6828	0.094564	0.047282
M1	-1.04946913607642	0.754703	-1.3906	0.166486	0.083243
M2	-0.72472249767663	0.752213	-0.9635	0.336924	0.168462
M3	0.00254117037458653	0.768175	0.0033	0.997365	0.498683
M4	-1.16696732931539	0.754424	-1.5468	0.124083	0.062042
M5	-0.065593006997021	0.755473	-0.0868	0.930931	0.465466
M6	-1.20991410656088	0.754338	-1.6039	0.110903	0.055451
M7	0.0952095811044339	0.76311	0.1248	0.900882	0.450441
M8	-0.92323399118414	0.770852	-1.1977	0.232996	0.116498
M9	0.306604585858594	0.767553	0.3995	0.690144	0.345072
M10	-0.964929050551642	0.766731	-1.2585	0.210234	0.105117
M11	-1.11710048861157	0.767795	-1.4549	0.147845	0.073923
t	-0.0018864249031574	0.003412	-0.5528	0.581229	0.290614

Multiple Linear Regression - Regression Statistics
Multiple R	0.616433194817533
R-squared	0.379989883672951
Adjusted R-squared	0.311574974285138
F-TEST (value)	5.55419698824659
F-TEST (DF numerator)	16
F-TEST (DF denominator)	145
p-value	3.63666030622767e-09
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	1.93955402328856
Sum Squared Residuals	545.471122341953

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	14	13.7547922296403	0.245207770359684
2	18	15.3644066218378	2.63559337816221
3	11	14.2734981863412	-3.27349818634124
4	12	13.6351364033619	-1.63513640336191
5	16	11.9821787165756	4.01782128342443
6	18	13.9579567345273	4.04204326547267
7	14	11.7106238302033	2.28937616979674
8	14	14.7003425089309	-0.700342508930904
9	15	16.151240492138	-1.15124049213796
10	15	14.0089812981117	0.99101870188834
11	17	15.0642053345256	1.93579466547437
12	19	16.1071609519693	2.89283904803074
13	10	13.1013262708401	-3.10132627084006
14	16	13.4706293428034	2.52937065719664
15	18	16.2044673421676	1.79553265783241
16	14	12.7387501703959	1.26124982960407
17	14	14.4788563248102	-0.478856324810153
18	17	15.0791466900749	1.92085330992511
19	14	16.025672375355	-2.02567237535501
20	16	13.3467670160147	2.65323298398533
21	18	16.8641620197113	1.13583798028872
22	11	13.2020257935074	-2.20202579350743
23	14	13.9140558638978	0.085944136102234
24	12	14.1335383509994	-2.13353835099942
25	17	15.0525656777561	1.94743432224387
26	9	15.9966161568537	-6.99661615685375
27	16	15.6366878500026	0.363312149997389
28	14	12.7126194535404	1.28738054645964
29	15	14.4480888323895	0.551911167610472
30	11	13.2885676870744	-2.28856768707445
31	16	16.2156307003588	-0.215630700358756
32	13	12.0963591933387	0.903640806661264
33	17	16.0746104598199	0.925389540180092
34	15	14.7715547789056	0.228445221094412
35	14	13.5568557725416	0.443144227458352
36	16	15.8127450262128	0.187254973787242
37	9	10.4718668947516	-1.47186689475155
38	15	14.3020594692255	0.697940530774509
39	17	15.6207727850023	1.37922721499765
40	13	14.5518103543228	-1.5518103543228
41	15	16.2211050516634	-1.22110505166344
42	16	13.1353014402609	2.86469855973915
43	16	16.4648449247546	-0.464844924754555
44	12	12.8585483225214	-0.858548322521357
45	12	15.7050817863304	-3.70508178633036
46	11	13.5045743137679	-2.50457431376794
47	15	14.8558448872059	0.144155112794118
48	15	15.368153519164	-0.368153519163958
49	17	13.1225418710443	3.87745812895568
50	13	14.8228139428797	-1.82281394287965
51	16	15.6361443194046	0.363855680595442
52	14	12.852282453692	1.14771754630804
53	11	12.3657186374211	-1.36571863742109
54	12	12.8818533189705	-0.881853318970485
55	12	14.7475247465433	-2.74752474654334
56	15	14.2495583122859	0.750441687714062
57	16	15.2910956716132	0.708904328386767
58	15	14.7216744114584	0.278325588541553
59	12	14.7109822598252	-2.71098225982516
60	12	13.9977095757946	-1.9977095757946
61	8	10.3229172045813	-2.32291720458132
62	13	14.6236432656473	-1.62364326564726
63	11	15.1574611181638	-4.15746111816381
64	14	12.3855270956954	1.61447290430455
65	15	14.1360528925753	0.863947107424682
66	10	14.4647265310104	-4.4647265310104
