Multiple Linear Regression - Estimated Regression Equation

Depression[t] = + 28.0319250600556 -0.0162764938429117Connected[t] + 0.00305274942489057Separate[t] -0.144083343591928Learning[t] -0.0466135490343518Software[t] -0.641378322065256Happiness[t] -0.121880686933211Belonging[t] + 0.130909410471364Belonging_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)	28.0319250600556	2.991789	9.3696	0	0
Connected	-0.0162764938429117	0.067978	-0.2394	0.811084	0.405542
Separate	0.00305274942489057	0.063806	0.0478	0.961903	0.480951
Learning	-0.144083343591928	0.114073	-1.2631	0.208471	0.104236
Software	-0.0466135490343518	0.116114	-0.4014	0.688647	0.344324
Happiness	-0.641378322065256	0.095854	-6.6912	0	0
Belonging	-0.121880686933211	0.062732	-1.9429	0.053855	0.026928
Belonging_Final	0.130909410471364	0.090592	1.445	0.150479	0.075239

Multiple Linear Regression - Regression Statistics
Multiple R	0.581866339640286
R-squared	0.338568437206384
Adjusted R-squared	0.308503366170311
F-TEST (value)	11.2611886664147
F-TEST (DF numerator)	7
F-TEST (DF denominator)	154
p-value	1.76930692319388e-11
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	2.6328617115281
Sum Squared Residuals	1067.52196197273

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	12	13.7982754542448	-1.79827545424476
2	11	9.32657830553867	1.67342169446133
3	14	14.6125980703651	-0.612598070365088
4	12	14.6919029738794	-2.69190297387944
5	21	11.4651805720986	9.53481942790137
6	12	10.312797466026	1.68720253397399
7	22	13.5995061867615	8.40049381323847
8	11	12.4593930578592	-1.45939305785922
9	10	12.2273659200577	-2.22736592005769
10	13	12.3739030721799	0.626096927820059
11	10	10.619139908646	-0.619139908646044
12	8	10.2373340081958	-2.23733400819577
13	15	15.5739744326327	-0.573974432632679
14	14	12.1714640395967	1.82853596040328
15	10	9.24890161000077	0.75109838999923
16	14	13.555567671742	0.444432328258013
17	14	12.6868490613918	1.31315093860816
18	11	9.52856955214178	1.47143044785822
19	10	12.9945224109822	-2.99452241098218
20	13	12.2475556215279	0.752444378472132
21	7	10.5720861458145	-3.57208614581452
22	14	15.1742587037778	-1.17425870377776
23	12	12.9287435548827	-0.928743554882747
24	14	15.0524593329875	-1.05245933298749
25	11	10.0480097925521	0.951990207447938
26	9	15.0367662544933	-6.03676625449332
27	11	10.8854678140681	0.114532185931865
28	15	13.1648628050355	1.83513719496448
29	14	11.4944004678199	2.50559953218005
30	13	15.6348091932846	-2.63480919328457
31	9	11.294270997927	-2.29427099792702
32	15	14.9887744568289	0.0112255431711478
33	10	11.1131721223103	-1.11317212231031
34	11	11.9372355443196	-0.937235544319606
35	13	12.4933052512702	0.506694748729773
36	8	13.1213718751578	-5.12137187515782
37	20	17.3267872527183	2.67321274728172
38	12	12.3250836610648	-0.325083661064816
39	10	10.7385421826178	-0.73854218261779
40	10	13.5420291733181	-3.54202917331815
41	9	12.006991588825	-3.00699158882496
42	14	11.3596449894239	2.6403550105761
43	8	11.4066364663852	-3.40663646638517
44	14	15.1035423452468	-1.10354234524684
45	11	14.4074809539141	-3.40748095391407
46	13	15.285589814494	-2.28558981449403
47	9	12.9955177424932	-3.99551774249325
48	11	12.1847015811421	-1.18470158114211
49	15	10.3194861546383	4.68051384536174
50	11	13.3465306412945	-2.3465306412945
51	10	11.3917099997813	-1.39170999978125
52	14	13.2104313246145	0.789568675385497
53	18	15.4334586445188	2.56654135548115
54	14	15.4519095396656	-1.45190953966564
55	11	15.4166630365736	-4.41666303657358
56	12	12.4996699192225	-0.499669919222525
57	13	11.245938679855	1.75406132014504
58	9	12.5105185174677	-3.51051851746771
59	10	13.9008692132683	-3.90086921326835
60	15	14.1954889683464	0.804511031653555
61	20	18.172210413423	1.82778958657697
62	12	12.820708079094	-0.820708079094002
63	12	14.0783963499523	-2.07839634995235
64	14	13.8453836263034	0.154616373696595
65	13	12.8262420358679	0.17375796413205
66	11	14.7701294635527	-3.77012946355272
67	17	14.7056359999339	2.2943640000661
68	12	13.2932610736262	-1.2932610736262
69	13	12.906288555803	0.0937114441969621
