Multiple Linear Regression - Estimated Regression Equation

connected[t] = + 30.0077097493809 + 0.267094674463107learning[t] + 0.133484251054619happiness[t] -0.0201783941181385depression[t] -0.0656407988678097month[t] -0.00409937096057251t + 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)	30.0077097493809	8.882802	3.3782	0.000922	0.000461
learning	0.267094674463107	0.121318	2.2016	0.029161	0.01458
happiness	0.133484251054619	0.133808	0.9976	0.320029	0.160015
depression	-0.0201783941181385	0.100087	-0.2016	0.840485	0.420243
month	-0.0656407988678097	0.959635	-0.0684	0.945553	0.472777
t	-0.00409937096057251	0.016807	-0.2439	0.807618	0.403809

Multiple Linear Regression - Regression Statistics
Multiple R	0.249308146172092
R-squared	0.0621545517477652
Adjusted R-squared	0.0320954027653217
F-TEST (value)	2.06774156460876
F-TEST (DF numerator)	5
F-TEST (DF denominator)	156
p-value	0.0722890459834615
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	3.32052426539283
Sum Squared Residuals	1720.03749794177

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	41	34.5117127419775	6.48828725802246
2	39	35.8630127927428	3.13698720725721
3	30	35.6652725054348	-5.6652725054348
4	31	34.7666354759127	-3.76663547591269
5	34	34.8477728876442	-0.847772887644241
6	35	35.025152891393	-0.0251528913930451
7	39	35.8879006218113	3.11209937818874
8	34	35.0373848882978	-1.03738488829778
9	36	34.9198534880469	1.08014651195314
10	37	35.122313609195	1.87768639080502
11	38	35.7128125971612	2.28718740283884
12	36	36.0160385165461	-0.0160385165461042
13	38	34.669332127267	3.33066787273301
14	39	35.4863166567523	3.51368334324773
15	33	36.0969940388366	-3.0969940388366
16	32	34.9440547382588	-2.94405473825878
17	36	34.9399553672982	1.06004463270179
18	38	36.7323173041714	1.26768269582855
19	39	35.8137542252389	3.18624577476106
20	32	35.481898825107	-3.48189882510698
21	32	35.8658383209645	-3.86583832096447
22	31	34.7861004337946	-3.7861004337946
23	39	36.0240946276235	2.97590537237652
24	37	34.9113859429281	2.08861405707193
25	39	35.9023376840581	3.09766231594188
26	41	34.8707210928969	6.12927890710313
27	36	35.4935600166192	0.506439983380755
28	33	34.8746838926138	-1.87468389261377
29	33	35.2913418412891	-2.29134184128907
30	34	34.2392945113019	-0.239294511301944
31	31	35.2504246465501	-4.25042464655013
32	27	33.9235181343275	-6.92351813432754
33	37	35.0884370871024	1.91156291289765
34	34	35.3313801688406	-1.33138016884062
35	34	34.6192504096629	-0.619250409662937
36	32	33.1133487901605	-1.11334879016054
37	29	32.7340029557893	-3.7340029557893
38	36	34.760614941954	1.23938505804602
39	29	35.5980302102651	-6.59803021026513
40	35	35.0599938350861	-0.0599938350860857
41	37	35.3430413603529	1.65695863964711
42	34	34.83734492093	-0.837344920930028
43	38	36.5568839614569	1.44311603854307
44	35	34.2952091747904	0.704790825209592
45	38	34.3516449861843	3.64835501381575
46	37	33.3724205525435	3.62757944745654
47	38	34.7842557856632	3.21574421433676
48	33	35.0068943009295	-2.0068943009295
49	36	35.4561445300687	0.543855469931285
50	38	34.464632382436	3.53536761756399
51	32	35.4153535076836	-3.41535350768364
52	32	34.5293827092151	-2.52938270921507
53	32	33.5099276596919	-1.50992765969187
54	34	34.7884048141109	-0.788404814110898
55	32	32.9095371053952	-0.909537105395181
56	37	34.6211854657959	2.37881453420414
57	39	35.264581300698	3.73541869930202
58	29	35.2077112551553	-6.20771125515535
59	37	34.5158860624497	2.48411393755033
60	35	34.6779893953615	0.322010604638485
61	30	32.9706823517393	-2.97068235173935
62	38	34.8638100868494	3.1361899131506
63	34	34.5927422137796	-0.592742213779594
64	31	34.4145494588204	-3.41454945882039
65	34	35.0983020819588	-1.09830208195879
66	35	34.7342329184245	0.265767081575496
67	36	35.0096421082728	0.990357891727174
68	30	35.2399189589576	-5.23991895895756
69	39	34.0135259002641	4.98647409973593
70	35	35.0576268330378	-0.0576268330377839
71	38	33.3376535583621	4.66234644163791
72	31	34.6285445991269	-3.6285445991269
73	34	35.5996964632004	-1.59969646320042
74	38	35.6561322745943	2.34386772540574