67	11	13.4506281197972	-2.45062811979724
68	12	14.0376204659057	-2.03762046590575
69	15	14.7527172026451	0.247282797354854
70	15	13.3294520162208	1.67054798377924
71	14	13.2704234062628	0.729576593737176
72	16	13.2482825132096	2.75171748679042
73	15	13.9628834391535	1.03711656084651
74	15	15.1861732164093	-0.18617321640933
75	13	15.6616815788024	-2.66168157880236
76	12	11.9447607103137	0.055239289686289
77	17	14.6797289756452	2.32027102435482
78	13	11.9956328110001	1.00436718899991
79	15	14.4217762757809	0.578223724219132
80	13	14.7615889475855	-1.76158894758553
81	15	15.7744604600426	-0.774460460042635
82	16	13.9653784809307	2.03462151906925
83	15	14.9153423465004	0.0846576534996258
84	16	15.0970201909723	0.90297980902773
85	15	13.7798001642699	1.22019983573008
86	14	13.9969688622393	0.00303113776067021
87	15	14.7963779546285	0.203622045371485
88	14	13.68158032877	0.318419671230044
89	13	13.1674275217246	-0.167427521724624
90	7	10.1854727876331	-3.18547278763314
91	17	14.3808543430923	2.61914565690767
92	13	12.6956496635239	0.30435033647608
93	15	15.1108706667682	-0.110870666768206
94	14	13.0856617976718	0.914338202328181
95	13	14.3322718399007	-1.33227183990066
96	16	15.7533138140173	0.246686185982674
97	12	12.605856218741	-0.605856218740962
98	14	14.7804286210361	-0.780428621036108
99	17	15.6808312418001	1.31916875819993
100	15	14.3672749750119	0.632725024988095
101	17	15.8666888925559	1.13331110744413
102	12	12.5416400334742	-0.541640033474242
103	16	15.7069479159132	0.293052084086837
104	11	14.0536528388447	-3.05365283884468
105	15	14.019431425153	0.980568574846966
106	9	11.595939492077	-2.59593949207704
107	16	14.5182053611704	1.48179463882964
108	15	13.8789645263809	1.12103547361908
109	10	12.4810518281872	-2.48105182818722
110	10	9.62508658047406	0.374913419525941
111	15	14.3235275344621	0.676472465537871
112	11	12.646749670617	-1.64674967061704
113	13	15.5880379366193	-2.5880379366193
114	14	11.5280913023491	2.47190869765091
115	18	15.0441158811067	2.95588411889327
116	16	15.3096008956788	0.690399104321161
117	14	13.9077286411846	0.0922713588153874
118	14	13.446793033906	0.553206966094015
119	14	14.5299404985319	-0.529940498531948
120	14	14.5564981732464	-0.55649817324644
121	12	12.1458647851035	-0.145864785103458
122	14	13.4649116755338	0.535088324466238
123	15	15.725888309977	-0.72588830997699
124	15	15.3579388846925	-0.357938884692536
125	15	15.1044753397571	-0.104475339757052
126	13	14.0772729516653	-1.07727295166532
127	17	17.0237559326953	-0.0237559326952548
128	17	15.2489165341548	1.75108346584525
129	19	15.6804490524671	3.3195509475329
130	15	13.4122893034112	1.58771069658876
131	13	13.9972224732897	-0.997222473289658
132	9	11.3734814996703	-2.37348149967029
133	15	14.9446420893246	0.0553579106754226
134	15	12.3930228484914	2.6069771515086
135	15	14.9734754516285	0.0265245483715351
136	16	13.1463446404182	2.85365535958178
137	11	10.1245011379008	0.875498862099166
138	14	12.6935153874479	1.3064846125521
139	11	12.6583804094296	-1.65838040942959
140	15	13.9077002291656	1.09229977083436
141	13	14.5090442920349	-1.50904429203487
142	15	14.0215353384901	0.978464661509882
143	16	13.140057266351	2.85994273364905
144	14	15.1045906539932	-1.10459065399316
145	15	13.8070944266803	1.19290557331973
146	16	14.8821361631967	1.11786383680333
147	16	14.9893934377309	1.01060656226906
148	11	12.9634959619387	-1.96349596193869
149	12	15.1204352163809	-3.12043521638091
150	9	11.1605786392064	-2.1605786392064
151	16	15.1492445449699	0.850755455030106
152	13	12.7336950720493	0.266304927950715
153	16	16.1591078300916	-0.159107830091647
154	12	13.9341399415412	-1.93413994154122
155	9	11.1945926899971	-2.19459268999714
156	13	12.56854120437	0.43145879562998
157	13	12.4467968999264	0.553203100073588
158	14	13.0911032333721	0.908896766627947
