Multiple Linear Regression - Estimated Regression Equation

Happiness[t] = + 7.80305927515177 + 17.4163705006130Pop[t] + 0.0579165349035982Age[t] -0.156072330488879Age_p[t] -0.0921950616972788Concern_over_mistakes[t] + 0.149224968338923Concern_over_mistakes_p[t] + 0.0116215720252558Doubts_about_actions[t] -0.44594773439194Doubts_about_actions_p[t] + 0.0441574359203689Parental_expectations[t] -0.00935434412190598Parental_expectations_p[t] + 0.0471039134932978Parental_criticism[t] -0.194860597403451Parental_criticism_p[t] + 0.151966046354645Popularity[t] -0.265853714177041Popularity_p[t] + 0.275841334364272Perceived_learning_competence[t] -0.419494182412067Perceived_learning_competence_p[t] -0.059154172572458Amotivation[t] -0.09235574763941Amotivation_p[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)	7.80305927515177	3.855283	2.024	0.045086	0.022543
Pop	17.4163705006130	5.139877	3.3885	0.000938	0.000469
Age	0.0579165349035982	0.080771	0.717	0.474672	0.237336
Age_p	-0.156072330488879	0.120191	-1.2985	0.196475	0.098238
Concern_over_mistakes	-0.0921950616972788	0.057377	-1.6068	0.110594	0.055297
Concern_over_mistakes_p	0.149224968338923	0.07632	1.9552	0.052768	0.026384
Doubts_about_actions	0.0116215720252558	0.116138	0.1001	0.920451	0.460225
Doubts_about_actions_p	-0.44594773439194	0.156561	-2.8484	0.005133	0.002567
Parental_expectations	0.0441574359203689	0.113091	0.3905	0.696857	0.348429
Parental_expectations_p	-0.00935434412190598	0.144955	-0.0645	0.948648	0.474324
Parental_criticism	0.0471039134932978	0.144518	0.3259	0.745012	0.372506
Parental_criticism_p	-0.194860597403451	0.176933	-1.1013	0.272855	0.136427
Popularity	0.151966046354645	0.097226	1.563	0.120557	0.060278
Popularity_p	-0.265853714177041	0.128616	-2.067	0.040779	0.02039
Perceived_learning_competence	0.275841334364272	0.136637	2.0188	0.045631	0.022816
Perceived_learning_competence_p	-0.419494182412067	0.182803	-2.2948	0.023399	0.011699
Amotivation	-0.059154172572458	0.171926	-0.3441	0.731369	0.365684
Amotivation_p	-0.09235574763941	0.190163	-0.4857	0.628048	0.314024

Multiple Linear Regression - Regression Statistics
Multiple R	0.551151442308679
R-squared	0.303767912358937
Adjusted R-squared	0.209831837042285
F-TEST (value)	3.2337726622595
F-TEST (DF numerator)	17
F-TEST (DF denominator)	126
p-value	7.93946563379944e-05
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	2.11904678725665
Sum Squared Residuals	565.785270109425

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	14	16.4449038106865	-2.44490381068653
2	18	15.7541897500416	2.24581024995843
3	11	13.6664783894794	-2.66647838947938
4	12	12.3264143694462	-0.326414369446192
5	16	15.3105723046397	0.689427695360279
6	18	15.9734671883796	2.02653281162036
7	14	15.846137955077	-1.84613795507701
8	14	14.4724372187036	-0.472437218703563
9	15	15.6398598635021	-0.639859863502078
10	15	12.3212337507793	2.67876624922068
11	17	14.6316845729493	2.36831542705073
12	19	14.1210850154642	4.87891498453579
13	10	13.8687769622295	-3.86877696222945
14	18	15.9785438903078	2.02145610969221
15	14	13.9655310745338	0.0344689254662466
16	14	14.437739941546	-0.437739941545996
17	17	14.3689284846416	2.63107151535841
18	14	15.1065775316393	-1.10657753163932
19	16	16.0046013562127	-0.00460135621266727
20	18	13.0205793072042	4.97942069279577
21	14	13.4773267079694	0.522673292030594
22	12	11.8088722476630	0.19112775233703
23	17	13.8985372125633	3.10146278743668
24	9	14.7711227710924	-5.77112277109235
25	16	15.5682321704595	0.431767829540484
26	14	12.9607127455222	1.03928725447783
27	11	13.5753866236095	-2.57538662360950
28	16	16.531157979698	-0.531157979697993
