Multiple Linear Regression - Estimated Regression Equation
Learning_p[t] = + 1.36685540574507e-16 -2.24130327401676e-16Pop[t] 0t 0Pop_t[t] 0Connected[t] 0Connected_p[t] 0Separate[t] 0Separate_p[t] + 1Learning[t] -1.92034237745733e-18Software[t] -8.89015228870144e-18Happiness[t] + 2.18919951146729e-18Happiness_p[t] -7.28235610420522e-18Depression[t] + 1.4446555024318e-17Depression_p[t] + 5.80567721635646e-19Belonging[t] -7.82099234232271e-19Belonging_p[t] + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)1.36685540574507e-1600.45710.6480060.324003
Pop-2.24130327401676e-160-0.59950.5493940.274697
t00010.5
Pop_t00010.5
Connected00010.5
Connected_p00010.5
Separate00010.5
Separate_p00010.5
Learning1017486132759686390400
Software-1.92034237745733e-180-0.33260.7397090.369855
Happiness-8.89015228870144e-180-1.10260.2712750.135638
Happiness_p2.18919951146729e-1800.20610.8369110.418456
Depression-7.28235610420522e-180-1.29930.1950390.09752
Depression_p1.4446555024318e-1701.89680.0590160.029508
Belonging5.80567721635646e-1900.33820.7354880.367744
Belonging_p-7.82099234232271e-190-0.35240.7248330.362416


Multiple Linear Regression - Regression Statistics
Multiple R1
R-squared1
Adjusted R-squared1
F-TEST (value)3.82527696498098e+33
F-TEST (DF numerator)15
F-TEST (DF denominator)248
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation1.66273983278766e-16
Sum Squared Residuals6.85646530381604e-30


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
11313-1.45145152277389e-18
216169.13382281187284e-17
319192.20080812421479e-16
415152.91131368272878e-16
51414-1.83785412959099e-17
613131.47592556469601e-16
71919-2.14814933356497e-17
815157.75199657230604e-17
91414-2.05182447936475e-15
1015159.62410813914866e-17
1116167.85385461039742e-17
1216161.07531583039445e-16
131616-1.29216766437425e-17
1416162.66834699914131e-17
151717-6.4936073361718e-18
1615151.325330699211e-17
1715154.24657846245047e-17
1820201.40677982937323e-16
1918188.79253859218245e-18
201616-2.8626478281246e-17
2116165.82748188361095e-17
2216163.77735641477304e-17
231919-1.52364038465625e-16
2416162.40251547160884e-18
2517173.74148914273145e-17
261717-1.75715879626839e-17
2716163.62099381836029e-17
2815159.0501729656722e-18
2916163.30078187093899e-17
3014141.07678824789097e-16
3115156.37198087735031e-17
3212121.39266515503507e-16
331414-3.95987452853688e-17
3416161.57782939346024e-17
3514143.49108358973607e-17
361010-2.28837617189125e-16
3710101.38298912807948e-16
381414-1.31415026081835e-18
391616-4.50670023380202e-17
401616-3.24048719677377e-17
4116163.15938321313444e-17
421414-1.58644527001878e-17
432020-1.13115475341791e-16
441414-8.4205038314338e-17
451414-3.76555848966257e-17
4611111.71658458255001e-16
4714147.78112582695865e-17
4815153.42530161207263e-17
491616-4.67461078036641e-17
5014141.61871146693924e-16
5116168.35525882758815e-17
521414-4.73561959356755e-18
5312122.04779445057439e-16
5416163.40527870555137e-17
5599-1.48036674294063e-16
5614146.11489634687792e-17
5716163.03583523892933e-17
5816164.97705904859719e-17
5915153.12105550153574e-17
6016161.01009962501312e-17
6112121.69064364291339e-16
6216165.88091682557375e-17
631616-2.0598932823686e-17
641414-6.08273341316093e-18
6516162.87364815093477e-17
6617172.86785999857939e-17
6718187.30435824472102e-17
681818-1.62372801622125e-16
6912122.33527753270681e-16
701616-1.33022756084014e-16
7110102.53162206071888e-16
7214148.52909694737138e-18
7318182.56535306277374e-17
7418181.3729797963058e-16
7516167.42932268971479e-19
761717-1.23894876598315e-16
7716168.4789353821386e-17
7816164.56905779004254e-17
