Multiple Linear Regression - Estimated Regression Equation

Software[t] = + 4.55992301497745 -0.047496183329279Connected[t] + 0.0332067483233368Separate[t] + 0.529019027360035Learning[t] -0.0399388089690363Happiness[t] -0.0231956678629946Depression[t] -0.000948402888831708Belonging_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)	4.55992301497745	2.505678	1.8198	0.070713	0.035357
Connected	-0.047496183329279	0.046821	-1.0144	0.311964	0.155982
Separate	0.0332067483233368	0.043794	0.7583	0.449451	0.224725
Learning	0.529019027360035	0.066733	7.9273	0	0
Happiness	-0.0399388089690363	0.074846	-0.5336	0.594373	0.297186
Depression	-0.0231956678629946	0.055013	-0.4216	0.673873	0.336937
Belonging_Final	-0.000948402888831708	0.020366	-0.0466	0.962918	0.481459

Multiple Linear Regression - Regression Statistics
Multiple R	0.551801768015629
R-squared	0.304485191185174
Adjusted R-squared	0.277562037295568
F-TEST (value)	11.3094176274319
F-TEST (DF numerator)	6
F-TEST (DF denominator)	155
p-value	1.8421963954296e-10
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	1.82038224683142
Sum Squared Residuals	513.637686309749

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	12	9.88384305807921	2.11615694192079
2	11	11.2120727939769	-0.212072793976896
3	15	13.5447360561843	1.45526394381572
4	6	11.322151196414	-5.32215119641397
5	13	10.4102123512722	2.58978764872781
6	10	9.69597814393623	0.30402185606377
7	12	12.6838036575605	-0.683803657560514
8	14	11.2150137182104	2.78498628178959
9	12	10.5448460463178	1.45515395368223
10	6	11.0545053259519	-5.05450532595189
11	10	11.2913935115925	-1.29139351159253
12	12	11.4676942872303	0.532305712769674
13	12	11.594452648576	0.405547351424017
14	11	11.438675150265	-0.438675150264977
15	15	12.2134015250146	2.78659847498538
16	12	11.1531280738648	0.846871926135211
17	10	10.9214009662248	-0.92140096622485
18	12	13.6119791769889	-1.61197917698888
19	11	12.6617862712644	-1.66178627126444
20	12	11.5922584028264	0.407741597173591
21	11	11.6800195259455	-0.680019525945482
22	12	11.7754589917039	0.224541008296116
23	13	13.1520011860091	-0.152001186009144
24	11	11.7228358895677	-0.72283588956769
25	9	11.7800822274171	-2.78008222741714
26	13	12.055733682681	0.944266317318984
27	10	11.5416464299835	-1.54164642998347
28	14	11.2076759928552	2.79232400714479
29	12	11.586176482927	0.413823517072977
30	10	10.6645415515056	-0.664541551505645
31	12	11.0583619993995	0.941638000600529
32	8	9.78993350988028	-1.78993350988028
33	10	10.2865420575347	-0.286542057534732
34	12	11.7325586704806	0.267441329519411
35	12	10.4470016854062	1.55299831459381
36	7	6.97268502111375	0.0273149788862498
37	6	8.64367962518416	-2.64367962518416
38	12	10.4339380197228	1.56606198027723
39	10	11.7217043702225	-1.72170437022254
40	10	11.666689614325	-1.66668961432501
41	10	11.4789633406015	-1.47896334060154
42	12	10.4416518387975	1.55834816120253
43	15	13.5421809602723	1.45781903972766
44	10	10.5662401288991	-0.566240128899148
45	10	10.3168724091065	-0.316872409106461
46	12	9.0052030276397	2.9947969723603
47	13	10.6077731465932	2.39222685340679
48	11	11.1590028045905	-0.159002804590477
49	11	11.5094935974213	-0.509493597421298
50	12	10.4069153847643	1.59308461523572
51	14	11.8534986732448	2.14650132675524
