Multiple Linear Regression - Estimated Regression Equation

Happiness[t] = + 13.5418192607468 + 0.0236875343095792Connected[t] + 0.0599170464092312Separate[t] + 0.100158690643845Learning[t] -0.0796049946788367Software[t] -0.34016858129956Depression[t] + 0.0523382523886976Belonging[t] -0.0402494950926348Belonging_Final[t] -1.04308022934069M1[t] -0.675853126651141M2[t] -0.00863759431825111M3[t] -1.12540140962164M4[t] -0.0047466453498684M5[t] -1.16617735315638M6[t] + 0.174722807443339M7[t] -0.796081789230753M8[t] + 0.228190847148109M9[t] -1.10780459080302M10[t] -1.1127438087348M11[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)	13.5418192607468	2.688148	5.0376	1e-06	1e-06
Connected	0.0236875343095792	0.052577	0.4505	0.653009	0.326504
Separate	0.0599170464092312	0.04885	1.2266	0.222005	0.111003
Learning	0.100158690643845	0.085977	1.165	0.245978	0.122989
Software	-0.0796049946788367	0.086997	-0.915	0.361718	0.180859
Depression	-0.34016858129956	0.05544	-6.1358	0	0
Belonging	0.0523382523886976	0.047941	1.0917	0.276792	0.138396
Belonging_Final	-0.0402494950926348	0.068906	-0.5841	0.56006	0.28003
M1	-1.04308022934069	0.760201	-1.3721	0.172177	0.086089
M2	-0.675853126651141	0.760575	-0.8886	0.375706	0.187853
M3	-0.00863759431825111	0.769145	-0.0112	0.991055	0.495528
M4	-1.12540140962164	0.756017	-1.4886	0.138797	0.069398
M5	-0.0047466453498684	0.759216	-0.0063	0.99502	0.49751
M6	-1.16617735315638	0.755106	-1.5444	0.124704	0.062352
M7	0.174722807443339	0.767709	0.2276	0.82029	0.410145
M8	-0.796081789230753	0.784562	-1.0147	0.311971	0.155985
M9	0.228190847148109	0.768882	0.2968	0.767063	0.383531
M10	-1.10780459080302	0.775446	-1.4286	0.155299	0.077649
M11	-1.1127438087348	0.768804	-1.4474	0.149982	0.074991

Multiple Linear Regression - Regression Statistics
Multiple R	0.623835595610296
R-squared	0.389170850350452
Adjusted R-squared	0.31228326507988
F-TEST (value)	5.06155641357359
F-TEST (DF numerator)	18
F-TEST (DF denominator)	143
p-value	8.5893293588768e-09
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	1.93855600480879
Sum Squared Residuals	537.393911880569

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	14	13.4974993019156	0.502500698084415
2	18	15.1405206275074	2.85947937249255
3	11	14.0513302476591	-3.05133024765908
4	12	13.9271549734614	-1.92715497346142
5	16	11.9094264372422	4.09057356275779
6	18	13.5569474272449	4.44305257275511
7	14	11.2465268006201	2.7534731993799
8	14	14.5690182801896	-0.569018280189591
9	15	15.8269372848301	-0.826937284830122
10	15	14.2758409498266	0.724159050173419
11	17	14.7539301641478	2.24606983585224
12	19	15.8557128284973	3.14428717150275
13	10	12.8568964703074	-2.85689647030739
14	16	13.5291839972933	2.47081600270674
15	18	16.0589427414605	1.9410572585395
16	14	12.5230785810638	1.47692141893624
17	14	14.3652812602964	-0.365281260296428
18	17	15.290968932544	1.70903106745596
19	14	16.1421382010196	-2.14213820101956
20	16	13.1804701746001	2.81952982539989
21	18	16.6550731358995	1.34492686410049
22	11	12.6986990265441	-1.69869902654407
23	14	13.9138965603826	0.0861034396174205
24	12	14.1612576261413	-2.16125762614132
25	17	14.9924127097268	2.00758729027322
26	9	15.6561500260502	-6.65615002605025
27	16	15.7946431276722	0.205356872327771