75	34	34.8306966584801	-0.8306966584801
76	39	34.7987805579829	4.20121944201709
77	37	35.3160781325412	1.68392186745885
78	34	34.6973281808895	-0.697328180889551
79	28	34.2396268651215	-6.23962686512145
80	37	34.8505565919135	2.14944340808649
81	33	35.0730689348259	-2.0730689348259
82	37	36.2910109068905	0.708989093109484
83	35	35.105226981141	-0.105226981141034
84	37	34.9069820044176	2.09301799558244
85	32	34.7693983824024	-2.76939838240237
86	33	34.8787310407321	-1.87873104073214
87	38	34.4739265719	3.52607342810003
88	33	34.8907106929291	-1.89071069292914
89	29	34.6925918885595	-5.69259188855953
90	33	33.4792435779812	-0.47924357798117
91	31	34.1903082412407	-3.19030824124071
92	36	34.9473884501409	1.05261154985908
93	35	34.9835196950628	0.0164803049372452
94	32	34.5384846103482	-2.53848461034818
95	29	33.9676036099975	-4.96760360999747
96	39	35.1450626214719	3.85493737852807
97	37	34.5061342757022	2.49386572429781
98	35	34.8698953774416	0.130104622558449
99	37	35.2662487596448	1.73375124035517
100	32	34.4811699317669	-2.48116993176695
101	38	35.2782284118418	2.72177158815817
102	37	34.4856374208993	2.51436257910067
103	36	36.1645673284822	-0.164567328482216
104	32	34.1777517240511	-2.17775172405115
105	33	34.8737920611815	-1.87379206118147
106	40	33.2069679781495	6.79303202185055
107	38	35.3670642153687	2.63293578463126
108	41	34.8614939482998	6.13850605170025
109	36	34.1445109173164	1.85548908268358
110	43	32.8904273014402	10.1095726985598
111	30	34.8239118247865	-4.8239118247865
112	31	34.2656970554893	-3.26569705548932
113	32	34.8763744375736	-2.87637443757364
114	32	33.8566670433427	-1.8566670433427
115	37	34.1799451844919	2.82005481550808
116	37	35.551802146437	1.44819785356297
117	33	34.1316419990422	-1.13164199904223
118	34	34.1477210221998	-0.147721022199799
119	33	33.9572405532487	-0.957240553248674
120	38	34.6333548409686	3.36664515903141
121	33	33.5610029445095	-0.561002944509461
122	31	34.6453344931656	-3.64533449316558
123	38	34.0339705322247	3.96602946777527
124	37	34.8916903670079	2.10830963299211
125	33	34.5599611392298	-1.55996113922979
126	31	34.5559879406231	-3.55598794062309
127	39	34.8792660817723	4.1207339182277
128	44	35.3689992715017	8.63100072849833
129	33	35.077500659606	-2.07750065960598
130	35	33.6978234728013	1.30217652719867
131	32	34.5354910858202	-2.53549108582023
132	28	32.2132811167993	-4.21328111679929
133	40	34.8144392401265	5.18556075987354
134	27	33.6410692007228	-6.64106920072276
135	37	34.2316943610428	2.76830563895718
136	32	34.5878171273637	-2.5878171273637
137	28	33.2005016051406	-5.20050160514057
138	34	34.3126498833333	-0.312649883333318
139	30	32.7993622731202	-2.79936227312018
140	35	33.6971865514319	1.30281344856811
141	31	32.3375615863915	-1.33756158639151
142	32	34.7775449014813	-2.77754490148131
143	30	34.5591215306397	-4.55912153063969
144	30	34.8625997947324	-4.86259979473237
145	31	34.7248900003633	-3.72489000036331
146	40	33.2718852277969	6.72811477220315
147	32	35.384364858423	-3.384364858423
148	36	33.3571924657557	2.64280753424434
149	32	34.3282181574753	-2.32821815747531
150	35	32.9609548570164	2.03904514298355
151	38	33.2312099788759	4.76879002112415
152	42	34.0612392564763	7.93876074352373
153	34	34.8861144660878	-0.886114466087767
154	35	34.2875429085543	0.712457091445695
155	35	33.2075526766767	1.79244732332331
156	33	32.6891900062003	0.310809993799696
157	36	34.6152885388359	1.3847114611641
158	32	33.6964731151957	-1.69647311519565
159	33	34.9545195307888	-1.9545195307888
160	34	34.4569661161999	-0.456966116199904
161	32	33.069398249269	-1.06939824926904
162	34	33.5062345920625	0.493765407937532

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
9	0.926233598893912	0.147532802212176	0.0737664011060882
10	0.882752851009637	0.234494297980726	0.117247148990363
11	0.813596930997423	0.372806138005153	0.186403069002577
12	0.74795036879616	0.504099262407681	0.252049631203841
13	0.777671003247714	0.444657993504572	0.222328996752286
14	0.71264018253108	0.574719634937839	0.28735981746892
