Multiple Linear Regression - Estimated Regression Equation
I3[t] = -6.12668574711217 + 0.558945291398803I1[t] + 0.227036009710999I2[t] + 0.10342160976733E1[t] + 0.0191455460759015E2[t] -0.0263588305502614E3[t] + 0.513498207819026A[t] + 0.00609024818330574Happiness[t] -0.0518473800633609`Depression\r`[t] + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)-6.126685747112174.288483-1.42860.1551470.077573
I10.5589452913988030.1118714.99632e-061e-06
I20.2270360097109990.1029352.20560.0289010.01445
E10.103421609767330.1162170.88990.3749160.187458
E20.01914554607590150.0891930.21470.8303230.415162
E3-0.02635883055026140.091963-0.28660.7747870.387393
A0.5134982078190260.1209814.24453.8e-051.9e-05
Happiness0.006090248183305740.1516830.04020.9680250.484013
`Depression\r`-0.05184738006336090.112959-0.4590.6468910.323446


Multiple Linear Regression - Regression Statistics
Multiple R0.613397762281821
R-squared0.376256814772346
Adjusted R-squared0.343642792015344
F-TEST (value)11.5366576388241
F-TEST (DF numerator)8
F-TEST (DF denominator)153
p-value9.52682377430847e-13
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation3.7272329021876
Sum Squared Residuals2125.51656139392


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
12116.78865398355264.21134601644737
21512.55850866081952.44149133918046
31813.32179626325984.6782037367402
41114.0557762656397-3.05577626563966
5814.0338485111221-6.03384851112208
61917.35878798076361.64121201923643
7415.3584899936647-11.3584899936647
82015.20387960299754.79612039700248
91616.9894235828506-0.989423582850612
101413.39108118359830.60891881640171
111011.5771905023916-1.57719050239156
121314.8719286862847-1.87192868628469
131411.26245436454162.73754563545839
14815.7280890691149-7.72808906911492
152318.83135003340644.1686499665936
161115.119877027642-4.11987702764199
1796.534557496394042.46544250360596
182418.24795777347485.75204222652523
19515.0586903450134-10.0586903450134
201515.0199095227383-0.019909522738349
2159.68166173517755-4.68166173517755
221914.15588686662044.84411313337958
2362.221133485170243.77886651482976
241314.3515120225943-1.3515120225943
251111.0722134089751-0.0722134089750904
261717.4071559180441-0.407155918044059
271717.3460928952005-0.346092895200477
2859.40805262085281-4.40805262085281
29911.8170506086167-2.81705060861674
301514.85864051264420.141359487355773
311716.01510591205030.984894087949741
321714.06646825556622.93353174443382
332018.99012319785911.00987680214091
341212.1474871652576-0.147487165257636
35711.0989148382247-4.09891483822474
361617.1118747821256-1.11187478212558
3779.84990749939573-2.84990749939573
381412.26655409853591.7334459014641
392420.24003587247443.75996412752559
401516.0101183050525-1.01011830505251
411513.84655833617521.15344166382476
421014.790773528538-4.79077352853795
431415.457903832017-1.45790383201698
441818.0143786932819-0.0143786932818921
451217.7116391930634-5.71163919306339
46914.3713139462055-5.37131394620551
47910.2962388518111-1.29623885181106
48817.6793483895436-9.67934838954356
491814.20871055779743.79128944220255
501010.2383211388444-0.238321138844417
511713.77628285857713.22371714142292
521410.42539990222073.57460009777928
531614.75733897260181.24266102739815
54109.13648496703880.863515032961204
551916.04512628614382.95487371385616
561012.6355223342904-2.63552233429036
571413.15481924113660.845180758863358
581015.0472995010411-5.04729950104113
59410.0927870690494-6.09278706904941
601914.31552940870784.68447059129218
61913.9225241605385-4.92252416053853
621212.2153166820505-0.215316682050493
631615.44802713960290.551972860397065
641116.2730891166085-5.27308911660846
651818.3143258192032-0.314325819203207
661115.3675133331142-4.36751333311421
672417.31244180240776.68755819759225
681713.85813263024843.14186736975165
