Multiple Linear Regression - Estimated Regression Equation

Happiness[t] = + 16.0606034156061 + 0.0191423359391710Age[t] -0.0115621244172054Concern_over_mistakes[t] -0.250443166783529Doubts_about_actions[t] + 0.0879285077749663Parental_expectations[t] -0.0909414328317329Parental_criticism[t] + 0.0351776347057642Popularity[t] + 0.0420782212752515Perceived_learning_competence[t] -0.143892749023934Amotivation[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)	16.0606034156061	2.475415	6.488	0	0
Age	0.0191423359391710	0.062121	0.3081	0.758447	0.379224
Concern_over_mistakes	-0.0115621244172054	0.038417	-0.301	0.763903	0.381952
Doubts_about_actions	-0.250443166783529	0.077967	-3.2122	0.001647	0.000824
Parental_expectations	0.0879285077749663	0.069261	1.2695	0.206435	0.103218
Parental_criticism	-0.0909414328317329	0.086108	-1.0561	0.292796	0.146398
Popularity	0.0351776347057642	0.063569	0.5534	0.580919	0.29046
Perceived_learning_competence	0.0420782212752515	0.089299	0.4712	0.638253	0.319126
Amotivation	-0.143892749023934	0.07338	-1.9609	0.051947	0.025974

Multiple Linear Regression - Regression Statistics
Multiple R	0.419576907453149
R-squared	0.176044781267948
Adjusted R-squared	0.127217805343086
F-TEST (value)	3.60548196838682
F-TEST (DF numerator)	8
F-TEST (DF denominator)	135
p-value	0.000793486487427386
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	2.22706924744676
Sum Squared Residuals	669.578053444616

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	14	15.0779522881879	-1.07795228818793
2	18	15.2704526613444	2.72954733865561
3	11	14.4783540692253	-3.47835406922526
4	12	12.5815235675167	-0.581523567516666
5	16	14.3764493011754	1.62355069882458
6	18	14.8651402925499	3.13485970745012
7	14	14.9349117583161	-0.934911758316131
8	14	14.5250987612011	-0.525098761201125
9	15	14.6233487799596	0.376651220040392
10	15	12.9415542508617	2.05844574913827
11	17	13.3857358731387	3.61426412686132
12	19	13.9038607260703	5.09613927392967
13	10	13.0394480669619	-3.03944806696189
14	18	16.2363384821039	1.76366151789606
15	14	11.7977630785502	2.20223692144981
16	14	14.6237786151202	-0.623778615120154
17	17	15.1325590660827	1.86744093391730
18	14	15.0529811587830	-1.05298115878296
19	16	14.9660071045525	1.03399289544749
20	18	13.5031645339563	4.49683546604375
21	14	13.3802154827307	0.619784517269298
22	12	12.9257332182720	-0.925733218271973
23	17	13.8210980862393	3.17890191376065
24	9	14.6648587410489	-5.66485874104889
25	16	14.5747010178424	1.42529898215757
26	14	13.2072737163034	0.792726283696607
27	11	14.5821600313076	-3.58216003130761
28	16	15.4453508760106	0.554649123989363
29	13	13.2210378228577	-0.221037822857698
30	17	14.5449958951211	2.45500410487893
31	15	14.5579694021628	0.442030597837232
32	14	14.8692849827572	-0.869284982757222
33	16	12.1614199045038	3.83858009549615
34	9	12.5172485435579	-3.51724854355791
35	15	13.1554616625264	1.84453833747362
36	17	15.5464871484718	1.45351285152818
37	13	13.4976758394431	-0.497675839443059
38	15	13.7539600426477	1.24603995735231
39	16	13.9223766986622	2.07762330133785
40	16	17.0005388760699	-1.00053887606991
41	12	13.8818619789282	-1.88186197892816
42	11	13.4296137885327	-2.42961378853269
43	15	15.236448799787	-0.236448799787013
44	17	14.8927094544706	2.10729054552944
45	13	14.3111454372712	-1.31114543727118
46	16	11.7608150818851	4.23918491811492
47	14	14.1940192507578	-0.194019250757793
48	11	13.4641094884327	-2.46410948843266
49	12	13.1752845451896	-1.17528454518956
50	12	13.9607429899927	-1.96074298999265
51	15	14.0216717679516	0.978328232048416
52	16	15.1279918472786	0.872008152721424