7913131.05946251446967e-16
8016165.21599456906539e-17
8116161.61374974103592e-17
8216165.94642266030468e-17
8315152.19616392678152e-17
8415155.54820539816556e-17
8516168.92658485863697e-18
8614141.75630800855819e-17
8716165.13884139509994e-17
8816162.03781258908467e-17
891515-1.03663657305183e-16
901212-4.2170810208847e-17
9117177.27105744266447e-17
9216163.76135746323378e-17
931515-3.82614885196352e-17
941313-1.40279670152558e-17
951616-3.12035376786387e-17
961616-1.28081722090695e-16
9716165.90476242008081e-17
981616-1.01306612964251e-16
9914142.21439905096732e-17
1001616-7.50898180015081e-17
10116165.36179649950678e-19
1022020-2.37155954962517e-16
1031515-3.8369631508224e-17
1041616-2.67013326189195e-17
1051313-3.67070062470712e-17
10617171.82034306386219e-16
1071616-3.84916675760016e-17
1081616-8.14526971637787e-17
1091212-9.22592492559904e-17
11016167.88197935604034e-17
1111616-6.86183445492531e-17
1121717-1.30380223653069e-17
1131313-5.86477358522615e-17
11412126.04288957434411e-17
1151818-6.05106549949209e-17
1161414-3.79376599438271e-17
1171414-4.47525503114943e-17
11813131.11979000559608e-18
1191616-1.83800595290055e-17
1201313-2.73641060669539e-17
1211616-6.00028728881568e-17
12213138.72923941850241e-17
1231616-8.92486389404245e-17
12415152.10827288571686e-17
1251616-6.39658135889376e-17
12615151.01163166115667e-17
12717179.82231628561124e-18
12815154.96981254429536e-17
1291212-9.90415651722252e-17
1301616-4.68132414647345e-17
1311010-1.74068569794559e-17
1321616-1.10885587182588e-16
13312129.15735735812237e-17
1341414-9.25334759980161e-18
1351515-5.15451391978378e-17
1361313-1.1615213376683e-16
13715157.28997776456746e-17
1381111-1.12448577436544e-16
13912126.25560341237487e-17
1401111-1.02348110850709e-16
14116161.12330964930187e-16
1421515-7.34012793830642e-17
1431717-2.09703061002804e-16
1441616-1.09115174332596e-16
14510105.18345097593176e-16
1461818-1.24025104083988e-16
1471313-3.38556418808434e-17
14816161.58635345205838e-16
1491313-4.00635756829946e-17
15010104.35155502661914e-17
1511515-3.43837688782738e-17
15216167.68108530534051e-17
15316161.34408472380051e-16
1541414-1.16326902664211e-16
15510105.63298345187444e-17
15617173.017028556686e-17
1571313-4.47710386545275e-17
1581515-9.33430813097778e-17
15916161.84316922000909e-16
1601212-1.06075721525982e-17
1611313-9.17217266143978e-17
16213134.56152158099252e-17
1631212-2.5874000376772e-17
1641717-8.10074867061527e-17
1651515-5.58380681886873e-17
16610101.5854474688277e-16
1671414-3.74444173054824e-17
16811113.84621735512178e-17
16913137.62599845374198e-17
1701616-1.17684548579949e-16
1711212-4.350007754772e-17
1721616-1.3640331422257e-17
17312121.29744768217893e-16
17499-9.12804241403528e-17
1751212-4.66862750548388e-17
1761515-9.59800703830095e-17
17712124.22139409726594e-17
1781212-1.52358147313267e-18
1791414-6.35805088406545e-17
18012121.5537334291736e-16
1811616-8.77183982453098e-17
18211113.08450984587646e-17
18319194.14959840735588e-16
1841515-2.62765880050525e-17
18588-1.48793006245311e-16
18616168.76784688049716e-18
1871717-9.58114996116628e-17
18812129.93119219664588e-17
18911112.08866822805811e-17
1901111-9.5186143950854e-17
1911414-1.88166065478576e-17
1921616-2.35361652590574e-17
1931212-7.90565546845695e-18
1941616-7.70005918191211e-17
19513131.98341791193701e-18
1961515-5.14694064145262e-17
1971616-2.35322351437047e-16
19816165.84401552501175e-17
1991414-8.16779411742105e-17
20016166.99425349019296e-17
20116161.03477152566704e-16
20214148.63208681605092e-17
20311111.32879525263642e-16
20412124.30498560151617e-17
2051515-1.55572316767153e-16