159	19	15.3197928898884	3.68020711011163
160	13	15.0157288972295	-2.01572889722954
161	12	12.7167045239811	-0.716704523981125
162	13	12.0102436853054	0.989756314694604

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
20	0.807853112534791	0.384293774930418	0.192146887465209
21	0.942938678945438	0.114122642109123	0.0570613210545616
22	0.932018979763963	0.135962040472075	0.0679810202360373
23	0.900148493707293	0.199703012585414	0.0998515062927068
24	0.981791418493283	0.0364171630134346	0.0182085815067173
25	0.992033444588222	0.0159331108235564	0.00796655541177822
26	0.999947564866386	0.000104870267227314	5.24351336136572e-05
27	0.999916307717258	0.000167384565484406	8.36922827422029e-05
28	0.999866552410364	0.000266895179272248	0.000133447589636124
29	0.999744636296059	0.000510727407882907	0.000255363703941454
30	0.9998863403324	0.00022731933519975	0.000113659667599875
31	0.999788539864159	0.00042292027168241	0.000211460135841205
32	0.999633792631176	0.00073241473764803	0.000366207368824015
33	0.999432466784155	0.00113506643168932	0.000567533215844662
34	0.999161628505242	0.00167674298951663	0.000838371494758313
35	0.998653714643775	0.00269257071245036	0.00134628535622518
36	0.997807545493178	0.00438490901364416	0.00219245450682208
37	0.99662691972432	0.0067461605513605	0.00337308027568025
38	0.996073363945796	0.00785327210840842	0.00392663605420421
39	0.996301155561627	0.00739768887674579	0.00369884443837289
40	0.994555525266706	0.0108889494665877	0.00544447473329384
41	0.99189425122771	0.0162114975445786	0.00810574877228931
42	0.993747031605417	0.0125059367891669	0.00625296839458347
43	0.99172533844276	0.0165493231144825	0.00827466155724124
44	0.988390400992264	0.0232191980154715	0.0116095990077357
45	0.99250171435108	0.0149965712978418	0.0074982856489209
46	0.991047177345519	0.0179056453089626	0.00895282265448132
47	0.987264555680969	0.0254708886380624	0.0127354443190312
48	0.98182096179707	0.036358076405861	0.0181790382029305
49	0.99603176197355	0.00793647605290128	0.00396823802645064
50	0.99478535986848	0.0104292802630391	0.00521464013151955
51	0.993087755111402	0.0138244897771956	0.00691224488859782
52	0.992121902759423	0.0157561944811532	0.00787809724057661
53	0.989675342653801	0.0206493146923977	0.0103246573461989
54	0.986473531619679	0.0270529367606428	0.0135264683803214
55	0.986962469860298	0.0260750602794041	0.0130375301397021
56	0.983680846422548	0.0326383071549046	0.0163191535774523
57	0.979710144449701	0.0405797111005975	0.0202898555502987
58	0.976512442159993	0.0469751156800147	0.0234875578400074
59	0.979502526640417	0.0409949467191651	0.0204974733595826
60	0.9788519023368	0.0422961953264001	0.0211480976632
61	0.976774349537012	0.0464513009259757	0.0232256504629878
62	0.97208258912148	0.0558348217570408	0.0279174108785204
63	0.985893110773977	0.0282137784520452	0.0141068892260226
64	0.987317516416388	0.0253649671672242	0.0126824835836121
65	0.985282118410895	0.0294357631782101	0.0147178815891051
66	0.995539664761525	0.00892067047695055	0.00446033523847527
67	0.995952291926521	0.008095416146958	0.004047708073479
68	0.995415021681323	0.00916995663735388	0.00458497831867694
69	0.994375641078475	0.0112487178430496	0.00562435892152478
70	0.99523825448203	0.00952349103594151	0.00476174551797076
71	0.994006451879493	0.0119870962410148	0.00599354812050742
72	0.996338453426668	0.00732309314666468	0.00366154657333234
73	0.995877029533512	0.00824594093297625	0.00412297046648813
74	0.994940244830426	0.0101195103391489	0.00505975516957444
75	0.996331288443118	0.00733742311376365	0.00366871155688183
76	0.994867615925513	0.0102647681489732	0.00513238407448659
77	0.99647703358598	0.00704593282803836	0.00352296641401918
78	0.995729885376958	0.00854022924608432	0.00427011462304216
79	0.99458113130487	0.0108377373902589	0.00541886869512947