29	13	12.2186271904323	0.781372809567731
30	17	15.0524052292497	1.94759477075034
31	15	15.6822476121662	-0.682247612166205
32	14	14.2757627709241	-0.275762770924058
33	16	11.4510107137883	4.54898928621168
34	9	11.6206886344894	-2.62068863448942
35	15	13.0738996467414	1.92610035325862
36	17	16.3944950210218	0.605504978978197
37	13	13.9194452468857	-0.919445246885724
38	15	14.2756763490710	0.724323650929016
39	16	15.2974497841682	0.702550215831777
40	16	16.0659978482457	-0.065997848245705
41	12	13.3956435702274	-1.39564357022737
42	11	13.3647940920151	-2.36479409201511
43	15	15.1253136743861	-0.125313674386131
44	17	15.0808544660365	1.91914553396351
45	13	14.1074912214962	-1.10749122149620
46	16	12.1624104318225	3.83758956817754
47	14	12.8878826608025	1.11211733919750
48	11	12.1390467713564	-1.13904677135642
49	12	12.6918401028865	-0.691840102886545
50	12	12.0617611816134	-0.0617611816133956
51	15	14.3958818811173	0.604118118882706
52	16	16.1805457428282	-0.180545742828208
53	15	15.338190943667	-0.338190943666999
54	12	14.3182556186467	-2.31825561864671
55	12	14.5678023348977	-2.56780233489766
56	8	12.0913631046910	-4.09136310469096
57	13	13.9499996294482	-0.949999629448203
58	11	14.1719838671055	-3.17198386710553
59	14	16.2529809586942	-2.25298095869415
60	15	13.1905701431104	1.80942985688959
61	10	12.4709057739645	-2.47090577396451
62	11	12.4483158070715	-1.44831580707154
63	12	14.2276371013400	-2.22763710133998
64	15	14.4638333817266	0.536166618273435
65	15	14.5445039769890	0.455496023011029
66	14	13.7141505316615	0.285849468338474
67	16	12.6906172282805	3.30938277171949
68	15	15.0593256490364	-0.0593256490363937
69	15	14.3420406650057	0.657959334994292
70	13	14.6631598442056	-1.66315984420558
71	17	14.7709482012146	2.22905179878537
72	13	12.7178968246213	0.282103175378710
73	15	11.7465401624124	3.25345983758762
74	13	14.3599790923522	-1.35997909235220
75	15	14.8487223470941	0.151277652905856
76	16	14.6729377356415	1.32706226435852
77	15	14.4067536482802	0.59324635171983
78	16	13.3596310079674	2.64036899203256
79	15	13.9583341481188	1.04166585188117
80	14	14.3193755762845	-0.319375576284458
81	15	12.4495158826618	2.55048411733815
82	7	11.0743902824004	-4.07439028240037
83	17	16.3395273344472	0.660472665552797
84	13	14.6977416730483	-1.69774167304829
85	15	13.8447720094466	1.15522799055341
86	14	14.0112754708934	-0.0112754708934258
87	13	13.4775057303095	-0.477505730309453
88	16	16.3508300171744	-0.350830017174373
89	12	13.8147797415958	-1.81477974159582
90	14	15.2288173552706	-1.22881735527064
91	17	12.5093683051598	4.49063169484016
92	15	14.0948319157220	0.905168084277952
93	17	13.1372109262309	3.8627890737691
94	12	14.4642925657112	-2.46429256571117
95	16	15.0734127486121	0.926587251387942
96	11	13.5846150084969	-2.58461500849692
97	15	12.6962856713824	2.30371432861762
98	9	13.1475683942831	-4.14756839428309
99	16	14.3207374251218	1.67926257487817
100	10	11.8142033109291	-1.81420331092914
101	10	12.6928516973584	-2.69285169735840
102	15	15.0703700173387	-0.0703700173386514
103	11	13.4967130072771	-2.49671300727713
104	13	15.4086513356288	-2.40865133562876
105	14	14.2477323247196	-0.247732324719573
106	18	15.3757356593952	2.62426434060484
107	16	14.6997733666157	1.30022663338427
108	14	12.9145808336005	1.08541916639951
109	14	15.3577004055355	-1.35770040553550
110	14	13.8825739553111	0.117426044688885
111	14	15.4281010931093	-1.42810109310932
112	12	13.7535048654012	-1.75350486540121
113	14	13.4811229943765	0.518877005623528
114	15	15.7405108149539	-0.740510814953864
115	15	14.9538852051491	0.0461147948509387
116	13	13.8076319769972	-0.807631976997153
117	17	14.9633509481369	2.03664905186309
