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*The author of this computation has been verified*
R Software Module: /rwasp_multipleregression.wasp (opens new window with default values)
Title produced by software: Multiple Regression
Date of computation: Wed, 01 Dec 2010 14:28:58 +0000
 
Cite this page as follows:
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/01/t129121369244vhdhf5dolj7j9.htm/, Retrieved Wed, 01 Dec 2010 15:28:24 +0100
 
BibTeX entries for LaTeX users:
@Manual{KEY,
    author = {{YOUR NAME}},
    publisher = {Office for Research Development and Education},
    title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2010/Dec/01/t129121369244vhdhf5dolj7j9.htm/},
    year = {2010},
}
@Manual{R,
    title = {R: A Language and Environment for Statistical Computing},
    author = {{R Development Core Team}},
    organization = {R Foundation for Statistical Computing},
    address = {Vienna, Austria},
    year = {2010},
    note = {{ISBN} 3-900051-07-0},
    url = {http://www.R-project.org},
}
 
Original text written by user:
 
IsPrivate?
No (this computation is public)
 
User-defined keywords:
 
Dataseries X:
» Textbox « » Textfile « » CSV «
162556 807 213118 6282154 29790 444 81767 4321023 87550 412 153198 4111912 84738 428 -26007 223193 54660 315 126942 1491348 42634 168 157214 1629616 40949 263 129352 1398893 45187 267 234817 1926517 37704 228 60448 983660 16275 129 47818 1443586 25830 104 245546 1073089 12679 122 48020 984885 18014 393 -1710 1405225 43556 190 32648 227132 24811 280 95350 929118 6575 63 151352 1071292 7123 102 288170 638830 21950 265 114337 856956 37597 234 37884 992426 17821 277 122844 444477 12988 73 82340 857217 22330 67 79801 711969 13326 103 165548 702380 16189 290 116384 358589 7146 83 134028 297978 15824 56 63838 585715 27664 236 74996 657954 11920 73 31080 209458 8568 34 32168 786690 14416 139 49857 439798 3369 26 87161 688779 11819 70 106113 574339 6984 40 80570 741409 4519 42 102129 597793 2220 12 301670 644190 18562 211 102313 377934 10327 74 88577 640273 5336 80 112477 697458 2365 83 191778 550608 4069 131 79804 207393 8636 203 128294 301607 13718 56 96448 345783 4525 89 93 etc...
 
Output produced by software:

Enter (or paste) a matrix (table) containing all data (time) series. Every column represents a different variable and must be delimited by a space or Tab. Every row represents a period in time (or category) and must be delimited by hard returns. The easiest way to enter data is to copy and paste a block of spreadsheet cells. Please, do not use commas or spaces to seperate groups of digits!


Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time27 seconds
R Server'George Udny Yule' @ 72.249.76.132


Multiple Linear Regression - Estimated Regression Equation
1[t] = -3391.17858864606 + 105.872732288592`2`[t] -0.0129238160950211`3`[t] + 0.00883702507798882`4`[t] + 3.86197934402415t + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0		2-tail p-value1-tail p-value
(Intercept)-3391.17858864606954.239242-3.55380.0004220.000211
`2`105.8727322885925.25080520.163100
`3`-0.01292381609502110.008774-1.47290.141520.07076
`4`0.008837025077988820.00087310.122300
t3.861979344024152.3017961.67780.0941170.047059


Multiple Linear Regression - Regression Statistics
Multiple R0.903346438799689
R-squared0.81603478849208
Adjusted R-squared0.814307415614072
F-TEST (value)472.413801838101
F-TEST (DF numerator)4
F-TEST (DF denominator)426
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation5093.25888789658
Sum Squared Residuals11050987878.2326