28	14	12.5407805458876	1.45921945411238
29	15	14.4520991622292	0.547900837770814
30	11	13.0779458969188	-2.07794589691875
31	16	15.8289710546179	0.171028945382111
32	13	12.2632142847049	0.736785715295122
33	17	15.6936508558796	1.30634914412037
34	15	14.5846867391197	0.415313260880307
35	14	13.2392850696611	0.760714930338873
36	16	15.6446482470382	0.355351752961835
37	9	10.5717698595048	-1.57176985950479
38	15	14.0462062886325	0.953793711367533
39	17	15.6085822978899	1.39141770211009
40	13	14.5484079949121	-1.54840799491211
41	15	16.137632139359	-1.13763213935895
42	16	12.9972733453711	3.0027266546289
43	16	16.1197963902802	-0.11979639028016
44	12	12.8697300642282	-0.869730064228191
45	12	15.1329916599772	-3.13299165997719
46	11	13.0808655264894	-2.08086552648935
47	15	14.643064188511	0.356935811488987
48	15	15.3194506496632	-0.319450649663228
49	17	13.4352453023156	3.56475469768436
50	13	14.5026869115115	-1.50268691151147
51	16	15.6517902275984	0.348209772401606
52	14	12.7124250316776	1.28757496832237
53	11	12.2040247150566	-1.2040247150566
54	12	12.6566746927878	-0.656674692787771
55	12	15.0017655764505	-3.00176557645045
56	15	14.4680713635992	0.531928636400828
57	16	15.0178944787386	0.982105521261361
58	15	14.560078741447	0.439921258553019
59	12	14.7775316327853	-2.77753163278528
60	12	14.0449723017412	-2.04497230174125
61	8	10.2142835927717	-2.21428359277173
62	13	14.5873463090955	-1.58734630909546
63	11	15.0605187612416	-4.06051876124159
64	14	12.4858894047386	1.51411059526138
65	15	13.9229970688027	1.07700293119726
66	10	14.5624496729493	-4.56244967294929
67	11	13.3357564154145	-2.33575641541446
68	12	14.0897653939569	-2.08976539395687
69	15	14.6827876839914	0.317212316008584
70	15	13.2857886848117	1.71421131518825
71	14	13.1644559445886	0.835544055411354
72	16	13.4750508868805	2.52494911311949
73	15	14.2144976361211	0.785502363878908
74	15	15.5107516448428	-0.510751644842808
75	13	15.2456812518827	-2.24568125188269
76	12	11.8756277571766	0.124372242823387
77	17	14.7088740428008	2.29112595719916
78	13	11.8228263702883	1.1771736297117
79	15	14.3001521174501	0.699847882549907
80	13	14.3237306674119	-1.3237306674119
81	15	15.8973822951496	-0.897382295149599
82	16	14.8036768383452	1.19632316165479
83	15	14.9656203928773	0.0343796071227446
84	16	14.9505821450144	1.04941785498557
85	15	13.8359985377326	1.16400146226743
86	14	14.0276999161927	-0.0276999161927164
87	15	15.1477995901464	-0.147799590146373
88	14	13.7214028207454	0.278597179254605
89	13	13.184139281065	-0.184139281064952
90	7	10.130954084458	-3.13095408445804
91	17	14.6403527313555	2.3596472686445
92	13	12.4199605839585	0.580039416041543
93	15	15.4593289284384	-0.459328928438398
94	14	12.6740457027538	1.32595429724622
95	13	14.1539764902371	-1.15397649023708
96	16	15.9826154005127	0.0173845994872993
97	12	12.4778623697042	-0.477862369704175
98	14	14.9276048895712	-0.927604889571163
99	17	15.6596474126952	1.34035258730478
100	15	14.6621489362737	0.337851063726275
101	17	15.8470758040679	1.15292419593205
102	12	12.6428292546157	-0.642829254615677
103	16	15.8690776457985	0.130922354201517
104	11	13.8301327565398	-2.83013275653977
105	15	14.4156460274657	0.584353972534306