52	10	10.5206951899794	-0.520695189979416
53	12	9.59215634435098	2.40784365564902
54	13	11.8235820652327	1.17641793476729
55	5	8.0952717829083	-3.0952717829083
56	6	10.3494414765148	-4.34944147651483
57	12	11.3176629901686	0.682337009831356
58	12	11.9281915125489	0.0718084874510565
59	11	11.1812888713566	-0.181288871356633
60	10	11.6229084294136	-1.62290842941358
61	7	9.59928207501813	-2.59928207501813
62	12	11.508171268268	0.491828731731974
63	14	11.8112403678466	2.18875963215345
64	11	10.7427607409249	0.257239259075135
65	12	11.50684330548	0.493156694519955
66	13	12.4185175738007	0.581482426199315
67	14	12.6611529252596	1.33884707474041
68	11	12.7574639718833	-1.75746397188333
69	12	9.44740499985938	2.55259500014062
70	12	11.6268563182283	0.373143681771693
71	8	8.33828452681129	-0.338284526811291
72	11	10.7374108943161	0.262589105683856
73	14	12.8163093034543	1.18369069654567
74	14	12.7699122934835	1.23008770651647
75	12	11.4841624167406	0.51583758325938
76	9	11.7306426413782	-2.73064264137818
77	13	11.4742335986058	1.52576640139416
78	11	11.483505820189	-0.483505820188991
79	12	10.191485682932	1.80851431706803
80	12	11.4041880515889	0.595811948411089
81	12	11.7544353285972	0.245564671402815
82	12	13.7738235931471	-1.7738235931471
83	12	11.7399894488768	0.260010551123215
84	12	10.8755220547845	1.12447794521551
85	11	11.1852001258344	-0.185200125834424
86	10	11.5810006573347	-1.58100065733472
87	9	10.5130936693636	-1.51309366936357
88	12	11.7085585846119	0.29144141538812
89	12	11.8110172526619	0.18898274733814
90	12	11.192999390193	0.807000609807015
91	9	9.60708263215154	-0.607082632151542
92	15	12.0075629967169	2.99243700328306
93	12	11.7790853678293	0.220914632170678
94	12	10.9525178297191	1.04748217028087
95	12	10.2602473728064	1.73975262719359
96	10	11.4285710167636	-1.42857101676364
97	13	11.5379271432154	1.46207285678464
98	9	11.533348029291	-2.53334802929098
99	12	11.4162626749177	0.58373732508234
100	10	10.7670891250694	-0.767089125069389
101	14	11.4612208647645	2.53877913523546
102	11	11.5360303374377	-0.5360303374377
103	15	13.6924047422078	1.3075952577922
104	11	11.1708073454112	-0.170807345411206
105	11	11.7371288313634	-0.737128831363391
106	12	9.7608874952732	2.2391125047268
107	12	11.9718794791296	0.0281205208703795
108	12	11.3609529762845	0.639047023715514
109	11	11.697980641234	-0.697980641234027
110	7	9.27596268465184	-2.27596268465184
111	12	11.7580781696829	0.24192183031713
112	14	11.8186768204876	2.18132317951244
113	11	12.5683262728418	-1.56832627284177
114	11	10.0956044235025	0.904395576497483
115	10	9.23800049153432	0.76199950846568
116	13	12.4662796953789	0.533720304621072
117	13	10.8119053101053	2.18809468989467
118	8	10.7771723628619	-2.77717236286189
119	11	10.2242952544441	0.775704745555905
120	12	11.4555749234684	0.544425076531637
121	11	10.2399479878504	0.76005201214964
122	13	11.5209187657258	1.47908123427424
123	12	10.02193035173	1.97806964826996
124	14	11.6995026926269	2.30049730737311
125	13	11.0603309625093	1.9396690374907
126	15	11.828736665335	3.17126333466503
127	10	10.7887859676196	-0.788785967619555
128	11	11.8058314400077	-0.805831440007747
129	9	11.0590222451392	-2.05902224513918
130	11	9.39925207758015	1.60074792241985
131	10	11.7859824964499	-1.78598249644985
