Multiple Linear Regression - Estimated Regression Equation

Happiness[t] = + 16.295785836819 -0.352003748191891Depression[t] + 0.0327823330796020Belonging[t] -0.0508921511278503ConcernOverMistakes[t] + 0.0834010628945067ParentalExpectations[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)	16.295785836819	1.664632	9.7894	0	0
Depression	-0.352003748191891	0.055802	-6.308	0	0
Belonging	0.0327823330796020	0.016405	1.9983	0.047742	0.023871
ConcernOverMistakes	-0.0508921511278503	0.031365	-1.6226	0.107066	0.053533
ParentalExpectations	0.0834010628945067	0.051379	1.6233	0.106919	0.053459

Multiple Linear Regression - Regression Statistics
Multiple R	0.577439805903951
R-squared	0.333436729442392
Adjusted R-squared	0.313237842455798
F-TEST (value)	16.5076783519652
F-TEST (DF numerator)	4
F-TEST (DF denominator)	132
p-value	5.43735056979244e-11
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	1.96470138552339
Sum Squared Residuals	509.526802524634

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	15	15.2405807169901	-0.240580716990116
2	9	10.4148072421445	-1.41480724214455
3	12	13.4016615091257	-1.40166150912573
4	15	15.5046361567662	-0.504636156766184
5	17	16.8386560090091	0.161343990990863
6	14	13.4962272595151	0.503772740484899
7	9	11.4130192150532	-2.41301921505324
8	11	9.98542425864777	1.01457574135223
9	13	14.5798724817562	-1.57987248175621
10	16	14.6111857282765	1.38881427172354
11	16	13.3513487151291	2.64865128487089
12	15	14.2365411737676	0.763458826232353
13	10	14.3210684364193	-4.32106843641928
14	16	15.0656236603749	0.934376339625117
15	12	15.2027205530160	-3.20272055301598
16	15	14.5314953897118	0.468504610288203
17	13	12.3979257794953	0.602074220504689
18	18	14.8981553956824	3.10184460431763
19	13	14.5301607976524	-1.53016079765241
20	17	13.6606695102863	3.33933048971367
21	14	13.6218328351118	0.378167164888222
22	13	14.9959555522953	-1.99595555229529
23	13	16.1514074813615	-3.15140748136155
24	15	15.4350710877115	-0.435071087711524
25	15	13.2322423442587	1.76775765574134
26	13	12.8661129236613	0.133887076338690
27	13	15.1487513019564	-2.14875130195644
28	16	13.4058506737881	2.59414932621192
29	14	15.4744871200173	-1.47448712001731
30	18	15.4761981724146	2.52380182758542
31	9	10.9160338834504	-1.91603388345043
32	16	15.8903119674658	0.109688032534207
33	16	15.1748131540376	0.825186845962405
34	17	15.3527799673215	1.64722003267853
35	13	15.1929392293385	-2.19293922933851
36	17	13.9140690951791	3.08593090482086
37	15	12.713828128838	2.28617187116201
38	14	14.1458890445015	-0.145889044501468
39	10	11.8571441790707	-1.85714417907066
40	13	14.3124340062302	-1.31243400623021
41	11	14.0987076177035	-3.09870761770346
42	11	13.6302470522245	-2.63024705222451
43	15	15.5107067561138	-0.510706756113806
44	15	15.5357942192208	-0.535794219220782
45	12	12.4310835138825	-0.431083513882478
46	17	15.2685586404881	1.73144135951187
47	15	13.3151453362853	1.68485466371471
48	16	15.5584512827904	0.441548717209623
49	14	13.4458656937605	0.554134306239527
50	17	14.4520622152074	2.54793778479259
51	10	10.1358970842751	-0.135897084275084
52	11	14.5378394103724	-3.53783941037237
53	15	14.1435454267364	0.856454573263645
54	15	14.8616623382729	0.138337661727071
55	7	10.9312207266023	-3.93122072660233
56	17	15.2683720009474	1.73162799905255
57	14	12.6006730610376	1.39932693896244
58	18	15.8398125339285	2.16018746607150
59	14	14.0411980246021	-0.0411980246020936
