Multiple Linear Regression - Estimated Regression Equation

belonging[t] = + 30.412552707353 + 0.616533594321869popularity[t] + 0.510913274781838hapiness[t] -0.430298147948814doubsaboutactions[t] + 0.226540094212896parentalexpectations[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)	30.412552707353	5.931119	5.1276	1e-06	0
popularity	0.616533594321869	0.19293	3.1956	0.00173	0.000865
hapiness	0.510913274781838	0.260515	1.9612	0.051873	0.025936
doubsaboutactions	-0.430298147948814	0.223642	-1.924	0.056407	0.028203
parentalexpectations	0.226540094212896	0.16801	1.3484	0.179748	0.089874

Multiple Linear Regression - Regression Statistics
Multiple R	0.407575041565467
R-squared	0.166117414507092
Adjusted R-squared	0.14194690478266
F-TEST (value)	6.87273112569805
F-TEST (DF numerator)	4
F-TEST (DF denominator)	138
p-value	4.48569440201219e-05
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	6.81522948809898
Sum Squared Residuals	6409.73471061264

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	42	44.9369863542805	-2.93698635428054
2	51	46.5328128669426	4.46718713305736
3	42	44.5794806322225	-2.57948063222247
4	46	44.8085839942633	1.19141600573670
5	41	38.9500748187993	2.04992518120068
6	49	42.5111682871394	6.48883171286065
7	47	44.9475052205085	2.05249477949147
8	33	43.4273686860097	-10.4273686860097
9	47	45.6669571379309	1.33304286206911
10	42	38.7713219577704	3.22867804222959
11	32	43.8726261734934	-11.8726261734934
12	53	50.1263882821805	2.87361171781952
13	41	41.0721140613763	-0.0721140613763252
14	41	46.3417851693583	-5.34178516935829
15	33	41.1997091238926	-8.19970912389262
16	37	39.9017992766049	-2.90179927660486
17	43	44.9772968332735	-1.97729683327349
18	33	38.3313122410941	-5.33131224109408
19	49	46.4346693015934	2.56533069840660
20	42	45.6591402681422	-3.6591402681422
21	43	37.8301105350398	5.16988946496025
22	37	36.6571054161354	0.342894583864567
23	43	46.1450483502170	-3.14504835021703
24	42	42.7701961594034	-0.770196159403397
25	43	40.7268773447206	2.27312265527941
26	46	47.0231672534775	-1.02316725347753
27	33	48.2790106514449	-15.2790106514449
28	42	44.8691132459055	-2.86911324590554
29	40	41.1949227038347	-1.19492270383467
30	44	42.2040130660934	1.79598693390657
31	42	46.8018865923787	-4.80188659237874
32	52	43.9334955407335	8.06650445926646
33	44	41.9629749830951	2.03702501690493
34	45	44.8813822513076	0.118617748692373
35	46	40.8627622900817	5.13723770991826
36	36	41.7584038007051	-5.7584038007051
37	45	45.8781977770110	-0.878197777010954
38	49	45.8453757145153	3.15462428548474
39	43	44.0207801242567	-1.02078012425666
40	43	43.9576934359398	-0.957693435939837
41	37	39.9924485943033	-2.99244859430326
42	32	34.5634361004407	-2.56343610044072
43	45	44.1569993540624	0.843000645937645
44	45	47.1818342393157	-2.18183423931565
45	45	44.9291694844916	0.0708305155083902
46	45	43.0120240464424	1.98797595355756
47	31	42.3902368501598	-11.3902368501598
48	33	42.1058753318975	-9.10587533189754
49	44	43.1680006981477	0.83199930185228
50	49	36.5264682415817	12.4735317584183
51	44	42.503339755044	1.49666024495603
52	41	38.5776039260532	2.42239607394679
53	44	42.8683338935993	1.13166610640072
54	38	41.9424219260015	-3.94242192600147
55	33	41.8595836469384	-8.85958364693841
56	47	43.0870512868701	3.91294871312985
57	37	40.0372053777565	-3.0372053777565
58	48	45.2411111255955	2.75888887440452
59	40	40.9656806131822	-0.965680613182238
60	50	45.5610025339463	4.43899746605369
61	54	48.1839091981331	5.8160908018669
62	43	47.1515754446479	-4.15157544464788
63	54	41.7912316943541	12.2087683056459
64	44	44.1697413725206	-0.169741372520612
65	47	42.1637025871002	4.83629741289975
