Multiple Linear Regression - Estimated Regression Equation

Connected[t] = + 29.4474536129401 + 0.266840966518791Learning[t] + 0.133404339807184Happiness[t] -0.020419774909484Depression[t] -0.00518057911389828t + 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)	29.4474536129401	3.426719	8.5935	0	0
Learning	0.266840966518791	0.120876	2.2076	0.028725	0.014363
Happiness	0.133404339807184	0.133379	1.0002	0.318756	0.159378
Depression	-0.020419774909484	0.099707	-0.2048	0.837996	0.418998
t	-0.00518057911389828	0.005692	-0.9101	0.364167	0.182083

Multiple Linear Regression - Regression Statistics
Multiple R	0.249251727193792
R-squared	0.0621264235090886
Adjusted R-squared	0.0382315553182373
F-TEST (value)	2.59999021601112
F-TEST (DF numerator)	4
F-TEST (DF denominator)	157
p-value	0.0382364588771699
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	3.30998209050868
Sum Squared Residuals	1720.08908599965

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	41	34.5338290569574	6.46617094304262
2	39	35.883208511538	3.11679148846203
3	30	35.6834611286017	-5.68346112860171
4	31	34.7851605730388	-3.7851605730388
5	34	34.8629784124495	-0.86297841244949
6	35	35.0415435206165	-0.0415435206165239
7	39	35.8995936322918	3.1004063677082
8	34	35.0516667111071	-1.05166671110706
9	36	34.933469280191	1.06653071980896
10	37	35.1338703428675	1.86612965713252
11	38	35.7235987346152	2.27640126538481
12	36	36.0260663849346	-0.0260663849346261
13	38	34.6773083231897	3.32269167681031
14	39	35.4929735578284	3.50702644217162
15	33	36.1031217244856	-3.10312172448557
16	32	34.9489627534674	-2.94896275346742
17	36	34.9437821743535	1.05621782564648
18	38	36.7342787719836	1.26572122801642
19	39	35.81562301532	3.18437698467997
20	32	35.4823098580545	-3.48230985805447
21	32	35.8664566080118	-3.86645660801184
22	31	34.7845072258813	-3.78450722588127
23	39	36.0209021155643	2.97909788443574
24	37	34.9075504074607	2.09244959253934
25	39	35.8974918186299	3.10250818137008
26	41	34.8659160708775	6.13408392912248
27	36	35.4868853540762	0.513114645923851
28	33	34.8663760291912	-1.86637602919116
29	33	35.2818605313127	-2.28186053131272
30	34	34.229800434842	-0.229800434841987
31	31	35.2401616209207	-4.24016162092073
32	27	33.911726473372	-6.91172647337201
33	37	35.0759440610718	1.92405593892815
34	34	35.3172169604717	-1.31721696047168
35	34	34.604110558694	-0.604110558694046
36	32	33.0999507681104	-1.0999507681104
37	29	32.7164254109888	-3.71642541098878
38	36	34.742392936069	1.25760706393098
39	29	35.578542519426	-6.57854251942604
40	35	35.0397445810834	-0.0397445810834052
41	37	35.3217924564934	1.67820754350664
42	34	34.8142354096016	-0.814235409601641
43	38	36.5326192790574	1.46738072094261
44	35	34.2702568921451	0.729743107854889
45	38	34.3263356377597	3.67366436224033
46	37	33.3463882694632	3.65361173053676
47	38	34.7570270487724	3.24297295122761
48	33	34.9778478863583	-1.97784788635831
49	36	35.4246378537396	0.575362146260365
50	38	34.4338370819974	3.56616291800264
51	32	35.3829712302521	-3.38297123025208
52	32	34.4956209388483	-2.49562093884829
53	32	33.4748663076373	-1.47486630763733
54	34	34.7521330340437	-0.75213303404371
55	32	32.9403250140267	-0.940325014026727
56	37	34.6491425120188	2.35085748798115
57	39	35.2906284308402	3.70937156915977
58	29	35.2337226115571	-6.23372261155709
59	37	34.5410682715934	2.45893172840664
60	35	34.7006297844508	0.299370215549164
61	30	32.9923691054856	-2.99236910548562
62	38	34.8849322907587	3.11506770924133
63	34	34.6129430320304	-0.61294303203041
64	31	34.4334539894815	-3.43345398948151
65	34	35.1157794581219	-1.11577945812186
66	35	34.7512576963098	0.248742303690194
67	36	35.023803774065	0.976196225935022
68	30	35.2541264093057	-5.25412640930568
69	39	34.0276932755911	4.97230672440889
70	35	35.0694567876429	-0.0694567876428877
71	38	33.3502458445185	4.64975415548146
72	31	34.6383982612752	-3.63839826127521
73	34	35.6080167582483	-1.60801675824826
74	38	35.6640955038628	2.33590449613719
75	34	34.8380045371875	-0.838004537187481
76	39	34.8029023855093	4.19709761449068