132	11	8.72153734817028	2.27846265182972
133	8	11.4783644614786	-3.47836446147856
134	11	9.63700357507371	1.36299642492629
135	12	10.5496303693437	1.45036963065632
136	12	10.9243006135232	1.07569938647677
137	9	9.83370114571178	-0.833701145711782
138	11	11.1188587865199	-0.118858786519914
139	10	9.27283132179983	0.727168678200169
140	8	9.4826437731848	-1.4826437731848
141	9	7.64549269257136	1.35450730742864
142	8	11.7710429206976	-3.7710429206976
143	9	11.1872235275761	-2.18722352757614
144	15	12.4028404785059	2.59715952149406
145	11	11.3945442991894	-0.39454429918937
146	8	8.03333970454682	-0.0333397045468161
147	13	12.4970259520156	0.502974047984359
148	12	10.1458408197901	1.85415918020995
149	12	11.7557141972169	0.244285802783111
150	9	9.99362639747544	-0.993626397475436
151	7	8.37268719570674	-1.37268719570674
152	13	10.7709126074682	2.22908739253175
153	9	11.7845471831157	-2.78454718311569
154	6	11.8575807717304	-5.85758077173042
155	8	10.5919041301486	-2.59190413014864
156	8	8.32705335127324	-0.327053351273243
157	15	12.0075629967169	2.99243700328306
158	6	10.2212781922162	-4.22127819221624
159	9	11.0590222451392	-2.05902224513918
160	11	11.6956390911945	-0.695639091194462
161	8	9.60630179447381	-1.60630179447381
162	8	10.0837813418109	-2.0837813418109

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
10	0.999851424477043	0.000297151045914864	0.000148575522957432
11	0.999584752312288	0.000830495375424223	0.000415247687712112
12	0.999508254631613	0.000983490736774578	0.000491745368387289
13	0.99906705256654	0.0018658948669192	0.000932947433459601
14	0.998320625925237	0.00335874814952584	0.00167937407476292
15	0.998016067059599	0.00396786588080289	0.00198393294040144
16	0.996627129089228	0.00674574182154437	0.00337287091077219
17	0.993941830414157	0.0121163391716853	0.00605816958584267
18	0.992559580413728	0.0148808391725447	0.00744041958627234
19	0.988841981649723	0.0223160367005543	0.0111580183502771
20	0.981908884202325	0.0361822315953507	0.0180911157976753
21	0.973403223192833	0.0531935536143345	0.0265967768071673
22	0.962349501406728	0.0753009971865446	0.0376504985932723
23	0.946492255914221	0.107015488171559	0.0535077440857793
24	0.927764067918632	0.144471864162735	0.0722359320813676
25	0.924925692523975	0.15014861495205	0.0750743074760248
26	0.943274441098196	0.113451117803608	0.0567255589018042
27	0.932912263502637	0.134175472994727	0.0670877364973635
28	0.939618910973164	0.120762178053673	0.0603810890268364
29	0.918841450300435	0.16231709939913	0.0811585496995648
30	0.89829275389737	0.20341449220526	0.10170724610263
31	0.879624582835873	0.240750834328254	0.120375417164127
32	0.89716923196924	0.205661536061519	0.10283076803076
33	0.868048238530524	0.263903522938952	0.131951761469476
34	0.833778780696771	0.332442438606459	0.166221219303229
35	0.824242227201685	0.351515545596631	0.175757772798315
36	0.787993593453302	0.424012813093395	0.212006406546698
37	0.825996526204315	0.348006947591369	0.174003473795685
38	0.817356412469574	0.365287175060851	0.182643587530426
39	0.806718212637905	0.38656357472419	0.193281787362095
40	0.787857151176946	0.424285697646108	0.212142848823054
41	0.763149743082059	0.473700513835883	0.236850256917941
42	0.748032627375557	0.503934745248886	0.251967372624443
