Multiple Linear Regression - Estimated Regression Equation

Software[t] = + 4.5104574109139 -0.0476502811001375Connected[t] + 0.033615813974464Separate[t] + 0.528535975192473Learning[t] -0.0406097034253699Happiness[t] -0.0224269391840146Depression[t] + 0.00391007197576475Belonging[t] -0.00626369092094975Belonging_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)	4.5104574109139	2.574743	1.7518	0.081797	0.040899
Connected	-0.0476502811001375	0.047004	-1.0138	0.312289	0.156145
Separate	0.033615813974464	0.044176	0.761	0.447844	0.223922
Learning	0.528535975192473	0.067169	7.8688	0	0
Happiness	-0.0406097034253699	0.075466	-0.5381	0.591271	0.295635
Depression	-0.0224269391840146	0.055865	-0.4014	0.688647	0.344324
Belonging	0.00391007197576475	0.044042	0.0888	0.929372	0.464686
Belonging_Final	-0.00626369092094975	0.06326	-0.099	0.921255	0.460628

Multiple Linear Regression - Regression Statistics
Multiple R	0.551834021342622
R-squared	0.30452078711117
Adjusted R-squared	0.272908095616223
F-TEST (value)	9.63286492577976
F-TEST (DF numerator)	7
F-TEST (DF denominator)	154
p-value	6.54508891528849e-10
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	1.82623628063756
Sum Squared Residuals	513.611398718401

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	12	9.87430108142183	2.12569891857817
2	11	11.2235250585375	-0.223525058537466
3	15	13.5339918411383	1.46600815886169
4	6	11.3193839691587	-5.31938396915873
5	13	10.4219513333832	2.57804866661678
6	10	9.69901806413087	0.300981935869128
7	12	12.6499189505108	-0.6499189505108
8	14	11.2192095084323	2.78079049156767
9	12	10.545168724653	1.45483127534703
10	6	11.0549138052263	-5.05491380522629
11	10	11.2857530462841	-1.28575304628407
12	12	11.4480027772661	0.551997222733896
13	12	11.5892745029769	0.410725497023086
14	11	11.4267826650356	-0.42678266503557
15	15	12.219851419521	2.78014858047904
16	12	11.1417882096627	0.858211790337311
17	10	10.9276692765871	-0.927669276587128
18	12	13.6166528988683	-1.61665289886833
19	11	12.6437729713974	-1.64377297139736
20	12	11.5740058312382	0.425994168761792
21	11	11.6648360666432	-0.664836066643154
22	12	11.7615631406725	0.23843685932747
23	13	13.1384638758318	-0.138463875831758
24	11	11.7009032351795	-0.700903235179519
25	9	11.7864070462344	-2.78640704623436
26	13	12.0686960125552	0.931303987444767
27	10	11.559551558222	-1.55955155822196
28	14	11.1990755096422	2.80092449035779
29	12	11.6038924215564	0.396107578443598
30	10	10.6472888421444	-0.64728884214435
31	12	11.0568683114543	0.943131688545682
32	8	9.78214942471264	-1.78214942471264
33	10	10.2826329467188	-0.282632946718843
34	12	11.7250734274722	0.274926572527795
35	12	10.4645101756171	1.5354898243829
36	7	6.9675640446936	0.0324359553064027
37	6	8.65660110003244	-2.65660110003244
38	12	10.4338803842506	1.56611961574938
39	10	11.7216664330209	-1.72166643302086
40	10	11.6631194479239	-1.66311944792389
41	10	11.4761698911984	-1.4761698911984
42	12	10.4530939616396	1.5469060383604
43	15	13.5214435981629	1.4785564018371
44	10	10.5593788207707	-0.559378820770704
45	10	10.3132003486076	-0.313200348607569
46	12	9.01492653687501	2.98507346312499
47	13	10.5840950915946	2.41590490840542
48	11	11.1582591710422	-0.158259171042193
49	11	11.5285250869533	-0.528525086953345