53	15	14.8167127993799	0.183287200620092
54	12	14.9747072136804	-2.97470721368041
55	12	14.4392776828147	-2.43927768281471
56	8	12.8347214829339	-4.83472148293395
57	13	15.3946704295832	-2.39467042958323
58	11	14.9065615455410	-3.90656154554104
59	14	14.6883104129871	-0.688310412987106
60	15	13.1756825446938	1.82431745530620
61	10	14.0598900072451	-4.05989000724508
62	11	12.7631232913734	-1.76312329137341
63	12	13.8717481205393	-1.87174812053932
64	15	13.1660194281387	1.83398057186127
65	15	14.5159213494338	0.484078650566199
66	14	13.7741067656847	0.225893234315285
67	16	13.2161996996528	2.78380030034716
68	15	14.9578968909679	0.0421031090321294
69	15	15.2697013986737	-0.269701398673676
70	13	14.848550480332	-1.84855048033201
71	17	14.8661384548628	2.13386154513725
72	13	13.4158267459841	-0.415826745984057
73	15	13.7863826161484	1.21361738385159
74	13	14.6005177994864	-1.60051779948635
75	15	14.0976568569614	0.902343143038571
76	16	14.5589597349070	1.44104026509302
77	15	14.5831975450757	0.416802454924332
78	16	14.2395514470958	1.76044855290416
79	15	14.3568511216736	0.643148878326449
80	14	14.7749855796484	-0.77498557964838
81	15	12.3345092456483	2.66549075435175
82	7	11.6855997390837	-4.6855997390837
83	17	15.0084355883792	1.99156441162081
84	13	14.5452660368803	-1.54526603688032
85	15	13.6603984349183	1.33960156508174
86	14	13.8786437840147	0.121356215985340
87	13	13.7439434803704	-0.7439434803704
88	16	15.2920855029073	0.707914497092714
89	12	14.176131274987	-2.17613127498700
90	14	15.5628880163819	-1.56288801638194
91	17	14.7194050239523	2.28059497604773
92	15	15.5194923230004	-0.519492323000411
93	17	13.260543871222	3.73945612877799
94	12	13.9681810482396	-1.96818104823960
95	16	15.3973361909104	0.602663809089637
96	11	14.1190627659778	-3.11906276597783
97	15	13.2691464766065	1.73085352339346
98	9	14.0890899483988	-5.08908994839878
99	16	14.7571298656708	1.2428701343292
100	10	13.1132570563521	-3.11325705635209
101	10	13.2577107599210	-3.25771075992098
102	15	14.9073124673474	0.092687532652553
103	11	13.9705819710362	-2.97058197103620
104	13	15.2290907699082	-2.22909076990817
105	14	13.2448114667880	0.755188533212036
106	18	14.6506184828741	3.34938151712589
107	16	15.1155946172844	0.884405382715643
108	14	12.3346016721198	1.66539832788022
109	14	13.1782142881395	0.821785711860506
110	14	13.2237871928536	0.776212807146425
111	14	14.348938141212	-0.348938141211985
112	12	13.7332718180091	-1.73327181800905
113	14	14.5052954315628	-0.505295431562779
114	15	14.3465288033002	0.653471196699786
115	15	14.9997548705920	0.000245129408036393
116	13	13.6097461096947	-0.609746109694739
117	17	14.9031351886011	2.09686481139894
118	17	15.382167334217	1.617832665783
119	19	14.9767898207555	4.02321017924451
120	15	13.8842209859511	1.11577901404888
121	13	14.0475514263170	-1.04755142631702
122	9	12.2024559719639	-3.20245597196392
123	15	15.0654718210993	-0.0654718210993186
124	15	14.5895060100700	0.41049398992995
125	16	13.8901066620519	2.10989333794814
126	11	13.3104871668195	-2.31048716681952
127	14	14.6190363894438	-0.619036389443828
128	11	12.6696218413593	-1.66962184135928
129	15	13.4092875684140	1.59071243158604
130	13	13.4213314060550	-0.42133140605503
131	16	12.7207767437889	3.27922325621113
132	14	14.7040927994066	-0.704092799406585
133	15	14.8253465477149	0.174653452285116
134	16	13.0549500241579	2.94504997584208
135	16	15.4706574542867	0.529342545713309
136	11	12.4370137923298	-1.43701379232980
137	13	14.0417290804259	-1.04172908042588
138	16	14.5747010178424	1.42529898215757
139	12	14.0188756070208	-2.01887560702079
140	9	11.4175931514257	-2.41759315142568