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast		Residuals
Prediction Error
1162556134813.23295084127742.7670491594
22979080752.2854491019-50962.2854491019
38755074597.139736644312952.8602633557
48473844246.270571662140491.7294283379
55466041516.546592254813143.4534077452
64263426787.764947830715846.2350521693
74094935170.71492156175778.28507843833
84518738897.68408534756289.31591465253
93770428693.97144015189010.02855984822
101627522444.0383162244-6169.0383162244
112583013971.590399197711858.4096008023
121267917654.4902977426-4975.49029774255
131801450707.1192229822-32693.1192229822
144355618363.942689146325192.0573108537
152481133289.4693440706-8478.46934407064
16657510851.5840712748-4276.5840712748
1771239394.59440010815-2271.59440010815
182195030829.8823978998-8879.88239789984
193759729736.90597552537860.09402447472
201782128353.0489733869-10532.0489733869
211298810929.73354366002058.26645634003
22223309047.6124798099813282.3875201900
231332611669.97612937071656.02387062927
241618929069.3358525902-12880.3358525902
2571466393.89351001315752.106489986849
26158246989.053454139988834.94654586002
272766426544.18116005121119.81883994883
28119205894.979684605946025.02031539406
2985686856.757652601141711.24234739886
301441614683.1538359888-267.153835988804
3133694441.538372056-1072.53837205600
32118197847.55925954023971.4407404598
3369846481.75408452118502.245915478825
3445195149.59878364938-630.598783649385
352220-191.5409405374672411.54094053747
361856221104.5370203265-2542.53702032647
37103279099.652535949091227.34746405091
3853369935.21698343846-4599.21698343846
3923657934.10848679435-5569.10848679435
40406911433.9934372727-7364.99343727273
41863619266.5877796455-10630.5877796455
42137184509.114379773729208.88562022628
4345259419.13208099745-4894.13208099745
4468697934.66137660965-1065.66137660965
4546283441.975135868261186.02486413174
4636891452.003427500032236.99657249997
4748912533.852084013842357.14791598616
48748914606.2960683665-7117.29606836654
4949015508.51553690459-607.515536904591
5022841874.02359977279409.976400227208
5131609626.88538503357-6466.88538503357
52415014047.5398998944-9897.53989989445
5372858983.85836315689-1698.85836315689
5411346254.97952958969-5120.97952958969
5546588932.60662872239-4274.60662872239
5623847772.02711600479-5388.02711600479
5737482583.391086356391164.60891364361
5853714618.33528009038752.664719909623
5912853966.8401400127-2681.84014001270
6093278136.041123026241190.95887697376
6155654537.761841783461027.23815821654
621528751.120585945018776.879414054982
6331221938.057835400011183.94216459999
6475617162.30651797259398.693482027411
6526754952.96965096952-2277.96965096952
661325325425.4446523027-12172.4446523027
67880-280.0906716284961160.09067162850
6820533741.55933130812-1688.55933130812
6914246222.8690658604-4798.8690658604
7040368337.31837552158-4301.31837552158
7130453503.14303517675-458.143035176745
7251193750.549812202351368.45018779765
7314311961.19405968852-530.19405968852
74554-298.647410830782852.647410830782
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761765199.8765262956991565.1234737043
7710121745.97704827555-733.977048275554
78810-789.6374984209541599.63749842095
7912804282.03919330997-3002.03919330997
80666-226.052746273067892.052746273067
8113802273.68077819962-893.68077819962
8246776515.31463039572-1838.31463039572
838761745.27451465866-869.274514658662
84814676.94241538396137.057584616040
85514533.699990905852-19.6999909058520
8656926467.65951310254-775.659513102544
87364210415.9459400951-6773.94594009508
88540111.782911467186428.217088532814
8920993066.41364022259-967.413640222591
90567515.9711594366651.0288405633401
9120013012.77829760544-1011.77829760544
9229493472.50320206677-523.503202066771
9322537343.94694905428-5090.94694905428
9465331626.086597870624906.91340212938
9518894212.63509804343-2323.63509804343
9630552705.51821116006349.481788839945
97272268.0349039306383.96509606936206
9814141330.4936800332583.5063199667511
992564887.1036937627041676.89630623730
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10112612014.88533597403-753.88533597403
102975-77.84333075625161052.84333075625
10333664072.0608089018-706.0608089018
104576-837.3061440253281413.30614402533
10516862344.62019145786-658.620191457862
1067461546.66027416939-800.660274169394
10731922438.77408476474753.225915235263
10820451969.0194082737475.9805917262602
10957023538.876820781852163.12317921815
1101932416.6045985115051515.39540148850
1119362101.96173812314-1165.96173812314
11234371315.133545553662121.86645444634
11351313172.514794803091958.48520519691
114239727.24535037469202369.75464962531
1151389285.5067834102851103.49321658972
11615033069.13633041819-1566.13633041819
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123158510883.1756247143-9298.17562471425
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149271-514.49874550819785.49874550819
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184378712.76203259428-334.76203259428
18523-173.849547681346196.849547681346
186638656.123973097158-18.1239730971579
18723002039.26489595224260.735104047759
