Multiple Linear Regression - Estimated Regression Equation

belonging[t] = + 33.7628490052607 + 0.576297541832057popularity[t] + 0.478113214787677hapiness[t] -1.43366386194624gender[t] -0.413115473681592doubsaboutactions[t] + 0.180267632695104parentalexpectations[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)	33.7628490052607	6.588503	5.1245	1e-06	0
popularity	0.576297541832057	0.195775	2.9437	0.003811	0.001906
hapiness	0.478113214787677	0.261714	1.8269	0.069898	0.034949
gender	-1.43366386194624	1.23424	-1.1616	0.247428	0.123714
doubsaboutactions	-0.413115473681592	0.223849	-1.8455	0.067122	0.033561
parentalexpectations	0.180267632695104	0.172462	1.0453	0.297743	0.148872

Multiple Linear Regression - Regression Statistics
Multiple R	0.417432508416781
R-squared	0.174249899083126
Adjusted R-squared	0.144113034086160
F-TEST (value)	5.78195174251427
F-TEST (DF numerator)	5
F-TEST (DF denominator)	137
p-value	7.09848962427984e-05
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	6.80662163087911
Sum Squared Residuals	6347.22342955535

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	42	44.0042598762073	-2.00425987620725
2	51	46.8367687387696	4.16323126123041
3	42	45.0386012280569	-3.03860122805688
4	46	45.3923196194003	0.607680380599712
5	41	38.4149149725497	2.58508502745032
6	49	41.7778084974571	7.22219150254293
7	47	45.1934317758985	1.80656822410153
8	33	44.0386878499175	-11.0386878499175
9	47	46.1327837725338	0.867216227466201
10	42	38.2152537175015	3.78474628249851
11	32	44.3480183377868	-12.3480183377868
12	53	50.1655430507007	2.83445694929927
13	41	40.27577216656	0.724227833440006
14	41	44.9498786437781	-3.9498786437781
15	33	42.0796463288628	-9.0796463288628
16	37	40.4644889486936	-3.46448894869356
17	43	44.0521720527685	-1.05217205276850
18	33	37.7220240244711	-4.72202402447114
19	49	46.6712786128107	2.32872138718934
20	42	44.6787417450835	-2.67874174508349
21	43	38.7576888909785	4.24231110902155
22	37	36.4056013010121	0.59439869898794
23	43	46.5573322358791	-3.55733223587911
24	42	41.9547835291927	0.0452164708072546
25	43	40.0991880224438	2.90081197755616
26	46	47.4532289560783	-1.45322895607832
27	33	47.088753357488	-14.088753357488
28	42	45.2142008290221	-3.21420082902206
29	40	41.8204287759848	-1.82042877598483
30	44	41.5325431236559	2.46745687634411
31	42	47.1507153422558	-5.1507153422558
32	52	42.8239196498810	9.17608035011904
33	44	42.4466075806803	1.55339241931970
34	45	44.0032753330561	0.996724666943933
35	46	41.5419768162453	4.45802318375466
36	36	41.0738754473343	-5.07387544733434
37	45	46.3291524266226	-1.32915242662256
38	49	46.2755876751802	2.72441232481981
39	43	43.1462177736761	-0.146217773676077
40	43	44.6153762793691	-1.61537627936906
41	37	40.6048050375166	-3.6048050375166
42	32	34.3959486579680	-2.39594865796796
43	45	44.6458639198794	0.354136080120617
44	45	45.976109817696	-0.97610981769596
45	45	45.4175455726492	-0.417545572649211
46	45	42.0572969164606	2.94270308353941
47	31	43.067735829719	-12.0677358297190
48	33	42.83154347166	-9.83154347166001
49	44	43.7740288537632	0.225971146236796
50	49	36.2125771639958	12.7874228360042
51	44	41.6957771079194	2.30422289208061
52	41	38.0885508362488	2.91144916375125
53	44	42.0894470431349	1.91055295686515
54	38	42.6157811952182	-4.61578119521817
55	33	42.4650166598824	-9.4650166598824
56	47	43.6521737602553	3.34782623974469
57	37	39.3905869405912	-2.39058694059117
58	48	45.9220284993284	2.07797150067163
59	40	40.4713674091024	-0.471367409102381
60	50	44.5440782311414	5.45592176885862
61	54	48.179740930135	5.82025906986496
62	43	47.5296596868481	-4.52965968684812
63	54	42.5919306727397	11.4080693272602
64	44	44.4871387518542	-0.487138751854244