20615152.72760470188797e-17
20716164.04492631127119e-17
20816161.07987396690478e-17
20911111.18472859845156e-16
2101515-1.26396416155576e-16
21112123.47324393686826e-17
21212121.47114331754982e-16
2131515-6.35884841715272e-17
21415151.2340877414657e-16
2151616-2.14273631647745e-16
21614141.95346419927467e-16
21717171.49632403006136e-16
2181414-1.31030858249358e-17
2191313-1.08420594899898e-17
22015154.10151998936579e-17
2211313-2.65867152102666e-17
2221414-1.36024061312366e-17
22315152.16863172817602e-17
22412121.39204405548261e-17
22513136.60683085541834e-17
22688-1.78018903032714e-16
22714143.81656199840313e-17
22814142.73411055272852e-18
2291111-6.87003940841005e-17
2301212-9.51662284624673e-17
2311313-5.82078385392791e-17
2321010-1.96810924806742e-16
2331616-2.36104508990807e-16
23418189.73731736612677e-18
23513133.05577261129989e-17
23611113.84827184694763e-17
23744-2.18483378261541e-16
2381313-8.32449428801257e-17
23916168.30388419490023e-17
24010101.08940410707996e-16
2411212-3.5932874020546e-17
24212124.04195641875445e-17
24310102.22482403451848e-17
2441313-1.21089488472482e-17
24515156.11484567379523e-17
24612125.6963162837555e-17
24714141.09173001732896e-16
24810101.02455589497642e-16
2491212-7.64051349140271e-17
25012126.26015063115869e-17
2511111-5.146819756764e-17
25210105.77712485380279e-17
25312129.78075005028212e-18
2541616-7.57701718367407e-17
25512123.71942887391307e-17
2561414-1.09480875236225e-17
25716162.18670411167949e-16
2581414-1.18134024224867e-16
25913137.48003792223316e-18
26044-3.52537230481938e-17
26115151.09714250069526e-16
2621111-4.23899059927633e-17
26311112.62897215568266e-17
2641414-9.99001456225595e-17


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
190.402288345890820.8045766917816410.597711654109179
200.5553196119182050.889360776163590.444680388081795
210.2194065744885510.4388131489771020.780593425511449
220.9210692100279430.1578615799441150.0789307899720573
230.9844252019493610.03114959610127810.015574798050639
240.9803355765788190.03932884684236280.0196644234211814
250.91498961248970.1700207750205990.0850103875102996
260.0003249937439700010.0006499874879400020.99967500625603
270.01216195050251990.02432390100503970.98783804949748
2813.71711121170752e-201.85855560585376e-20
290.9299524074178360.1400951851643280.0700475925821639
300.008188830437872450.01637766087574490.991811169562128
310.9836950655178230.03260986896435460.0163049344821773
320.227775462286060.4555509245721190.772224537713941
330.9999999958369728.32605643792285e-094.16302821896143e-09
348.45639605661226e-091.69127921132245e-080.999999991543604
350.7929277735966070.4141444528067860.207072226403393
360.07506219553691290.1501243910738260.924937804463087
379.97515352223561e-071.99503070444712e-060.999999002484648
380.3008170599855050.6016341199710110.699182940014495
390.9522187818431880.09556243631362330.0477812181568116
403.34542976825003e-096.69085953650006e-090.99999999665457
415.1622663195582e-061.03245326391164e-050.99999483773368
420.9999999999999976.21058167798393e-153.10529083899196e-15
430.9999999993079311.384138672244e-096.92069336122e-10
440.5599278736423940.8801442527152120.440072126357606
450.9987770520902950.002445895819409940.00122294790970497
460.9996983310915230.000603337816954060.00030166890847703
470.067979258402330.135958516804660.93202074159767
480.9999999980719323.85613524211471e-091.92806762105735e-09
4916.66466807386733e-383.33233403693366e-38
500.9744669403474590.05106611930508180.0255330596525409
519.39779328489027e-091.87955865697805e-080.999999990602207
520.9541131445521370.09177371089572610.0458868554478631