188149-62.7738108527951211.773810852795
189226-403.04808391859629.04808391859
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1940-639.66774009896639.66774009896
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1960-631.943781410912631.943781410912
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1980-624.219822722864624.219822722864
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200472740.659414015815-268.659414015815
2010-612.633884690791612.633884690791
2020-608.771905346767608.771905346767
2030-604.909926002743604.909926002743
204203670.165173628171-467.165173628171
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20763-413.69660431043476.69660431043
2080-585.600029282623585.600029282623
20911362578.09342731872-1442.09342731872
210265-334.771669186399599.771669186399
2110-574.01409125055574.01409125055
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213267767.833967304474-500.833967304474
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2171585.6814386826218-70.6814386826218
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2190-331.372791921172331.372791921172
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221288-380.526557124839668.526557124839
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2233-421.743045531604424.743045531604
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22520-413.440115598409433.440115598409
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229192-378.50729787201570.50729787201
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3420-68.094797183387568.0947971833875
3430-64.232817839363664.2328178393636
3440-60.370838495339760.3708384953397
3456211256.88169394479-635.881693944791
3460-52.64687980729152.646879807291
347119186.117545299031-67.1175452990306
3480-44.922921119243344.9229211192433
3490-41.060941775218541.0609417752185
35015951056.77925349082538.220746509175
351312340.956104540384-28.9561045403843
35260694.650820195808-634.650820195808
3535871138.84285337347-551.842853373465
35413556.399835244446278.6001647555538
3550-17.889065711074217.8890657110742
3560-14.027086367050314.0270863670503
3575141406.36326012554-892.363260125545
3580-6.303127679001596.30312767900159
3590-2.441148334977702.44114833497770
36001.42083100904620-1.42083100904620
3611428.906958326655-427.906958326655
36209.1447896970949-9.1447896970949
363013.0067690411188-13.0067690411188
36417632907.68428965275-1144.68428965275
365180996.497706018052-816.497706018052
366024.5927070731914-24.5927070731914
367028.4546864172153-28.4546864172153
368032.3166657612401-32.3166657612401
369036.178645105264-36.178645105264
370218782.678555807925-564.678555807925
371043.9026037933118-43.9026037933118
372448871.537469618135-423.537469618135
373227774.803157137359-547.803157137359
374174249.811721181098-75.8117211810982
375059.3505211694091-59.3505211694091
376063.212500513433-63.212500513433
3771211113.545635925-992.545635925
378607877.221643535415-270.221643535415
37922121173.150981881131038.84901811887
380078.6604178895295-78.6604178895295
381082.5223972335534-82.5223972335534
3825301844.68063868027-1314.68063868027
3835711512.02078980017-941.020789800174
384094.108335265626-94.108335265626
385781360.08614510669-1282.08614510669
38624892397.8848447056991.1151552943088
387131540.312451594871-409.312451594871
388923715.888247128215207.111752871785
38972424.858578292874-352.858578292874
390572926.083199250837-354.083199250837
3913971215.54193274741-818.541932747414
392450572.861476289156-122.861476289156
393622512.431175305197109.568824694803
3946941135.05919825183-441.059198251834
3953425515.3881308669352909.61186913306
396562735.737927037281-173.737927037281
39749172365.339758892722551.66024110728
398144225758.4282770896-24316.4282770896
399529683.482048280749-154.482048280749
40021264260.98567149517-2134.98567149517
4011061253.745368870727807.254631129273
4027761125.41430681182-349.414306811823
403611659.355455194269-48.3554551942689
40415261961.55050090240-435.550500902405
405592530.37308132178861.6269186782124
40611821317.51788485871-135.517884858709
4076211268.10639888040-647.106398880397
4089891384.74146132617-395.74146132617
4094381021.79042664365-583.79042664365
410726-345.5960394524111071.59603945241
41113036062.31407203259-4759.31407203259
41274192141.687519516655277.31248048335
41311641434.93075206088-270.930752060882
41433104584.48424021938-1274.48424021938
4151920-188.5872839684552108.58728396846
416965-716.9958127178821681.99581271788
41732563796.84941682896-540.84941682896
41811352102.56723400335-967.567234003349
41912702306.4609260004-1036.4609260004
420661-336.523489098692997.523489098692
4211013-321.204129005271334.20412900527
42228447262.62998886578-4418.62998886578
423115284893.946481483726634.05351851628
4246526-730.2001014547137256.20010145471
42522642064.53026920289199.469730797105
42651097972.36127104056-2863.36127104056
4273999196.6607169949743802.33928300503
4283562424768.623156981010855.3768430190
42992522866.478192658166385.52180734184
430152369666.656679540855569.34332045915
431180735162.5781683954412910.4218316046


