Multiple Linear Regression - Estimated Regression Equation

Happiness[t] = + 15.4893520503043 + 0.0216155702168623Connected[t] + 0.0649005494285598Separate[t] + 0.0731669569957836Learning[t] -0.0475755057203567Software[t] -0.385554294834322Depression[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)	15.4893520503043	2.277804	6.8001	0	0
Connected	0.0216155702168623	0.050678	0.4265	0.670312	0.335156
Separate	0.0649005494285598	0.04706	1.3791	0.16984	0.08492
Learning	0.0731669569957836	0.085303	0.8577	0.392358	0.196179
Software	-0.0475755057203567	0.086735	-0.5485	0.584121	0.29206
Depression	-0.385554294834322	0.050539	-7.6288	0	0

Multiple Linear Regression - Regression Statistics
Multiple R	0.559914901167637
R-squared	0.313504696549565
Adjusted R-squared	0.291501641951794
F-TEST (value)	14.2482351782799
F-TEST (DF numerator)	5
F-TEST (DF denominator)	156
p-value	1.75743863906064e-11
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	1.96762793629027
Sum Squared Residuals	603.963312524505

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	14	14.5954241417700	-0.595424141769973
2	18	14.8154203763069	3.18457962369312
3	11	13.6881178562438	-2.68811785624375
4	12	14.4865526407722	-2.48655264077222
5	16	10.9348173985899	5.06518260141014
6	18	13.9767767870524	4.02322321294757
7	14	10.6813479489678	3.31865205103223
8	14	14.7510512487800	-0.751051248779952
9	15	15.1369201890644	-0.136920189064369
10	15	14.5551945143819	0.444805485618133
11	17	15.1620340572161	1.83796594278386
12	19	15.9894621432960	3.01053785670398
13	10	13.3987137693181	-3.39871376931805
14	16	14.0481607883753	1.95183921162473
15	18	15.2786489310972	2.72135106890282
16	14	13.4516065869983	0.548393413001706
17	14	13.5683193298779	0.431680670122103
18	17	15.4283004249242	1.57169957507585
19	14	15.7367118817041	-1.73671188170413
20	16	13.8454272893998	2.15457271060016
21	18	16.2712291135547	1.72877088644531
22	11	13.3733568749201	-2.37335687492010
23	14	14.9436192375906	-0.943619237590552
24	12	14.0698301973701	-2.06983019737010
25	17	14.9837383447434	2.01626165525662
26	9	15.6077760519643	-6.60777605196432
27	16	14.9928508196623	1.00714918033767
28	14	13.2521190486544	0.74788095134564
29	15	13.5463891142109	1.45361088578906
30	11	13.9023760767113	-2.90237607671127
31	16	15.0332597438102	0.966740256189755
32	13	12.8638750435452	0.136124956454824
33	17	14.9940845730077	2.00591542699229
34	15	14.984269766645	0.015730233354991
35	14	13.6125234169849	0.387476583015122
36	16	15.4174742286397	0.582525771360257
37	9	10.8632512578279	-1.86325125782788
38	15	14.2360105005386	0.763989499461395
39	17	14.9674939252644	2.03250607473563
40	13	15.2269884454227	-2.22698844542267
41	15	15.5908733312622	-0.590873331262156
42	16	13.4216707704362	2.57832922956377
43	16	16.0528334956947	-0.0528334956946907
44	12	13.5384373520938	-1.53843735209381
45	12	14.4354442001046	-2.43544420010457
46	11	13.7823720037909	-2.78237200379091
47	15	15.7777323163263	-0.777732316326299
48	15	14.7423610968670	0.257638903132960
49	17	13.5977597828904	3.40224021710964
50	13	14.5998953863781	-1.59989538637809
51	16	15.2963424590335	0.703657540966547
52	14	13.2788889931575	0.721111006842455
53	11	11.6898885366737	-0.689888536673653
54	12	13.8449319258502	-1.84493192585024
55	12	14.4373957201405	-2.43739572014050