118	17	15.7830556443950	1.21694435560503
119	19	15.3272861965998	3.67271380340016
120	15	14.4112736577084	0.588726342291602
121	13	13.3930813795265	-0.393081379526461
122	9	11.0329011410282	-2.03290114102822
123	15	15.4803261391011	-0.480326139101051
124	15	14.2408972415409	0.759102758459076
125	16	14.6698347845364	1.33016521546355
126	11	11.9532693758456	-0.953269375845617
127	14	13.6633150508708	0.33668494912919
128	11	12.9528328761856	-1.95283287618557
129	15	15.5498237842772	-0.54982378427716
130	13	12.0610673678835	0.938932632116483
131	16	13.8102043113500	2.18979568865003
132	14	15.2203160934167	-1.22031609341668
133	15	14.5516631824448	0.448336817555191
134	16	15.1576435446834	0.842356455316636
135	16	14.8470828962593	1.15291710374066
136	11	11.9896549580181	-0.98965495801812
137	13	14.3663242279658	-1.36632422796584
138	16	15.5682321704595	0.431767829540484
139	12	13.1734417187557	-1.17344171875566
140	9	11.4050765582403	-2.40507655824028
141	13	11.6786420211317	1.32135797886827
142	13	14.6977416730483	-1.69774167304829
143	19	15.3272861965998	3.67271380340016
144	13	15.8422351949844	-2.84223519498437

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
21	0.943301244428447	0.113397511143106	0.0566987555715528
22	0.98423296160775	0.0315340767844996	0.0157670383922498
23	0.971239997500362	0.0575200049992764	0.0287600024996382
24	0.986953391097773	0.0260932178044547	0.0130466089022273
25	0.975434540797141	0.0491309184057173	0.0245654592028586
26	0.971867029009981	0.0562659419800373	0.0281329709900187
27	0.960228580111234	0.0795428397775322	0.0397714198887661
28	0.94433440623263	0.111331187534740	0.0556655937673699
29	0.924928563767615	0.15014287246477	0.075071436232385
30	0.92788659610135	0.144226807797301	0.0721134038986507
31	0.896118950452477	0.207762099095046	0.103881049547523
32	0.905508051110253	0.188983897779494	0.094491948889747
33	0.96337205040892	0.0732558991821609	0.0366279495910804
34	0.950946861876897	0.0981062762462064	0.0490531381231032
35	0.947560890200473	0.104878219599055	0.0524391097995274
36	0.928868899644877	0.142262200710247	0.0711311003551234
37	0.92781626381196	0.144367472376081	0.0721837361880405
38	0.925887321522612	0.148225356954775	0.0741126784773877
39	0.903013349884683	0.193973300230634	0.0969866501153168
40	0.872960851496963	0.254078297006074	0.127039148503037
41	0.858402238539462	0.283195522921076	0.141597761460538
42	0.87805993612833	0.243880127743341	0.121940063871671
43	0.847017201127069	0.305965597745863	0.152982798872931
44	0.833510219295858	0.332979561408284	0.166489780704142
45	0.816219982928694	0.367560034142613	0.183780017071306
46	0.835456266183868	0.329087467632264	0.164543733816132
47	0.80219197447196	0.39561605105608	0.19780802552804
48	0.874519956128545	0.250960087742910	0.125480043871455
49	0.844457599680325	0.311084800639350	0.155542400319675
50	0.81436990242759	0.371260195144820	0.185630097572410
51	0.774315927787588	0.451368144424823	0.225684072212412
52	0.737390849784539	0.525218300430922	0.262609150215461
53	0.69280374617528	0.614392507649441	0.307196253824720
54	0.69615738479118	0.607685230417638	0.303842615208819
55	0.706037015082325	0.58792596983535	0.293962984917675
56	0.8259081196424	0.348183760715201	0.174091880357601
57	0.807540062079463	0.384919875841074	0.192459937920537
58	0.838319492352599	0.323361015294802	0.161680507647401
59	0.855107717105286	0.289784565789428	0.144892282894714
60	0.884899786344764	0.230200427310471	0.115100213655236
61	0.887828255626977	0.224343488746046	0.112171744373023
62	0.895259140353008	0.209481719293984	0.104740859646992
63	0.887664414752807	0.224671170494386	0.112335585247193