65	47	41.4846309470944	5.51536905290556
66	33	42.920346022228	-9.92034602222798
67	45	46.7182062462211	-1.71820624622112
68	33	34.3969332011189	-1.39693320111894
69	44	45.5840202417591	-1.58402024175911
70	47	44.9072303150742	2.09276968492577
71	45	40.320391742162	4.679608257838
72	43	41.782476529187	1.21752347081298
73	43	38.1449121622487	4.85508783775133
74	33	44.4236756570102	-11.4236756570102
75	46	43.8551276162629	2.14487238373706
76	47	43.8937556454775	3.10624435452245
77	47	42.603024690897	4.39697530910302
78	0	40.8443202073073	-40.8443202073073
79	43	43.9339183209542	-0.933918320954231
80	46	42.5846458224672	3.41535417753283
81	36	37.6845083783094	-1.68450837830939
82	42	38.7801182696698	3.21988173033017
83	44	43.3244341931839	0.675565806816119
84	47	47.3470839963446	-0.347083996344561
85	41	39.5343753863885	1.46562461361146
86	47	44.4894468096627	2.51055319033731
87	46	45.0783730159141	0.921626984085934
88	47	47.2318141047555	-0.231814104755542
89	46	47.0663239787966	-1.06632397879663
90	46	44.2541932817382	1.74580671826182
91	36	44.9833220743376	-8.98332207433755
92	30	40.2635041789879	-10.2635041789879
93	48	42.3118464376086	5.68815356239138
94	45	40.786087424135	4.21391257586502
95	49	45.565611162557	3.43438883744299
96	55	47.1119280975496	7.88807190245038
97	11	41.2106358874803	-30.2106358874803
98	52	45.8976278737389	6.10237212626114
99	33	35.8460503522182	-2.84605035221816
100	47	48.4024792961153	-1.40247929611528
101	33	39.5825444075711	-6.58254440757113
102	44	44.4244490685566	-0.424449068556609
103	42	40.4258609194790	1.57413908052104
104	55	42.8519735532771	12.1480264467229
105	42	44.2853286544892	-2.28532865448918
106	46	44.9994230957312	1.0005769042688
107	46	46.9155594434609	-0.915559443460863
108	47	45.5699704335528	1.43002956644724
109	33	43.4866317181834	-10.4866317181834
110	53	49.7252325374682	3.27476746253175
111	42	42.2572971430153	-0.257297143015258
112	44	44.0353952489580	-0.0353952489580468
113	55	44.9434007412378	10.0565992587622
114	40	35.4674449791323	4.53255502086767
115	46	45.3200370280216	0.67996297197837
116	53	45.8805423091942	7.11945769080578
117	44	45.870432834188	-1.87043283418797
118	35	40.6678336923207	-5.66783369232071
119	40	39.7329699714004	0.267030028599579
120	44	45.0966228796246	-1.09662287962459
121	46	46.7482594466916	-0.748259446691554
122	45	42.4945197572417	2.50548024275826
123	53	45.1926583643521	7.8073416356479
124	45	43.5121944823426	1.48780551765740
125	48	42.7836312950986	5.21636870490143
126	46	44.4753970014563	1.52460299854366
127	55	41.7597081789892	13.2402918210108
128	47	49.7343574693235	-2.73435746932351
129	43	42.6559438706948	0.344056129305151
130	38	38.0828982613678	-0.0828982613678303
131	40	40.2315434785775	-0.231543478577502
132	47	42.2529378720195	4.74706212798049
133	47	42.1068413684137	4.89315863158632
134	42	40.7197661683714	1.28023383162857
135	53	42.5732128328035	10.4267871671965
136	43	44.0521720527685	-1.05217205276850
137	44	44.8536655636319	-0.853665563631855
138	42	43.2926230380161	-1.29262303801609
139	51	44.5581280393477	6.44187196065227
140	54	42.9524659381300	11.0475340618700
141	41	42.0995565181411	-1.09955651814110
142	51	42.8128256317237	8.18717436827628
143	51	44.4987828731226	6.50121712687743

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
9	0.625479598830677	0.749040802338646	0.374520401169323
10	0.48978863462332	0.97957726924664	0.51021136537668
11	0.474338660514287	0.948677321028573	0.525661339485713
12	0.369242547572502	0.738485095145003	0.630757452427498
13	0.28139104572854	0.56278209145708	0.71860895427146
14	0.192075279610892	0.384150559221784	0.807924720389108