531.32036612928931e-062.64073225857862e-060.999998679633871
540.2245981518667970.4491963037335940.775401848133203
550.9999999999999725.58405117295423e-142.79202558647712e-14
560.003435965875617690.006871931751235370.996564034124382
570.9995640440229120.0008719119541752420.000435955977087621
580.6056303994652220.7887392010695560.394369600534778
590.9959327138127510.008134572374497210.0040672861872486
604.90330117263184e-059.80660234526368e-050.999950966988274
6112.83223115071108e-331.41611557535554e-33
620.9999979601036974.07979260668682e-062.03989630334341e-06
6313.5028916671508e-191.7514458335754e-19
647.06709236608769e-141.41341847321754e-130.999999999999929
651.54773334266328e-103.09546668532656e-100.999999999845227
662.47264810314444e-244.94529620628889e-241
670.6986658045693960.6026683908612070.301334195430604
681.15861258576554e-052.31722517153109e-050.999988413874142
698.37622982836868e-141.67524596567374e-130.999999999999916
703.74178160002837e-117.48356320005673e-110.999999999962582
711.70205694153655e-173.4041138830731e-171
720.9999960875941787.82481164389571e-063.91240582194785e-06
730.000364110925979730.000728221851959460.99963588907402
740.9999999977127964.57440743687688e-092.28720371843844e-09
750.4660774750989990.9321549501979980.533922524901001
760.9996583524832150.0006832950335691560.000341647516784578
770.9998606550868870.0002786898262250160.000139344913112508
782.6833313665706e-235.3666627331412e-231
790.08275274271516010.165505485430320.91724725728484
800.0001294397225945220.0002588794451890440.999870560277406
811.17551959287488e-132.35103918574977e-130.999999999999882
820.8281718698189040.3436562603621910.171828130181096
830.9999999994759361.04812780928e-095.24063904640001e-10
840.001350186761394020.002700373522788050.998649813238606
850.8230703578558320.3538592842883360.176929642144168
865.27606702574724e-091.05521340514945e-080.999999994723933
876.63648623371417e-091.32729724674283e-080.999999993363514
880.9999758175905794.83648188416528e-052.41824094208264e-05
891.97353094268119e-053.94706188536238e-050.999980264690573
900.47577272021990.95154544043980.5242272797801
913.24697087922979e-076.49394175845957e-070.999999675302912
921.30716268965404e-072.61432537930809e-070.999999869283731
930.999718274572370.0005634508552606680.000281725427630334
942.24332243514111e-124.48664487028222e-120.999999999997757
950.2987844753815490.5975689507630980.701215524618451
960.103424687022210.206849374044420.89657531297779
970.08045869448956230.1609173889791250.919541305510438
980.9999999998984522.03096663603641e-101.0154833180182e-10
991.99563483359068e-083.99126966718135e-080.999999980043652
1000.9994787170362580.001042565927484310.000521282963742157
1010.01944797991608290.03889595983216590.980552020083917
1025.63957045055609e-321.12791409011122e-311
1030.9999999996265697.46860964247596e-103.73430482123798e-10
1040.9999999998974222.05156872163919e-101.0257843608196e-10
1050.04541579916701180.09083159833402360.954584200832988
1060.05139166611389370.1027833322277870.948608333886106
1070.999999909254881.81490239874159e-079.07451199370795e-08
1082.46092768054643e-094.92185536109285e-090.999999997539072
1090.9557675193713030.08846496125739360.0442324806286968
1108.85430035815885e-381.77086007163177e-371
1110.9100433430807150.1799133138385710.0899566569192854
1124.02264989991461e-098.04529979982922e-090.99999999597735
1130.9999500357734049.99284531911442e-054.99642265955721e-05
1143.85943207318273e-087.71886414636545e-080.999999961405679
1151.10343223125912e-072.20686446251824e-070.999999889656777
1160.8550715126435740.2898569747128530.144928487356426
