Multiple Linear Regression - Estimated Regression Equation

Learning[t] = + 5.75297936491273 -0.0282568887487843month[t] + 0.113576967565404Connected[t] -0.0200904826801223Separate[t] + 0.542745611256127Software[t] + 0.0596364628099267Happiness[t] -0.0704181393331173Depression[t] + 0.036427902180297Belonging[t] -0.0529848894217246Belonging_Final[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)	5.75297936491273	3.715964	1.5482	0.123645	0.061823
month	-0.0282568887487843	0.308202	-0.0917	0.92707	0.463535
Connected	0.113576967565404	0.047329	2.3997	0.01761	0.008805
Separate	-0.0200904826801223	0.045392	-0.4426	0.658678	0.329339
Software	0.542745611256127	0.069203	7.8428	0	0
Happiness	0.0596364628099267	0.076632	0.7782	0.437644	0.218822
Depression	-0.0704181393331173	0.057102	-1.2332	0.219392	0.109696
Belonging	0.036427902180297	0.045263	0.8048	0.422179	0.211089
Belonging_Final	-0.0529848894217246	0.064685	-0.8191	0.413994	0.206997

Multiple Linear Regression - Regression Statistics
Multiple R	0.597281724924451
R-squared	0.356745458928728
Adjusted R-squared	0.323111234558988
F-TEST (value)	10.6066206554086
F-TEST (DF numerator)	8
F-TEST (DF denominator)	153
p-value	8.61755111714047e-12
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	1.85629928851646
Sum Squared Residuals	527.21459842765

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	13	16.1298871909862	-3.12988719098625
2	16	15.9849024041899	0.0150975958101213
3	19	16.1930169966061	2.80698300339387
4	15	11.7519499613048	3.24805003869518
5	14	15.4792474818291	-1.47924748182913
6	13	14.8982185716239	-1.89821857162391
7	19	15.0742607941765	3.92573920582352
8	15	16.6137489839327	-1.61374898393271
9	14	15.8989289259795	-1.89892892597955
10	15	12.4513923854856	2.54860761451438
11	16	15.210426448153	0.789573551846969
12	16	16.2056621680204	-0.205662168020368
13	16	15.3797692033982	0.62023079660177
14	16	15.3218673043115	0.678132695688522
15	17	17.3748468930913	-0.374846893091318
16	15	15.0375105708466	-0.0375105708465517
17	15	14.5688280335456	0.431171966454438
18	20	16.1477928250854	3.85220717491464
19	18	15.4246668424533	2.57533315754673
20	16	15.2108642162993	0.789135783700652
21	16	15.2527365564957	0.747263443504294
22	16	14.7256050866408	1.27439491335921
23	19	16.4289218798701	2.57107812012989
24	16	14.6969932819345	1.30300671806546
25	17	14.786789829446	2.21321017055403
26	17	16.8950278198149	0.10497218018505
27	16	14.9814816101481	1.01851838985185
28	15	16.0626264994801	-1.06262649948007
29	16	15.4624180400323	0.5375819599677
30	14	13.9746540386173	0.0253459613826816
31	15	15.6083599244513	-0.608359924451314
32	12	12.2019222280761	-0.201922228076089
33	14	15.1233355996756	-1.1233355996756
34	16	15.4485909031628	0.551409096837173
35	14	15.6602911917052	-1.66029119170525
36	7	12.9152478891545	-5.91524788915454
37	10	10.8889504374052	-0.888950437405246
38	14	15.7949596849761	-1.79495968497612
39	16	14.2379047017887	1.76209529821132
40	16	14.597583933006	1.40241606699403
41	16	15.0577042584062	0.942295741593818
42	14	15.5793326532885	-1.57933265328847
43	20	17.92232451385	2.07767548614998
44	14	14.2198343594375	-0.219834359437496
45	14	14.9087126469597	-0.908712646959749
46	11	15.6090626583327	-4.60906265833273
47	14	16.4370033401999	-2.43700334019989
48	15	14.9485677681328	0.0514322318672124
49	16	15.2220487639025	0.777951236097505
50	14	16.033091146378	-2.03309114637805
51	16	16.5096063780609	-0.509606378060878
52	14	14.1282023583104	-0.128202358310439
53	12	14.7060832465641	-2.70608324656406
54	16	15.203547492717	0.796452507283037
55	9	11.5325027780148	-2.53250277801477
56	14	12.6423534208995	1.35764657910053
57	16	16.1081323561665	-0.108132356166457
58	16	15.0983581280381	0.901641871961943
59	15	15.3403022878421	-0.340302287842074
60	16	14.1492093036089	1.85079069639109
61	12	11.4465534267629	0.55344657323713
62	16	15.9953478460453	0.00465215395471908
63	16	16.4871677899959	-0.487167789995944
64	14	14.3591071719428	-0.359107171942833
65	16	15.4198862442758	0.58011375572415
66	17	15.8976871175734	1.10231288242662
