Multiple Linear Regression - Estimated Regression Equation

Depression [t] = + 24.1568693472891 -0.048698971906455Connected[t] + 0.0212697039878104Separate[t] -0.73207250482067Happiness[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)	24.1568693472891	2.675306	9.0296	0	0
Connected	-0.048698971906455	0.067524	-0.7212	0.471849	0.235925
Separate	0.0212697039878104	0.064264	0.331	0.741102	0.370551
Happiness	-0.73207250482067	0.091736	-7.9802	0	0

Multiple Linear Regression - Regression Statistics
Multiple R	0.546383336681775
R-squared	0.29853475060351
Adjusted R-squared	0.285215790171931
F-TEST (value)	22.4142681508154
F-TEST (DF numerator)	3
F-TEST (DF denominator)	158
p-value	3.81550346872928e-12
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	2.67682813705154
Sum Squared Residuals	1132.13460229911

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	12	12.7194451831719	-0.719445183171919
2	11	9.76093488377522	1.23906511622478
3	14	15.3875422766414	-1.38754227664143
4	12	14.5642313919387	-2.56423139193869
5	21	11.5749232728879	9.42507672711211
6	12	9.89192165943761	2.10807834056239
7	22	12.6679551990701	9.33204480092991
8	11	13.0177985785414	-2.01779857854142
9	10	12.16705842592	-2.16705842592003
10	13	12.182168565977	0.817831434022999
11	10	10.5204366565145	-0.520436656514534
12	8	9.21749870264953	-1.21749870264953
13	15	15.7300230062105	-0.730023006210466
14	14	11.3526981173434	2.64730188265658
15	10	10.159477235153	-0.159477235153001
16	14	13.0513874103909	0.948612589609106
17	14	12.8353218187773	1.16467818122274
18	11	10.6693245844292	0.330675415570794
19	10	12.8168431269848	-2.81684312698476
20	13	11.5659726967617	1.43402730323826
21	7	10.1230973911082	-3.12309739110821
22	14	15.2537644887837	-1.25376448878374
23	12	12.8168431269848	-0.816843126984761
24	14	14.3996557844268	-0.399655784426821
25	11	10.4930073885959	0.506992611404111
26	9	16.2521894833483	-7.25218948334834
27	11	11.4349859210994	-0.434985921099355
28	15	13.0877672544357	1.91223274556432
29	14	12.2706159336638	1.72938406633623
30	13	15.15020698104	-2.15020698103999
31	9	11.529592852717	-2.52959285271696
32	15	14.005685070756	0.994314929243971
33	10	10.569135628421	-0.569135628420989
34	11	12.3069957777086	-1.30699577770856
35	13	12.8901803546146	0.109819645385447
36	8	11.5872424007496	-3.58724240074956
37	20	16.815307442238	3.18469255776201
38	12	12.1245190179444	-0.124519017944405
39	10	10.9587274036726	-0.958727403672629
40	10	13.6373629994922	-3.6373629994922
41	9	12.0545503420501	-3.05455034205014
42	14	11.4898444569366	2.51015554306336
43	8	11.273778865323	-3.27377886532301
44	14	14.3694355043129	-0.36943550431287
45	11	14.1169900686545	-3.11699006865445
46	13	15.0466494732962	-2.04664947329625
47	9	12.1547392980584	-3.15473929805836
48	11	12.2918856376516	-1.29188563765158
49	15	10.7667225282421	4.23327747175788
50	11	13.469996379785	-2.46999637978502
51	10	11.6935909206886	-1.69359092068861
52	14	12.9875782984275	1.01242170157254
53	18	15.2476049248529	2.7523950751471
54	14	14.5244829961584	-0.524482996158376
55	11	14.4942627160444	-3.49426271604442
56	12	12.0545503420501	-0.0545503420501392
57	13	11.2676193013922	1.73238069860782
58	9	12.4866815252774	-3.4866815252774
59	10	14.3358466724634	-4.33584667246339
60	15	14.3907052083007	0.609294791699321
61	20	17.4348718631888	2.56512813681123
62	12	13.5125357877606	-1.51253578776064
63	12	15.1927463890156	-3.19274638901561
64	14	13.142625790273	0.857374209727029
65	13	12.1793775537817	0.820622446218306
66	11	15.9186593299054	-4.91865932990545
67	17	15.0953484452027	1.9046515547973
68	12	14.4853121399183	-2.48531213991828
69	13	12.1273100301397	0.872689969860288
70	14	12.2582968058021	1.7417031941979
71	13	12.8230026909156	0.176997309084405
72	15	11.7422898925951	3.25771010740494
73	13	12.3495351856842	0.650464814315823
74	10	12.197278706034	-2.19727870603398
75	11	13.5584437474718	-2.55844374747179
76	19	14.1108305047236	4.88916949527638
77	13	10.6967538523479	2.30324614765215
78	17	13.643522563423	3.35647743657697
79	13	12.4715713852204	0.528428614779576