106	9	11.0912333885881	-2.09123338858809
107	16	14.5178627027905	1.48213729720953
108	15	14.0396424213763	0.960357578623659
109	10	12.5709745711477	-2.57097457114771
110	10	10.0817441894812	-0.0817441894811905
111	15	14.4854176859255	0.514582314074452
112	11	12.6155872442189	-1.61558724421887
113	13	16.2289050013754	-3.22890500137544
114	14	11.9808939991625	2.01910600083749
115	18	15.0399726930887	2.96002730691131
116	16	15.273693879353	0.72630612064702
117	14	14.0514094874081	-0.0514094874081292
118	14	13.8719627306605	0.128037269339494
119	14	14.5936121346874	-0.593612134687446
120	14	14.6404301147931	-0.640430114793107
121	12	12.3192699891059	-0.319269989105903
122	14	13.1495843393045	0.850415660695499
123	15	15.8596531556732	-0.859653155673191
124	15	15.4224057707189	-0.422405770718911
125	15	14.9113158660432	0.0886841339567667
126	13	13.9968234078691	-0.996823407869108
127	17	17.0394036387198	-0.0394036387198468
128	17	15.6521636702678	1.34783632973218
129	19	15.8589686276712	3.14103137232879
130	15	13.1417750795587	1.85822492044134
131	13	14.2545109163481	-1.25451091634805
132	9	11.2893208994391	-2.28932089943914
133	15	15.4057530604746	-0.405753060474594
134	15	12.3187681810567	2.68123181894325
135	15	15.0729608592093	-0.0729608592092801
136	16	12.8552870361808	3.14471296381922
137	11	9.77827154437156	1.22172845562844
138	14	12.7493110850331	1.25068891496686
139	11	12.8047963720491	-1.80479637204905
140	15	14.1748590354367	0.825140964563255
141	13	14.5653320092836	-1.5653320092836
142	15	14.2912409165721	0.708759083427851
143	16	13.5441452794938	2.45585472050621
144	14	15.1440082250437	-1.14400822504374
145	15	13.4345744553235	1.56542554467648
146	16	14.7381707323768	1.26182926762321
147	16	14.6808924547411	1.31910754525886
148	11	12.9616085721338	-1.96160857213376
149	12	15.1318190267411	-3.13181902674109
150	9	11.2136817252037	-2.21368172520365
151	16	15.6312903631357	0.368709636864285
152	13	12.8851898457535	0.114810154246494
153	16	16.7425975252669	-0.742597525266862
154	12	14.6401056752832	-2.64010567528317
155	9	11.4781085234895	-2.4781085234895
156	13	12.4523082538588	0.547691746141177
157	13	12.1729621438485	0.827037856151482
158	14	13.7835819470837	0.216418052916265
159	19	15.6221401862049	3.37785981379515
160	13	15.1481953308108	-2.14819533081078
161	12	13.2181386505488	-1.21813865054881
162	13	12.3204201055537	0.679579894446278

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
22	0.984674503751012	0.0306509924979767	0.0153254962489884
23	0.980133690703059	0.0397326185938826	0.0198663092969413
24	0.984756078239196	0.0304878435216083	0.0152439217608041
25	0.982352329035722	0.0352953419285556	0.0176476709642778
26	0.999933441000011	0.000133117999978931	6.65589999894656e-05
27	0.999924498517948	0.000151002964103535	7.55014820517676e-05
28	0.999920522488637	0.000158955022726529	7.94775113632647e-05
29	0.999843979140867	0.000312041718266482	0.000156020859133241
30	0.999911722806668	0.000176554386664257	8.82771933321285e-05
31	0.999862543372048	0.000274913255903705	0.000137456627951853
32	0.999819119694992	0.000361760610015895	0.000180880305007948
33	0.999672451484282	0.000655097031436829	0.000327548515718415
34	0.999538241622893	0.000923516754213293	0.000461758377106646