77	37	35.3204211883695	1.67957881163055
78	34	34.6999441503889	-0.699944150388882
79	28	34.2427284509709	-6.24272845097091
80	37	34.852941191437	2.14705880856304
81	33	35.0737297421185	-2.07372974211846
82	37	36.2897371437964	0.710262856203609
83	35	35.1042081337096	-0.10420813370963
84	37	34.9043316031557	2.09566839684433
85	32	34.7657466842346	-2.76574668423459
86	33	34.8735829569228	-1.87358295692282
87	38	34.4681247845785	3.53187521542148
88	33	34.8836415736045	-1.8836415736045
89	29	34.683797329955	-5.68379732995497
90	33	33.4684113211128	-0.468411321112791
91	31	34.1805292146997	-3.18052921469971
92	36	34.9350965591321	1.06490344086793
93	35	34.9707232429327	0.0292767570672889
94	32	34.5244578076739	-2.52445780767387
95	29	33.9542898302626	-4.95428983026263
96	39	35.1294253952172	3.87057460478283
97	37	34.4885285823271	2.51147141767288
98	35	34.852255557375	0.147744442624996
99	37	35.2472879976827	1.75271200231734
100	32	34.4620365808263	-2.46203658082629
101	38	35.2573466143643	2.74265338563566
102	37	34.4626256867576	2.53737431324238
103	36	36.1401054325856	-0.140105432585559
104	32	34.1541180967513	-2.15411809675127
105	33	34.8472969688375	-1.84729696883748
106	40	33.1799081265957	6.82009187340434
107	38	35.3392799914831	2.66072000851692
108	41	34.8317552314958	6.16824476850422
109	36	34.1799727282554	1.82002727174455
110	43	32.923650308881	10.076349691119
111	30	34.8570530439731	-4.85705304397306
112	31	34.2978353307209	-3.29783533072094
113	32	34.9079834973781	-2.90798349737814
114	32	33.8871642923583	-1.88716429235832
115	37	34.2100194306828	2.78998056931718
116	37	35.5799155208863	1.42008447911373
117	33	34.1588832964449	-1.1588832964449
118	34	34.1741224922405	-0.174122492240489
119	33	33.9837800462457	-0.983780046245736
120	38	34.6566037172313	3.34339628276869
121	33	33.5840915589467	-0.584091558946668
122	31	34.666662333913	-3.66666233391299
123	38	34.0556225197784	3.94437748022164
124	37	34.9122241649493	2.08777583505072
125	33	34.5789432945881	-1.57894329458814
126	31	34.5737950023787	-3.57379500237867
127	39	34.8966501407032	4.10334985929683
128	44	35.3843119448079	8.61568805519212
129	33	35.0918383373613	-2.09183833736128
130	35	33.7116779496433	1.28832205035669
131	32	34.5478921068092	-2.54789210680918
132	28	32.2242703951684	-4.22427039516844
133	40	34.8247594031052	5.17524059689477
134	27	33.6501160833688	-6.65011608336875
135	37	34.2398767620209	2.76012323797911
136	32	34.594101939414	-2.59410193941399
137	28	33.2044397540412	-5.20443975404124
138	34	34.3169321015718	-0.31693210157183
139	30	32.8033350871423	-2.80333508714225
140	35	33.7007117083233	1.2992882916767
141	31	32.3409388086104	-1.34093880861038
142	32	34.7781341910801	-2.77813419108015
143	30	34.5578378856167	-4.5578378856167
144	30	34.860370109745	-4.86037010974499
145	31	34.7217529039195	-3.72175290391948
146	40	33.2693506404095	6.73064935959049
147	32	35.3784780185365	-3.37847801853645
148	36	33.3516511328832	2.6483488671168
149	32	34.3212373429518	-2.32123734295183
150	35	32.9519626455841	2.04803735441587
151	38	33.2230279699305	4.77697203006947
152	42	34.0497403294416	7.95025967055838
153	34	34.8749719355439	-0.874971935543934
154	35	34.2749146724728	0.725085327527151
155	35	33.1929007165334	1.80709928346657
156	33	32.6743934054826	0.325606594517413
157	36	34.5983589167287	1.40164108327132
158	32	33.6796385862563	-1.67963858625628
159	33	34.9364209639443	-1.93642096394434
160	34	34.4384948623251	-0.438494862325095
161	32	33.0487681031435	-1.04876810314349
162	34	33.4846723801745	0.515327619825462

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
8	0.908508483928956	0.182983032142088	0.091491516071044
9	0.864691644245106	0.270616711509787	0.135308355754893
10	0.810713488373715	0.37857302325257	0.189286511626285
11	0.728392077118633	0.543215845762733	0.271607922881367
12	0.657551153685223	0.684897692629553	0.342448846314777
13	0.700658127284306	0.598683745431389	0.299341872715694
14	0.631315635631295	0.73736872873741	0.368684364368705
15	0.655233887415698	0.689532225168603	0.344766112584302