80	9	13.4123468317524	-4.41234683175243
81	11	12.3344250456272	-1.3344250456272
82	10	11.4500960611563	-1.45009606115633
83	9	12.2582968058021	-3.2582968058021
84	12	11.3437475412173	0.656252458782721
85	12	12.340584609558	-0.340584609558035
86	13	12.9601490305088	0.0398509694911812
87	13	12.1547392980584	0.845260701941643
88	12	13.0239581424722	-1.02395814247225
89	15	13.9082871269431	1.09171287305688
90	22	18.1271959722291	3.87280402777087
91	13	10.9676779797988	2.03232202020123
92	15	13.5673943235979	1.43260567640207
93	13	12.3433756217533	0.656624378246658
94	15	12.9450388904518	2.05496110954816
95	10	13.8657477189675	-3.8657477189675
96	11	11.3101587093678	-0.310158709367801
97	16	14.3145769684756	1.68542303152442
98	11	12.8627510866959	-1.86275108669591
99	11	10.6329447403844	0.36705525961558
100	10	12.3831240175337	-2.38312401753366
101	10	10.6267851764536	-0.626785176453586
102	16	14.3145769684756	1.68542303152442
103	12	11.477525329075	0.522474670925024
104	11	15.1412564049139	-4.14125640491385
105	16	12.3982341575906	3.60176584240937
106	19	16.3008884552548	2.69911154474521
107	11	11.3375879772864	-0.337587977286445
108	16	12.008642382339	3.99135761766101
109	15	15.8274209500234	-0.827420950023374
110	24	15.6354160745929	8.36458392540714
111	14	12.4379825533709	1.56201744662906
112	15	15.2963038967594	-0.296303896759359
113	11	13.953617547114	-2.95361754711405
114	15	13.0513874103909	1.94861258960911
115	12	9.90087223556375	2.09912776443625
116	10	11.3224778372295	-1.32247783722947
117	14	13.1515763663991	0.848423633600888
118	13	13.1028773944927	-0.102877394492657
119	9	13.0452278464601	-4.04522784646006
120	15	12.8230026909156	2.17699730908441
121	15	14.551912264077	0.44808773592298
122	14	12.9724681583705	1.02753184162951
123	11	12.1547392980584	-1.15473929805836
124	8	12.182168565977	-4.182168565977
125	11	12.2280765256881	-1.22807652568815
126	11	13.832158887118	-2.83215888711802
127	8	10.4930073885959	-2.49300738859589
128	10	10.3984004569783	-0.398400456978286
129	11	9.40613502634452	1.59386497365548
130	13	12.1732179898509	0.826782010149141
131	11	13.7834599152116	-2.78345991521156
132	20	16.8852761181323	3.11472388186775
133	10	12.0148019462698	-2.01480194626983
134	15	12.4990006531391	2.50099934686093
135	12	12.182168565977	-0.182168565977001
136	14	11.5021635847983	2.49783641520169
137	23	15.2084340686128	7.79156593138719
138	14	12.9965288745536	1.00347112544639
139	16	15.3875422766414	0.612457723358565
140	11	12.1944876938387	-1.19448769383867
141	12	13.8746982950936	-1.87469829509364
142	10	12.340584609558	-2.34058460955803
143	14	11.7059100485503	2.29408995144972
144	12	13.1913247621794	-1.19132476217943
145	12	12.1553168375986	-0.155316837598576
146	11	11.1551112175223	-0.155111217522294
147	12	11.4596241768227	0.540375823177307
148	13	15.1166181491905	-2.11661814919051
149	11	14.4729930120566	-3.47299301205661
150	19	16.5443833147871	2.45561668521293
151	12	11.4226667932377	0.577333206762313
152	17	13.3815490120983	3.61845098790174
153	9	11.5961929768757	-2.5961929768757
154	12	14.4970537282397	-2.49705372823973
155	19	16.5869227227627	2.41307727723731
156	18	13.6922215353295	4.30777846467051
157	15	13.5673943235979	1.43260567640207
158	14	13.1364662263421	0.863533773657864
159	11	9.40613502634452	1.59386497365548
160	9	13.6647922674108	-4.66479226741084
161	18	14.5580718280079	3.44192817199215
162	16	13.7498710833621	2.25012891663791

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
7	0.999751510137812	0.000496979724375756	0.000248489862187878
8	0.999687059549789	0.000625880900422106	0.000312940450211053
9	0.99970527205805	0.000589455883899908	0.000294727941949954
10	0.999290170514986	0.00141965897002828	0.000709829485014142
11	0.999206401741466	0.00158719651706751	0.000793598258533755
12	0.998969470258118	0.00206105948376308	0.00103052974188154
13	0.99817979197987	0.00364041604026055	0.00182020802013028
14	0.997042436210843	0.00591512757831443	0.00295756378915721
15	0.994746551368834	0.0105068972623318	0.00525344863116592
16	0.991363896676737	0.017272206646527	0.0086361033232635