141	13	11.487566079174	1.51243392082600
142	13	14.5452660368803	-1.54526603688032
143	19	14.9767898207555	4.02321017924451
144	13	15.5205134149569	-2.52051341495688

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
12	0.290779630480904	0.581559260961807	0.709220369519096
13	0.187883584731516	0.375767169463032	0.812116415268484
14	0.178308138533829	0.356616277067657	0.821691861466171
15	0.137998000379250	0.275996000758501	0.86200199962075
16	0.172672998386777	0.345345996773554	0.827327001613223
17	0.833921665080817	0.332156669838367	0.166078334919183
18	0.78720934746902	0.42558130506196	0.21279065253098
19	0.767747430857905	0.464505138284191	0.232252569142095
20	0.812335050671468	0.375329898657064	0.187664949328532
21	0.793618405077571	0.412763189844858	0.206381594922429
22	0.77602215990357	0.447955680192860	0.223977840096430
23	0.785059837315354	0.429880325369293	0.214940162684646
24	0.899159647310014	0.201680705379972	0.100840352689986
25	0.871442408276538	0.257115183446923	0.128557591723462
26	0.867671896553391	0.264656206893218	0.132328103446609
27	0.926044574458823	0.147910851082353	0.0739554255411766
28	0.900855846579912	0.198288306840176	0.0991441534200878
29	0.889384898392732	0.221230203214535	0.110615101607268
30	0.903464642311989	0.193070715376022	0.096535357688011
31	0.87368218817357	0.252635623652859	0.126317811826429
32	0.844166316558119	0.311667366883762	0.155833683441881
33	0.853896575813262	0.292206848373475	0.146103424186738
34	0.88243044231252	0.235139115374960	0.117569557687480
35	0.86137384480167	0.277252310396658	0.138626155198329
36	0.846342096531941	0.307315806936118	0.153657903468059
37	0.818210419789273	0.363579160421453	0.181789580210727
38	0.793236079327734	0.413527841344531	0.206763920672266
39	0.78888020981107	0.422239580377858	0.211119790188929
40	0.786233596071662	0.427532807856676	0.213766403928338
41	0.755380524419074	0.489238951161853	0.244619475580926
42	0.79525994990422	0.409480100191559	0.204740050095779
43	0.75664160795373	0.486716784092539	0.243358392046270
44	0.737028264568997	0.525943470862006	0.262971735431003
45	0.69779075109785	0.604418497804299	0.302209248902150
46	0.734685860979064	0.530628278041873	0.265314139020936
47	0.70392694310056	0.592146113798879	0.296073056899439
48	0.831832538776803	0.336334922446394	0.168167461223197
49	0.815440532873867	0.369118934252266	0.184559467126133
50	0.824826953440399	0.350346093119202	0.175173046559601
51	0.801102589058004	0.397794821883992	0.198897410941996
52	0.777298063539023	0.445403872921953	0.222701936460977
53	0.736969264762087	0.526061470475826	0.263030735237913
54	0.767724868934725	0.46455026213055	0.232275131065275
55	0.768054159159622	0.463891681680756	0.231945840840378
56	0.894447369972184	0.211105260055631	0.105552630027816
57	0.907516675603997	0.184966648792005	0.0924833243960027
58	0.94309961367395	0.113800772652101	0.0569003863260505
59	0.929361607554557	0.141276784890887	0.0706383924454433
60	0.925721379648822	0.148557240702357	0.0742786203511783
61	0.957111209959232	0.0857775800815369	0.0428887900407684
62	0.96157264993067	0.076854700138658	0.038427350069329
63	0.957980887083947	0.084038225832106	0.042019112916053
64	0.954350181743478	0.0912996365130441	0.0456498182565221
65	0.94179529360297	0.116409412794060	0.0582047063970298
66	0.925607145125994	0.148785709748013	0.0743928548740063
67	0.936231371199482	0.127537257601037	0.0637686288005185
68	0.922136576227811	0.155726847544378	0.0778634237721892
69	0.90225578111051	0.195488437778979	0.0977442188894894
70	0.89721661610838	0.205566767783239	0.102783383891619
71	0.894608666453212	0.210782667093576	0.105391333546788