60	14	15.450462949883	-1.45046294988299
61	9	15.4095723355089	-6.40957233550893
62	14	14.6379137192611	-0.637913719261112
63	11	12.4819594077577	-1.48195940775766
64	16	13.7214622813693	2.27853771863075
65	17	15.4823555535345	1.51764444646553
66	12	14.6430610156450	-2.64306101564496
67	15	14.1121302002215	0.887869799778519
68	15	15.2496285585010	-0.249628558501041
69	16	15.5155816902150	0.484418309784973
70	16	15.9792541033650	0.0207458966349813
71	11	12.8087378250599	-1.80873782505990
72	12	13.3139323547559	-1.31393235475590
73	14	13.8329953927971	0.167004607202922
74	15	15.2409409200754	-0.24094092007536
75	17	15.1766424436822	1.82335755631784
76	19	14.9786822554385	4.02131774456146
77	15	14.3316375095302	0.668362490469764
78	16	13.8683415567181	2.13165844328187
79	14	14.5093689115154	-0.509368911515423
80	16	11.1604398940993	4.83956010590073
81	15	14.3683877310000	0.631612269000046
82	17	14.4188685930322	2.58113140696781
83	12	14.5309485470859	-2.53094854708591
84	18	14.7135168731581	3.28648312684194
85	13	14.6911657454067	-1.69116574540674
86	14	12.8009236588097	1.19907634119033
87	14	14.2921346954522	-0.292134695452183
88	14	14.2303837926478	-0.230383792647757
89	12	14.3319109308432	-2.33191093084318
90	14	12.7376494021790	1.26235059782103
91	12	13.5245111188314	-1.52451111883137
92	15	14.4260003631263	0.573999636873744
93	11	12.1422682995793	-1.14226829957934
94	15	14.9611192800162	0.0388807199838129
95	14	14.0141271468152	-0.0141271468152189
96	15	13.7683702868543	1.23162971314568
97	16	14.8981716529350	1.10182834706496
98	14	10.4671902325933	3.53280976740666
99	18	16.1804628328586	1.81953716714136
100	14	15.4175081122892	-1.41750811228917
101	13	12.9951547432446	0.00484525675543712
102	14	12.9693663124764	1.03063368752364
103	14	14.9275166829977	-0.927516682997748
104	17	15.2722693648180	1.72773063518203
105	12	13.4324593684951	-1.43245936849512
106	16	13.780136084242	2.21986391575800
107	10	12.9081459950452	-2.90814599504515
108	13	14.6985871940664	-1.69858719406643
109	15	15.01083096412	-0.0108309641199875
110	16	14.9762377208747	1.02376227912530
111	14	13.1534905068801	0.846509493119878
112	13	12.7830710048217	0.216928995178302
113	17	14.9335872823454	2.06641271765463
114	14	13.7370245258287	0.262975474171276
115	16	13.1576993020778	2.84230069792216
116	12	14.5951623639331	-2.59516236393305
117	16	13.7096791676986	2.29032083230141
118	8	10.5082467927768	-2.50824679277680
119	9	12.1718704937023	-3.17187049370232
120	13	12.5990498494429	0.400950150557129
121	19	15.3531391113764	3.64686088862363
122	11	12.4399425936265	-1.43994259362648
123	15	15.1675783449186	-0.167578344918592
124	11	13.9316320706015	-2.9316320706015
125	15	15.6892909365432	-0.68929093654317
126	16	15.647274122412	0.352725877588004
127	15	13.0229947989599	1.97700520104013
128	12	13.1447540966964	-1.14475409669643
129	16	14.1142166539263	1.88578334607368
130	15	13.7653605301857	1.23463946981429
131	13	14.6876254033649	-1.68762540336491
132	14	14.4955329176756	-0.495532917675576
133	11	13.3142925578411	-2.31429255784111
134	15	14.1872732932648	0.8127267067352
135	14	12.5795186575630	1.42048134243703
136	13	15.6456335945343	-2.64563359453432
137	15	16.1068593508943	-1.10685935089426

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
8	0.0732841630127285	0.146568326025457	0.926715836987272
9	0.0413584146224721	0.0827168292449442	0.958641585377528
10	0.181623260368474	0.363246520736949	0.818376739631526