64	0.862590277417047	0.274819445165905	0.137409722582953
65	0.837419607093023	0.325160785813953	0.162580392906977
66	0.810012639251043	0.379974721497914	0.189987360748957
67	0.86165200408684	0.27669599182632	0.13834799591316
68	0.831527259690885	0.336945480618230	0.168472740309115
69	0.822268157107777	0.355463685784446	0.177731842892223
70	0.824156142776244	0.351687714447513	0.175843857223756
71	0.84185049113295	0.3162990177341	0.15814950886705
72	0.809586082128986	0.380827835742029	0.190413917871014
73	0.875090117997394	0.249819764005212	0.124909882002606
74	0.881271567115005	0.237456865769991	0.118728432884995
75	0.853324663657492	0.293350672685016	0.146675336342508
76	0.833572038552104	0.332855922895791	0.166427961447896
77	0.799160491523575	0.40167901695285	0.200839508476425
78	0.80998376612644	0.380032467747119	0.190016233873559
79	0.780494427013727	0.439011145972546	0.219505572986273
80	0.737726772899324	0.524546454201352	0.262273227100676
81	0.782147287941674	0.435705424116652	0.217852712058326
82	0.85886701413298	0.28226597173404	0.14113298586702
83	0.827105975177522	0.345788049644957	0.172894024822478
84	0.812641122634996	0.374717754730008	0.187358877365004
85	0.786013941503025	0.42797211699395	0.213986058496975
86	0.742397062793308	0.515205874413384	0.257602937206692
87	0.696579125820716	0.606841748358567	0.303420874179284
88	0.64756414449169	0.704871711016619	0.352435855508309
89	0.628105338025415	0.74378932394917	0.371894661974585
90	0.59238095208388	0.815238095832241	0.407619047916121
91	0.745030899273056	0.509938201453888	0.254969100726944
92	0.702786322336079	0.594427355327842	0.297213677663921
93	0.858458880221833	0.283082239556334	0.141541119778167
94	0.860509924195528	0.278980151608944	0.139490075804472
95	0.85644019206129	0.287119615877422	0.143559807938711
96	0.877399010729529	0.245201978540943	0.122600989270471
97	0.928711753809792	0.142576492380415	0.0712882461902077
98	0.967727634879842	0.0645447302403161	0.0322723651201580
99	0.971657780167688	0.056684439664624	0.028342219832312
100	0.962680579877633	0.0746388402447343	0.0373194201223672
101	0.955678120749645	0.0886437585007098	0.0443218792503549
102	0.937179251703054	0.125641496593892	0.0628207482969459
103	0.938586674236967	0.122826651526066	0.0614133257630328
104	0.969359527409302	0.0612809451813961	0.0306404725906981
105	0.962588049832229	0.0748239003355426	0.0374119501677713
106	0.952722668936845	0.0945546621263105	0.0472773310631553
107	0.95338292524435	0.0932341495112992	0.0466170747556496
108	0.980981643446963	0.0380367131060748	0.0190183565530374
109	0.972242452666677	0.0555150946666459	0.0277575473333230
110	0.983938746652355	0.0321225066952893	0.0160612533476447
111	0.977943910459217	0.044112179081566	0.022056089540783
112	0.97359331383682	0.0528133723263609	0.0264066861631805
113	0.978940109043986	0.0421197819120272	0.0210598909560136
114	0.96896231457732	0.0620753708453598	0.0310376854226799
115	0.946498386281995	0.107003227436010	0.0535016137180052
116	0.913333563826761	0.173332872346478	0.0866664361732388
117	0.903775875321915	0.192448249356171	0.0962241246780853
118	0.955724996965757	0.0885500060684863	0.0442750030342432
119	0.943789655697362	0.112420688605276	0.0562103443026379
120	0.95674543562426	0.086509128751479	0.0432545643757395
121	0.911405549136428	0.177188901727144	0.0885944508635718
122	0.825738173839069	0.348523652321862	0.174261826160931
123	0.679798054988813	0.640403890022373	0.320201945011187

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	0	0	OK
5% type I error level	7	0.0679611650485437	NOK
10% type I error level	25	0.242718446601942	NOK