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
811.71075369330065e-258.55376846650326e-26
916.65416218898276e-363.32708109449138e-36
1018.69259080806658e-384.34629540403329e-38
1112.08590613500832e-391.04295306750416e-39
1211.36221272352972e-386.8110636176486e-39
1311.39768124033521e-556.98840620167605e-56
1412.29520069022906e-781.14760034511453e-78
1513.31776783580989e-791.65888391790495e-79
1612.2762758732359e-791.13813793661795e-79
1712.03683996329001e-811.01841998164500e-81
1811.02941323699276e-805.14706618496378e-81
1914.01420163373768e-922.00710081686884e-92
2014.59767537538771e-932.29883768769385e-93
2112.93777994310743e-981.46888997155371e-98
2216.77510752593266e-1123.38755376296633e-112
2312.75499426433101e-1121.37749713216550e-112
2418.04676329947166e-1144.02338164973583e-114
2511.67668804264253e-1138.38344021321265e-114
2611.10103186060233e-1205.50515930301165e-121
2713.54734330836972e-1241.77367165418486e-124
2811.36257347597617e-1266.81286737988084e-127
2911.51088223974341e-1287.55441119871706e-129
3015.40104790102132e-1292.70052395051066e-129
3111.50644825597067e-1287.53224127985335e-129
3219.51944031249053e-1314.75972015624526e-131
3318.0603142973503e-1324.03015714867515e-132
3412.02481067625512e-1311.01240533812756e-131
3511.33000140189837e-1306.65000700949187e-131
3616.62815428236406e-1313.31407714118203e-131
3715.14043538719526e-1332.57021769359763e-133
3811.51033404044185e-1327.55167020220924e-133
3914.87018002710353e-1322.43509001355176e-132
4011.85005755973265e-1329.25028779866323e-133
4112.27221546025801e-1331.13610773012901e-133
4211.71704339260647e-1398.58521696303237e-140
4311.35352581272360e-1386.76762906361798e-139
4416.8276905726677e-1383.41384528633385e-138
4517.03982473730426e-1383.51991236865213e-138
4611.01102698077854e-1375.05513490389272e-138
4715.01024389983059e-1372.50512194991529e-137
4811.97864862110092e-1369.8932431055046e-137
4916.2356956379245e-1363.11784781896225e-136
5012.27719601033147e-1351.13859800516574e-135
5111.41809772790906e-1347.09048863954528e-135
5211.29809425528781e-1346.49047127643906e-135
5316.9805349421606e-1343.4902674710803e-134
5413.26318598872557e-1331.63159299436279e-133
5511.52439552748792e-1337.62197763743962e-134
5617.38787436223115e-1333.69393718111557e-133
5718.62667683866604e-1364.31333841933302e-136
5814.4487294303251e-1362.22436471516255e-136
5911.41838084774040e-1357.09190423870199e-136
6013.25000205681327e-1361.62500102840663e-136
6115.0292960444031e-1372.51464802220155e-137
6218.90779980124935e-1374.45389990062468e-137
6311.34469718623461e-1366.72348593117306e-137
6411.51383306030867e-1367.56916530154333e-137
6519.37430983295745e-1364.68715491647873e-136
6616.0393028360724e-1363.0196514180362e-136
6711.94932491438896e-1359.74662457194478e-136
6811.10767315430347e-1345.53836577151735e-135
6919.43803980596961e-1354.71901990298481e-135
7015.8089940085048e-1342.9044970042524e-134
7112.42883272254701e-1331.21441636127351e-133
7214.72188111132785e-1342.36094055566393e-134
7311.51980714567322e-1337.59903572836608e-134
7416.11689834150925e-1333.05844917075462e-133
7513.08255011428445e-1321.54127505714222e-132
7611.09541069932975e-1315.47705349664873e-132
7714.73258198660654e-1312.36629099330327e-131
7811.56672157654763e-1307.83360788273813e-131
7915.3130579017876e-1302.6565289508938e-130
8011.97474292994672e-1299.87371464973362e-130
8111.05568980174153e-1285.27844900870765e-129
8214.54385620225638e-1282.27192810112819e-128
8317.9758494461618e-1283.9879247230809e-128
8413.55034372780543e-1271.77517186390272e-127
8511.71231117787771e-1268.56155588938857e-127
8614.69157056840922e-1262.34578528420461e-126
8711.91498095411519e-1259.57490477057596e-126
8818.06345792093117e-1254.03172896046558e-125
8912.12188437857299e-1241.06094218928649e-124
9011.00742401380613e-1235.03712006903067e-124
9115.4177548518769e-1232.70887742593845e-123
9212.50528100132930e-1221.25264050066465e-122
9311.37779378835316e-1216.88896894176581e-122
9415.90878347780494e-1222.95439173890247e-122
9512.93563972243172e-1211.46781986121586e-121
9615.65176746025193e-1212.82588373012597e-121
9712.81955154550383e-1201.40977577275191e-120
9811.36238039372514e-1196.81190196862572e-120
9915.38962339330832e-1192.69481169665416e-119
10012.06297278149793e-1181.03148639074896e-118
10119.5475143713792e-1184.7737571856896e-118
10212.2005851211866e-1171.1002925605933e-117
10317.04289602729969e-1173.52144801364984e-117
10412.02485061596496e-1161.01242530798248e-116
10519.56783600352018e-1164.78391800176009e-116
10612.87903489975512e-1151.43951744987756e-115
10714.17427106324052e-1152.08713553162026e-115
10814.32266296717006e-1152.16133148358503e-115
10911.38105482934973e-1146.90527414674864e-115
11015.70001930338959e-1142.85000965169480e-114
11112.34325960486908e-1131.17162980243454e-113
11218.90222316667521e-1134.45111158333760e-113
11313.28300016091106e-1121.64150008045553e-112
11411.23609491644960e-1116.18047458224801e-112
11512.09696871543649e-1111.04848435771825e-111
11611.07510502655884e-1105.37552513279418e-111
11715.10180042553442e-1102.55090021276721e-110
11817.90380614945083e-1103.95190307472541e-110
11912.84098985833378e-1091.42049492916689e-109
12011.43917260340454e-1087.19586301702268e-109
12114.72183380983624e-1092.36091690491812e-109
12212.17895893116689e-1081.08947946558345e-108
12314.47176193521763e-1102.23588096760881e-110
12411.3482008487217e-1096.7410042436085e-110
12512.30690579252041e-1091.15345289626020e-109
12619.25538352207022e-1094.62769176103511e-109
12714.31884896399319e-1082.15942448199659e-108
12812.14671283927677e-1071.07335641963839e-107
12911.04278213197992e-1065.21391065989958e-107
13014.8188996083168e-1062.4094498041584e-106
13112.35109980801370e-1051.17554990400685e-105
13218.07253408610446e-1054.03626704305223e-105
13313.69060759231543e-1041.84530379615771e-104