11	0.479599440400899	0.959198880801798	0.520400559599101
12	0.363089465915866	0.726178931831731	0.636910534084134
13	0.585625709398543	0.828748581202914	0.414374290601457
14	0.536707821802155	0.92658435639569	0.463292178197845
15	0.623805106967883	0.752389786064234	0.376194893032117
16	0.546800243505382	0.906399512989237	0.453199756494618
17	0.459870221212666	0.919740442425332	0.540129778787334
18	0.526222067849517	0.947555864300965	0.473777932150483
19	0.449589374433823	0.899178748867647	0.550410625566177
20	0.510097440916511	0.979805118166978	0.489902559083489
21	0.432525774054861	0.865051548109721	0.567474225945139
22	0.515737820999333	0.968524358001333	0.484262179000667
23	0.62944895768676	0.74110208462648	0.37055104231324
24	0.570708460295176	0.858583079409647	0.429291539704824
25	0.53575239661337	0.928495206773259	0.464247603386630
26	0.471269115158822	0.942538230317645	0.528730884841178
27	0.452756220029514	0.905512440059029	0.547243779970486
28	0.520055938184432	0.959888123631135	0.479944061815568
29	0.471813535241607	0.943627070483214	0.528186464758393
30	0.512832754785012	0.974334490429975	0.487167245214988
31	0.496174036446225	0.99234807289245	0.503825963553775
32	0.434160999169758	0.868321998339516	0.565839000830242
33	0.377969013896649	0.755938027793298	0.622030986103351
34	0.402880894462131	0.805761788924262	0.597119105537869
35	0.406780348526123	0.813560697052247	0.593219651473877
36	0.518169439522365	0.963661120955269	0.481830560477635
37	0.588799113936846	0.822401772126308	0.411200886063154
38	0.535052506701184	0.929894986597633	0.464947493298816
39	0.510669284505735	0.97866143098853	0.489330715494265
40	0.4813400144886	0.9626800289772	0.5186599855114
41	0.575654128332074	0.848691743335852	0.424345871667926
42	0.622263335303044	0.755473329393911	0.377736664696956
43	0.57058584864392	0.85882830271216	0.42941415135608
44	0.518282124291765	0.96343575141647	0.481717875708235
45	0.465570133825168	0.931140267650335	0.534429866174832
46	0.468942269884758	0.937884539769515	0.531057730115242
47	0.480621713446976	0.961243426893951	0.519378286553025
48	0.439631908280094	0.879263816560188	0.560368091719906
49	0.390919647308881	0.781839294617761	0.60908035269112
50	0.420242228811847	0.840484457623694	0.579757771188153
51	0.380393346052336	0.760786692104672	0.619606653947664
52	0.479790002388065	0.95958000477613	0.520209997611935
53	0.438148094573044	0.876296189146089	0.561851905426956
54	0.387688051977723	0.775376103955446	0.612311948022277
55	0.539735762637849	0.920528474724303	0.460264237362151
56	0.521304635542008	0.957390728915984	0.478695364457992
57	0.505515460524605	0.98896907895079	0.494484539475395
58	0.515009960856588	0.969980078286824	0.484990039143412
59	0.464209765559933	0.928419531119867	0.535790234440066
60	0.447954860009965	0.895909720019929	0.552045139990035
61	0.848327156520388	0.303345686959224	0.151672843479612
62	0.821389668195662	0.357220663608676	0.178610331804338
63	0.80489744225482	0.390205115490361	0.195102557745181
64	0.81671215117164	0.366575697656721	0.183287848828361
65	0.802065876860183	0.395868246279634	0.197934123139817
66	0.826184732149248	0.347630535701505	0.173815267850752
67	0.799815293725088	0.400369412549823	0.200184706274912
68	0.763316564996774	0.473366870006451	0.236683435003226
69	0.725450449811901	0.549099100376198	0.274549550188099
70	0.681924442251647	0.636151115496705	0.318075557748353