50	12	10.4117232601718	1.58827673982821
51	14	11.8515230849059	2.14847691509409
52	10	10.5225406766449	-0.522540676644908
53	12	9.6015883065832	2.39841169341681
54	13	11.7773254780715	1.22267452192849
55	5	8.10500712881499	-3.10500712881499
56	6	10.347109885371	-4.34710988537104
57	12	11.3177834967856	0.682216503214374
58	12	11.9160243368809	0.0839756631190745
59	11	11.190116652862	-0.190116652862015
60	10	11.6228566504585	-1.62285665045847
61	7	9.59800276566633	-2.59800276566633
62	12	11.5214200432732	0.478579956726817
63	14	11.8268563884989	2.17314361150106
64	11	10.7359921662694	0.264007833730558
65	12	11.4927600153244	0.507239984675606
66	13	12.4246858053931	0.575314194606921
67	14	12.652273361793	1.34772663820703
68	11	12.7744077238441	-1.77440772384409
69	12	9.44677922800112	2.55322077199888
70	12	11.6266555402349	0.373344459765051
71	8	8.32156214862119	-0.321562148621191
72	11	10.7284860242677	0.271513975732291
73	14	12.8303750570365	1.16962494296355
74	14	12.7774750417953	1.2225249582047
75	12	11.4951894582621	0.504810541737896
76	9	11.7381390628484	-2.73813906284843
77	13	11.4702088914228	1.52979110857724
78	11	11.4740221449451	-0.4740221449451
79	12	10.1952937588971	1.80470624110291
80	12	11.3862730797129	0.613726920287076
81	12	11.7696670620867	0.230332937913348
82	12	13.8387949577148	-1.83879495771478
83	12	11.7278193073437	0.272180692656298
84	12	10.8819765188691	1.11802348113089
85	11	11.1842796788729	-0.184279678872921
86	10	11.5832599823992	-1.58325998239919
87	9	10.5209606727743	-1.52096067277427
88	12	11.7065722423052	0.293427757694769
89	12	11.8009927632823	0.199007236717744
90	12	11.2020653663306	0.797934633669447
91	9	9.60129000644368	-0.601290006443678
92	15	11.9959767707738	3.00402322922623
93	12	11.7897715474391	0.210228452560861
94	12	10.9699596369733	1.03004036302669
95	12	10.2742581041526	1.72574189584743
96	10	11.4408020531153	-1.44080205311527
97	13	11.5348348910729	1.46516510892712
98	9	11.5429870614637	-2.54298706146366
99	12	11.4259076649961	0.574092335003935
100	10	10.7709421160586	-0.770942116058564
101	14	11.4671566639129	2.5328433360871
102	11	11.537947797134	-0.537947797134037
103	15	13.6973175772501	1.3026824227499
104	11	11.1565174978989	-0.156517497898942
105	11	11.752116117169	-0.752116117169022
106	12	9.76859428286186	2.23140571713815
107	12	11.9677322075304	0.0322677924696399
108	12	11.3646880562456	0.635311943754397
109	11	11.6901173477808	-0.690117347780795
110	7	9.26340022143179	-2.26340022143179
111	12	11.7710446030505	0.228955396949462
112	14	11.829828261292	2.17017173870797
113	11	12.5739692245957	-1.57396922459566
114	11	10.1406801536022	0.859319846397823
115	10	9.23544045265891	0.764559547341086
116	13	12.4670165353155	0.532983464684458
117	13	10.8040634360511	2.19593656394888
118	8	10.7725006456168	-2.77250064561678
119	11	10.2218609482543	0.77813905174568
120	12	11.4689551767201	0.531044823279859
121	11	10.233472486602	0.766527513398023
122	13	11.5240239684628	1.47597603153722
123	12	10.035646365322	1.96435363467801
124	14	11.6955844763388	2.30441552366117
125	13	11.0558552760882	1.94414472391178
126	15	11.8390758982933	3.16092410170667
127	10	10.7934651285417	-0.793465128541668
128	11	11.8090819413974	-0.809081941397355
129	9	11.0426665806976	-2.04266658069758
