Multiple Linear Regression - Estimated Regression Equation

Learning[t] = + 11.5281494403163 + 0.122832529602809Connected[t] + 0.0576554749209971Happiness[t] -0.126916587598543Depression[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)	11.5281494403163	2.496828	4.6171	8e-06	4e-06
Connected	0.122832529602809	0.051279	2.3954	0.017774	0.008887
Happiness	0.0576554749209971	0.087613	0.6581	0.511451	0.255725
Depression	-0.126916587598543	0.064492	-1.9679	0.050824	0.025412

Multiple Linear Regression - Regression Statistics
Multiple R	0.302708695881518
R-squared	0.0916325545622892
Adjusted R-squared	0.0743850714210668
F-TEST (value)	5.31280731292804
F-TEST (DF numerator)	3
F-TEST (DF denominator)	158
p-value	0.00162848847127917
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	2.17072356257095
Sum Squared Residuals	744.502444045911

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	13	15.848460751743	-2.84846075174299
2	16	15.9603341798199	0.0396658201801298
3	19	14.070503326152	4.92949667384802
4	15	14.5048245058729	0.495175494127132
5	14	13.9616947059784	0.0383052940216023
6	13	15.3420874738101	-2.34208747381009
7	19	14.3336298165519	4.66637018344809
8	15	15.1155496321218	-0.115549632121834
9	14	15.545786753847	-1.54578675384699
10	15	15.2878695206542	-0.287869520654173
11	16	15.9067627628946	0.0932372371053941
12	16	16.0302418287281	-0.0302418287280672
13	16	14.8685915004549	1.13140849954509
14	16	15.4642734671822	0.535726532817754
15	17	15.3502555898016	1.64974441019844
16	15	14.4891348101206	0.510865189879414
17	15	14.9804649285318	0.0195350714681764
18	20	15.7798461752961	4.22015382470394
19	18	15.8566288677344	2.14337113226558
20	16	14.7313623475611	1.26863765243888
21	16	15.6081728229944	0.391827177005624
22	16	14.1933358557548	1.80666414424521
23	19	15.6027956925373	3.39720430746266
24	16	14.9879865082926	1.01201349170736
25	17	15.9026787048989	1.09732129510113
26	17	15.9409331399336	1.0590668600664
27	16	15.4765256411694	0.523474358830553
28	15	14.4850507521249	0.514949247875148
29	16	14.6696228146444	1.33037718535561
30	14	14.6887500321618	-0.688750032161757
31	15	15.1161961683525	-0.116196168352486
32	12	13.690400099587	-1.690400099587
33	14	15.7839302332918	-1.7839302332918
34	16	15.1732051070428	0.826794892957169
35	14	14.8617164569247	-0.861716456924748
36	7	15.3659452855538	-8.36594528555384
37	10	13.0708603211159	-3.07086032111591
38	14	15.2919535786499	-1.29195357864991
39	16	14.8012699964693	1.19873000353068
40	16	15.3076432744022	0.692356725597811
41	16	15.7955358710483	0.204464128951655
42	14	14.8501108191682	-0.850110819168199
43	20	16.1029404631707	3.89705953682931
44	14	14.742321449087	-0.74232144908702
45	14	15.4915688006911	-1.49156880069108
46	11	15.0572476209702	-4.05724762097018
47	14	15.9183684006512	-1.91836840065115
48	15	15.05037257744	-0.0503725774400218
49	16	15.0265147656963	0.973485234303728
50	14	15.5492242756121	-1.54922427561207
51	16	15.1121121103568	0.887887889643247
52	14	14.4891348101206	-0.489134810120586
53	12	13.8085020349634	-1.80850203496342
54	16	14.6194889194842	1.38051108051579
55	9	14.7545736230742	-5.75457362307422
56	14	15.4147861082527	-1.41478610825272
57	16	15.5911900547808	0.408809945219211
58	16	14.8128756342259	1.18712436577413
59	15	15.4956528586868	-0.495652858686811
60	16	14.6154048614885	1.38459513851152
61	12	13.1360373757977	-1.13603737579773
62	16	15.4223076880135	0.577692311986469
63	16	14.8156666197603	1.1843333802397
64	14	14.3663022805178	-0.366302280517777
65	16	14.9193719318457	1.08062806815426
66	17	15.0077602620407	1.99223973795934
67	18	14.4267487409732	3.5732512590268
68	18	14.3819919762701	3.61800802372994
69	12	15.5335345798598	-3.53353457985979
70	16	14.91528787385	1.08471212614999
71	10	15.353046575336	-5.35304657533599
72	14	14.3546966427612	-0.354696642761228
73	18	14.9193719318457	3.08062806815425
74	18	15.7914518130526	2.20854818694739
75	16	15.0578941572008	0.942105842799163
76	17	14.5990686295055	2.40093137049446
77	16	15.4031804704962	0.596819529503833
78	16	14.2963946316096	1.70360536839042