80	0.99427656423422	0.011446871531562	0.005723435765781
81	0.99245857818387	0.015082843632261	0.00754142181613052
82	0.992511750552925	0.0149764988941509	0.00748824944707547
83	0.989522918754432	0.020954162491135	0.0104770812455675
84	0.98690264077151	0.0261947184569785	0.0130973592284893
85	0.98522585854877	0.0295482829024586	0.0147741414512293
86	0.980659037619144	0.0386819247617125	0.0193409623808563
87	0.976545889294607	0.0469082214107868	0.0234541107053934
88	0.969630023692589	0.0607399526148227	0.0303699763074113
89	0.960861318242296	0.0782773635154076	0.0391386817577038
90	0.972114841262717	0.0557703174745667	0.0278851587372834
91	0.979348265751559	0.0413034684968827	0.0206517342484414
92	0.97258412686975	0.0548317462604995	0.0274158731302497
93	0.964066488112173	0.0718670237756533	0.0359335118878266
94	0.957765363384325	0.0844692732313508	0.0422346366156754
95	0.949569594951224	0.100860810097553	0.0504304050487764
96	0.93526591903918	0.129468161921641	0.0647340809608204
97	0.917192640165949	0.165614719668102	0.0828073598340508
98	0.910922182721948	0.178155634556105	0.0890778172780523
99	0.898678994780001	0.202642010439998	0.101321005219999
100	0.881471483226102	0.237057033547796	0.118528516773898
101	0.87703142677941	0.245937146441179	0.12296857322059
102	0.849812163803264	0.300375672393472	0.150187836196736
103	0.818475388932732	0.363049222134536	0.181524611067268
104	0.884871727812727	0.230256544374546	0.115128272187273
105	0.861227695405602	0.277544609188796	0.138772304594398
106	0.873622759200747	0.252754481598506	0.126377240799253
107	0.862982763987115	0.274034472025769	0.137017236012885
108	0.866779760623856	0.266440478752288	0.133220239376144
109	0.885713505370728	0.228572989258545	0.114286494629272
110	0.860529788082273	0.278940423835454	0.139470211917727
111	0.83508129541311	0.32983740917378	0.16491870458689
112	0.832466794201282	0.335066411597436	0.167533205798718
113	0.848160048343656	0.303679903312687	0.151839951656344
114	0.887055477178004	0.225889045643992	0.112944522821996
115	0.921639185644525	0.156721628710949	0.0783608143554746
116	0.911297693311317	0.177404613377366	0.0887023066886829
117	0.883365100695017	0.233269798609967	0.116634899304983
118	0.850591843975521	0.298816312048958	0.149408156024479
119	0.810724573248369	0.378550853503262	0.189275426751631
120	0.766871327783875	0.466257344432251	0.233128672216125
121	0.717930810761385	0.564138378477229	0.282069189238615
122	0.711019614831109	0.577960770337782	0.288980385168891
123	0.729512894446287	0.540974211107426	0.270487105553713
124	0.669349990047687	0.661300019904625	0.330650009952313
125	0.618345468865662	0.763309062268676	0.381654531134338
126	0.636333704945489	0.727332590109022	0.363666295054511
127	0.570651477290937	0.858697045418126	0.429348522709063
128	0.532036569767578	0.935926860464845	0.467963430232422
129	0.581960037412356	0.836079925175288	0.418039962587644
130	0.532403335428453	0.935193329143095	0.467596664571547
131	0.466320726309482	0.932641452618964	0.533679273690518
132	0.483215350511475	0.96643070102295	0.516784649488525
133	0.399228694734846	0.798457389469692	0.600771305265154
134	0.33647594930436	0.672951898608721	0.66352405069564
135	0.304395329337348	0.608790658674697	0.695604670662652
136	0.388904245273712	0.777808490547423	0.611095754726288
137	0.56393072726341	0.87213854547318	0.43606927273659
138	0.572502362219567	0.854995275560867	0.427497637780433
139	0.46571796953957	0.93143593907914	0.53428203046043
140	0.418583497827364	0.837166995654729	0.581416502172636
141	0.651983337147433	0.696033325705134	0.348016662852567
142	0.511205016162739	0.977589967674522	0.488794983837261

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	24	0.195121951219512	NOK
5% type I error level	64	0.520325203252033	NOK
10% type I error level	71	0.577235772357724	NOK