16	0.678834356814865	0.642331286370271	0.321165643185135
17	0.600145869759216	0.799708260481568	0.399854130240784
18	0.5554319001713	0.889136199657401	0.4445680998287
19	0.555707880076253	0.888584239847493	0.444292119923747
20	0.598371544599724	0.803256910800552	0.401628455400276
21	0.606217302666087	0.787565394667826	0.393782697333913
22	0.578013272324507	0.843973455350985	0.421986727675493
23	0.605381182896263	0.789237634207475	0.394618817103737
24	0.578641367331185	0.842717265337629	0.421358632668815
25	0.563244397822547	0.873511204354905	0.436755602177453
26	0.687449795667816	0.625100408664367	0.312550204332183
27	0.628617504577888	0.742764990844223	0.371382495422112
28	0.598564115155848	0.802871769688303	0.401435884844152
29	0.565683044457532	0.868633911084935	0.434316955542468
30	0.504133547182268	0.991732905635464	0.495866452817732
31	0.522722577907368	0.954554844185264	0.477277422092632
32	0.607022089803191	0.785955820393618	0.392977910196809
33	0.610902466088596	0.778195067822808	0.389097533911404
34	0.55520526839751	0.88958946320498	0.44479473160249
35	0.502057438818917	0.995885122362166	0.497942561181083
36	0.458199224359211	0.916398448718422	0.541800775640789
37	0.42200663365133	0.84401326730266	0.57799336634867
38	0.397175416151534	0.794350832303068	0.602824583848466
39	0.504387911374107	0.991224177251786	0.495612088625893
40	0.453773850212026	0.907547700424051	0.546226149787974
41	0.43123112975891	0.862462259517821	0.56876887024109
42	0.387081071031832	0.774162142063665	0.612918928968168
43	0.346830110018183	0.693660220036365	0.653169889981817
44	0.315561131265374	0.631122262530748	0.684438868734626
45	0.347710517490141	0.695421034980282	0.652289482509859
46	0.383874361110272	0.767748722220544	0.616125638889728
47	0.38765904066329	0.77531808132658	0.61234095933671
48	0.351441336031105	0.702882672062209	0.648558663968895
49	0.315025359444681	0.630050718889362	0.684974640555319
50	0.323565149823477	0.647130299646954	0.676434850176523
51	0.322737959242341	0.645475918484682	0.677262040757659
52	0.294384122740214	0.588768245480428	0.705615877259786
53	0.255921063220064	0.511842126440128	0.744078936779936
54	0.218222364403679	0.436444728807359	0.781777635596321
55	0.18434022351427	0.36868044702854	0.81565977648573
56	0.177198377911006	0.354396755822013	0.822801622088994
57	0.194768990084921	0.389537980169843	0.805231009915079
58	0.293298810677931	0.586597621355862	0.706701189322069
59	0.274784822698196	0.549569645396392	0.725215177301804
60	0.236648511450556	0.473297022901111	0.763351488549444
61	0.221740842698076	0.443481685396152	0.778259157301924
62	0.219773309264568	0.439546618529135	0.780226690735432
63	0.187876153801215	0.37575230760243	0.812123846198785
64	0.182434102872694	0.364868205745388	0.817565897127306
65	0.154366659039038	0.308733318078077	0.845633340960962
66	0.12869565798999	0.257391315979981	0.87130434201001
67	0.108556178337808	0.217112356675616	0.891443821662192
68	0.144445437754802	0.288890875509603	0.855554562245198
69	0.200238617016509	0.400477234033019	0.799761382983491
70	0.169767188465732	0.339534376931463	0.830232811534268
71	0.209694416868082	0.419388833736165	0.790305583131918
72	0.209508211572738	0.419016423145475	0.790491788427262
73	0.182669136995669	0.365338273991338	0.817330863004331
74	0.169851791367507	0.339703582735014	0.830148208632493
75	0.143117784568916	0.286235569137831	0.856882215431084
76	0.16665909901439	0.33331819802878	0.83334090098561
77	0.147076450467816	0.294152900935632	0.852923549532184
78	0.122709362951239	0.245418725902478	0.877290637048761
79	0.185412279442369	0.370824558884738	0.814587720557631
80	0.16979863118065	0.339597262361299	0.83020136881935
81	0.151005437060146	0.302010874120291	0.848994562939854
82	0.12709742473722	0.25419484947444	0.87290257526278
83	0.104667985596056	0.209335971192113	0.895332014403944
84	0.0939276034207715	0.187855206841543	0.906072396579229
85	0.0866345537562484	0.173269107512497	0.913365446243752
86	0.0739965571807849	0.14799311436157	0.926003442819215
87	0.0777501530741372	0.155500306148274	0.922249846925863