79	13	14.1823767542289	-1.18237675422889
80	16	15.6802249212064	0.319775078793649
81	16	15.05037257744	0.949627422559978
82	20	15.7262747583708	4.2737252416292
83	16	15.5498708118427	0.450129188157274
84	15	15.4724415831737	-0.472441583173713
85	15	14.8006234602387	0.199376539761331
86	16	14.7388839273219	1.26111607267806
87	14	15.410702050257	-1.41070205025698
88	16	14.8658005149205	1.13419948507952
89	16	13.9360651587926	2.06393484120738
90	15	13.1930463144881	1.80695368551193
91	12	14.6661852928793	-2.66618529287931
92	17	14.7958928660123	2.20410713398772
93	16	15.0422044614486	0.957795538551445
94	15	14.362218222522	0.637781777477957
95	13	14.5706480967853	-1.57064809678533
96	16	15.8450232299779	0.154976770022125
97	16	14.7341533330956	1.26584666690445
98	16	15.2383821617246	0.761617838275356
99	16	15.6570136456933	0.342986354306747
100	14	15.0544566354358	-1.05445663543576
101	16	15.9067627628946	0.0932372371053941
102	16	14.7341533330956	1.26584666690445
103	20	15.3496090535709	4.6503909464291
104	15	14.6969181481532	0.303081851846776
105	16	14.4157896394473	1.58421036055269
106	13	14.5489347343454	-1.54893473434536
107	17	15.7221907003751	1.27780929962493
108	16	15.3984498762698	0.601550123730219
109	16	14.6229264412493	1.37707355875071
110	12	14.3405048600821	-2.34050486008207
111	16	14.301125225836	1.69887477416404
112	16	14.0664192681562	1.93358073184376
113	17	14.8122290979952	2.18777090200478
114	13	14.362218222522	-1.36221822252204
115	12	15.5877525330157	-3.58775253301571
116	18	15.7262747583708	2.2737252416292
117	14	14.6119673397234	-0.611967339723396
118	14	14.8617164569247	-0.861716456924748
119	13	15.2465502777161	-2.24655027771611
120	16	15.0992134001389	0.900786599861101
121	13	14.3697398022829	-1.36973980228286
122	16	14.3663022805178	1.63369771948222
123	13	15.6645352254541	-2.66453522545407
124	16	15.9224524586469	0.0775475413531116
125	15	15.05037257744	-0.0503725774400218
126	16	14.6893965683924	1.31060343160759
127	15	16.2834284676945	-1.2834284676945
128	17	16.6437579405115	0.356242059488538
129	15	15.280994477124	-0.28099447712401
130	12	15.0422044614486	-3.04220446144855
131	16	14.8122290979952	1.18777090200478
132	10	12.9480277915131	-2.94802779151311
133	16	16.0371168722582	-0.0371168722582304
134	12	13.805711049429	-1.80571104942899
135	14	15.4147861082527	-1.41478610825272
136	15	14.6044457599626	0.39555424003742
137	13	12.6825889785595	0.31741102144053
138	15	14.7347998693262	0.265200130673795
139	11	13.8166701509549	-2.81667015095489
140	12	15.2960376366456	-3.29603763664564
141	8	14.5624799807939	-6.56247998079387
142	16	15.0544566354358	0.945543364564245
143	15	14.358780700757	0.641219299243038
144	17	14.4973029261121	2.50269707388795
145	16	14.6777909306359	1.32220906936414
146	10	15.9678557595807	-5.96785575958068
147	18	14.8582789351597	3.14172106484033
148	13	14.9344150913674	-1.93441509136738
149	16	14.7545736230742	1.24542637692578
150	13	13.9347720863313	-0.934772086331314
151	10	15.5952741127765	-5.59527411277652
152	15	15.2790548684321	-0.279054868432054
153	16	15.4846937571609	0.515306242839086
154	16	14.9961546242841	1.00384537571589
155	14	13.9347720863313	0.0652279136686864
156	10	14.0466455144082	-4.04664551440823
157	17	14.7958928660123	2.20410713398772
158	13	14.4891348101206	-1.48913481012059
159	15	15.280994477124	-0.28099447712401
160	16	15.3117273323979	0.688272667602077
161	12	13.8661575098844	-1.86615750988442
162	13	14.4233112192081	-1.42331121920812

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
7	0.867910216239857	0.264179567520287	0.132089783760143
8	0.768747211157113	0.462505577685775	0.231252788842887
9	0.657763629748202	0.684472740503595	0.342236370251798
10	0.533811437392519	0.932377125214963	0.466188562607481
11	0.527206075146179	0.945587849707641	0.47279392485382
12	0.537045588450931	0.925908823098138	0.462954411549069
13	0.437532376834591	0.875064753669181	0.562467623165409
14	0.352112885520623	0.704225771041245	0.647887114479377
15	0.336035901342791	0.672071802685582	0.663964098657209