72	0.872113217040825	0.25577356591835	0.127886782959175
73	0.855108018488725	0.289783963022549	0.144891981511275
74	0.848412425981181	0.303175148037639	0.151587574018819
75	0.822979148585482	0.354041702829036	0.177020851414518
76	0.811357720532735	0.37728455893453	0.188642279467265
77	0.776285841062497	0.447428317875007	0.223714158937503
78	0.758489063757123	0.483021872485754	0.241510936242877
79	0.719806700956339	0.560386598087322	0.280193299043661
80	0.680595330718434	0.638809338563131	0.319404669281565
81	0.709414011406127	0.581171977187746	0.290585988593873
82	0.814726249066258	0.370547501867483	0.185273750933742
83	0.801575036833426	0.396849926333148	0.198424963166574
84	0.781313758531684	0.437372482936632	0.218686241468316
85	0.757545845733953	0.484908308532094	0.242454154266047
86	0.715364856931384	0.569270286137233	0.284635143068616
87	0.674893569910924	0.650212860178153	0.325106430089076
88	0.641171340296407	0.717657319407186	0.358828659703593
89	0.63251971039876	0.734960579202479	0.367480289601240
90	0.610365463516837	0.779269072966325	0.389634536483163
91	0.609956487043298	0.780087025913405	0.390043512956702
92	0.564882706982104	0.870234586035791	0.435117293017896
93	0.729625823892482	0.540748352215036	0.270374176107518
94	0.709079239849097	0.581841520301805	0.290920760150902
95	0.675801376398512	0.648397247202977	0.324198623601488
96	0.707526800681546	0.584946398636909	0.292473199318454
97	0.717231637419171	0.565536725161658	0.282768362580829
98	0.904924042353916	0.190151915292168	0.0950759576460841
99	0.890213909749804	0.219572180500393	0.109786090250196
100	0.887117254402918	0.225765491194164	0.112882745597082
101	0.897056404431083	0.205887191137834	0.102943595568917
102	0.867970066720104	0.264059866559792	0.132029933279896
103	0.891725614212195	0.216548771575611	0.108274385787805
104	0.920178500783419	0.159642998433161	0.0798214992165806
105	0.913696786878292	0.172606426243416	0.0863032131217082
106	0.914464581653407	0.171070836693186	0.0855354183465928
107	0.897732152060325	0.204535695879351	0.102267847939675
108	0.923986132112931	0.152027735774137	0.0760138678870685
109	0.905852174447105	0.188295651105790	0.0941478255528952
110	0.907774169491522	0.184451661016957	0.0922258305084784
111	0.88103082835466	0.237938343290681	0.118969171645341
112	0.868523311464361	0.262953377071277	0.131476688535639
113	0.833666691429483	0.332666617141035	0.166333308570517
114	0.787234413894714	0.425531172210572	0.212765586105286
115	0.749509330426372	0.500981339147256	0.250490669573628
116	0.689184159122917	0.621631681754167	0.310815840877083
117	0.74280699126987	0.514386017460261	0.257193008730130
118	0.763351025980554	0.473297948038892	0.236648974019446
119	0.769998729828486	0.460002540343028	0.230001270171514
120	0.77688592130833	0.44622815738334	0.22311407869167
121	0.791061730743556	0.417876538512889	0.208938269256444
122	0.748624681643359	0.502750636713283	0.251375318356641
123	0.693839973144876	0.612320053710249	0.306160026855124
124	0.615922410368186	0.768155179263627	0.384077589631814
125	0.543402695802292	0.913194608395416	0.456597304197708
126	0.458501767774394	0.917003535548787	0.541498232225606
127	0.374299950852689	0.748599901705378	0.625700049147311
128	0.31636802311401	0.63273604622802	0.68363197688599
129	0.248029179099755	0.496058358199511	0.751970820900244
130	0.285723457089042	0.571446914178084	0.714276542910958
131	0.759825364923038	0.480349270153925	0.240174635076962
132	0.695616816753318	0.608766366493364	0.304383183246682

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	0	0	OK
10% type I error level	4	0.0330578512396694	OK