56	15	14.4781785556490	0.521821444350952
57	16	14.126537379775	1.87346262022500
58	15	15.4525988569437	-0.452598856943663
59	12	15.3441787714259	-3.34417877142593
60	12	13.3641175206796	-1.36411752067962
61	8	10.7889235880303	-2.78892358803027
62	13	14.4904761043925	-1.49047610439246
63	11	14.3737633615129	-3.37376336151285
64	14	13.5342006643631	0.465799335636875
65	15	13.823757880405	1.17624211959499
66	10	15.0314767881373	-5.0314767881373
67	11	12.6355569417665	-1.63555694176653
68	12	14.0571571163696	-2.05715711636956
69	15	14.2232728483632	0.77672715163678
70	15	13.8492224523589	1.15077754764110
71	14	13.9860231893220	0.0139768106780217
72	16	13.3433480178145	2.65665198218552
73	15	14.3941451783843	0.605854821615662
74	15	15.7670714426119	-0.767071442611874
75	13	14.3352642723594	-1.33526427235941
76	12	11.7695028872117	0.230497112788324
77	17	14.2304323819066	2.76956761809341
78	13	12.3291162067881	0.670883793211928
79	15	13.4745635881165	1.52543641188352
80	13	15.1712195726786	-2.17121957267864
81	15	14.8977536469996	0.102246353000413
82	16	15.7922391495416	0.207760850458387
83	15	15.7769939265305	-0.776993926530516
84	16	14.3307930277513	1.66920697224875
85	15	14.3351912318159	0.664808768184144
86	14	13.8972933216289	0.102706678371143
87	15	14.4258171598704	0.574182840129564
88	14	14.3823982533081	-0.382398253308145
89	13	13.0094719890806	-0.00947198908060875
90	7	10.3887877985406	-3.38878779854058
91	17	13.9334726060752	3.06652739392485
92	13	13.0912214204334	-0.0912214204333582
93	15	14.4943789449075	0.505621055092534
94	14	12.7415495450212	1.25845045497883
95	13	14.5879414934078	-1.58794149340775
96	16	15.1225980797415	0.877401920258526
97	12	12.9439683985465	-0.943968398546507
98	14	14.7592085574516	-0.759208557451583
99	17	14.8544148290099	2.14558517099008
100	15	15.2105094690662	-0.210509469066193
101	17	15.2962347814775	1.70376521852249
102	12	13.0391194099872	-1.03911940998722
103	16	14.7918879230665	1.20811207693352
104	11	14.3313422300788	-3.33134223007882
105	15	13.212259326834	1.78774067316599
106	9	11.4855252111415	-2.48552521114145
107	16	15.0140979056511	0.985902094348878
108	15	13.3376083828486	1.66239161715145
109	10	13.4030581346047	-3.40305813460468
110	10	10.4363165135120	-0.436316513512027
111	15	13.5464429529889	1.45355704701109
112	11	13.0224526675022	-2.02245266750218
113	13	15.3213832866417	-2.32138328664166
114	14	12.9672938838928	1.03270611610724
115	18	14.2713437176332	3.72865628236683
116	16	15.2089264332583	0.79107356674167
117	14	13.8067835404989	0.193216459501065
118	14	14.4518309341519	-0.451830934151903
119	14	15.4320363219727	-1.43203632197268
120	14	13.4636143187466	0.536385681253391
121	12	13.2485116518239	-1.24851165182386
122	14	13.0661791714855	0.9338208285145
123	15	14.9810322753822	0.0189677246177731
124	15	16.1755288997864	-1.17552889978641
125	15	14.4525084371406	0.547491562859352
126	13	14.5170943411191	-1.51709434111911
127	17	15.9464918095344	1.05350819046558
128	17	15.8365233252212	1.16347667477879
129	19	14.9673132071649	4.03268679283513
130	15	13.7300822272162	1.26991777278379
131	13	14.7765874399378	-1.77658743993776
132	9	10.6686587084378	-1.66865870843779
133	15	15.6898195056619	-0.689819505661932
134	15	12.5913474275270	2.40865257247301