17	0.985989794752693	0.0280204104946141	0.0140102052473071
18	0.97860937041175	0.0427812591765006	0.0213906295882503
19	0.980310194555444	0.0393796108891128	0.0196898054445564
20	0.971128574880477	0.0577428502390457	0.0288714251195229
21	0.975866471999038	0.0482670560019237	0.0241335280009618
22	0.966300227666247	0.0673995446675059	0.0336997723337529
23	0.954375330250926	0.0912493394981479	0.0456246697490739
24	0.93654701879451	0.126905962410979	0.0634529812054896
25	0.91887682441545	0.1622463511691	0.0811231755845498
26	0.982350725701349	0.0352985485973026	0.0176492742986513
27	0.975361440715216	0.0492771185695689	0.0246385592847844
28	0.970603671145542	0.0587926577089159	0.0293963288544579
29	0.962693931223856	0.0746121375522885	0.0373060687761442
30	0.952881840816776	0.0942363183664475	0.0471181591832238
31	0.951860466010995	0.0962790679780104	0.0481395339890052
32	0.940227596375782	0.119544807248436	0.0597724036242178
33	0.923996830615147	0.152006338769706	0.0760031693848528
34	0.909350000755439	0.181299998489123	0.0906499992445614
35	0.885194138939437	0.229611722121125	0.114805861060563
36	0.906378942885895	0.187242114228209	0.0936210571141047
37	0.932072842721774	0.135854314556453	0.0679271572782263
38	0.912590943429029	0.174818113141941	0.0874090565709705
39	0.895151578351206	0.209696843297588	0.104848421648794
40	0.905161641250898	0.189676717498205	0.0948383587491025
41	0.9062389379017	0.187522124196599	0.0937610620982996
42	0.901034318913051	0.197931362173898	0.0989656810869492
43	0.906549824210411	0.186900351579179	0.0934501757895894
44	0.884111186081583	0.231777627836834	0.115888813918417
45	0.877459927605968	0.245080144788063	0.122540072394032
46	0.859840482592103	0.280319034815795	0.140159517407897
47	0.869334346558676	0.261331306882649	0.130665653441324
48	0.847370511580785	0.305258976838431	0.152629488419215
49	0.876609192114534	0.246781615770932	0.123390807885466
50	0.865229807714949	0.269540384570103	0.134770192285051
51	0.855058304751128	0.289883390497744	0.144941695248872
52	0.832716960846798	0.334566078306404	0.167283039153202
53	0.844831012964384	0.310337974071231	0.155168987035616
54	0.81499095860684	0.370018082786321	0.18500904139316
55	0.827594722820834	0.344810554358331	0.172405277179166
56	0.796099085685029	0.407801828629942	0.203900914314971
57	0.777665434823047	0.444669130353907	0.222334565176953
58	0.802743150104118	0.394513699791763	0.197256849895881
59	0.840871437201098	0.318257125597805	0.159128562798902
60	0.817245228930322	0.365509542139357	0.182754771069678
61	0.833737739591054	0.332524520817893	0.166262260408946
62	0.81184384430477	0.37631231139046	0.18815615569523
63	0.819623671403985	0.360752657192031	0.180376328596015
64	0.79118607071254	0.417627858574919	0.20881392928746
65	0.759956540310894	0.480086919378211	0.240043459689106
66	0.830151640217264	0.339696719565472	0.169848359782736
67	0.824884501143132	0.350230997713736	0.175115498856868
68	0.820855478099784	0.358289043800432	0.179144521900216
69	0.793787677912696	0.412424644174608	0.206212322087304
70	0.774856931377295	0.45028613724541	0.225143068622705
71	0.740474218736171	0.519051562527658	0.259525781263829
72	0.757738538910885	0.48452292217823	0.242261461089115
73	0.722568548287607	0.554862903424785	0.277431451712393
74	0.711397153638157	0.577205692723687	0.288602846361843
75	0.710313499101002	0.579373001797996	0.289686500898998
76	0.804559744207077	0.390880511585846	0.195440255792923
77	0.797107730851124	0.405784538297752	0.202892269148876
78	0.816160964153243	0.367678071693514	0.183839035846757
79	0.786104272484807	0.427791455030386	0.213895727515193
80	0.849781769180139	0.300436461639722	0.150218230819861
81	0.828534207853878	0.342931584292244	0.171465792146122
82	0.807239799408943	0.385520401182114	0.192760200591057
83	0.822845872367823	0.354308255264353	0.177154127632177
84	0.793036827950105	0.413926344099791	0.206963172049895
85	0.75917787321605	0.481644253567901	0.24082212678395
86	0.722579069421563	0.554841861156874	0.277420930578437
87	0.687046372424938	0.625907255150123	0.312953627575062