66	33	43.6658376700268	-10.6658376700268
67	45	46.4193756776139	-1.41937567761391
68	33	34.6190402034134	-1.6190402034134
69	44	45.0829171528135	-1.08291715281352
70	47	44.4488551199754	2.55114488002456
71	45	41.1449123184207	3.85508768157934
72	43	42.4480757676692	0.551924232330809
73	43	37.221059526062	5.77894047393797
74	33	43.6833602773896	-10.6833602773896
75	46	43.2333163698479	2.76668363015209
76	47	43.5129031303589	3.48709686964110
77	47	42.0383248456606	4.96167515433936
78	0	41.522157968918	-41.522157968918
79	43	43.3867239225719	-0.386723922571923
80	46	43.4195518162210	2.58044818377904
81	36	38.1700994808881	-2.17009948088806
82	42	39.3400624877549	2.65993751224505
83	44	42.7451851355430	1.25481486445695
84	47	47.0131272314588	-0.0131272314588052
85	41	40.2712280573135	0.728771942686462
86	47	44.0816494914968	2.91835050850321
87	46	44.5395102688272	1.46048973117281
88	47	46.8672022640789	0.132797735921066
89	46	46.7690586987297	-0.769058698729703
90	46	45.1810490558561	0.81895094414394
91	36	44.776563398115	-8.77656339811497
92	30	39.8667423995724	-9.86674239957245
93	48	43.0799029859706	4.92009701402945
94	45	41.5524284258925	3.44757157410751
95	49	45.1863084889702	3.81369151102983
96	55	46.8974610587467	8.10253894125329
97	11	42.0305196381786	-31.0305196381786
98	52	45.5512909652188	6.4487090347812
99	33	36.2801765566226	-3.28017655662258
100	47	48.1961782035352	-1.19617820353519
101	33	38.7213115723564	-5.72131157235639
102	44	44.0010343646638	-0.00103436466376364
103	42	39.6222125160939	2.37778748390614
104	55	42.2267834442637	12.7732165557363
105	42	43.7039191656366	-1.70391916563656
106	46	44.7612639429821	1.23873605701787
107	46	46.6862204196666	-0.68622041966665
108	47	46.6003516908729	0.399648309127147
109	33	42.8758164789434	-9.87581647894343
110	53	49.464296438058	3.53570356194200
111	42	42.9914768205022	-0.991476820502178
112	44	43.4598564640608	0.540143535939195
113	55	45.9185082560041	9.08149174399586
114	40	35.7311876173843	4.26881238261573
115	46	46.3562889892971	-0.356288989297095
116	53	45.5109863173790	7.48901368262104
117	44	45.3194972690451	-1.31949726904513
118	35	39.9618555151909	-4.96185551519093
119	40	39.0034499383886	0.996550061611378
120	44	44.8112801595495	-0.811280159549488
121	46	46.1017074214931	-0.101707421493107
122	45	42.0032854620883	2.99671453791174
123	53	44.6298311332344	8.37016886676562
124	45	44.7284418804864	0.271558119513565
125	48	42.0655648529044	5.93443514709564
126	46	45.5990840295561	0.400915970443874
127	55	41.1374239019232	13.8625760980768
128	47	49.6001813834191	-2.60018138341915
129	43	41.8162427182145	1.18375728178551
130	38	38.5850923425507	-0.585092342550694
131	40	40.9131069599403	-0.913106959940305
132	47	41.5774336185995	5.4225663814005
133	47	41.4315028200663	5.56849717993371
134	42	41.615509283056	0.384490716944030
135	53	43.3717587518836	9.62824124811636
136	43	44.9772968332735	-1.97729683327349
137	44	44.4160330574797	-0.416033057479743
138	42	42.689575201417	-0.68957520141703
139	51	44.043567995887	6.95643200411302
140	54	42.2443118827799	11.7556881172201
141	41	43.0598229419331	-2.05982294193311
142	51	43.686402389427	7.31359761057296
143	51	43.9554644525565	7.04453554744353

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
8	0.597440620714478	0.805118758571044	0.402559379285522
9	0.475728075470647	0.951456150941293	0.524271924529353
10	0.362864486345942	0.725728972691883	0.637135513654058
11	0.353397989648564	0.706795979297127	0.646602010351436
12	0.28705494551777	0.57410989103554	0.71294505448223
13	0.262535586235171	0.525071172470342	0.737464413764829
14	0.205008434192043	0.410016868384085	0.794991565807957
15	0.232827008341727	0.465654016683454	0.767172991658273