67	18	16.0922218839943	1.90777811600571
68	18	14.6629544704338	3.33704552956622
69	12	15.8698834104958	-3.86988341049582
70	16	15.4120567043363	0.587943295663665
71	10	13.4338517380073	-3.43385173800731
72	14	14.3145765357063	-0.314576535706347
73	18	16.5334336228893	1.46656637711072
74	18	17.1455592350002	0.85444076499977
75	16	15.7139054732823	0.286094526717688
76	17	13.8775737325263	3.12242626747375
77	16	16.3550903284348	-0.355090328434813
78	16	14.4397798991329	1.56022010086712
79	13	14.8344777371261	-1.83447773712611
80	16	16.0033787094052	-0.00337870940516579
81	16	15.5685871340011	0.431412865998926
82	20	16.7651063476103	3.23489365238973
83	16	15.6780485370973	0.321951462902658
84	15	16.0127720309633	-1.01277203096326
85	15	14.733001844788	0.266998155211959
86	16	14.257234889631	1.74276511036905
87	14	14.2144006920536	-0.214400692053646
88	16	15.3263740331022	0.673625966897797
89	16	14.5718017194826	1.42819828051738
90	15	14.2082708955402	0.791729104459763
91	12	13.4730655989737	-1.47306559897372
92	17	16.9950773262088	0.00492267379117193
93	16	15.4815965727044	0.518403427295559
94	15	15.2777389354317	-0.277738935431694
95	13	15.169410386292	-2.16941038629203
96	16	15.2076371924497	0.792362807550259
97	16	15.8494066595658	0.150593340434225
98	16	14.1718922837739	1.82810771622611
99	16	16.1492349207599	-0.149234920759932
100	14	14.3306533767156	-0.330653376715642
101	16	17.3553554421742	-1.35535544217415
102	16	14.8036572669313	1.19634273306874
103	20	17.4073407878138	2.59265921218621
104	15	14.5728193947239	0.427180605276148
105	16	14.5604944886173	1.43950551138273
106	13	15.3870414692802	-2.38704146928025
107	17	16.0539303213555	0.946069678644474
108	16	15.9323721806411	0.0676278193588523
109	16	14.5849140447142	1.41508595528583
110	12	12.3021051907114	-0.302105190711376
111	16	15.0071118169415	0.992888183058528
112	16	15.8908077287927	0.109192271207325
113	17	14.5435263309862	2.45647366901377
114	13	14.9921541234457	-1.9921541234457
115	12	14.9238074002447	-2.92380740024473
116	18	16.6601582376924	1.33984176230764
117	14	15.5381859417024	-1.53818594170243
118	14	13.0084656435661	0.991534356433905
119	13	14.9747923571653	-1.97479235716531
120	16	15.7190058708734	0.280994129126558
121	13	14.3232751022776	-1.32327510227757
122	16	15.6848185668973	0.315181433102675
123	13	16.0166004302169	-3.0166004302169
124	16	17.1171910834514	-1.11719108345143
125	15	16.0462026349978	-1.04620263499776
126	16	16.8576836656374	-0.857683665637436
127	15	15.4992899104087	-0.499289910408683
128	17	16.328438050819	0.671561949181044
129	15	13.8808577298809	1.11914227011908
130	12	15.0234050908313	-3.02340509083126
131	16	14.2310338065885	1.76896619341155
132	10	13.3910831929673	-3.39108319296729
133	16	14.1701153142268	1.82988468577321
134	12	13.991168762107	-1.99116876210698
135	14	15.7301563886678	-1.73015638866784
136	15	15.1824150705959	-0.18241507059592
137	13	12.3482747046653	0.651725295334732
138	15	14.5177112149833	0.482288785016659
139	11	13.243955172699	-2.24395517269898
140	12	13.4364303932935	-1.43643039329351
141	8	13.4442412081347	-5.44424120813469
142	16	13.1727328340795	2.82726716592048
143	15	13.4053974715002	1.59460252849984
144	17	16.6302300349203	0.369769965079671
145	16	14.916589918762	1.08341008123798
146	10	14.2401473551524	-4.24014735515238
147	18	16.0055198493271	1.99448015067291
148	13	15.2616848807395	-2.2616848807395
149	16	15.2308415826853	0.769158417314687
150	13	13.1081348614777	-0.108134861477708
151	10	13.1993639781136	-3.19936397811361
152	15	16.5186683196254	-1.51866831962543
153	16	14.1877202735803	1.81227972641974
154	16	12.0806428893732	3.91935711062677
155	14	12.5384513444053	1.46154865559468
156	10	12.6127617408854	-2.61276174088537
157	17	16.9950773262088	0.00492267379117193
158	13	11.7022307818717	1.29776921812829
159	15	13.8808577298809	1.11914227011908
160	16	15.1585588378701	0.841441162129917
161	12	12.6024817935443	-0.60248179354427
162	13	12.6755390124536	0.32446098754644

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