88	0.652245606539751	0.695508786920498	0.347754393460249
89	0.616721337462316	0.766557325075368	0.383278662537684
90	0.664646274135492	0.670707451729017	0.335353725864508
91	0.654778465960286	0.690443068079427	0.345221534039714
92	0.622558882654336	0.754882234691329	0.377441117345664
93	0.582192215135079	0.835615569729841	0.41780778486492
94	0.560055180480308	0.879889639039383	0.439944819519692
95	0.614080402033808	0.771839195932384	0.385919597966192
96	0.569753007541843	0.860493984916314	0.430246992458157
97	0.539288790255282	0.921422419489436	0.460711209744718
98	0.522788674410985	0.95442265117803	0.477211325589015
99	0.476648824562684	0.953297649125367	0.523351175437316
100	0.464065082877339	0.928130165754679	0.535934917122661
101	0.419975841425352	0.839951682850704	0.580024158574648
102	0.388638682502058	0.777277365004116	0.611361317497942
103	0.345816296338331	0.691632592676661	0.654183703661669
104	0.449485930467368	0.898971860934737	0.550514069532632
105	0.506327189488056	0.987345621023887	0.493672810511944
106	0.491629102226915	0.983258204453829	0.508370897773085
107	0.444765442710905	0.88953088542181	0.555234557289095
108	0.500846769757817	0.998306460484366	0.499153230242183
109	0.474873822054742	0.949747644109483	0.525126177945259
110	0.849394382537371	0.301211234925259	0.150605617462629
111	0.829517595215811	0.340964809568379	0.170482404784189
112	0.799751640913232	0.400496718173536	0.200248359086768
113	0.797166267800184	0.405667464399632	0.202833732199816
114	0.776637371531068	0.446725256937864	0.223362628468932
115	0.774270722612472	0.451458554775056	0.225729277387528
116	0.744003052377384	0.511993895245233	0.255996947622616
117	0.716085172554312	0.567829654891377	0.283914827445688
118	0.675242160215823	0.649515679568353	0.324757839784177
119	0.737054799239775	0.52589040152045	0.262945200760225
120	0.731673579301129	0.536652841397742	0.268326420698871
121	0.68718887205349	0.625622255893019	0.31281112794651
122	0.644797281523612	0.710405436952775	0.355202718476388
123	0.597014831873154	0.805970336253692	0.402985168126846
124	0.64413681710185	0.711726365796299	0.35586318289815
125	0.613998996802306	0.772002006395388	0.386001003197694
126	0.649979010882349	0.700041978235301	0.350020989117651
127	0.651910645937986	0.696178708124029	0.348089354062015
128	0.602866659752024	0.794266680495952	0.397133340247976
129	0.587433848043964	0.825132303912071	0.412566151956035
130	0.532125970846033	0.935748058307934	0.467874029153967
131	0.573047743044142	0.853904513911717	0.426952256955858
132	0.54396627688275	0.912067446234499	0.45603372311725
133	0.507128098221448	0.985743803557105	0.492871901778552
134	0.475020604198399	0.950041208396798	0.524979395801601
135	0.412943693324047	0.825887386648093	0.587056306675953
136	0.378466603976455	0.75693320795291	0.621533396023545
137	0.678420602308489	0.643158795383023	0.321579397691511
138	0.621551069354977	0.756897861290046	0.378448930645023
139	0.559368263991764	0.881263472016472	0.440631736008236
140	0.50763902549839	0.984721949003221	0.49236097450161
141	0.463775640202293	0.927551280404585	0.536224359797707
142	0.445931438690504	0.891862877381009	0.554068561309496
143	0.43854788072638	0.87709576145276	0.56145211927362
144	0.369059049877922	0.738118099755845	0.630940950122078
145	0.297362600776094	0.594725201552187	0.702637399223906
146	0.251583130733201	0.503166261466401	0.748416869266799
147	0.189359806873271	0.378719613746541	0.810640193126729
148	0.190765949083758	0.381531898167516	0.809234050916242
149	0.286002688696639	0.572005377393278	0.713997311303361
150	0.213013692929105	0.42602738585821	0.786986307070895
151	0.146073546569559	0.292147093139118	0.853926453430441
152	0.234095400396112	0.468190800792224	0.765904599603888
153	0.180331957288677	0.360663914577355	0.819668042711323
154	0.156861695765267	0.313723391530535	0.843138304234733
155	0.0903673542779089	0.180734708555818	0.909632645722091

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	8	0.0536912751677852	NOK
5% type I error level	16	0.10738255033557	NOK
10% type I error level	23	0.154362416107383	NOK