691814.23776643785353.7622335621465
7099.50559291632528-0.505592916325278
711914.59272114444344.40727885555658
721815.38069584135532.61930415864465
731213.6666583642052-1.66665836420521
742319.06165346445933.93834653554066
752217.21120341215414.78879658784589
761411.45331552976982.54668447023025
771411.65313834914732.34686165085268
781614.86070058632131.13929941367867
792318.00798752212434.99201247787569
8079.81421372243942-2.81421372243942
811018.4275838307451-8.42758383074512
821210.54881888659421.45118111340582
831215.1240439164227-3.12404391642267
841213.5490565022799-1.54905650227987
851713.65536275850043.34463724149957
862117.72431954664113.27568045335887
871616.2120257044635-0.212025704463468
881114.5199133814633-3.51991338146334
891411.68137732036922.3186226796308
901314.7185320016373-1.71853200163735
9199.29145645122718-0.291456451227177
921918.09507739375530.904922606244663
931314.7470073797008-1.74700737970077
941914.69558706866344.30441293133662
951312.92476740676980.075232593230176
961314.5033767227507-1.50337672275072
971315.5819448917486-2.58194489174859
981412.93811551881051.06188448118953
991211.94027486522340.0597251347765582
1002219.86947132931462.13052867068544
1011112.971971859192-1.97197185919202
102513.3291080693156-8.32910806931561
1031816.67217282377241.32782717622755
1041915.35502468440863.64497531559141
1051413.35056995197880.649430048021183
1061514.39601982514670.603980174853273
1071212.7439717998442-0.743971799844232
1081915.72482963535753.27517036464255
1091513.74433563061291.25566436938705
1101714.68317902397642.31682097602361
111814.9625925862247-6.96259258622471
1121014.9221081097-4.9221081097
1131212.0057497990257-0.00574979902571159
1141212.7613993881254-0.761399388125431
1152017.07951490486552.92048509513449
1161210.56227898720961.43772101279038
1171211.37999780336330.620002196636709
1181414.7860502208166-0.786050220816584
119613.5140855383662-7.5140855383662
120109.891984556891050.108015443108946
1211814.00763483555563.99236516444444
1221815.28464541654612.71535458345387
123710.6602878486117-3.66028784861168
1241814.49752888114413.50247111885587
125920.228725657145-11.228725657145
1261715.72073015362171.27926984637831
1272217.10810972161264.89189027838742
1281113.0515620765383-2.05156207653826
1291510.94008087676074.05991912323935
1301715.53879794806061.46120205193938
1311512.04026152225372.95973847774634
1322216.82153212389355.17846787610653
13399.48928857012745-0.489288570127449
1341311.15502686764371.84497313235631
1352016.7640161297623.23598387023804
1361415.0397137129615-1.0397137129615
1371417.7357926402913-3.73579264029129
1381211.97875742696510.0212425730349382
1392016.34865837924763.65134162075237
1402017.13794466617372.86205533382632
141810.5691085707593-2.56910857075926
1421714.55675155721422.44324844278582
14397.147052198281511.85294780171849
1441814.16163506852933.83836493147073
1452219.13591037668152.86408962331851
1461012.2490428408529-2.24904284085291
1471315.1686080540861-2.16860805408608
1481517.6540383274489-2.6540383274489
1491814.43015361464533.56984638535475
1501816.07952649689491.92047350310509
1511213.921327202056-1.92132720205596
1521214.8233563992011-2.82335639920115
1532018.21501411603641.78498588396358
1541216.0491016510208-4.04910165102077
1551616.0981067422462-0.0981067422462444
1561613.32817819278332.67182180721667
1571812.44806861871275.55193138128725
1581615.84735611530040.152643884699615
1591314.8750631325607-1.87506313256072
1601713.44469209165883.55530790834124
1611310.73394105571072.26605894428927
1621712.34277821496354.6572217850365


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
120.8697264242666690.2605471514666620.130273575733331
130.7998776092454960.4002447815090070.200122390754504
140.8060972495499960.3878055009000080.193902750450004