70	14	12.1782564288185	1.82174357118151
71	13	14.3242869724282	-1.32428697242824
72	15	12.5898426775239	2.41015732247613
73	13	11.1421328558883	1.85786714411172
74	10	11.498425338794	-1.49842533879403
75	11	12.6658270523158	-1.66582705231576
76	19	13.5873517942137	5.41264820578627
77	13	10.825361971506	2.17463802849404
78	17	13.7674054402197	3.23259455978035
79	13	12.3856269768364	0.614373023163554
80	9	14.0479582007702	-5.04795820077017
81	11	11.5125874396328	-0.512587439632772
82	10	10.1861960447225	-0.18619604472254
83	9	12.3272232863662	-3.32722328636616
84	12	11.2795841276983	0.720415872301701
85	12	12.3048013148419	-0.304801314841931
86	13	12.6065998969801	0.393400103019936
87	13	12.2249838902413	0.775016109758725
88	12	12.8430294902949	-0.8430294902949
89	15	14.1934338986379	0.806566101362088
90	22	17.4827370624569	4.51726293754312
91	13	11.7098419262581	1.29015807374189
92	15	13.7955744510425	1.20442554895745
93	13	11.7390595729378	1.26094042706218
94	15	12.1860803638768	2.81391963612316
95	10	13.2834123168995	-3.28341231689952
96	11	10.8758059761169	0.124194023883097
97	16	14.1480287699157	1.85197123008433
98	11	12.367870360924	-1.36787036092402
99	11	10.1766767683571	0.823323231642862
100	10	12.2758997795279	-2.27589977952787
101	10	10.2899538785473	-0.289953878547267
102	16	14.0155519411943	1.98444805880574
103	12	10.1634307052218	1.83656929477818
104	11	15.3214634072101	-4.32146340721015
105	16	11.6992686474132	4.30073135258684
106	19	16.3531014521086	2.64689854789135
107	11	11.1392420266071	-0.139242026607136
108	16	11.9738510012157	4.02614899878425
109	15	16.0594052052423	-1.05940520524232
110	24	17.3119438288729	6.68805617112711
111	14	11.5823975929262	2.41760240707381
112	15	14.3558529829596	0.64414701704043
113	11	12.8106730420164	-1.81067304201645
114	15	13.0552263848403	1.94477361515968
115	12	10.683352942923	1.31664705707701
116	10	10.5223129730452	-0.52231297304517
117	14	13.7529247347496	0.247075265250363
118	13	13.4596285103321	-0.459628510332111
119	9	13.3249458195299	-4.32494581952992
120	15	11.9100804304604	3.08991956953958
121	15	15.2638335722661	-0.263833572266107
122	14	12.4780725163251	1.52192748367488
123	11	11.7010816639075	-0.701081663907469
124	8	11.8569113363132	-3.8569113363132
125	11	12.1951681981938	-1.1951681981938
126	11	12.8098075865427	-1.80980758654274
127	8	10.1947684143828	-2.19476841438281
128	10	10.3100624306707	-0.310062430670654
129	11	9.90360264149986	1.09639735850014
130	13	12.6851691146641	0.314830885335913
131	11	13.3470972809805	-2.34709728098046
132	20	17.1401349214288	2.85986507857122
133	10	11.8319203021611	-1.83192030216111
134	15	13.1357499837797	1.86425001622027
135	12	12.3511570849608	-0.351157084960815
136	14	11.560923521528	2.43907647847197
137	23	16.0340302202413	6.96596977975873
138	14	13.7517867601024	0.248213239897576
139	16	16.5445349341713	-0.544534934171252
140	11	13.2794703647723	-2.27947036477227
141	12	14.681611534838	-2.68161153483798
142	10	13.0544074679659	-3.05440746796585
143	14	11.2430007086322	2.75699929136778
144	12	11.979019567874	0.0209804321260404
145	12	11.7958296076958	0.204170392304208
146	11	11.7523419961418	-0.752341996141819
147	12	11.0217821016392	0.978217898360798
148	13	15.7299790451009	-2.72997904510094
149	11	13.9252579002798	-2.92525790027984
150	19	16.619468186117	2.38053181388298
151	12	12.0816344550512	-0.0816344550512346
152	17	12.8802875936309	4.11971240636909
153	9	11.3213772127863	-2.32137721278631
154	12	14.2843549482132	-2.28435494821325
155	19	16.622898406728	2.37710159327202
156	18	14.6074623336178	3.39253766638217
157	15	13.7955744510425	1.20442554895745
158	14	13.7113049678657	0.288695032134259
159	11	9.90360264149986	1.09639735850014
160	9	12.8586137589459	-3.85861375894593
161	18	14.1269679279711	3.87303207202892
162	16	14.6165786861657	1.38342131383433

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
11	0.842969506615882	0.314060986768237	0.157030493384118
12	0.998268505027293	0.00346298994541389	0.00173149497270695
13	0.996003552159906	0.00799289568018868	0.00399644784009434