135	15	14.5821288178983	0.417871182101734
136	16	13.1920043892841	2.80799561071594
137	11	9.17764221207729	1.82235778792271
138	14	13.6722143320095	0.327785667990505
139	11	12.5695511392106	-1.56955113921062
140	15	14.7088178834745	0.291182116525516
141	13	13.9614585234978	-0.96145852349778
142	15	15.3221932956414	-0.322193295641354
143	16	13.6160025131542	2.3839974868458
144	14	14.3128925319208	-0.312892531920831
145	15	13.6728365748806	1.32716342511938
146	16	14.4758601722815	1.52413982771845
147	16	14.0052372453626	1.99476275463743
148	11	13.9719908969942	-2.97199089699418
149	12	14.5516353296399	-2.55163532963993
150	9	11.5201738772182	-2.52017387721821
151	16	14.6138546381623	1.38614536183766
152	13	12.7231260966578	0.276873903342167
153	16	15.9630054229033	0.0369945770967159
154	12	15.0355851752068	-3.03558517520681
155	9	11.7707174387915	-2.77071743879147
156	13	11.6256711169233	1.37432888307674
157	13	13.0912214204334	-0.0912214204333582
158	14	13.8503279050431	0.149672094956893
159	19	14.9673132071649	4.03268679283513
160	13	15.4784511148912	-2.47845111489121
161	12	12.0099916584122	-0.0099916584121995
162	13	12.9623988949389	0.0376011050610872

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
9	0.610384536324888	0.779230927350224	0.389615463675112
10	0.697694753005909	0.604610493988182	0.302305246994091
11	0.60133736106553	0.797325277868941	0.398662638934470
12	0.837510118435455	0.324979763129089	0.162489881564545
13	0.971178285658212	0.0576434286835757	0.0288217143417878
14	0.969003983338667	0.0619920333226657	0.0309960166613329
15	0.986461702507744	0.027076594984512	0.013538297492256
16	0.97796589466562	0.0440682106687614	0.0220341053343807
17	0.968789972929166	0.062420054141668	0.031210027070834
18	0.964863491588869	0.070273016822263	0.0351365084111315
19	0.95899647331651	0.0820070533669787	0.0410035266834893
20	0.948293502106552	0.103412995786896	0.0517064978934478
21	0.94022719959051	0.119545600818981	0.0597728004094907
22	0.96430397169394	0.0713920566121196	0.0356960283060598
23	0.953712524635104	0.0925749507297923	0.0462874753648962
24	0.950067273582667	0.099865452834667	0.0499327264173335
25	0.936994885726581	0.126010228546837	0.0630051142734187
26	0.999304202358273	0.00139159528345385	0.000695797641726925
27	0.99892492081625	0.00215015836749926	0.00107507918374963
28	0.998270873708441	0.00345825258311753	0.00172912629155877
29	0.997476553497488	0.00504689300502335	0.00252344650251167
30	0.998858671557668	0.00228265688466337	0.00114132844233168
31	0.998239272813728	0.00352145437254362	0.00176072718627181
32	0.997430900316827	0.00513819936634663	0.00256909968317332
33	0.99688543569227	0.00622912861545985	0.00311456430772993
34	0.995286337375697	0.00942732524860632	0.00471366262430316
35	0.99331203604572	0.0133759279085593	0.00668796395427964
36	0.990336164997295	0.0193276700054101	0.00966383500270503
37	0.992421822821826	0.0151563543563488	0.00757817717817441
38	0.989338064758038	0.0213238704839241	0.0106619352419621
39	0.988772532623797	0.0224549347524059	0.0112274673762030
40	0.989547221968181	0.0209055560636378	0.0104527780318189
41	0.98582809550672	0.0283438089865612	0.0141719044932806
42	0.98630329712292	0.0273934057541603	0.0136967028770801
43	0.981254967327316	0.037490065345367	0.0187450326726835