150.8016006101914240.3967987796171510.198399389808576
160.7577213335304260.4845573329391470.242278666469574
170.7194287524047880.5611424951904240.280571247595212
180.8530635865734120.2938728268531770.146936413426588
190.9732082937837940.05358341243241160.0267917062162058
200.9579561878592390.08408762428152260.0420438121407613
210.960089757623840.07982048475231910.0399102423761596
220.949538039863380.1009239202732390.0504619601366196
230.9532174956847030.09356500863059440.0467825043152972
240.9416505447695280.1166989104609430.0583494552304716
250.9185334181969280.1629331636061430.0814665818030715
260.9394177091791530.1211645816416940.060582290820847
270.9158396538629040.1683206922741920.0841603461370961
280.925607478092250.14878504381550.07439252190775
290.9075420674087410.1849158651825180.0924579325912591
300.8835455802910910.2329088394178180.116454419708909
310.8520143448804150.2959713102391710.147985655119585
320.8590459548225150.2819080903549710.140954045177485
330.8300714068624130.3398571862751730.169928593137587
340.8069802414821810.3860395170356380.193019758517819
350.8672472392553160.2655055214893680.132752760744684
360.8430447154617010.3139105690765970.156955284538299
370.8155088704276610.3689822591446790.184491129572339
380.7853266920626680.4293466158746640.214673307937332
390.7753113299519190.4493773400961620.224688670048081
400.7326873609448940.5346252781102110.267312639055106
410.6858403034123390.6283193931753220.314159696587661
420.6881092829472360.6237814341055280.311890717052764
430.650855823544980.6982883529100410.34914417645502
440.622208645072520.7555827098549590.37779135492748
450.6695234863249380.6609530273501230.330476513675062
460.677283446075960.645433107848080.32271655392404
470.6393352518372580.7213294963254840.360664748162742
480.8650548146104110.2698903707791780.134945185389589
490.8933446077296580.2133107845406840.106655392270342
500.8703050856941540.2593898286116910.129694914305846
510.8780674309773670.2438651380452660.121932569022633
520.8790651092003660.2418697815992670.120934890799634
530.8713515074604250.257296985079150.128648492539575
540.8526559059810890.2946881880378210.147344094018911
550.8431377472430830.3137245055138330.156862252756917
560.8214738201182140.3570523597635730.178526179881786
570.791122357804970.417755284390060.20887764219503
580.8297216815671240.3405566368657520.170278318432876
590.8676595362456150.2646809275087710.132340463754385
600.9220064243162980.1559871513674050.0779935756837023
610.9292425042145820.1415149915708370.0707574957854184
620.9117191822481990.1765616355036030.0882808177518013
630.8972975215666240.2054049568667510.102702478433376
640.9109240502159730.1781518995680550.0890759497840275
650.9036239815316880.1927520369366250.0963760184683125
660.9083385570304510.1833228859390990.0916614429695494
670.9543931676286240.09121366474275180.0456068323713759
680.9523499434031120.09530011319377660.0476500565968883
690.9520780522067970.09584389558640520.0479219477932026
700.9391067949993090.1217864100013820.060893205000691
710.9458646954587070.1082706090825850.0541353045412925
720.9401431336916760.1197137326166480.0598568663083241
730.9293778213745150.1412443572509710.0706221786254854
740.9321862569827620.1356274860344750.0678137430172376
750.9404466009446640.1191067981106710.0595533990553357
760.9359852530430760.1280294939138480.0640147469569239
770.9272238159141770.1455523681716460.0727761840858228
780.9112800415614010.1774399168771980.0887199584385989
790.9249915040249060.1500169919501880.0750084959750939
800.9159927416906910.1680145166186170.0840072583093086
810.9679755815477390.06404883690452290.0320244184522615
820.9599147541035810.08017049179283780.0400852458964189
830.9575672904719560.08486541905608790.0424327095280439