13411.61703711135888e-1038.08518555679439e-104
13516.89035218688408e-1033.44517609344204e-103
13613.11931611753586e-1021.55965805876793e-102
13711.49761732746609e-1017.48808663733044e-102
13816.82409715541069e-1013.41204857770534e-101
13912.62552941840527e-1001.31276470920264e-100
14011.17461826166418e-995.87309130832089e-100
14115.24878191033206e-992.62439095516603e-99
14212.33025091509821e-981.16512545754910e-98
14311.02258618292287e-975.11293091461433e-98
14414.66855823696054e-972.33427911848027e-97
14512.1678085596241e-961.08390427981205e-96
14619.84362702964409e-964.92181351482204e-96
14714.28186950487171e-952.14093475243586e-95
14811.94990983253464e-949.74954916267322e-95
14917.94921470262818e-943.97460735131409e-94
15013.40858745986111e-931.70429372993056e-93
15111.50294444091096e-927.5147222045548e-93
15215.72128633341256e-922.86064316670628e-92
15312.53052796818909e-911.26526398409455e-91
15411.10183494154625e-905.50917470773124e-91
15514.72965114713811e-902.36482557356906e-90
15611.98424268236339e-899.92121341181695e-90
15718.2896930126903e-894.14484650634515e-89
15813.48540459775242e-881.74270229887621e-88
15911.32582910437026e-876.6291455218513e-88
16015.4638021763481e-872.73190108817405e-87
16112.24175606805356e-861.12087803402678e-86
16219.15685404272928e-864.57842702136464e-86
16313.72347462474617e-851.86173731237308e-85
16411.54153586719157e-847.70767933595787e-85
16515.6720446406403e-842.83602232032015e-84
16612.29107159490914e-831.14553579745457e-83
16719.16707444814624e-834.58353722407312e-83
16812.26246155702969e-821.13123077851484e-82
16915.2454707459865e-822.62273537299325e-82
17012.06405976002663e-811.03202988001332e-81
17118.08425930143795e-814.04212965071897e-81
17213.25479906325640e-801.62739953162820e-80
17311.26322528388294e-796.31612641941468e-80
17415.1225296164379e-792.56126480821895e-79
17511.97057819049319e-789.85289095246593e-79
17617.88855762956559e-783.94427881478279e-78
17712.74189734046045e-801.37094867023023e-80
17811.06527567662869e-795.32637838314344e-80
17914.17443884058398e-792.08721942029199e-79
18011.62853663230065e-788.14268316150323e-79
18116.27947073364692e-783.13973536682346e-78
18212.51742753406820e-771.25871376703410e-77
18318.09977310079056e-774.04988655039528e-77
18412.87221397342119e-761.43610698671059e-76
18511.13885245685808e-755.6942622842904e-76
18614.23137212976614e-752.11568606488307e-75
18711.12435914050525e-745.62179570252626e-75
18814.39452598615993e-742.19726299307997e-74
18911.69044294891886e-738.45221474459428e-74
19016.3113446219971e-733.15567231099855e-73
19112.39371096975624e-721.19685548487812e-72
19218.8530659813574e-724.4265329906787e-72
19313.39013633850436e-711.69506816925218e-71
19411.24255683912431e-706.21278419562153e-71
19514.64371472132498e-702.32185736066249e-70
19611.68619651700348e-698.4309825850174e-70
19715.22029340735522e-692.61014670367761e-69
19811.87952814003108e-689.39764070015539e-69
19916.73522317066302e-683.36761158533151e-68
20011.60005405410997e-678.00027027054983e-68
20115.72302875972611e-672.86151437986305e-67
20212.03735536973605e-661.01867768486802e-66
20317.21848176095664e-663.60924088047832e-66
20412.64347729271051e-651.32173864635525e-65
20519.2231630827692e-654.6115815413846e-65
20613.3378833717864e-641.6689416858932e-64
20711.18773784329469e-635.93868921647343e-64
20814.12434926128662e-632.06217463064331e-63
20911.34135263203372e-626.70676316016861e-63
21014.66511887845526e-622.33255943922763e-62
21111.59564572274713e-617.97822861373565e-62
21215.43137135541609e-612.71568567770805e-61
21311.86601354054305e-609.33006770271525e-61
21416.46408064099808e-603.23204032049904e-60
21512.19356980726704e-591.09678490363352e-59
21617.45924762806057e-593.72962381403028e-59
21712.56979903797009e-581.28489951898505e-58
21818.58612351155124e-584.29306175577562e-58
21912.87869638042523e-571.43934819021261e-57
22019.1649018464153e-574.58245092320765e-57
22113.06473009433012e-561.53236504716506e-56
22219.95731774293666e-564.97865887146833e-56
22313.24703102985209e-551.62351551492604e-55
22411.05754841338839e-545.28774206694197e-55
22513.41369304901207e-541.70684652450603e-54
22611.05353308135377e-535.26766540676884e-54
22713.4739058306927e-531.73695291534635e-53
22811.10171383347762e-525.50856916738809e-53
22913.53531592726406e-521.76765796363203e-52
23011.11044307309737e-515.55221536548683e-52
23113.58911256714016e-511.79455628357008e-51
23211.08522600410298e-505.42613002051488e-51
23313.36050451671348e-501.68025225835674e-50
23411.06615085152282e-495.33075425761408e-50
23513.27354712709191e-491.63677356354596e-49
23619.99645610947147e-494.99822805473574e-49
23713.03826588636747e-481.51913294318374e-48
23819.47247783504856e-484.73623891752428e-48
23912.85124184847485e-471.42562092423742e-47
24018.5382272235216e-474.2691136117608e-47
24112.54363136827067e-461.27181568413533e-46
24217.69191789793302e-463.84595894896651e-46
24312.26851171893131e-451.13425585946565e-45
24416.8909565654893e-453.44547828274465e-45
24511.07259069776443e-445.36295348882215e-45
24613.11232679914101e-441.55616339957050e-44
24718.98237136370301e-444.49118568185150e-44
24812.645353566394e-431.322676783197e-43
24917.57381250106239e-433.78690625053120e-43
25012.15669330636368e-421.07834665318184e-42
25116.3758708169517e-423.18793540847585e-42
25211.79798122024017e-418.98990610120084e-42
25315.14356816897803e-412.57178408448902e-41
25419.94226408531689e-414.97113204265844e-41
25511.12572395624945e-405.62861978124725e-41
25613.19445187406346e-401.59722593703173e-40
25719.04724142198798e-404.52362071099399e-40
25812.43307603482732e-391.21653801741366e-39
25916.81739543192161e-393.40869771596081e-39
26011.90008565457799e-389.50042827288993e-39
26115.26754100525401e-382.63377050262701e-38
26211.4524816967591e-377.2624084837955e-38