14	0.994248109849938	0.0115037803001248	0.00575189015006239
15	0.992329286086666	0.0153414278266669	0.00767071391333347
16	0.986033347098322	0.0279333058033559	0.0139666529016779
17	0.985071947286132	0.0298561054277367	0.0149280527138684
18	0.975340509215983	0.0493189815680343	0.0246594907840172
19	0.985068979139394	0.0298620417212114	0.0149310208606057
20	0.976422534950975	0.0471549300980509	0.0235774650490254
21	0.98550587293612	0.0289882541277598	0.0144941270638799
22	0.982349283798822	0.0353014324023564	0.0176507162011782
23	0.973163415791815	0.0536731684163707	0.0268365842081854
24	0.964801138190501	0.0703977236189973	0.0351988618094986
25	0.949525777512728	0.100948444974543	0.0504742224872717
26	0.963827690038481	0.0723446199230388	0.0361723099615194
27	0.965210424689654	0.0695791506206924	0.0347895753103462
28	0.952596056365951	0.0948078872680988	0.0474039436340494
29	0.964207406107305	0.0715851877853909	0.0357925938926954
30	0.962000369337914	0.0759992613241721	0.037999630662086
31	0.961113594212973	0.0777728115740529	0.0388864057870265
32	0.950795039625717	0.098409920748565	0.0492049603742825
33	0.937914472690221	0.124171054619558	0.0620855273097791
34	0.927938634813493	0.144122730373014	0.0720613651865068
35	0.912919178999373	0.174161642001254	0.0870808210006272
36	0.936860358408597	0.126279283182806	0.0631396415914032
37	0.965637939613293	0.0687241207734146	0.0343620603867073
38	0.953517038492523	0.0929659230149548	0.0464829615074774
39	0.941605532217129	0.116788935565742	0.0583944677828708
40	0.946893802948226	0.106212394103547	0.0531061970517737
41	0.946437524152302	0.107124951695397	0.0535624758476983
42	0.945053353777199	0.109893292445601	0.0549466462228006
43	0.955560455733272	0.0888790885334567	0.0444395442667284
44	0.942919575122959	0.114160849754083	0.0570804248770415
45	0.941523177074652	0.116953645850696	0.0584768229253481
46	0.931491136332344	0.137017727335312	0.0685088636676562
47	0.946118866932278	0.107762266135445	0.0538811330677223
48	0.933267223433529	0.133465553132941	0.0667327765664706
49	0.952584501335013	0.0948309973299735	0.0474154986649867
50	0.945999521431841	0.108000957136319	0.0540004785681593
51	0.93861168164048	0.12277663671904	0.0613883183595198
52	0.924648148137111	0.150703703725778	0.0753518518628888
53	0.928993508943382	0.142012982113236	0.0710064910566179
54	0.915646463047551	0.168707073904898	0.084353536952449
55	0.936443078814952	0.127113842370096	0.0635569211850481
56	0.921969868222305	0.15606026355539	0.0780301317776951
57	0.912668903549816	0.174662192900367	0.0873310964501835
58	0.927943310489425	0.144113379021149	0.0720566895105747
59	0.942218210167606	0.115563579664788	0.0577817898323938
60	0.93091020645357	0.138179587092859	0.0690897935464297
61	0.931739383928379	0.136521232143243	0.0682606160716214
62	0.916276488083789	0.167447023832422	0.083723511916211
63	0.90771371066031	0.18457257867938	0.0922862893396901
64	0.886247043885785	0.22750591222843	0.113752956114215
65	0.861522106288796	0.276955787422408	0.138477893711204
66	0.882530089288984	0.234939821422032	0.117469910711016
67	0.88148140730874	0.23703718538252	0.11851859269126
68	0.865871561553405	0.268256876893189	0.134128438446595
69	0.840003345605567	0.319993308788866	0.159996654394433
70	0.824312407486767	0.351375185026466	0.175687592513233
71	0.803048314544956	0.393903370910088	0.196951685455044
72	0.795667107604999	0.408665784790001	0.204332892395001
73	0.77822666688051	0.44354666623898	0.22177333311949
74	0.757677813111666	0.484644373776668	0.242322186888334
75	0.738256545271879	0.523486909456242	0.261743454728121
76	0.850981976629279	0.298036046741441	0.149018023370721
77	0.843690702950133	0.312618594099733	0.156309297049867
78	0.859468090653313	0.281063818693375	0.140531909346687
79	0.83386102283967	0.33227795432066	0.16613897716033
80	0.908239932041749	0.183520135916502	0.091760067958251
81	0.888248794512845	0.223502410974311	0.111751205487155
82	0.865618169638221	0.268763660723558	0.134381830361779
83	0.880925001943063	0.238149996113875	0.119074998056937