130	11	9.39967815683661	1.60032184316339
131	10	11.7914634959918	-1.79146349599182
132	11	8.73080633827149	2.26919366172851
133	8	11.4843377035926	-3.48433770359264
134	11	9.63286334519974	1.36713665480026
135	12	10.5472483161872	1.45275168381275
136	12	10.9134645286763	1.0865354713237
137	9	9.82868087243896	-0.828680872438958
138	11	11.0956874897645	-0.0956874897644672
139	10	9.25777513396797	0.742224866032029
140	8	9.47192203705678	-1.47192203705678
141	9	7.65407421128651	1.34592578871349
142	8	11.7561888370001	-3.75618883700011
143	9	11.1971916865423	-2.19719168654233
144	15	12.4092454982301	2.59075450176987
145	11	11.3977149594834	-0.397714959483352
146	8	8.03893797140226	-0.0389379714022622
147	13	12.4908164183439	0.509183581656068
148	12	10.1345113883703	1.86548861162966
149	12	11.7554270956875	0.244572904312479
150	9	9.99507759363662	-0.995077593636617
151	7	8.37762520015308	-1.37762520015308
152	13	10.7862884517931	2.21371154820689
153	9	11.7935304626767	-2.79353046267673
154	6	11.8597729909134	-5.85977299091341
155	8	10.5939959816378	-2.59399598163781
156	8	8.31937444704162	-0.31937444704162
157	15	11.9959767707738	3.00402322922623
158	6	10.2183444704624	-4.21834447046237
159	9	11.0426665806976	-2.04266658069758
160	11	11.7018587155815	-0.701858715581503
161	8	9.62889376062547	-1.62889376062547
162	8	10.0663928465821	-2.06639284658212

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
11	0.99984527763933	0.000309444721339209	0.000154722360669604
12	0.999738776165858	0.000522447668283149	0.000261223834141575
13	0.9993762089404	0.00124758211920055	0.000623791059600274
14	0.998978611694347	0.00204277661130656	0.00102138830565328
15	0.998827712463321	0.0023445750733589	0.00117228753667945
16	0.997888435751084	0.00422312849783278	0.00211156424891639
17	0.99613879358041	0.00772241283918073	0.00386120641959036
18	0.995239947716748	0.00952010456650442	0.00476005228325221
19	0.992490904669081	0.0150181906618387	0.00750909533091937
20	0.987331713346931	0.0253365733061376	0.0126682866530688
21	0.980449244102258	0.0391015117954834	0.0195507558977417
22	0.972111734016676	0.0557765319666486	0.0278882659833243
23	0.95866187222908	0.08267625554184	0.04133812777092
24	0.941455203986034	0.117089592027931	0.0585447960139657
25	0.939724832060897	0.120550335878206	0.0602751679391029
26	0.943808005234562	0.112383989530875	0.0561919947654377
27	0.94434847328965	0.111303053420701	0.0556515267103503
28	0.951029936159701	0.097940127680597	0.0489700638402985
29	0.932602662223359	0.134794675553282	0.0673973377766411
30	0.912464938216625	0.175070123566751	0.0875350617833753
31	0.89587822170228	0.20824355659544	0.10412177829772
32	0.912752413785146	0.174495172429708	0.0872475862148541
33	0.886393476046195	0.227213047907609	0.113606523953805
34	0.854862578058271	0.290274843883459	0.145137421941729
35	0.840988186877898	0.318023626244204	0.159011813122102
36	0.804102330737957	0.391795338524086	0.195897669262043
37	0.845392430013446	0.309215139973108	0.154607569986554
38	0.83662368930035	0.326752621399299	0.16337631069965
39	0.826399834306282	0.347200331387435	0.173600165693718
40	0.808340126461541	0.383319747076917	0.191659873538459
41	0.784505302363684	0.430989395272631	0.215494697636316