16	0.27676084062102	0.553521681242039	0.72323915937898
17	0.214143975950893	0.428287951901786	0.785856024049107
18	0.515436327260828	0.969127345478343	0.484563672739172
19	0.517982401001359	0.964035197997282	0.482017598998641
20	0.445002170870358	0.890004341740716	0.554997829129642
21	0.37476470751188	0.74952941502376	0.62523529248812
22	0.311639247941096	0.623278495882192	0.688360752058904
23	0.369796385033404	0.739592770066809	0.630203614966596
24	0.309323917847593	0.618647835695186	0.690676082152407
25	0.261753906626454	0.523507813252908	0.738246093373546
26	0.21078296303364	0.421565926067281	0.78921703696636
27	0.165660468520885	0.33132093704177	0.834339531479115
28	0.133959893099823	0.267919786199645	0.866040106900177
29	0.103695759105437	0.207391518210873	0.896304240894563
30	0.103051476890997	0.206102953781994	0.896948523109003
31	0.0782285946925479	0.156457189385096	0.921771405307452
32	0.0972222449371819	0.194444489874364	0.902777755062818
33	0.096503664106032	0.193007328212064	0.903496335893968
34	0.0743348336276227	0.148669667255245	0.925665166372377
35	0.0653192945767713	0.130638589153543	0.934680705423229
36	0.646282913052244	0.707434173895512	0.353717086947756
37	0.761368648291184	0.477262703417632	0.238631351708816
38	0.737949332581189	0.524101334837621	0.262050667418811
39	0.730766461198894	0.538467077602213	0.269233538801106
40	0.689417321843606	0.621165356312787	0.310582678156394
41	0.64099220052428	0.718015598951441	0.35900779947572
42	0.602389898114847	0.795220203770306	0.397610101885153
43	0.699272445588738	0.601455108822524	0.300727554411262
44	0.665686324163745	0.668627351672509	0.334313675836255
45	0.653806625583251	0.692386748833497	0.346193374416749
46	0.775418270937586	0.449163458124828	0.224581729062414
47	0.767113999934475	0.465772000131049	0.232886000065525
48	0.72709578066922	0.54580843866156	0.27290421933078
49	0.689623519271677	0.620752961456646	0.310376480728323
50	0.66964767365728	0.660704652685439	0.33035232634272
51	0.635806627372671	0.728386745254659	0.364193372627329
52	0.590866026684789	0.818267946630422	0.409133973315211
53	0.579189044575846	0.841621910848308	0.420810955424154
54	0.550709544234973	0.898580911530054	0.449290455765027
55	0.774434196577776	0.451131606844447	0.225565803422224
56	0.755973134518808	0.488053730962383	0.244026865481192
57	0.719682093118637	0.560635813762726	0.280317906881363
58	0.70673829007572	0.586523419848561	0.29326170992428
59	0.667645056310837	0.664709887378325	0.332354943689163
60	0.640295290419519	0.719409419160962	0.359704709580481
61	0.606523016993504	0.786953966012992	0.393476983006496
62	0.56281691868146	0.87436616263708	0.43718308131854
63	0.53610318684539	0.927793626309221	0.46389681315461
64	0.49011697030327	0.980233940606539	0.50988302969673
65	0.454611986433513	0.909223972867026	0.545388013566487
66	0.453757978699476	0.907515957398952	0.546242021300524
67	0.51855904307331	0.962881913853381	0.48144095692669
68	0.609965825364828	0.780068349270344	0.390034174635172
69	0.689542952528567	0.620914094942866	0.310457047471433
70	0.657294629273989	0.685410741452022	0.342705370726011
71	0.839794342933533	0.320411314132934	0.160205657066467
72	0.811239789176867	0.377520421646265	0.188760210823133
73	0.839426879555569	0.321146240888861	0.16057312044443
74	0.83915631494245	0.321687370115101	0.16084368505755
75	0.815054004163866	0.369891991672269	0.184945995836134
76	0.820610221273887	0.358779557452225	0.179389778726113
77	0.792992924501777	0.414014150996446	0.207007075498223
78	0.780852584202153	0.438294831595695	0.219147415797847
79	0.755523217638353	0.488953564723294	0.244476782361647
80	0.718988725486086	0.562022549027827	0.281011274513914
81	0.687153750130675	0.625692499738649	0.312846249869325
82	0.795209523851822	0.409580952296356	0.204790476148178
83	0.762792774390848	0.474414451218304	0.237207225609152
84	0.728637371811807	0.542725256376386	0.271362628188193
85	0.68980851474053	0.620382970518939	0.31019148525947
86	0.663135322805938	0.673729354388125	0.336864677194062