84	0.857845187852388	0.284309624295223	0.142154812147612
85	0.8299357170047	0.340128565990599	0.170064282995299
86	0.798831729939358	0.402336540121285	0.201168270060642
87	0.767177926448663	0.465644147102675	0.232822073551337
88	0.733955589796783	0.532088820406435	0.266044410203217
89	0.697465351997849	0.605069296004302	0.302534648002151
90	0.770701048015499	0.458597903969003	0.229298951984501
91	0.74410689956593	0.51178620086814	0.25589310043407
92	0.712336009559808	0.575327980880384	0.287663990440192
93	0.684285588811115	0.631428822377769	0.315714411188885
94	0.686453448305639	0.627093103388722	0.313546551694361
95	0.710904606157855	0.57819078768429	0.289095393842145
96	0.668408104947017	0.663183790105966	0.331591895052983
97	0.643101396217379	0.713797207565242	0.356898603782621
98	0.614358550598021	0.771282898803958	0.385641449401979
99	0.571581374277883	0.856837251444233	0.428418625722117
100	0.556737826126796	0.886524347746408	0.443262173873204
101	0.50849615848491	0.983007683030181	0.49150384151509
102	0.482468428441165	0.964936856882329	0.517531571558835
103	0.471020286890204	0.942040573780407	0.528979713109796
104	0.594736882002643	0.810526235994715	0.405263117997357
105	0.714246512121457	0.571506975757087	0.285753487878543
106	0.702962272869356	0.594075454261288	0.297037727130644
107	0.6579518955452	0.6840962089096	0.3420481044548
108	0.737201562367634	0.525596875264732	0.262798437632366
109	0.712788967169065	0.574422065661869	0.287211032830935
110	0.894627323929315	0.21074535214137	0.105372676070685
111	0.8964737618676	0.2070524762648	0.1035262381324
112	0.872390486343937	0.255219027312126	0.127609513656063
113	0.851160367821361	0.297679264357278	0.148839632178639
114	0.881985665428594	0.236028669142812	0.118014334571406
115	0.866438520493018	0.267122959013963	0.133561479506982
116	0.835881144541006	0.328237710917987	0.164118855458994
117	0.830592268134499	0.338815463731001	0.169407731865501
118	0.796174372325734	0.407651255348533	0.203825627674266
119	0.844604931156095	0.31079013768781	0.155395068843905
120	0.868385738545581	0.263228522908837	0.131614261454419
121	0.83718056709849	0.32563886580302	0.16281943290151
122	0.806754517117462	0.386490965765075	0.193245482882537
123	0.766895606569461	0.466208786861078	0.233104393430539
124	0.777437601427812	0.445124797144377	0.222562398572188
125	0.745042296753181	0.509915406493638	0.254957703246819
126	0.716958049570298	0.566083900859403	0.283041950429702
127	0.715690566531499	0.568618866937002	0.284309433468501
128	0.698262651029887	0.603474697940226	0.301737348970113
129	0.654383072796453	0.691233854407095	0.345616927203547
130	0.594655801642603	0.810688396714794	0.405344198357397
131	0.572474284349023	0.855051431301955	0.427525715650977
132	0.534653013348719	0.930693973302562	0.465346986651281
133	0.475866724046484	0.951733448092969	0.524133275953516
134	0.432197622623413	0.864395245246826	0.567802377376587
135	0.369632092422268	0.739264184844536	0.630367907577732
136	0.319093438625791	0.638186877251582	0.680906561374209
137	0.623020966372324	0.753958067255352	0.376979033627676
138	0.54877094191796	0.902458116164081	0.45122905808204
139	0.473125045297455	0.946250090594909	0.526874954702546
140	0.417887799015976	0.835775598031952	0.582112200984024
141	0.406289867760832	0.812579735521663	0.593710132239168
142	0.359243269087186	0.718486538174372	0.640756730912814
143	0.368799422462793	0.737598844925586	0.631200577537207
144	0.286718657146382	0.573437314292764	0.713281342853618
145	0.214319238407169	0.428638476814337	0.785680761592831
146	0.310550722415169	0.621101444830338	0.689449277584831
147	0.225691776182641	0.451383552365283	0.774308223817359
148	0.450191741260263	0.900383482520527	0.549808258739737
149	0.528008068318587	0.943983863362826	0.471991931681413
150	0.389158039377046	0.778316078754092	0.610841960622954
151	0.544622238199205	0.910755523601589	0.455377761800795

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	2	0.0141843971631206	NOK
5% type I error level	11	0.0780141843971631	NOK
10% type I error level	24	0.170212765957447	NOK