1177.5214567813668e-211.50429135627336e-201
1180.0008819455150194170.001763891030038830.999118054484981
11913.64858735516655e-201.82429367758327e-20
1209.05887699030417e-091.81177539806083e-080.999999990941123
1210.9999999999706495.87009379933526e-112.93504689966763e-11
1229.01155161647999e-151.802310323296e-140.999999999999991
1230.9993037655884470.001392468823106250.000696234411553123
1244.88723627929409e-319.77447255858819e-311
12512.2312844893789e-171.11564224468945e-17
12611.97226843654285e-219.86134218271423e-22
1270.006847395636398310.01369479127279660.993152604363602
1280.6700776665920130.6598446668159750.329922333407987
1291.63603678227241e-403.27207356454482e-401
1303.99713952509614e-287.99427905019229e-281
1312.0236859850622e-284.0473719701244e-281
1323.02869668027751e-236.05739336055501e-231
1336.12535841654327e-261.22507168330865e-251
1342.54561479658834e-085.09122959317668e-080.999999974543852
1350.000602938004128160.001205876008256320.999397061995872
1360.007511147186289360.01502229437257870.992488852813711
1370.999999999999617.79626476979923e-133.89813238489962e-13
1380.9999999999099381.80124089413312e-109.00620447066562e-11
1399.2821992267036e-151.85643984534072e-140.999999999999991
1401.0376847598637e-072.0753695197274e-070.999999896231524
1410.9372306177559440.1255387644881120.0627693822440561
1420.6387847706656380.7224304586687240.361215229334362
1430.2315698916610290.4631397833220590.768430108338971
1440.9660219072513660.06795618549726810.0339780927486341
1450.2799549036535760.5599098073071520.720045096346424
1461.6576029868166e-423.31520597363319e-421
1470.0387969682574010.0775939365148020.961203031742599
1482.02515261138506e-214.05030522277012e-211
1490.9999999999999141.72058702809162e-138.60293514045811e-14
1500.7493703559277590.5012592881444820.250629644072241
1510.9999999999999911.72811274358611e-148.64056371793056e-15
1520.0002053944455700460.0004107888911400930.99979460555443
1533.25535806263963e-486.51071612527927e-481
1540.9858552038415010.02828959231699790.0141447961584989
1552.58142915431639e-115.16285830863278e-110.999999999974186
15611.49023420917783e-267.45117104588917e-27
15714.68225982959741e-172.3411299147987e-17
1580.9785261208078120.04294775838437670.0214738791921884
15914.01763313027514e-312.00881656513757e-31
1600.0002131433999440630.0004262867998881270.999786856600056
1615.9550520689763e-161.19101041379526e-150.999999999999999
1621.64688767434609e-133.29377534869217e-130.999999999999835
1636.70017643553115e-171.34003528710623e-161
1643.83843035710517e-137.67686071421033e-130.999999999999616
1651.51994022412039e-173.03988044824078e-171
1661.28016620446872e-252.56033240893743e-251
1670.5930881287413840.8138237425172310.406911871258616
1682.60321712083954e-135.20643424167908e-130.99999999999974
1693.23001622025456e-426.46003244050912e-421
1700.9999999868479562.63040877600586e-081.31520438800293e-08
1712.53986103914762e-295.07972207829524e-291
1723.47918468813283e-356.95836937626566e-351
1730.9999999999999853.07955141578191e-141.53977570789096e-14
1748.21141488423181e-901.64228297684636e-891
1756.25132849804714e-281.25026569960943e-271
1767.43628455566725e-161.48725691113345e-150.999999999999999
1770.003269021103849980.006538042207699950.99673097889615
1783.59699468959486e-107.19398937918973e-100.999999999640301
17912.36600663296867e-231.18300331648434e-23
1800.01915439653316480.03830879306632950.980845603466835
18111.41303783616803e-207.06518918084016e-21
1825.76088519119062e-241.15217703823812e-231
1830.9999999999897632.04733734391415e-111.02366867195708e-11