35	0.99953019038611	0.000939619227779685	0.000469809613889843
36	0.999163836639357	0.00167232672128612	0.000836163360643058
37	0.999000754566183	0.00199849086763364	0.000999245433816821
38	0.998603595821895	0.00279280835621065	0.00139640417810532
39	0.998330761842672	0.00333847631465616	0.00166923815732808
40	0.997881961667444	0.00423607666511276	0.00211803833255638
41	0.996869832141009	0.0062603357179823	0.00313016785899115
42	0.996825139147221	0.00634972170555811	0.00317486085277905
43	0.995055765507167	0.00988846898566514	0.00494423449283257
44	0.994205313363122	0.0115893732737565	0.00579468663687823
45	0.99703149275729	0.00593701448542049	0.00296850724271024
46	0.996850185941657	0.00629962811668602	0.00314981405834301
47	0.995190206190631	0.0096195876187376	0.0048097938093688
48	0.993489217120961	0.0130215657580787	0.00651078287903934
49	0.996040667739845	0.00791866452031014	0.00395933226015507
50	0.995021669058131	0.00995666188373789	0.00497833094186894
51	0.992680081867159	0.014639836265682	0.00731991813284098
52	0.990552921890353	0.0188941562192943	0.00944707810964713
53	0.988960037526577	0.0220799249468459	0.011039962473423
54	0.984797910987681	0.0304041780246383	0.0152020890123192
55	0.989792621430566	0.0204147571388684	0.0102073785694342
56	0.985784244313018	0.0284315113739644	0.0142157556869822
57	0.98051096880788	0.0389780623842398	0.0194890311921199
58	0.975001041832888	0.0499979163342236	0.0249989581671118
59	0.983828463015931	0.0323430739681383	0.0161715369840692
60	0.987660269538451	0.0246794609230971	0.0123397304615486
61	0.988091678282493	0.023816643435014	0.011908321717507
62	0.9866449349873	0.0267101300254006	0.0133550650127003
63	0.995415479803189	0.0091690403936226	0.0045845201968113
64	0.994430336515701	0.0111393269685971	0.00556966348429856
65	0.992755752459026	0.0144884950819485	0.00724424754097423
66	0.998949391086921	0.00210121782615836	0.00105060891307918
67	0.99918356586845	0.00163286826309974	0.000816434131549871
68	0.999233915825533	0.00153216834893494	0.000766084174467471
69	0.998820764742117	0.00235847051576563	0.00117923525788281
70	0.998683169217937	0.002633661564126	0.001316830782063
71	0.998145427413286	0.00370914517342796	0.00185457258671398
72	0.998469535636973	0.00306092872605413	0.00153046436302706
73	0.997922645918115	0.00415470816376975	0.00207735408188487
74	0.997076270012868	0.00584745997426355	0.00292372998713177
75	0.997983765104378	0.00403246979124477	0.00201623489562238
76	0.997023799119986	0.00595240176002715	0.00297620088001358
77	0.997716130041162	0.00456773991767533	0.00228386995883767
78	0.99704776002805	0.00590447994390106	0.00295223997195053
79	0.9958570325572	0.0082859348855993	0.00414296744279965
80	0.995870016981887	0.00825996603622657	0.00412998301811329
81	0.994856826703398	0.0102863465932035	0.00514317329660177
82	0.993158469958729	0.0136830600825421	0.00684153004127104
83	0.990310599427133	0.0193788011457339	0.00968940057286696
84	0.987184040101346	0.0256319197973073	0.0128159598986537
85	0.985028225625871	0.0299435487482576	0.0149717743741288
86	0.980328937797851	0.039342124404298	0.019671062202149
87	0.974125522642001	0.0517489547159983	0.0258744773579991