16	0.169006793876959	0.338013587753917	0.830993206123041
17	0.137693072652727	0.275386145305455	0.862306927347273
18	0.0966812150311128	0.193362430062226	0.903318784968887
19	0.100276166445054	0.200552332890109	0.899723833554946
20	0.07739960400775	0.1547992080155	0.92260039599225
21	0.0833503092307999	0.166700618461600	0.9166496907692
22	0.056293215013495	0.11258643002699	0.943706784986505
23	0.0432324141286542	0.0864648282573083	0.956767585871346
24	0.0308293951175297	0.0616587902350594	0.96917060488247
25	0.0246656143087032	0.0493312286174063	0.975334385691297
26	0.0159987688551355	0.0319975377102709	0.984001231144864
27	0.0451527092970399	0.0903054185940799	0.95484729070296
28	0.0341103289641478	0.0682206579282956	0.965889671035852
29	0.0230987699602323	0.0461975399204646	0.976901230039768
30	0.0153109332107159	0.0306218664214318	0.984689066789284
31	0.0118023922170776	0.0236047844341553	0.988197607782922
32	0.0130085883731660	0.0260171767463321	0.986991411626834
33	0.00852149255993075	0.0170429851198615	0.99147850744007
34	0.0055707203137654	0.0111414406275308	0.994429279686235
35	0.00481862253266961	0.00963724506533922	0.99518137746733
36	0.00325469351434969	0.00650938702869937	0.99674530648565
37	0.00212529412368423	0.00425058824736846	0.997874705876316
38	0.00154901634082213	0.00309803268164426	0.998450983659178
39	0.000988871411542903	0.00197774282308581	0.999011128588457
40	0.000604641312048233	0.00120928262409647	0.999395358687952
41	0.000374525413936076	0.000749050827872152	0.999625474586064
42	0.000216379258019646	0.000432758516039293	0.99978362074198
43	0.000153166864095342	0.000306333728190684	0.999846833135905
44	8.96631314683946e-05	0.000179326262936789	0.999910336868532
45	5.01279095161707e-05	0.000100255819032341	0.999949872090484
46	6.1385710442343e-05	0.000122771420884686	0.999938614289558
47	0.000106408672410746	0.000212817344821492	0.99989359132759
48	0.000362386625719256	0.000724773251438511	0.99963761337428
49	0.000245619524845623	0.000491239049691245	0.999754380475154
50	0.00306958380063952	0.00613916760127905	0.99693041619936
51	0.00225122436172797	0.00450244872345594	0.997748775638272
52	0.00160614781214924	0.00321229562429847	0.99839385218785
53	0.00104039883206646	0.00208079766413292	0.998959601167934
54	0.000834140842124923	0.00166828168424985	0.999165859157875
55	0.00146312234683071	0.00292624469366143	0.99853687765317
56	0.00112218210364044	0.00224436420728087	0.99887781789636
57	0.000761853790977201	0.00152370758195440	0.999238146209023
58	0.000603312780229307	0.00120662556045861	0.99939668721977
59	0.000399330026100266	0.000798660052200533	0.9996006699739
60	0.000331364864212417	0.000662729728424833	0.999668635135788
61	0.000345808211289995	0.00069161642257999	0.99965419178871
62	0.000253078934663712	0.000506157869327424	0.999746921065336
63	0.00118399445194412	0.00236798890388824	0.998816005548056
64	0.000769500803247529	0.00153900160649506	0.999230499196752
65	0.000658717049196801	0.00131743409839360	0.999341282950803
66	0.00123965506416688	0.00247931012833377	0.998760344935833
67	0.000825939669807051	0.00165187933961410	0.999174060330193
68	0.000553175605460668	0.00110635121092134	0.99944682439454
69	0.000356027226452397	0.000712054452904793	0.999643972773548
70	0.000247977325311045	0.000495954650622089	0.999752022674689
71	0.00017787854968241	0.00035575709936482	0.999822121450318
72	0.000110831621502511	0.000221663243005022	0.999889168378498
73	9.55563696450313e-05	0.000191112739290063	0.999904443630355
74	0.000193419371844867	0.000386838743689734	0.999806580628155
75	0.000133421555773419	0.000266843111546839	0.999866578444227