71	0.683998205190294	0.632003589619413	0.316001794809706
72	0.659624735257503	0.680750529484993	0.340375264742497
73	0.613048843087564	0.773902313824871	0.386951156912436
74	0.56523245494708	0.86953509010584	0.43476754505292
75	0.558743574393523	0.882512851212954	0.441256425606477
76	0.705263351019125	0.58947329796175	0.294736648980875
77	0.665145438731063	0.669709122537874	0.334854561268937
78	0.6701069583107	0.6597860833786	0.3298930416893
79	0.626361622219987	0.747276755560025	0.373638377780013
80	0.850462996831906	0.299074006336188	0.149537003168094
81	0.824003920935552	0.351992158128896	0.175996079064448
82	0.849414255486803	0.301171489026393	0.150585744513197
83	0.869552150226566	0.260895699546867	0.130447849773434
84	0.92326164590972	0.153476708180559	0.0767383540902793
85	0.91763037540818	0.164739249183639	0.0823696245918196
86	0.902902821728002	0.194194356543995	0.0970971782719977
87	0.878001173749225	0.243997652501549	0.121998826250775
88	0.84887026884961	0.302259462300781	0.151129731150390
89	0.86081227043935	0.278375459121302	0.139187729560651
90	0.844645074417291	0.310709851165418	0.155354925582709
91	0.839102760163104	0.321794479673792	0.160897239836896
92	0.80698426574348	0.386031468513041	0.193015734256521
93	0.775266677281568	0.449466645436863	0.224733322718432
94	0.732849387510732	0.534301224978536	0.267150612489268
95	0.699477295347295	0.601045409305411	0.300522704652705
96	0.673627692663029	0.652744614673942	0.326372307336971
97	0.642672767626638	0.714654464746724	0.357327232373362
98	0.833416483087699	0.333167033824602	0.166583516912301
99	0.85965176160142	0.280696476797161	0.140348238398581
100	0.833695115446326	0.332609769107347	0.166304884553674
101	0.793834547035877	0.412330905928247	0.206165452964123
102	0.758560280825116	0.482879438349768	0.241439719174884
103	0.71678279227986	0.566434415440279	0.283217207720140
104	0.704500990924244	0.590998018151511	0.295499009075756
105	0.67664915182558	0.646701696348839	0.323350848174419
106	0.780243678425236	0.439512643149528	0.219756321574764
107	0.813170472681997	0.373659054636006	0.186829527318003
108	0.802927594851541	0.394144810296917	0.197072405148459
109	0.760367988460329	0.479264023079343	0.239632011539671
110	0.726052715566932	0.547894568866137	0.273947284433068
111	0.678223478729696	0.643553042540608	0.321776521270304
112	0.613840172677905	0.77231965464419	0.386159827322095
113	0.610614789885845	0.77877042022831	0.389385210114155
114	0.541787518370017	0.916424963259966	0.458212481629983
115	0.660865630097632	0.678268739804737	0.339134369902368
116	0.730232479766025	0.539535040467949	0.269767520233975
117	0.677534503280607	0.644930993438785	0.322465496719392
118	0.744642015101051	0.510715969797898	0.255357984898949
119	0.739864885143378	0.520270229713244	0.260135114856622
120	0.74661197070844	0.506776058583119	0.253388029291559
121	0.945317135775299	0.109365728449403	0.0546828642247014
122	0.934434685878776	0.131130628242448	0.065565314121224
123	0.891634511376772	0.216730977246456	0.108365488623228
124	0.92814891030849	0.143702179383022	0.0718510896915108
125	0.88214377164656	0.235712456706880	0.117856228353440
126	0.80440866803698	0.391182663926041	0.195591331963020
127	0.70876471306956	0.58247057386088	0.29123528693044
128	0.680948516831039	0.638102966337923	0.319051483168961
129	0.578552934539392	0.842894130921216	0.421447065460608

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	1	0.00819672131147541	OK