15	0.728549888724036	0.542900222551928	0.271450111275964
16	0.745041899897134	0.509916200205731	0.254958100102866
17	0.670454972179386	0.659090055641228	0.329545027820614
18	0.625163269224827	0.749673461550347	0.374836730775173
19	0.622224274105848	0.755551451788303	0.377775725894152
20	0.659158492594574	0.681683014810852	0.340841507405426
21	0.663640738576976	0.672718522846048	0.336359261423024
22	0.634501676637344	0.730996646725311	0.365498323362656
23	0.658175456452936	0.683649087094128	0.341824543547064
24	0.630785098417953	0.738429803164093	0.369214901582047
25	0.614177705380622	0.771644589238757	0.385822294619378
26	0.729293529374999	0.541412941250003	0.270706470625001
27	0.672735127502937	0.654529744994127	0.327264872497063
28	0.642599472919273	0.714801054161454	0.357400527080727
29	0.609482661048342	0.781034677903315	0.390517338951658
30	0.547979846444184	0.904040307111632	0.452020153555816
31	0.564880733911955	0.870238532176089	0.435119266088045
32	0.645582894775227	0.708834210449547	0.354417105224773
33	0.647941151576842	0.704117696846316	0.352058848423158
34	0.593015077580738	0.813969844838524	0.406984922419262
35	0.539792064219769	0.920415871560461	0.460207935780231
36	0.495349878940056	0.990699757880113	0.504650121059944
37	0.45890860129401	0.91781720258802	0.54109139870599
38	0.432532645301027	0.865065290602054	0.567467354698973
39	0.540640505163189	0.918718989673622	0.459359494836811
40	0.489476557470173	0.978953114940346	0.510523442529827
41	0.465292462810418	0.930584925620836	0.534707537189582
42	0.420455585234864	0.840911170469728	0.579544414765136
43	0.37775220077821	0.75550440155642	0.62224779922179
44	0.344655972915982	0.689311945831964	0.655344027084018
45	0.374899957964263	0.749799915928525	0.625100042035737
46	0.409233528521585	0.818467057043169	0.590766471478415
47	0.411363927654798	0.822727855309596	0.588636072345202
48	0.374292286647622	0.748584573295245	0.625707713352378
49	0.336432987409653	0.672865974819306	0.663567012590347
50	0.343969213131044	0.687938426262089	0.656030786868956
51	0.342583889316496	0.685167778632992	0.657416110683504
52	0.314118277725571	0.628236555451142	0.685881722274429
53	0.275512438029936	0.551024876059872	0.724487561970064
54	0.236688284270071	0.473376568540143	0.763311715729929
55	0.200551737081017	0.401103474162035	0.799448262918983
56	0.184189860791774	0.368379721583548	0.815810139208226
57	0.176836814528248	0.353673629056496	0.823163185471752
58	0.310575206097973	0.621150412195946	0.689424793902027
59	0.287223697379837	0.574447394759674	0.712776302620163
60	0.247556279957055	0.495112559914109	0.752443720042945
61	0.234963621707405	0.46992724341481	0.765036378292595
62	0.229016126044093	0.458032252088186	0.770983873955907
63	0.197749958256101	0.395499916512202	0.802250041743899
64	0.193468088911679	0.386936177823358	0.806531911088321
65	0.164031859400875	0.32806371880175	0.835968140599125
66	0.137423064157955	0.274846128315909	0.862576935842045
67	0.116142033898393	0.232284067796787	0.883857966101607
68	0.153097800734476	0.306195601468953	0.846902199265524
69	0.208074401061814	0.416148802123627	0.791925598938186
70	0.176337894838852	0.352675789677703	0.823662105161148
71	0.21310252011339	0.426205040226781	0.78689747988661
72	0.213337837710728	0.426675675421456	0.786662162289272
73	0.18587164611647	0.37174329223294	0.81412835388353
74	0.172355838074323	0.344711676148646	0.827644161925677
75	0.145345188349327	0.290690376698654	0.854654811650673
76	0.169694362587313	0.339388725174626	0.830305637412687
77	0.149613124459765	0.299226248919531	0.850386875540235
78	0.124701934489872	0.249403868979744	0.875298065510128
79	0.188532010755218	0.377064021510436	0.811467989244782
80	0.172259267892671	0.344518535785343	0.827740732107329
81	0.153123324714808	0.306246649429617	0.846876675285192
82	0.128941782472614	0.257883564945228	0.871058217527386
83	0.106119090100221	0.212238180200442	0.893880909899779
84	0.0950742622935845	0.190148524587169	0.904925737706415
85	0.0877097694688495	0.175419538937699	0.912290230531151
86	0.0748674487410779	0.149734897482156	0.925132551258922