88	0.965996320080744	0.0680073598385119	0.0340036799192559
89	0.956373062306066	0.0872538753878672	0.0436269376939336
90	0.970782132875468	0.0584357342490635	0.0292178671245317
91	0.973889742875521	0.052220514248958	0.026110257124479
92	0.965597224596812	0.0688055508063766	0.0344027754031883
93	0.955697181103215	0.0886056377935706	0.0443028188967853
94	0.948540336947137	0.102919326105727	0.0514596630528634
95	0.938535971355432	0.122928057289136	0.0614640286445682
96	0.920908233278736	0.158183533442527	0.0790917667212636
97	0.89986555585632	0.20026888828736	0.10013444414368
98	0.899177940003847	0.201644119992306	0.100822059996153
99	0.881494522103826	0.237010955792348	0.118505477896174
100	0.860304601640809	0.279390796718382	0.139695398359191
101	0.858185172053456	0.283629655893088	0.141814827946544
102	0.830992063748099	0.338015872503802	0.169007936251901
103	0.793828684534925	0.412342630930151	0.206171315465075
104	0.88553644635148	0.22892710729704	0.11446355364852
105	0.862988533933939	0.274022932132121	0.13701146606606
106	0.87094160028717	0.25811679942566	0.12905839971283
107	0.857863848858258	0.284272302283484	0.142136151141742
108	0.86078246392148	0.278435072157039	0.13921753607852
109	0.878183427658619	0.243633144682761	0.121816572341381
110	0.845880922122169	0.308238155755663	0.154119077877831
111	0.809482914456636	0.381034171086729	0.190517085543364
112	0.784432355623644	0.431135288752712	0.215567644376356
113	0.790777291122169	0.418445417755662	0.209222708877831
114	0.969258591843628	0.0614828163127442	0.0307414081563721
115	0.986805573245143	0.026388853509715	0.0131944267548575
116	0.989013909850615	0.0219721802987698	0.0109860901493849
117	0.983808561714696	0.0323828765706072	0.0161914382853036
118	0.975845188924136	0.0483096221517275	0.0241548110758637
119	0.964566272710731	0.0708674545785372	0.0354337272892686
120	0.956515251327735	0.0869694973445291	0.0434847486722646
121	0.937578431115813	0.124843137768373	0.0624215688841867
122	0.926631714493193	0.146736571013614	0.0733682855068072
123	0.901139511654153	0.197720976691694	0.0988604883458468
124	0.87506892186188	0.24986215627624	0.12493107813812
125	0.835476386922178	0.329047226155643	0.164523613077822
126	0.786243600950117	0.427512798099766	0.213756399049883
127	0.72622369207743	0.54755261584514	0.27377630792257
128	0.755658919566318	0.488682160867364	0.244341080433682
129	0.711154272783143	0.577691454433714	0.288845727216857
130	0.680040732332875	0.63991853533425	0.319959267667125
131	0.60486193245547	0.790276135089061	0.39513806754453
132	0.526559799995574	0.946880400008852	0.473440200004426
133	0.442265939141394	0.884531878282789	0.557734060858606
134	0.376287459465075	0.752574918930149	0.623712540534925
135	0.289690767000216	0.579381534000431	0.710309232999784
136	0.253754388985107	0.507508777970215	0.746245611014893
137	0.453206609523181	0.906413219046362	0.546793390476819
138	0.388996459742879	0.777992919485757	0.611003540257121
139	0.268328699845435	0.53665739969087	0.731671300154565
140	0.660470540221629	0.679058919556742	0.339529459778371

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	39	0.327731092436975	NOK
5% type I error level	69	0.579831932773109	NOK
10% type I error level	79	0.663865546218487	NOK