42	0.768456494450726	0.463087011098547	0.231543505549274
43	0.766621268570969	0.466757462858063	0.233378731429031
44	0.725509168985755	0.54898166202849	0.274490831014245
45	0.682367104468763	0.635265791062475	0.317632895531237
46	0.743492864836465	0.51301427032707	0.256507135163535
47	0.752718107785084	0.494563784429833	0.247281892214916
48	0.709722570799576	0.580554858400848	0.290277429200424
49	0.672648203586945	0.654703592826109	0.327351796413055
50	0.658340894017514	0.683318211964973	0.341659105982486
51	0.662941816994012	0.674116366011976	0.337058183005988
52	0.616677611611851	0.766644776776299	0.383322388388149
53	0.642404076655365	0.715191846689269	0.357595923344635
54	0.608556121733435	0.782887756533129	0.391443878266565
55	0.698451746676686	0.603096506646628	0.301548253323314
56	0.853549224916107	0.292901550167787	0.146450775083893
57	0.827172042262793	0.345655915474415	0.172827957737207
58	0.794109306688078	0.411781386623843	0.205890693311922
59	0.758373691600922	0.483252616798156	0.241626308399078
60	0.746373390244611	0.507253219510778	0.253626609755389
61	0.763250383157356	0.473499233685287	0.236749616842644
62	0.727695307793456	0.544609384413087	0.272304692206544
63	0.740549608902745	0.518900782194511	0.259450391097255
64	0.700546428118841	0.598907143762318	0.299453571881159
65	0.666018123130624	0.667963753738751	0.333981876869376
66	0.624394020192826	0.751211959614347	0.375605979807174
67	0.604952214407708	0.790095571184585	0.395047785592292
68	0.589627700118002	0.820744599763995	0.410372299881998
69	0.607092951484994	0.785814097030011	0.392907048515006
70	0.563456387827535	0.87308722434493	0.436543612172465
71	0.521856636810802	0.956286726378396	0.478143363189198
72	0.479223503606812	0.958447007213624	0.520776496393188
73	0.449122928273152	0.898245856546305	0.550877071726848
74	0.424353393269617	0.848706786539234	0.575646606730383
75	0.39804520782304	0.796090415646081	0.60195479217696
76	0.448108123877749	0.896216247755498	0.551891876122251
77	0.435551106025378	0.871102212050755	0.564448893974622
78	0.39336493659824	0.786729873196479	0.60663506340176
79	0.39765985161791	0.795319703235821	0.60234014838209
80	0.374050417360411	0.748100834720822	0.625949582639589
81	0.332350333124554	0.664700666249108	0.667649666875446
82	0.340625559293921	0.681251118587842	0.659374440706079
83	0.304154927540921	0.608309855081842	0.695845072459079
84	0.277207745314489	0.554415490628978	0.722792254685511
85	0.23989211653176	0.47978423306352	0.76010788346824
86	0.231614216558557	0.463228433117114	0.768385783441443
87	0.231049828303854	0.462099656607708	0.768950171696146
88	0.197635371458038	0.395270742916076	0.802364628541962
89	0.167954207328648	0.335908414657297	0.832045792671352
90	0.14638177451221	0.292763549024421	0.85361822548779
91	0.125881851042602	0.251763702085204	0.874118148957398
92	0.177411367731209	0.354822735462419	0.822588632268791
93	0.152960476755327	0.305920953510654	0.847039523244673
94	0.137346008031296	0.274692016062593	0.862653991968704
95	0.131068384436088	0.262136768872177	0.868931615563912
96	0.123999259062138	0.247998518124276	0.876000740937862
97	0.115807331336032	0.231614662672063	0.884192668663969
98	0.148022239852711	0.296044479705421	0.851977760147289
99	0.123547704453257	0.247095408906514	0.876452295546743