840.9481547507316480.1036904985367040.0518452492683522
850.9452506781983620.1094986436032750.0547493218016376
860.942632783517340.114734432965320.0573672164826599
870.9276088833103850.144782233379230.0723911166896149
880.9278690876860730.1442618246278540.0721309123139271
890.917450817670990.165098364658020.0825491823290098
900.9033527746724120.1932944506551770.0966472253275883
910.887599102850710.2248017942985810.112400897149291
920.8654350242996010.2691299514007980.134564975700399
930.8439906981839330.3120186036321350.156009301816067
940.853702580953910.2925948380921790.14629741904609
950.824372361914190.351255276171620.17562763808581
960.7960407921111160.4079184157777670.203959207888884
970.781555129266420.4368897414671610.21844487073358
980.7465085490760590.5069829018478830.253491450923941
990.7055828538191740.5888342923616530.294417146180826
1000.6764883172083790.6470233655832410.323511682791621
1010.6438964360959060.7122071278081890.356103563904094
1020.8549037745957710.2901924508084580.145096225404229
1030.8283775001006090.3432449997987820.171622499899391
1040.8351791477306970.3296417045386070.164820852269303
1050.8045438486191530.3909123027616940.195456151380847
1060.7731365601029040.4537268797941930.226863439897097
1070.7391693269463590.5216613461072830.260830673053641
1080.7188131788865850.562373642226830.281186821113415
1090.6847945493828130.6304109012343740.315205450617187
1100.6482852620884060.7034294758231880.351714737911594
1110.7286553863703110.5426892272593770.271344613629689
1120.7625469780429460.4749060439141090.237453021957054
1130.7334339849748540.5331320300502930.266566015025146
1140.704328016640970.5913439667180590.29567198335903
1150.7050317316970910.5899365366058190.294968268302909
1160.6610129455941530.6779741088116950.338987054405847
1170.6102353232631470.7795293534737050.389764676736853
1180.5573133755496320.8853732489007350.442686624450368
1190.8436694462790920.3126611074418170.156330553720908
1200.8099849597240540.3800300805518930.190015040275946
1210.8040338153787180.3919323692425650.195966184621282
1220.7727173611382740.4545652777234510.227282638861726
1230.8068959605545320.3862080788909360.193104039445468
1240.7780201322427760.4439597355144490.221979867757224
1250.9944407236184640.01111855276307110.00555927638153553
1260.9915263859227930.0169472281544150.00847361407720751
1270.9890902217409330.0218195565181350.0109097782590675
1280.9835305371739450.03293892565210970.0164694628260548
1290.9793759420828830.04124811583423470.0206240579171173
1300.9707134579600910.0585730840798180.029286542039909
1310.9582843920750050.08343121584999030.0417156079249952
1320.9620186360439490.07596272791210290.0379813639560515
1330.9506260541897290.09874789162054120.0493739458102706
1340.9342028559068590.1315942881862820.0657971440931409
1350.9225458571238520.1549082857522950.0774541428761476
1360.8927490950851940.2145018098296120.107250904914806
1370.9030110426586180.1939779146827640.0969889573413822
1380.8648025819846280.2703948360307440.135197418015372
1390.890314137733350.21937172453330.10968586226665
1400.86113880303450.2777223939310.1388611969655
1410.8588470382675120.2823059234649770.141152961732488
1420.807113293085810.3857734138283790.19288670691419
1430.7339274148095320.5321451703809370.266072585190468
1440.786381492551650.42723701489670.21361850744835
1450.861328479287970.277343041424060.13867152071203
1460.904943086539180.190113826921640.0950569134608201
1470.8363097026845290.3273805946309420.163690297315471
1480.751885476135630.4962290477287410.24811452386437
1490.6590146606490720.6819706787018560.340985339350928
1500.5518854657012930.8962290685974150.448114534298707


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level00OK
5% type I error level50.0359712230215827OK
10% type I error level190.136690647482014NOK