43	0.74797747881314	0.504045042373721	0.25202252118686
44	0.705438925664044	0.589122148671912	0.294561074335956
45	0.661179812936741	0.677640374126518	0.338820187063259
46	0.728715544343096	0.542568911313808	0.271284455656904
47	0.734832474027695	0.53033505194461	0.265167525972305
48	0.690834071048011	0.618331857903977	0.309165928951989
49	0.653045243777791	0.693909512444419	0.346954756222209
50	0.638997405870345	0.72200518825931	0.361002594129655
51	0.644532285807241	0.710935428385518	0.355467714192759
52	0.597923815966798	0.804152368066405	0.402076184033202
53	0.626044890413787	0.747910219172426	0.373955109586213
54	0.590836663820803	0.818326672358394	0.409163336179197
55	0.684400844713234	0.631198310573532	0.315599155286766
56	0.844484725236873	0.311030549526253	0.155515274763126
57	0.817329777460819	0.365340445078363	0.182670222539181
58	0.783428306649307	0.433143386701385	0.216571693350693
59	0.7470599225431	0.505880154913801	0.2529400774569
60	0.735641372070292	0.528717255859416	0.264358627929708
61	0.75369890050626	0.49260219898748	0.24630109949374
62	0.717573642577751	0.564852714844499	0.282426357422249
63	0.732748038386095	0.53450392322781	0.267251961613905
64	0.692528328153188	0.614943343693624	0.307471671846812
65	0.657703589602515	0.684592820794969	0.342296410397485
66	0.616281699277426	0.767436601445149	0.383718300722574
67	0.596181903551855	0.80763619289629	0.403818096448145
68	0.579153651738497	0.841692696523005	0.420846348261503
69	0.597104424471131	0.805791151057738	0.402895575528869
70	0.553315693483334	0.893368613033332	0.446684306516666
71	0.513268336278616	0.973463327442768	0.486731663721384
72	0.470033380158765	0.940066760317531	0.529966619841235
73	0.442162248100645	0.88432449620129	0.557837751899355
74	0.417935304907469	0.835870609814938	0.582064695092531
75	0.392450977130494	0.784901954260988	0.607549022869506
76	0.440488365320747	0.880976730641493	0.559511634679253
77	0.42621826482458	0.852436529649161	0.57378173517542
78	0.38550064308146	0.77100128616292	0.61449935691854
79	0.391024883154774	0.782049766309548	0.608975116845226
80	0.367923846366708	0.735847692733416	0.632076153633292
81	0.32733659265401	0.654673185308019	0.67266340734599
82	0.322921426909697	0.645842853819394	0.677078573090303
83	0.284873432871979	0.569746865743958	0.715126567128021
84	0.259606089091173	0.519212178182345	0.740393910908827
85	0.223873090393003	0.447746180786007	0.776126909606996
86	0.215995007581193	0.431990015162387	0.784004992418807
87	0.215987594872769	0.431975189745538	0.784012405127231
88	0.183981056837357	0.367962113674714	0.816018943162643
89	0.156158472059015	0.31231694411803	0.843841527940985
90	0.135466985449922	0.270933970899843	0.864533014550078
91	0.116026247505586	0.232052495011172	0.883973752494414
92	0.160483207346457	0.320966414692914	0.839516792653543
93	0.140182757628693	0.280365515257386	0.859817242371307
94	0.124891012393688	0.249782024787377	0.875108987606312
95	0.120954678831403	0.241909357662807	0.879045321168597
96	0.112762424181913	0.225524848363827	0.887237575818087
97	0.103996325592294	0.207992651184587	0.896003674407706
98	0.128600277057323	0.257200554114645	0.871399722942677
99	0.107199209349448	0.214398418698895	0.892800790650553
100	0.0906117504618421	0.181223500923684	0.909388249538158