44	0.979955554401584	0.0400888911968312	0.0200444455984156
45	0.984191591291725	0.0316168174165510	0.0158084087082755
46	0.988428139344799	0.0231437213104027	0.0115718606552013
47	0.984454041514929	0.0310919169701425	0.0155459584850712
48	0.978897390778568	0.0422052184428637	0.0211026092214319
49	0.987054319310723	0.0258913613785544	0.0129456806892772
50	0.985341394041754	0.0293172119164926	0.0146586059582463
51	0.980614005629716	0.0387719887405673	0.0193859943702837
52	0.974581892720378	0.0508362145592431	0.0254181072796216
53	0.968794738379996	0.0624105232400088	0.0312052616200044
54	0.96836521220702	0.0632695755859608	0.0316347877929804
55	0.970841579464537	0.0583168410709264	0.0291584205354632
56	0.96272746457092	0.0745450708581605	0.0372725354290802
57	0.96076684637725	0.0784663072454991	0.0392331536227495
58	0.950320046062205	0.0993599078755893	0.0496799539377946
59	0.966942357316818	0.0661152853663635	0.0330576426831817
60	0.962883325495661	0.0742333490086779	0.0371166745043390
61	0.972997305582211	0.0540053888355773	0.0270026944177886
62	0.969617805597308	0.0607643888053835	0.0303821944026918
63	0.98193954774556	0.0361209045088797	0.0180604522544398
64	0.976402268943361	0.0471954621132777	0.0235977310566388
65	0.971370929002428	0.0572581419951431	0.0286290709975716
66	0.994003462638368	0.0119930747232637	0.00599653736163187
67	0.993398160944323	0.0132036781113540	0.00660183905567702
68	0.993843691806439	0.0123126163871229	0.00615630819356147
69	0.991986361743055	0.0160272765138910	0.00801363825694548
70	0.990166592537628	0.0196668149247444	0.00983340746237221
71	0.986770192019729	0.0264596159605421	0.0132298079802710
72	0.98974405633396	0.0205118873320813	0.0102559436660407
73	0.986627834996308	0.0267443300073836	0.0133721650036918
74	0.982750826300367	0.0344983473992665	0.0172491736996333
75	0.98031342832297	0.039373143354058	0.019686571677029
76	0.97414936972899	0.0517012605420204	0.0258506302710102
77	0.980295361560843	0.0394092768783134	0.0197046384391567
78	0.974910154625375	0.0501796907492509	0.0250898453746255
79	0.971904586479246	0.056190827041507	0.0280954135207535
80	0.976044897834906	0.0479102043301887	0.0239551021650943
81	0.96870350539882	0.0625929892023598	0.0312964946011799
82	0.959714467802454	0.0805710643950919	0.0402855321975460
83	0.950762533941635	0.0984749321167307	0.0492374660583653
84	0.946269823093454	0.107460353813091	0.0537301769065455
85	0.933878268817473	0.132243462365053	0.0661217311825267
86	0.917572079156132	0.164855841687736	0.0824279208438682
87	0.89974807999574	0.200503840008520	0.100251920004260
88	0.878503855046042	0.242992289907916	0.121496144953958
89	0.8536528999544	0.2926942000912	0.1463471000456
90	0.895166517577366	0.209666964845268	0.104833482422634
91	0.923018111035449	0.153963777929103	0.0769818889645513
92	0.904526280004947	0.190947439990107	0.0954737199950534
93	0.88638823995236	0.227223520095281	0.113611760047641
94	0.871294234444382	0.257411531111235	0.128705765555618
95	0.864764793802535	0.270470412394930	0.135235206197465
96	0.841324363215982	0.317351273568037	0.158675636784018
97	0.817174596603026	0.365650806793949	0.182825403396974
98	0.793733346364088	0.412533307271824	0.206266653635912
99	0.795667793483921	0.408664413032158	0.204332206516079