88	0.0661893393561471	0.132378678712294	0.933810660643853
89	0.0961438385754472	0.192287677150894	0.903856161424553
90	0.0789684427099687	0.157936885419937	0.921031557290031
91	0.0797205033581918	0.159441006716384	0.920279496641808
92	0.066017453715764	0.132034907431528	0.933982546284236
93	0.0529861650655954	0.105972330131191	0.947013834934405
94	0.0493264856018004	0.0986529712036008	0.9506735143982
95	0.0676242217233905	0.135248443446781	0.93237577827661
96	0.0720558457959242	0.144111691591848	0.927944154204076
97	0.0651438404047274	0.130287680809455	0.934856159595273
98	0.051793915825986	0.103587831651972	0.948206084174014
99	0.0430895148426613	0.0861790296853227	0.956910485157339
100	0.0403585601041349	0.0807171202082698	0.959641439895865
101	0.0360015337166939	0.0720030674333877	0.963998466283306
102	0.0317375315457164	0.0634750630914329	0.968262468454284
103	0.0242248387748805	0.048449677549761	0.97577516122512
104	0.021089604417294	0.042179208834588	0.978910395582706
105	0.0178681457529144	0.0357362915058288	0.982131854247086
106	0.038108721013183	0.076217442026366	0.961891278986817
107	0.0336507874866009	0.0673015749732018	0.966349212513399
108	0.0586585777265181	0.117317155453036	0.941341422273482
109	0.0508151903663746	0.101630380732749	0.949184809633625
110	0.331559700284608	0.663119400569215	0.668440299715392
111	0.354024885819205	0.708049771638411	0.645975114180795
112	0.332852244716017	0.665704489432035	0.667147755283983
113	0.312041617428543	0.624083234857086	0.687958382571457
114	0.277430730615292	0.554861461230583	0.722569269384708
115	0.259297987932642	0.518595975865284	0.740702012067358
116	0.230079459953682	0.460158919907365	0.769920540046318
117	0.19482692581709	0.38965385163418	0.80517307418291
118	0.161346192573423	0.322692385146846	0.838653807426577
119	0.13888402165853	0.277768043317061	0.861115978341469
120	0.163223387200905	0.326446774401811	0.836776612799095
121	0.133617670989231	0.267235341978463	0.866382329010769
122	0.123101420372457	0.246202840744914	0.876898579627543
123	0.12940333014734	0.258806660294679	0.87059666985266
124	0.111367701887328	0.222735403774656	0.888632298112672
125	0.0902253880185308	0.180450776037062	0.909774611981469
126	0.087697332095387	0.175394664190774	0.912302667904613
127	0.0911018013915958	0.182203602783192	0.908898198608404
128	0.38563146482604	0.771262929652079	0.61436853517396
129	0.338078189786961	0.676156379573923	0.661921810213039
130	0.313528743438547	0.627057486877093	0.686471256561453
131	0.270891066620741	0.541782133241482	0.729108933379259
132	0.271108992067145	0.542217984134289	0.728891007932855
133	0.464786146461052	0.929572292922104	0.535213853538948
134	0.566104059297517	0.867791881404966	0.433895940702483
135	0.622904064118284	0.754191871763431	0.377095935881716
136	0.566505506291738	0.866988987416525	0.433494493708262
137	0.587000549862025	0.82599890027595	0.412999450137975
138	0.533966633031413	0.932066733937174	0.466033366968587
139	0.540652131772701	0.918695736454599	0.4593478682273
140	0.483145297848971	0.966290595697941	0.516854702151029
141	0.548518501285965	0.902962997428069	0.451481498714035
142	0.487642904337089	0.975285808674179	0.512357095662911
143	0.519780907064992	0.960438185870017	0.480219092935008
144	0.577365927081104	0.845268145837793	0.422634072918896
145	0.669138235582657	0.661723528834685	0.330861764417343
146	0.691879930063118	0.616240139873764	0.308120069936882
147	0.813593971408964	0.372812057182073	0.186406028591036
148	0.744768931466464	0.510462137067072	0.255231068533536
149	0.825958149238738	0.348083701522525	0.174041850761262
150	0.828494456546855	0.34301108690629	0.171505543453145
151	0.869177371168422	0.261645257663156	0.130822628831578
152	0.997184514269723	0.00563097146055411	0.00281548573027705
153	0.988374549097643	0.0232509018047139	0.0116254509023569
154	0.955721008378929	0.0885579832421429	0.0442789916210714

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	1	0.00680272108843537	OK
5% type I error level	5	0.0340136054421769	OK
10% type I error level	13	0.0884353741496599	OK