87	0.0783113902716961	0.156622780543392	0.921688609728304
88	0.0666556666385023	0.133311333277005	0.933344333361498
89	0.0967052138010439	0.193410427602088	0.903294786198956
90	0.0797127355948779	0.159425471189756	0.920287264405122
91	0.0821166926798035	0.164233385359607	0.917883307320197
92	0.0682271780608267	0.136454356121653	0.931772821939173
93	0.0551711969517032	0.110342393903406	0.944828803048297
94	0.0527310969393132	0.105462193878626	0.947268903060687
95	0.0776865132420293	0.155373026484059	0.922313486757971
96	0.0807739842868216	0.161547968573643	0.919226015713178
97	0.0724663374775528	0.144932674955106	0.927533662522447
98	0.058711054531992	0.117422109063984	0.941288945468008
99	0.0488217072262639	0.0976434144525278	0.951178292773736
100	0.0513636332077558	0.102727266415512	0.948636366792244
101	0.0445910560756951	0.0891821121513903	0.955408943924305
102	0.0381554633533163	0.0763109267066326	0.961844536646684
103	0.0299714817021905	0.0599429634043809	0.97002851829781
104	0.0332117016958757	0.0664234033917514	0.966788298304124
105	0.0410081778369742	0.0820163556739484	0.958991822163026
106	0.0558579697555972	0.111715939511194	0.944142030244403
107	0.0503152230606129	0.100630446121226	0.949684776939387
108	0.0547351111954021	0.109470222390804	0.945264888804598
109	0.0472888664683496	0.0945777329366992	0.95271113353165
110	0.310285202054276	0.620570404108552	0.689714797945724
111	0.335869686823318	0.671739373646635	0.664130313176682
112	0.315138607984343	0.630277215968686	0.684861392015657
113	0.293686875544381	0.587373751088762	0.706313124455619
114	0.258967802595193	0.517935605190386	0.741032197404807
115	0.241956094889281	0.483912189778562	0.758043905110719
116	0.213602822055017	0.427205644110035	0.786397177944983
117	0.179501414486647	0.359002828973293	0.820498585513353
118	0.147491199475963	0.294982398951926	0.852508800524037
119	0.126019672665406	0.252039345330812	0.873980327334594
120	0.148288165521072	0.296576331042144	0.851711834478928
121	0.120310140630643	0.240620281261287	0.879689859369357
122	0.109978413254519	0.219956826509038	0.890021586745481
123	0.11546656216934	0.23093312433868	0.88453343783066
124	0.0985747148624784	0.197149429724957	0.901425285137522
125	0.0790464773497496	0.158092954699499	0.92095352265025
126	0.0763304060627154	0.152660812125431	0.923669593937285
127	0.0790087242024975	0.158017448404995	0.920991275797503
128	0.351499455237563	0.702998910475126	0.648500544762437
129	0.304962962844212	0.609925925688424	0.695037037155788
130	0.280584855985933	0.561169711971866	0.719415144014067
131	0.239605517114507	0.479211034229013	0.760394482885493
132	0.238679374475542	0.477358748951084	0.761320625524458
133	0.421180773012597	0.842361546025194	0.578819226987403
134	0.519531296724717	0.960937406550567	0.480468703275283
135	0.575103145820398	0.849793708359205	0.424896854179602
136	0.516183219229971	0.967633561540058	0.483816780770029
137	0.534676832948923	0.930646334102154	0.465323167051077
138	0.479503133764962	0.959006267529923	0.520496866235038
139	0.483753233155871	0.967506466311743	0.516246766844129
140	0.424872105794575	0.849744211589151	0.575127894205425
141	0.486243500643192	0.972487001286383	0.513756499356808
142	0.423567332676523	0.847134665353047	0.576432667323477
143	0.451452127891543	0.902904255783087	0.548547872108456
144	0.504561086407204	0.990877827185593	0.495438913592796
145	0.594208250205263	0.811583499589474	0.405791749794737
146	0.613711323157182	0.772577353685636	0.386288676842818
147	0.743868371517753	0.512263256964495	0.256131628482247
148	0.659319464100465	0.68136107179907	0.340680535899535
149	0.745868029607814	0.508263940784372	0.254131970392186
150	0.74028984783611	0.519420304327781	0.25971015216389
151	0.781227693388097	0.437544613223806	0.218772306611903
152	0.988491130348059	0.0230177393038825	0.0115088696519412
153	0.956526226627436	0.0869475467451278	0.0434737733725639

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	1	0.00689655172413793	OK
10% type I error level	9	0.0620689655172414	OK