12	0.758909692611693	0.482180614776613	0.241090307388307
13	0.621786631986117	0.756426736027767	0.378213368013884
14	0.581760463357661	0.836479073284678	0.418239536642339
15	0.461529334370621	0.923058668741243	0.538470665629379
16	0.361264099622209	0.722528199244418	0.638735900377791
17	0.298301232278281	0.596602464556563	0.701698767721719
18	0.507288353898752	0.985423292202496	0.492711646101248
19	0.423984824837541	0.847969649675083	0.576015175162459
20	0.335082781243585	0.67016556248717	0.664917218756415
21	0.265183039994633	0.530366079989267	0.734816960005367
22	0.242530315275424	0.485060630550848	0.757469684724576
23	0.442412294867684	0.884824589735368	0.557587705132316
24	0.4793851810649	0.9587703621298	0.5206148189351
25	0.469757607058247	0.939515214116494	0.530242392941753
26	0.429218011847715	0.85843602369543	0.570781988152285
27	0.491155965131596	0.982311930263192	0.508844034868404
28	0.494035997089612	0.988071994179225	0.505964002910388
29	0.475196614137723	0.950393228275446	0.524803385862277
30	0.517195080331069	0.965609839337862	0.482804919668931
31	0.456100092921843	0.912200185843685	0.543899907078157
32	0.406981414922854	0.813962829845707	0.593018585077146
33	0.379810556357532	0.759621112715064	0.620189443642468
34	0.346109323653537	0.692218647307075	0.653890676346463
35	0.296838174886241	0.593676349772482	0.703161825113759
36	0.857228215723504	0.285543568552993	0.142771784276496
37	0.832099356264902	0.335801287470196	0.167900643735098
38	0.823955326335071	0.352089347329858	0.176044673664929
39	0.845135511858917	0.309728976282166	0.154864488141083
40	0.830249252551953	0.339501494896095	0.169750747448047
41	0.802299795349441	0.395400409301117	0.197700204650559
42	0.774997879974895	0.45000424005021	0.225002120025105
43	0.803308722851849	0.393382554296302	0.196691277148151
44	0.764789533608033	0.470420932783934	0.235210466391967
45	0.736774880216628	0.526450239566745	0.263225119783372
46	0.878993975862137	0.242012048275726	0.121006024137863
47	0.919977463806876	0.160045072386249	0.0800225361931244
48	0.8989197390829	0.2021605218342	0.1010802609171
49	0.885621005219799	0.228757989560402	0.114378994780201
50	0.881801865538489	0.236396268923022	0.118198134461511
51	0.854560625789751	0.290878748420498	0.145439374210249
52	0.823493771543181	0.353012456913637	0.176506228456819
53	0.836860241205071	0.326279517589858	0.163139758794929
54	0.825086272472812	0.349827455054377	0.174913727527189
55	0.836758684955846	0.326482630088307	0.163241315044154
56	0.812209531870147	0.375580936259706	0.187790468129853
57	0.778979212291977	0.442041575416047	0.221020787708023
58	0.757932273703124	0.484135452593751	0.242067726296876
59	0.719542983085361	0.560914033829278	0.280457016914639
60	0.725044826413072	0.549910347173855	0.274955173586928
61	0.694784774542492	0.610430450915016	0.305215225457508
62	0.659607066228564	0.680785867542871	0.340392933771436
63	0.62236829064265	0.755263418714699	0.37763170935735
64	0.575435158363705	0.849129683272589	0.424564841636295
65	0.533904065621453	0.932191868757093	0.466095934378547
66	0.493779231445548	0.987558462891096	0.506220768554452
67	0.47948957205132	0.95897914410264	0.52051042794868
68	0.56592296949158	0.86815406101684	0.43407703050842
69	0.745842336749401	0.508315326501198	0.254157663250599
70	0.708789273772568	0.582421452454864	0.291210726227432
71	0.829852738933639	0.340294522132722	0.170147261066361
72	0.798091647355207	0.403816705289586	0.201908352644793
73	0.78861859796748	0.42276280406504	0.21138140203252
74	0.769095896716474	0.461808206567052	0.230904103283526
75	0.732420164600835	0.53515967079833	0.267579835399165
76	0.769658126741203	0.460683746517594	0.230341873258797
77	0.735762003728617	0.528475992542766	0.264237996271383
78	0.719409764710143	0.561180470579714	0.280590235289857
79	0.731352661962717	0.537294676074565	0.268647338037283
80	0.691341490915168	0.617317018169664	0.308658509084832
81	0.651595643357373	0.696808713285254	0.348404356642627
82	0.783474489432791	0.433051021134419	0.216525510567209