100	0.105061236516352	0.210122473032704	0.894938763483648
101	0.124138934110099	0.248277868220198	0.875861065889901
102	0.103054476632645	0.20610895326529	0.896945523367355
103	0.0977773359553872	0.195554671910774	0.902222664044613
104	0.0802676797901853	0.160535359580371	0.919732320209815
105	0.0665995158594831	0.133199031718966	0.933400484140517
106	0.0676469410628423	0.135293882125685	0.932353058937158
107	0.0535229437704108	0.107045887540822	0.946477056229589
108	0.0463271169573186	0.0926542339146372	0.953672883042681
109	0.0366409349780599	0.0732818699561198	0.96335906502194
110	0.0373147317562737	0.0746294635125474	0.962685268243726
111	0.028712208685536	0.057424417371072	0.971287791314464
112	0.0312556925455701	0.0625113850911403	0.96874430745443
113	0.0279982995078361	0.0559965990156723	0.972001700492164
114	0.0221729921874912	0.0443459843749824	0.977827007812509
115	0.0171744283399109	0.0343488566798218	0.982825571660089
116	0.0129818189723855	0.025963637944771	0.987018181027615
117	0.019785632074381	0.039571264148762	0.980214367925619
118	0.0225294522634235	0.0450589045268469	0.977470547736576
119	0.0171594270042404	0.0343188540084808	0.98284057299576
120	0.0131591680970503	0.0263183361941006	0.98684083190295
121	0.0108130685481078	0.0216261370962156	0.989186931451892
122	0.00892227212582196	0.0178445442516439	0.991077727874178
123	0.0104389051705807	0.0208778103411615	0.989561094829419
124	0.0165778124263341	0.0331556248526683	0.983422187573666
125	0.0174268004241893	0.0348536008483786	0.982573199575811
126	0.0415921928293497	0.0831843856586995	0.95840780717065
127	0.0313862793369959	0.0627725586739918	0.968613720663004
128	0.023777081309852	0.0475541626197039	0.976222918690148
129	0.0197797750377559	0.0395595500755119	0.980220224962244
130	0.0185698763737446	0.0371397527474892	0.981430123626255
131	0.0147722237920407	0.0295444475840815	0.985227776207959
132	0.0171636821778034	0.0343273643556069	0.982836317822197
133	0.026394470155207	0.052788940310414	0.973605529844793
134	0.0290119304345573	0.0580238608691145	0.970988069565443
135	0.0321153095684959	0.0642306191369919	0.967884690431504
136	0.026263825158068	0.052527650316136	0.973736174841932
137	0.0223502193726632	0.0447004387453265	0.977649780627337
138	0.0162686101019646	0.0325372202039291	0.983731389898035
139	0.0164806388425592	0.0329612776851184	0.983519361157441
140	0.0113977299598	0.0227954599196	0.9886022700402
141	0.0362561295450204	0.0725122590900407	0.96374387045498
142	0.0381519554969965	0.0763039109939929	0.961848044503004
143	0.026984229651314	0.0539684593026279	0.973015770348686
144	0.2950704996964	0.5901409993928	0.7049295003036
145	0.318911408397566	0.637822816795132	0.681088591602434
146	0.637808546516978	0.724382906966043	0.362191453483022
147	0.642779804553687	0.714440390892627	0.357220195446313
148	0.911311886571181	0.177376226857638	0.088688113428819
149	0.918488060117674	0.163023879764652	0.0815119398823261
150	0.83979569947952	0.32040860104096	0.16020430052048
151	0.72604067872963	0.54791864254074	0.27395932127037

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	8	0.0567375886524823	NOK
5% type I error level	32	0.226950354609929	NOK
10% type I error level	50	0.354609929078014	NOK