101	0.110136117472689	0.220272234945379	0.889863882527311
102	0.0910507375823853	0.182101475164771	0.908949262417615
103	0.0873000680496933	0.174600136099387	0.912699931950307
104	0.0736538920434171	0.147307784086834	0.926346107956583
105	0.0622898972830233	0.124579794566047	0.937710102716977
106	0.0636398628309533	0.127279725661907	0.936360137169047
107	0.0501105233400193	0.100221046680039	0.949889476659981
108	0.0441470412429711	0.0882940824859422	0.955852958757029
109	0.0352845382632723	0.0705690765265446	0.964715461736728
110	0.0368018699446159	0.0736037398892318	0.963198130055384
111	0.0289791432753655	0.0579582865507309	0.971020856724635
112	0.0325112614604269	0.0650225229208537	0.967488738539573
113	0.0293089277001342	0.0586178554002684	0.970691072299866
114	0.0232171251968368	0.0464342503936735	0.976782874803163
115	0.0182173815946796	0.0364347631893593	0.98178261840532
116	0.0137897085589168	0.0275794171178335	0.986210291441083
117	0.021654281150081	0.0433085623001619	0.978345718849919
118	0.0248654548376402	0.0497309096752805	0.97513454516236
119	0.0190699669350889	0.0381399338701779	0.980930033064911
120	0.0148746144021492	0.0297492288042984	0.985125385597851
121	0.0123518219645227	0.0247036439290454	0.987648178035477
122	0.010345904117888	0.020691808235776	0.989654095882112
123	0.0123105603395404	0.0246211206790809	0.98768943966046
124	0.0193278922089446	0.0386557844178891	0.980672107791055
125	0.0203504442999047	0.0407008885998094	0.979649555700095
126	0.0488580200973046	0.0977160401946092	0.951141979902695
127	0.037347471530282	0.074694943060564	0.962652528469718
128	0.0286346572337094	0.0572693144674188	0.971365342766291
129	0.0240241883365378	0.0480483766730755	0.975975811663462
130	0.022607074436804	0.045214148873608	0.977392925563196
131	0.0183252567250869	0.0366505134501738	0.981674743274913
132	0.0207995084309825	0.041599016861965	0.979200491569017
133	0.0328436708629951	0.0656873417259903	0.967156329137005
134	0.0357572730494277	0.0715145460988553	0.964242726950572
135	0.0398361355072505	0.0796722710145009	0.960163864492749
136	0.033806545853706	0.067613091707412	0.966193454146294
137	0.0292956390379524	0.0585912780759048	0.970704360962048
138	0.0212962972614162	0.0425925945228325	0.978703702738584
139	0.0207792051324328	0.0415584102648655	0.979220794867567
140	0.0149015553377942	0.0298031106755885	0.985098444662206
141	0.0476229603979843	0.0952459207959686	0.952377039602016
142	0.0509879019120572	0.101975803824114	0.949012098087943
143	0.0375233229725506	0.0750466459451012	0.962476677027449
144	0.35499712456637	0.70999424913274	0.64500287543363
145	0.396920484729776	0.793840969459552	0.603079515270224
146	0.708748098742694	0.582503802514612	0.291251901257306
147	0.707464782727141	0.585070434545718	0.292535217272859
148	0.867589372637628	0.264821254724743	0.132410627362372
149	0.867640636112575	0.26471872777485	0.132359363887425
150	0.787201516317637	0.425596967364725	0.212798483682363
151	0.670687602544238	0.658624794911525	0.329312397455762
152	0.674572385116034	0.650855229767932	0.325427614883966

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	7	0.048951048951049	NOK
5% type I error level	30	0.20979020979021	NOK
10% type I error level	48	0.335664335664336	NOK