83	0.747926660517725	0.504146678964549	0.252073339482275
84	0.722096246423037	0.555807507153927	0.277903753576963
85	0.681479464518887	0.637041070962226	0.318520535481113
86	0.669938050703596	0.660123898592808	0.330061949296404
87	0.627098862699655	0.745802274600691	0.372901137300345
88	0.587009389409658	0.825981221180683	0.412990610590342
89	0.568375280137793	0.863249439724414	0.431624719862207
90	0.532172598883795	0.93565480223241	0.467827401116205
91	0.519521654399045	0.96095669120191	0.480478345600955
92	0.482803975510764	0.965607951021527	0.517196024489236
93	0.439713578078711	0.879427156157422	0.560286421921289
94	0.397060874551359	0.794121749102718	0.602939125448641
95	0.415369283348758	0.830738566697516	0.584630716651242
96	0.378526757904308	0.757053515808616	0.621473242095692
97	0.338791117211641	0.677582234423283	0.661208882788359
98	0.334139470749469	0.668278941498938	0.665860529250531
99	0.292296060619464	0.584592121238929	0.707703939380536
100	0.254114757488067	0.508229514976133	0.745885242511933
101	0.230647881451743	0.461295762903485	0.769352118548257
102	0.21269922619582	0.42539845239164	0.78730077380418
103	0.260035762206808	0.520071524413616	0.739964237793192
104	0.222542743045502	0.445085486091004	0.777457256954498
105	0.214246593826043	0.428493187652086	0.785753406173957
106	0.231611353038837	0.463222706077674	0.768388646961163
107	0.209475817942311	0.418951635884623	0.790524182057688
108	0.187440831399831	0.374881662799662	0.812559168600169
109	0.180282038129006	0.360564076258012	0.819717961870994
110	0.165751705332195	0.33150341066439	0.834248294667805
111	0.145909747264278	0.291819494528555	0.854090252735722
112	0.122075327129798	0.244150654259595	0.877924672870202
113	0.141634926363832	0.283269852727663	0.858365073636168
114	0.126626046518684	0.253252093037368	0.873373953481316
115	0.164035676395232	0.328071352790465	0.835964323604768
116	0.154998611979124	0.309997223958249	0.845001388020876
117	0.133832654528185	0.267665309056371	0.866167345471815
118	0.115204592348022	0.230409184696044	0.884795407651978
119	0.116740481427905	0.23348096285581	0.883259518572095
120	0.106360138129616	0.212720276259232	0.893639861870384
121	0.089319392060683	0.178638784121366	0.910680607939317
122	0.0708241095044067	0.141648219008813	0.929175890495593
123	0.0800788571588726	0.160157714317745	0.919921142841127
124	0.0634210115006567	0.126842023001313	0.936578988499343
125	0.0507582275116755	0.101516455023351	0.949241772488325
126	0.0383106150323996	0.0766212300647992	0.9616893849676
127	0.0287417471282855	0.057483494256571	0.971258252871715
128	0.023195126165182	0.046390252330364	0.976804873834818
129	0.0178268160684757	0.0356536321369514	0.982173183931524
130	0.0246854311528225	0.049370862305645	0.975314568847177
131	0.0208496941493091	0.0416993882986181	0.979150305850691
132	0.033400942065284	0.066801884130568	0.966599057934716
133	0.0356386213118992	0.0712772426237985	0.964361378688101
134	0.0481725267543959	0.0963450535087917	0.951827473245604
135	0.0376607770941673	0.0753215541883346	0.962339222905833
136	0.0258600529450186	0.0517201058900372	0.974139947054981
137	0.0176903976953989	0.0353807953907978	0.982309602304601
138	0.0117978494786906	0.0235956989573812	0.988202150521309
139	0.0223860303803978	0.0447720607607957	0.977613969619602
140	0.0190035108652523	0.0380070217305046	0.980996489134748
141	0.644372050832405	0.71125589833519	0.355627949167595
142	0.578952957592025	0.84209408481595	0.421047042407975
143	0.490935442521133	0.981870885042265	0.509064557478867
144	0.407096330467502	0.814192660935005	0.592903669532498
145	0.315134375979227	0.630268751958455	0.684865624020773
146	0.450221427294704	0.900442854589408	0.549778572705296
147	0.344117621809518	0.688235243619035	0.655882378190482
148	0.604983620668869	0.790032758662261	0.395016379331131
149	0.545485570132542	0.909028859734916	0.454514429867458
150	0.388021220684155	0.776042441368309	0.611978779315845

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	8	0.0575539568345324	NOK
10% type I error level	15	0.107913669064748	NOK