26314.09324573809753e-372.04662286904876e-37
26411.11698648410844e-365.58493242054218e-37
26513.03379289344494e-361.51689644672247e-36
26618.19522256868363e-364.09761128434181e-36
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31812.5106633611173e-161.25533168055865e-16
31915.31787986294688e-162.65893993147344e-16
32011.10395262647103e-155.51976313235516e-16
3210.9999999999999992.27712159112737e-151.13856079556368e-15
3220.9999999999999984.66687445574164e-152.33343722787082e-15
3230.9999999999999959.50276551348024e-154.75138275674012e-15
3240.999999999999991.92237196780204e-149.61185983901021e-15
3250.999999999999983.86338063755340e-141.93169031877670e-14
3260.9999999999999617.75830553362062e-143.87915276681031e-14
3270.9999999999999231.53883213986992e-137.69416069934959e-14
3280.9999999999998483.03176425788262e-131.51588212894131e-13
3290.9999999999997035.93276351119939e-132.96638175559970e-13
3300.9999999999994231.15306364298907e-125.76531821494535e-13
3310.9999999999988872.22567085556982e-121.11283542778491e-12
3320.9999999999978674.26634896330983e-122.13317448165492e-12
3330.999999999995948.12111220509508e-124.06055610254754e-12
3340.9999999999922361.55278754580569e-117.76393772902847e-12
3350.999999999985362.92805862463827e-111.46402931231914e-11
3360.9999999999727495.45024424950736e-112.72512212475368e-11
3370.9999999999485041.02991850179368e-105.14959250896841e-11
3380.9999999999051551.89689914818914e-109.4844957409457e-11
3390.9999999998257633.4847338341549e-101.74236691707745e-10
3400.9999999996774386.45123301741058e-103.22561650870529e-10
3410.999999999406691.18661876510047e-095.93309382550234e-10
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3480.9999999685936096.28127826326232e-083.14063913163116e-08
3490.9999999464926981.07014603969927e-075.35073019849633e-08
3500.999999917052041.65895920610838e-078.29479603054188e-08
3510.9999998633662272.73267546031279e-071.36633773015639e-07
3520.9999997681580324.63683935408028e-072.31841967704014e-07
3530.9999996207275427.58544915225465e-073.79272457612733e-07
3540.9999993797623321.24047533669721e-066.20237668348605e-07
3550.9999989944717812.01105643776769e-061.00552821888384e-06
3560.9999983834472133.23310557422883e-061.61655278711442e-06
3570.9999973376434075.3247131868753e-062.66235659343765e-06
3580.9999957789421468.44211570725815e-064.22105785362908e-06
3590.9999933646730641.32706538714290e-056.63532693571448e-06
3600.9999896591416562.06817166877765e-051.03408583438882e-05
3610.999983789378453.24212431008755e-051.62106215504377e-05
3620.9999751581657454.96836685096186e-052.48418342548093e-05
3630.9999622661544227.54676911564012e-053.77338455782006e-05
3640.9999422993013830.0001154013972346975.77006986173487e-05
3650.9999122345601240.0001755308797512388.77654398756188e-05
3660.9998700179508850.0002599640982290180.000129982049114509
3670.9998092359570250.0003815280859490420.000190764042974521
3680.9997225832318530.0005548335362937870.000277416768146894
3690.9996002741505010.0007994516989979830.000399725849498991
3700.9994215729648430.001156854070313360.000578427035156681
3710.9991814407189750.001637118562049390.000818559281024694
3720.9988620126522020.002275974695596980.00113798734779849
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3770.9942328379351630.01153432412967450.00576716206483726
3780.9924475314503190.01510493709936280.00755246854968139
3790.9912931565858840.01741368682823280.0087068434141164
3800.9886896405982530.02262071880349400.0113103594017470
3810.9854522157618680.02909556847626430.0145477842381321
3820.9806190671724120.03876186565517540.0193809328275877
3830.9751825946573640.0496348106852730.0248174053426365
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3870.9382555783559220.1234888432881560.0617444216440782
3880.9273810318775840.1452379362448310.0726189681224156
3890.9124949572167140.1750100855665720.0875050427832859
3900.8963113450646730.2073773098706540.103688654935327
3910.8768587514095060.2462824971809880.123141248590494
3920.8552739962525870.2894520074948260.144726003747413
3930.8289075090844420.3421849818311170.171092490915558
3940.8113655651446240.3772688697107520.188634434855376
3950.8109618357774380.3780763284451240.189038164222562
3960.7863539800907170.4272920398185660.213646019909283
3970.8113666275648480.3772667448703030.188633372435152
3980.999413026331780.001173947336440310.000586973668220155
3990.9990276593473020.001944681305396850.000972340652698426
4000.9984607381278620.003078523744276840.00153926187213842
4010.9977372079890420.004525584021916130.00226279201095806
4020.9964908926993740.007018214601251140.00350910730062557
4030.9946007724895050.01079845502098920.0053992275104946
4040.9912203047997030.01755939040059330.00877969520029667
4050.9865361119594450.02692777608111050.0134638880405552
4060.9804174498607810.03916510027843740.0195825501392187
4070.9707784787487130.05844304250257350.0292215212512867
4080.9578759747516730.08424805049665490.0421240252483274
4090.9396743772551780.1206512454896440.0603256227448219
4100.9182080073595840.1635839852808330.0817919926404165
4110.9167186392567810.1665627214864380.0832813607432188
4120.9485737863512870.1028524272974270.0514262136487135
4130.9237497652760960.1525004694478080.0762502347239041
4140.9001299291589220.1997401416821570.0998700708410785
4150.8641954258373310.2716091483253380.135804574162669
4160.833772044268840.3324559114623210.166227955731161
4170.8383153746157710.3233692507684570.161684625384229
4180.788764717740350.4224705645192980.211235282259649
4190.7131481918835450.573703616232910.286851808116455
4200.6877045742938460.6245908514123070.312295425706154
4210.7737841240998440.4524317518003120.226215875900156
4220.6682212969498590.6635574061002820.331778703050141
4230.6291731240455060.7416537519089870.370826875954494