87	0.638922504036387	0.722154991927225	0.361077495963613
88	0.607598192703428	0.784803614593144	0.392401807296572
89	0.603447877948645	0.793104244102709	0.396552122051355
90	0.592009803401246	0.815980393197507	0.407990196598754
91	0.611348839989441	0.777302320021118	0.388651160010559
92	0.618717296039875	0.762565407920249	0.381282703960125
93	0.585392389375375	0.829215221249249	0.414607610624625
94	0.545975431102204	0.908049137795591	0.454024568897796
95	0.526056597518118	0.947886804963764	0.473943402481882
96	0.481930254116795	0.96386050823359	0.518069745883205
97	0.460336003380767	0.920672006761534	0.539663996619233
98	0.421114147333943	0.842228294667886	0.578885852666057
99	0.379359744745184	0.758719489490368	0.620640255254816
100	0.34558594033833	0.691171880676659	0.65441405966167
101	0.304615661649503	0.609231323299007	0.695384338350497
102	0.287921741711581	0.575843483423162	0.712078258288419
103	0.476128713064318	0.952257426128636	0.523871286935682
104	0.429561061657386	0.859122123314772	0.570438938342614
105	0.425417746238437	0.850835492476874	0.574582253761563
106	0.404092997716243	0.808185995432485	0.595907002283757
107	0.388757660531362	0.777515321062723	0.611242339468638
108	0.382867240639113	0.765734481278227	0.617132759360887
109	0.36689198963538	0.733783979270759	0.63310801036462
110	0.369285672649862	0.738571345299723	0.630714327350138
111	0.358381881996066	0.716763763992132	0.641618118003934
112	0.355646149482058	0.711292298964116	0.644353850517942
113	0.358059267374834	0.716118534749668	0.641940732625166
114	0.323694736616909	0.647389473233819	0.676305263383091
115	0.369923922196376	0.739847844392752	0.630076077803624
116	0.399677905078291	0.799355810156582	0.600322094921709
117	0.353504090146009	0.707008180292018	0.646495909853991
118	0.310357579585464	0.620715159170927	0.689642420414536
119	0.311272142075535	0.622544284151069	0.688727857924465
120	0.308041551729207	0.616083103458413	0.691958448270793
121	0.272204556511294	0.544409113022589	0.727795443488706
122	0.26416218605623	0.52832437211246	0.73583781394377
123	0.259332763449769	0.518665526899538	0.740667236550231
124	0.218323764644299	0.436647529288599	0.781676235355701
125	0.180823562665339	0.361647125330679	0.819176437334661
126	0.158752510095364	0.317505020190728	0.841247489904636
127	0.131479964505096	0.262959929010192	0.868520035494904
128	0.122618775478605	0.245237550957209	0.877381224521395
129	0.0973363187194191	0.194672637438838	0.902663681280581
130	0.0997180232641797	0.199436046528359	0.90028197673582
131	0.0841401132096668	0.168280226419334	0.915859886790333
132	0.0941590359788976	0.188318071957795	0.905840964021102
133	0.080572565227156	0.161145130454312	0.919427434772844
134	0.0780533464406623	0.156106692881325	0.921946653559338
135	0.0600552134322038	0.120110426864408	0.939944786567796
136	0.0459269128731783	0.0918538257463566	0.954073087126822
137	0.0332450029973684	0.0664900059947368	0.966754997002632
138	0.0252951055167588	0.0505902110335176	0.974704894483241
139	0.0315397553374087	0.0630795106748173	0.968460244662591
140	0.0333816229841689	0.0667632459683378	0.966618377015831
141	0.404724140967714	0.809448281935429	0.595275859032286
142	0.337097313150571	0.674194626301142	0.662902686849429
143	0.27336422557581	0.54672845115162	0.72663577442419
144	0.238719994052763	0.477439988105525	0.761280005947237
145	0.192350645132134	0.384701290264269	0.807649354867866
146	0.365455794018702	0.730911588037404	0.634544205981298
147	0.542841843297224	0.914316313405551	0.457158156702776
148	0.57047074520397	0.859058509592061	0.42952925479603
149	0.475590902797366	0.951181805594731	0.524409097202634
150	0.380855367444827	0.761710734889654	0.619144632555173
151	0.91196792180201	0.176064156395981	0.0880320781979904
152	0.959592640926638	0.0808147181467236	0.0404073590733618
153	0.915822941369558	0.168354117260883	0.0841770586304417
154	0.834638501686216	0.330722996627568	0.165361498313784
155	0.705953174842718	0.588093650314564	0.294046825157282

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	6	0.0402684563758389	OK