100	0.76031445143032	0.47937109713936	0.23968554856968
101	0.750139008127513	0.499721983744974	0.249860991872487
102	0.720849210185643	0.558301579628715	0.279150789814357
103	0.702644568939777	0.594710862120446	0.297355431060223
104	0.80176152213414	0.39647695573172	0.19823847786586
105	0.81860973089584	0.362780538208321	0.181390269104161
106	0.848127387233613	0.303745225532775	0.151872612766387
107	0.823840016853126	0.352319966293749	0.176159983146874
108	0.829746801280426	0.340506397439148	0.170253198719574
109	0.88427338744642	0.231453225107161	0.115726612553580
110	0.860101552025911	0.279796895948178	0.139898447974089
111	0.857485663558765	0.285028672882470	0.142514336441235
112	0.850653218582409	0.298693562835182	0.149346781417591
113	0.844810459792905	0.31037908041419	0.155189540207095
114	0.820938169631635	0.358123660736729	0.179061830368365
115	0.886880605550286	0.226238788899427	0.113119394449714
116	0.861596080480604	0.276807839038792	0.138403919519396
117	0.842351711970607	0.315296576058786	0.157648288029393
118	0.808826438387924	0.382347123224151	0.191173561612076
119	0.795390577831738	0.409218844336524	0.204609422168262
120	0.764476658820438	0.471046682359124	0.235523341179562
121	0.727886711758426	0.544226576483148	0.272113288241574
122	0.68450082862825	0.6309983427435	0.31549917137175
123	0.635651177598462	0.728697644803076	0.364348822401538
124	0.593058167704078	0.813883664591844	0.406941832295922
125	0.538003162864335	0.92399367427133	0.461996837135665
126	0.515376074484044	0.969247851031911	0.484623925515956
127	0.461249030640761	0.922498061281523	0.538750969359239
128	0.437303974997241	0.874607949994482	0.562696025002759
129	0.634963287482515	0.730073425034971	0.365036712517486
130	0.593460485661681	0.813079028676637	0.406539514338319
131	0.591438694513771	0.817122610972459	0.408561305486229
132	0.58029271418835	0.8394145716233	0.41970728581165
133	0.518440510065116	0.963118979869769	0.481559489934884
134	0.507838317885237	0.984323364229526	0.492161682114763
135	0.459078276327237	0.918156552654474	0.540921723672763
136	0.495988723710652	0.991977447421303	0.504011276289348
137	0.454180068633283	0.908360137266565	0.545819931366717
138	0.39537266574439	0.79074533148878	0.60462733425561
139	0.353036592314713	0.706073184629426	0.646963407685287
140	0.287369836863365	0.574739673726729	0.712630163136635
141	0.283893370426812	0.567786740853623	0.716106629573188
142	0.223670079669777	0.447340159339554	0.776329920330223
143	0.252724079476739	0.505448158953478	0.747275920523261
144	0.192040993644147	0.384081987288294	0.807959006355853
145	0.147848800993597	0.295697601987193	0.852151199006403
146	0.108484152267255	0.216968304534509	0.891515847732745
147	0.197810955969729	0.395621911939459	0.80218904403027
148	0.631913912458567	0.736172175082866	0.368086087541433
149	0.676265062495184	0.647469875009632	0.323734937504816
150	0.570899813553849	0.858200372892301	0.429100186446151
151	0.504722831749453	0.990554336501095	0.495277168250547
152	0.363077299053851	0.726154598107702	0.636922700946149
153	0.266137821380696	0.532275642761392	0.733862178619304

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	9	0.0620689655172414	NOK
5% type I error level	42	0.289655172413793	NOK
10% type I error level	68	0.468965517241379	NOK