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level3740.899038461538462NOK
5% type I error level3850.92548076923077NOK
10% type I error level3890.935096153846154NOK
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Dec/01/t129121369244vhdhf5dolj7j9/103h6x1291213708.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/01/t129121369244vhdhf5dolj7j9/103h6x1291213708.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/01/t129121369244vhdhf5dolj7j9/1ey931291213708.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/01/t129121369244vhdhf5dolj7j9/1ey931291213708.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/01/t129121369244vhdhf5dolj7j9/2ey931291213708.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/01/t129121369244vhdhf5dolj7j9/2ey931291213708.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/01/t129121369244vhdhf5dolj7j9/3pp861291213708.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/01/t129121369244vhdhf5dolj7j9/3pp861291213708.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/01/t129121369244vhdhf5dolj7j9/4pp861291213708.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/01/t129121369244vhdhf5dolj7j9/4pp861291213708.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/01/t129121369244vhdhf5dolj7j9/5pp861291213708.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/01/t129121369244vhdhf5dolj7j9/5pp861291213708.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/01/t129121369244vhdhf5dolj7j9/6hyqr1291213708.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/01/t129121369244vhdhf5dolj7j9/6hyqr1291213708.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/01/t129121369244vhdhf5dolj7j9/7s7pu1291213708.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/01/t129121369244vhdhf5dolj7j9/7s7pu1291213708.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/01/t129121369244vhdhf5dolj7j9/8s7pu1291213708.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/01/t129121369244vhdhf5dolj7j9/8s7pu1291213708.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/01/t129121369244vhdhf5dolj7j9/9s7pu1291213708.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/01/t129121369244vhdhf5dolj7j9/9s7pu1291213708.ps (open in new window)