76	9.3171584665127e-05	0.000186343169330254	0.999906828415335
77	8.30506922662771e-05	0.000166101384532554	0.999916949307734
78	0.892829438936245	0.214341122127509	0.107170561063755
79	0.868065884836799	0.263868230326403	0.131934115163201
80	0.843299472589571	0.313401054820857	0.156700527410429
81	0.82592270301237	0.348154593975259	0.174077296987629
82	0.796929709209897	0.406140581580206	0.203070290790103
83	0.760838971006644	0.478322057986711	0.239161028993356
84	0.721637713164158	0.556724573671684	0.278362286835842
85	0.67847398170123	0.643052036597541	0.321526018298770
86	0.655991971532385	0.68801605693523	0.344008028467615
87	0.63307041244207	0.733859175115861	0.366929587557930
88	0.584799647910457	0.830400704179087	0.415200352089543
89	0.542441755020813	0.915116489958374	0.457558244979187
90	0.51847896343144	0.96304207313712	0.48152103656856
91	0.584429503631593	0.831140992736815	0.415570496368407
92	0.65528967681803	0.689420646363939	0.344710323181969
93	0.640665923995563	0.718668152008873	0.359334076004437
94	0.611795896457293	0.776408207085415	0.388204103542707
95	0.570608003609361	0.858783992781278	0.429391996390639
96	0.580474612049945	0.83905077590011	0.419525387950055
97	0.998901652824894	0.00219669435021304	0.00109834717510652
98	0.99853839299037	0.00292321401925804	0.00146160700962902
99	0.998933283245663	0.00213343350867461	0.00106671675433731
100	0.998776389496303	0.00244722100739492	0.00122361050369746
101	0.99918152634753	0.00163694730494003	0.000818473652470016
102	0.998649814421303	0.0027003711573945	0.00135018557869725
103	0.998014610303334	0.00397077939333199	0.00198538969666600
104	0.99893166949303	0.00213666101393892	0.00106833050696946
105	0.998902675280419	0.0021946494391619	0.00109732471958095
106	0.998177525319184	0.00364494936163095	0.00182247468081548
107	0.997295827399732	0.00540834520053618	0.00270417260026809
108	0.99582980452548	0.00834039094904015	0.00417019547452008
109	0.998088934175428	0.00382213164914441	0.00191106582457220
110	0.996968215583728	0.00606356883254367	0.00303178441627184
111	0.995594759713668	0.00881048057266382	0.00440524028633191
112	0.993799862060218	0.012400275879563	0.0062001379397815
113	0.9937656149891	0.0124687700217979	0.00623438501089893
114	0.990691388748725	0.0186172225025497	0.00930861125127484
115	0.986148777466078	0.0277024450678433	0.0138512225339217
116	0.982739686935138	0.0345206261297233	0.0172603130648616
117	0.985860501391398	0.0282789972172035	0.0141394986086017
118	0.98633746120822	0.027325077583561	0.0136625387917805
119	0.98929796855311	0.0214040628937810	0.0107020314468905
120	0.982339238252573	0.0353215234948535	0.0176607617474268
121	0.9792848587304	0.0414302825391996	0.0207151412695998
122	0.969265419403	0.0614691611939989	0.0307345805969994
123	0.966307441955381	0.0673851160892385	0.0336925580446193
124	0.948882221427397	0.102235557145206	0.051117778572603
125	0.924860196261282	0.150279607477437	0.0751398037387184
126	0.890747254653248	0.218505490693504	0.109252745346752
127	0.912432463554567	0.175135072890867	0.0875675364454334
128	0.907029226512845	0.185941546974310	0.0929707734871552
129	0.900250677797774	0.199498644404451	0.0997493222022257
130	0.865157092536118	0.269685814927764	0.134842907463882
131	0.93766797189188	0.124664056216240	0.0623320281081202
132	0.888947850802238	0.222104298395525	0.111052149197762
133	0.813060503810084	0.373878992379831	0.186939496189916
134	0.687672393367932	0.624655213264136	0.312327606632068
135	0.532105840866852	0.935788318266296	0.467894159133148

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	58	0.453125	NOK
5% type I error level	76	0.59375	NOK
10% type I error level	82	0.640625	NOK