15	0.171661427117480	0.343322854234961	0.82833857288252
16	0.125844022450331	0.251688044900662	0.874155977549669
17	0.144721649968746	0.289443299937492	0.855278350031254
18	0.0983061725848849	0.196612345169770	0.901693827415115
19	0.114338625660729	0.228677251321458	0.88566137433927
20	0.100355345061709	0.200710690123417	0.899644654938291
21	0.117473136842153	0.234946273684305	0.882526863157847
22	0.0814774426745284	0.162954885349057	0.918522557325472
23	0.0626062325093802	0.125212465018760	0.93739376749062
24	0.0461221575759448	0.0922443151518895	0.953877842424055
25	0.0364422938838964	0.0728845877677928	0.963557706116104
26	0.0242733352926843	0.0485466705853686	0.975726664707316
27	0.0600328475122006	0.120065695024401	0.9399671524878
28	0.0465530033764704	0.0931060067529408	0.95344699662353
29	0.0322644290169215	0.064528858033843	0.967735570983078
30	0.021885400922732	0.043770801845464	0.978114599077268
31	0.0171853466829018	0.0343706933658037	0.982814653317098
32	0.0192589611838021	0.0385179223676043	0.980741038816198
33	0.0128339538011562	0.0256679076023124	0.987166046198844
34	0.00848461382060335	0.0169692276412067	0.991515386179397
35	0.00730537334364158	0.0146107466872832	0.992694626656358
36	0.00491177241641232	0.00982354483282465	0.995088227583588
37	0.0032527911652132	0.0065055823304264	0.996747208834787
38	0.00236295507723269	0.00472591015446538	0.997637044922767
39	0.00152424228584383	0.00304848457168765	0.998475757714156
40	0.000946264288637114	0.00189252857727423	0.999053735711363
41	0.000595651408963467	0.00119130281792693	0.999404348591037
42	0.000347862533781218	0.000695725067562437	0.999652137466219
43	0.000243585395748413	0.000487170791496826	0.999756414604252
44	0.000139895356023047	0.000279790712046094	0.999860104643977
45	7.86207430430635e-05	0.000157241486086127	0.999921379256957
46	9.93624592464402e-05	0.000198724918492880	0.999900637540754
47	0.000177055510202218	0.000354111020404435	0.999822944489798
48	0.000566704699634688	0.00113340939926938	0.999433295300365
49	0.000397170271791237	0.000794340543582473	0.999602829728209
50	0.0044244395442087	0.0088488790884174	0.995575560455791
51	0.00321309209460319	0.00642618418920638	0.996786907905397
52	0.00230252549001735	0.00460505098003470	0.997697474509983
53	0.00152203883988141	0.00304407767976283	0.998477961160119
54	0.00120395913717537	0.00240791827435075	0.998796040862825
55	0.00204356865281831	0.00408713730563662	0.997956431347182
56	0.00163860073497579	0.00327720146995158	0.998361399265024
57	0.00110806384769146	0.00221612769538293	0.998891936152309
58	0.000917739650250278	0.00183547930050056	0.99908226034975
59	0.000599281338231905	0.00119856267646381	0.999400718661768
60	0.000497624690026418	0.000995249380052836	0.999502375309974
61	0.000533329253905136	0.00106665850781027	0.999466670746095
62	0.000400558965733979	0.000801117931467958	0.999599441034266
63	0.00188341861353910	0.00376683722707821	0.998116581386461
64	0.00124204751161695	0.0024840950232339	0.998757952488383
65	0.00107889834091087	0.00215779668182175	0.99892110165909
66	0.00186592272656233	0.00373184545312467	0.998134077273438
67	0.00126569957793323	0.00253139915586647	0.998734300422067
68	0.000855590040042557	0.00171118008008511	0.999144409959957
69	0.00056457342228636	0.00112914684457272	0.999435426577714
70	0.000398911826995469	0.000797823653990937	0.999601088173005
71	0.00030133700853065	0.0006026740170613	0.99969866299147
72	0.000190551569050373	0.000381103138100746	0.99980944843095
73	0.000155192316221530	0.000310384632443060	0.999844807683778
74	0.000339927224344043	0.000679854448688086	0.999660072775656
75	0.000237952979395825	0.000475905958791649	0.999762047020604