 
Parameters (Session):
par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ;
 
Parameters (R input):
par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ;
 
R code (references can be found in the software module):
library(lattice)
library(lmtest)
n25 <- 25 #minimum number of obs. for Goldfeld-Quandt test
par1 <- as.numeric(par1)
x <- t(y)
k <- length(x[1,])
n <- length(x[,1])
x1 <- cbind(x[,par1], x[,1:k!=par1])
mycolnames <- c(colnames(x)[par1], colnames(x)[1:k!=par1])
colnames(x1) <- mycolnames #colnames(x)[par1]
x <- x1
if (par3 == 'First Differences'){
x2 <- array(0, dim=c(n-1,k), dimnames=list(1:(n-1), paste('(1-B)',colnames(x),sep='')))
for (i in 1:n-1) {
for (j in 1:k) {
x2[i,j] <- x[i+1,j] - x[i,j]
}
}
x <- x2
}
if (par2 == 'Include Monthly Dummies'){
x2 <- array(0, dim=c(n,11), dimnames=list(1:n, paste('M', seq(1:11), sep ='')))
for (i in 1:11){
x2[seq(i,n,12),i] <- 1
}
x <- cbind(x, x2)
}
if (par2 == 'Include Quarterly Dummies'){
x2 <- array(0, dim=c(n,3), dimnames=list(1:n, paste('Q', seq(1:3), sep ='')))
for (i in 1:3){
x2[seq(i,n,4),i] <- 1
}
x <- cbind(x, x2)
}
k <- length(x[1,])
if (par3 == 'Linear Trend'){
x <- cbind(x, c(1:n))
colnames(x)[k+1] <- 't'
}
x
k <- length(x[1,])
df <- as.data.frame(x)
(mylm <- lm(df))
(mysum <- summary(mylm))
if (n > n25) {
kp3 <- k + 3
nmkm3 <- n - k - 3
gqarr <- array(NA, dim=c(nmkm3-kp3+1,3))
numgqtests <- 0
numsignificant1 <- 0
numsignificant5 <- 0
numsignificant10 <- 0
for (mypoint in kp3:nmkm3) {
j <- 0
numgqtests <- numgqtests + 1
for (myalt in c('greater', 'two.sided', 'less')) {
j <- j + 1
gqarr[mypoint-kp3+1,j] <- gqtest(mylm, point=mypoint, alternative=myalt)$p.value
}
if (gqarr[mypoint-kp3+1,2] < 0.01) numsignificant1 <- numsignificant1 + 1
if (gqarr[mypoint-kp3+1,2] < 0.05) numsignificant5 <- numsignificant5 + 1
if (gqarr[mypoint-kp3+1,2] < 0.10) numsignificant10 <- numsignificant10 + 1
}
gqarr
}
bitmap(file='test0.png')
plot(x[,1], type='l', main='Actuals and Interpolation', ylab='value of Actuals and Interpolation (dots)', xlab='time or index')
points(x[,1]-mysum$resid)
grid()
dev.off()
bitmap(file='test1.png')
plot(mysum$resid, type='b', pch=19, main='Residuals', ylab='value of Residuals', xlab='time or index')
grid()
dev.off()
bitmap(file='test2.png')
hist(mysum$resid, main='Residual Histogram', xlab='values of Residuals')
grid()
dev.off()
bitmap(file='test3.png')
densityplot(~mysum$resid,col='black',main='Residual Density Plot', xlab='values of Residuals')
dev.off()
bitmap(file='test4.png')
qqnorm(mysum$resid, main='Residual Normal Q-Q Plot')
qqline(mysum$resid)
grid()
dev.off()
(myerror <- as.ts(mysum$resid))
bitmap(file='test5.png')
dum <- cbind(lag(myerror,k=1),myerror)
dum
dum1 <- dum[2:length(myerror),]
dum1
z <- as.data.frame(dum1)
z
plot(z,main=paste('Residual Lag plot, lowess, and regression line'), ylab='values of Residuals', xlab='lagged values of Residuals')
lines(lowess(z))
abline(lm(z))
grid()
dev.off()
bitmap(file='test6.png')
acf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Autocorrelation Function')
grid()
dev.off()
bitmap(file='test7.png')
pacf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Partial Autocorrelation Function')
grid()
dev.off()
bitmap(file='test8.png')
opar <- par(mfrow = c(2,2), oma = c(0, 0, 1.1, 0))
plot(mylm, las = 1, sub='Residual Diagnostics')
par(opar)
dev.off()
if (n > n25) {
bitmap(file='test9.png')
plot(kp3:nmkm3,gqarr[,2], main='Goldfeld-Quandt test',ylab='2-sided p-value',xlab='breakpoint')
grid()
dev.off()
}
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Estimated Regression Equation', 1, TRUE)
a<-table.row.end(a)
myeq <- colnames(x)[1]
myeq <- paste(myeq, '[t] = ', sep='')
for (i in 1:k){
if (mysum$coefficients[i,1] > 0) myeq <- paste(myeq, '+', '')
myeq <- paste(myeq, mysum$coefficients[i,1], sep=' ')
if (rownames(mysum$coefficients)[i] != '(Intercept)') {
myeq <- paste(myeq, rownames(mysum$coefficients)[i], sep='')
if (rownames(mysum$coefficients)[i] != 't') myeq <- paste(myeq, '[t]', sep='')
}
}
myeq <- paste(myeq, ' + e[t]')
a<-table.row.start(a)
a<-table.element(a, myeq)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,hyperlink('http://www.xycoon.com/ols1.htm','Multiple Linear Regression - Ordinary Least Squares',''), 6, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Variable',header=TRUE)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'S.D.',header=TRUE)
a<-table.element(a,'T-STAT<br />H0: parameter = 0',header=TRUE)
a<-table.element(a,'2-tail p-value',header=TRUE)
a<-table.element(a,'1-tail p-value',header=TRUE)
a<-table.row.end(a)
for (i in 1:k){
a<-table.row.start(a)
a<-table.element(a,rownames(mysum$coefficients)[i],header=TRUE)
a<-table.element(a,mysum$coefficients[i,1])
a<-table.element(a, round(mysum$coefficients[i,2],6))
a<-table.element(a, round(mysum$coefficients[i,3],4))
a<-table.element(a, round(mysum$coefficients[i,4],6))
a<-table.element(a, round(mysum$coefficients[i,4]/2,6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Regression Statistics', 2, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Multiple R',1,TRUE)
a<-table.element(a, sqrt(mysum$r.squared))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'R-squared',1,TRUE)
a<-table.element(a, mysum$r.squared)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Adjusted R-squared',1,TRUE)
a<-table.element(a, mysum$adj.r.squared)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (value)',1,TRUE)
a<-table.element(a, mysum$fstatistic[1])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (DF numerator)',1,TRUE)
a<-table.element(a, mysum$fstatistic[2])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (DF denominator)',1,TRUE)
a<-table.element(a, mysum$fstatistic[3])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'p-value',1,TRUE)
a<-table.element(a, 1-pf(mysum$fstatistic[1],mysum$fstatistic[2],mysum$fstatistic[3]))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Residual Statistics', 2, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Residual Standard Deviation',1,TRUE)
a<-table.element(a, mysum$sigma)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Sum Squared Residuals',1,TRUE)
a<-table.element(a, sum(myerror*myerror))
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable3.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Actuals, Interpolation, and Residuals', 4, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Time or Index', 1, TRUE)
a<-table.element(a, 'Actuals', 1, TRUE)
a<-table.element(a, 'Interpolation<br />Forecast', 1, TRUE)
a<-table.element(a, 'Residuals<br />Prediction Error', 1, TRUE)
a<-table.row.end(a)
for (i in 1:n) {
a<-table.row.start(a)
a<-table.element(a,i, 1, TRUE)
a<-table.element(a,x[i])
a<-table.element(a,x[i]-mysum$resid[i])
a<-table.element(a,mysum$resid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable4.tab')
if (n > n25) {
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Goldfeld-Quandt test for Heteroskedasticity',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'p-values',header=TRUE)
a<-table.element(a,'Alternative Hypothesis',3,header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'breakpoint index',header=TRUE)
a<-table.element(a,'greater',header=TRUE)
a<-table.element(a,'2-sided',header=TRUE)
a<-table.element(a,'less',header=TRUE)
a<-table.row.end(a)
for (mypoint in kp3:nmkm3) {
a<-table.row.start(a)
a<-table.element(a,mypoint,header=TRUE)
a<-table.element(a,gqarr[mypoint-kp3+1,1])
a<-table.element(a,gqarr[mypoint-kp3+1,2])
a<-table.element(a,gqarr[mypoint-kp3+1,3])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable5.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Description',header=TRUE)
a<-table.element(a,'# significant tests',header=TRUE)
a<-table.element(a,'% significant tests',header=TRUE)
a<-table.element(a,'OK/NOK',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'1% type I error level',header=TRUE)
a<-table.element(a,numsignificant1)
a<-table.element(a,numsignificant1/numgqtests)
if (numsignificant1/numgqtests < 0.01) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'5% type I error level',header=TRUE)
a<-table.element(a,numsignificant5)
a<-table.element(a,numsignificant5/numgqtests)
if (numsignificant5/numgqtests < 0.05) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'10% type I error level',header=TRUE)
a<-table.element(a,numsignificant10)
a<-table.element(a,numsignificant10/numgqtests)
if (numsignificant10/numgqtests < 0.1) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable6.tab')
}
 




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Software written by Ed van Stee & Patrick Wessa


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