1842.3562239951615e-324.712447990323e-321
1858.91516987275113e-191.78303397455023e-181
1860.1428478189700430.2856956379400870.857152181029957
1870.001638024533459960.003276049066919930.99836197546654
1885.57689119998738e-651.11537823999748e-641
1890.1629097926412980.3258195852825970.837090207358702
1901.21709975568818e-092.43419951137637e-090.9999999987829
1913.45217498786514e-076.90434997573029e-070.999999654782501
1921.46107455685421e-092.92214911370842e-090.999999998538925
1931.25699173002184e-262.51398346004368e-261
1940.09830682372185650.1966136474437130.901693176278143
1950.9999960911901047.81761979149998e-063.90880989574999e-06
19613.37701604961216e-201.68850802480608e-20
1970.8968380595500960.2063238808998080.103161940449904
1980.01659040942303840.03318081884607670.983409590576962
1990.03196883379594310.06393766759188620.968031166204057
2000.9999536822056259.26355887509922e-054.63177943754961e-05
2010.9999999999999991.20903618697438e-156.04518093487192e-16
2020.9997448798252460.0005102403495084260.000255120174754213
2030.001217885342805330.002435770685610660.998782114657195
2040.2583257249720980.5166514499441960.741674275027902
2050.5667517040373630.8664965919252750.433248295962637
2060.7264526047691420.5470947904617160.273547395230858
2072.52712265688843e-145.05424531377686e-140.999999999999975
2080.9489062142579640.1021875714840710.0510937857420357
2091.87573600738136e-073.75147201476272e-070.999999812426399
2106.02441862742376e-511.20488372548475e-501
2110.9999998642509612.71498078699179e-071.3574903934959e-07
2121.11676956350019e-132.23353912700038e-130.999999999999888
2130.0312606735458190.06252134709163790.968739326454181
2140.9999695973578616.08052842772823e-053.04026421386412e-05
2150.9951930251530.009613949693999110.00480697484699956
2162.09201122846258e-174.18402245692516e-171
2170.1028641334233680.2057282668467360.897135866576632
2181.68882768614764e-143.37765537229527e-140.999999999999983
2190.9989539675600970.002092064879806520.00104603243990326
2200.9873900627919420.02521987441611530.0126099372080577
2210.004965420067442350.00993084013488470.995034579932558
2228.64022300649583e-071.72804460129917e-060.999999135977699
2230.2322668472402110.4645336944804220.767733152759789
2244.59472394006803e-289.18944788013606e-281
2251.73842839198542e-053.47685678397084e-050.99998261571608
2260.9999996039193667.92161267158628e-073.96080633579314e-07
2272.02349653777178e-754.04699307554356e-751
2280.01799357239539220.03598714479078440.982006427604608
2290.9594394331303660.08112113373926810.0405605668696341
2300.01006704706729590.02013409413459180.989932952932704
2310.7244755472250720.5510489055498550.275524452774928
2320.9999792855514994.14288970020791e-052.07144485010396e-05
2333.20392018702718e-076.40784037405437e-070.999999679607981
2340.03348710860785330.06697421721570660.966512891392147
2359.32318339285568e-381.86463667857114e-371
2361.76160151408192e-363.52320302816383e-361
2370.08048616131855670.1609723226371130.919513838681443
2386.96810822832765e-211.39362164566553e-201
2390.0719695893901230.1439391787802460.928030410609877
2404.67178843092058e-069.34357686184117e-060.999995328211569
2412.90490447052788e-085.80980894105576e-080.999999970950955
2420.001735040479231990.003470080958463970.998264959520768
2430.940908445235620.118183109528760.0590915547643798
2445.0907906434921e-281.01815812869842e-271
2450.009007921825806910.01801584365161380.990992078174193


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level1530.674008810572687NOK
5% type I error level1690.744493392070485NOK
10% type I error level1800.79295154185022NOK