76	0.000164171763506551	0.000328343527013102	0.999835828236493
77	0.000147613137363427	0.000295226274726853	0.999852386862637
78	0.895765879239366	0.208468241521267	0.104234120760634
79	0.871536685851211	0.256926628297578	0.128463314148789
80	0.849033315550944	0.301933368898112	0.150966684449056
81	0.832311290034144	0.335377419931711	0.167688709965856
82	0.804666708916257	0.390666582167485	0.195333291083743
83	0.768370056234955	0.463259887530089	0.231629943765045
84	0.730195616494612	0.539608767010776	0.269804383505388
85	0.687106366796466	0.625787266407068	0.312893633203534
86	0.660107309729117	0.679785380541767	0.339892690270883
87	0.638865525486242	0.722268949027517	0.361134474513758
88	0.591136008230444	0.817727983539111	0.408863991769556
89	0.549962971564927	0.900074056870145	0.450037028435073
90	0.518301177254985	0.96339764549003	0.481698822745015
91	0.587563984971085	0.82487203005783	0.412436015028915
92	0.662472876937075	0.675054246125851	0.337527123062925
93	0.643619335086792	0.712761329826415	0.356380664913208
94	0.621559295856643	0.756881408286714	0.378440704143357
95	0.579326705380457	0.841346589239085	0.420673294619543
96	0.584887752033363	0.830224495933274	0.415112247966637
97	0.998529304112251	0.00294139177549745	0.00147069588774873
98	0.998021377107474	0.00395724578505237	0.00197862289252619
99	0.998517000651073	0.00296599869785316	0.00148299934892658
100	0.998283791478668	0.00343241704266308	0.00171620852133154
101	0.99885410165978	0.00229179668043973	0.00114589834021987
102	0.998129210647506	0.00374157870498806	0.00187078935249403
103	0.99726721218381	0.00546557563237986	0.00273278781618993
104	0.998413010877918	0.00317397824416377	0.00158698912208188
105	0.998393982653714	0.00321203469257201	0.00160601734628601
106	0.997364296080438	0.00527140783912368	0.00263570391956184
107	0.99616526112611	0.00766947774778048	0.00383473887389024
108	0.994058855097942	0.0118822898041155	0.00594114490205773
109	0.997546025614996	0.00490794877000809	0.00245397438500404
110	0.996153821946647	0.00769235610670508	0.00384617805335254
111	0.994132555303736	0.0117348893925270	0.00586744469626352
112	0.992105286486273	0.0157894270274544	0.0078947135137272
113	0.993234058281636	0.0135318834367274	0.00676594171836368
114	0.99076594005831	0.0184681198833785	0.00923405994168925
115	0.985298988740902	0.0294020225181955	0.0147010112590977
116	0.980537996974147	0.0389240060517069	0.0194620030258534
117	0.985886636101466	0.0282267277970688	0.0141133638985344
118	0.988752618193024	0.0224947636139524	0.0112473818069762
119	0.994915974257321	0.0101680514853573	0.00508402574267863
120	0.990966249035018	0.0180675019299635	0.00903375096498175
121	0.989187878645253	0.0216242427094938	0.0108121213547469
122	0.993758473418765	0.0124830531624707	0.00624152658123534
123	0.99378960246765	0.0124207950646997	0.00621039753234983
124	0.991870673756406	0.0162586524871871	0.00812932624359357
125	0.985117712902062	0.0297645741958761	0.0148822870979380
126	0.972965053553615	0.0540698928927708	0.0270349464463854
127	0.957188567054805	0.0856228658903897	0.0428114329451948
128	0.961471489415025	0.0770570211699497	0.0385285105849748
129	0.983176279830487	0.0336474403390265	0.0168237201695132
130	0.971796168726139	0.0564076625477226	0.0282038312738613
131	0.95039050098662	0.0992189980267622	0.0496094990133811
132	0.906213123271643	0.187573753456715	0.0937868767283573
133	0.846983848070659	0.306032303858682	0.153016151929341
134	0.728984590377958	0.542030819244083	0.271015409622042

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	55	0.436507936507937	NOK
5% type I error level	79	0.626984126984127	NOK
10% type I error level	88	0.698412698412698	NOK