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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 12:56:55 +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/t1291208166s09stulgq5bmt68.htm/, Retrieved Wed, 01 Dec 2010 13:56:18 +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/t1291208166s09stulgq5bmt68.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 «
1 162556 1081 807 213118 6282154 1 29790 309 444 81767 4321023 1 87550 458 412 153198 4111912 0 84738 588 428 -26007 223193 1 54660 302 315 126942 1491348 1 42634 156 168 157214 1629616 0 40949 481 263 129352 1398893 1 45187 353 267 234817 1926517 1 37704 452 228 60448 983660 1 16275 109 129 47818 1443586 0 25830 115 104 245546 1073089 0 12679 110 122 48020 984885 1 18014 239 393 -1710 1405225 0 43556 247 190 32648 227132 1 24811 505 280 95350 929118 0 6575 159 63 151352 1071292 0 7123 109 102 288170 638830 1 21950 519 265 114337 856956 1 37597 248 234 37884 992426 0 17821 373 277 122844 444477 1 12988 119 73 82340 857217 1 22330 84 67 79801 711969 0 13326 102 103 165548 702380 0 16189 295 290 116384 358589 0 7146 105 83 134028 297978 0 15824 64 56 63838 585715 1 27664 282 236 74996 657954 0 11920 182 73 31080 209458 0 8568 37 34 32168 786690 0 14416 361 139 49857 439798 1 3369 28 26 87161 688779 1 11819 85 70 106113 574339 1 6984 45 40 80570 741409 1 4519 49 42 102129 597793 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 time28 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135


Multiple Linear Regression - Estimated Regression Equation
group[t] = + 0.141829395088363 -3.30450842805763e-06costs[t] -0.000396266602596711trades[t] + 0.00163242981862731orders[t] + 9.16354136508386e-07dividends[t] + 1.18426873582471e-07wealth[t] + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)0.1418293950883630.0546662.59450.0098010.0049
costs-3.30450842805763e-064e-06-0.79320.428110.214055
trades-0.0003962666025967110.000384-1.0320.3026440.151322
orders0.001632429818627310.0008092.01760.044260.02213
dividends9.16354136508386e-071e-061.26160.2078030.103901
wealth1.18426873582471e-0701.36780.1720920.086046


Multiple Linear Regression - Regression Statistics
Multiple R0.247742376698528
R-squared0.0613762852122355
Adjusted R-squared0.050333653273556
F-TEST (value)5.5581210668853
F-TEST (DF numerator)5
F-TEST (DF denominator)425
p-value5.66819583613931e-05
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.437304029136044
Sum Squared Residuals81.2747959069127


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
111.43293580773021-0.432935807730206
211.23239332153249-0.232393321532494
310.9709351671081320.0290648328918682
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810.7318121380925460.268187861907454
910.3822012569019820.617798743098018
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1400.266997703192944-0.266997703192944
1510.5142138582294050.485786141770595
1600.425500734457257-0.425500734457257
1700.581326574540565-0.581326574540565
1810.5024867730647410.497513226935259
1910.4535493203829270.546450679617073
2000.552521996417692-0.552521996417692
2110.347892219567380.65210778043262
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2600.283456472626497-0.283456472626497
2710.4705620592010130.529437940798987
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2900.276999633455811-0.276999633455811
3000.275817673172989-0.275817673172989
3110.3234845030573070.676515496942693
3210.3486150946941380.651384905305862
3310.3278493065494350.672150693450565
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33300.234819885647591-0.234819885647591
33400.238543039571190-0.238543039571190
33500.235663839646542-0.235663839646542
33600.238329590420845-0.238329590420845
33700.231679883027697-0.231679883027697
33800.234819885647591-0.234819885647591
33900.235953769662144-0.235953769662144
34000.244950642760967-0.244950642760967
34100.247176502226114-0.247176502226114
34200.234819885647591-0.234819885647591
34300.234819885647591-0.234819885647591
34400.234819885647591-0.234819885647591
34500.234124903583879-0.234124903583879
34600.234819885647591-0.234819885647591
34700.234092389956732-0.234092389956732
34800.234819885647591-0.234819885647591
34900.234819885647591-0.234819885647591
35000.239609365445689-0.239609365445689
35100.231585925511453-0.231585925511453
35200.242298538748743-0.242298538748743
35300.24464038666036-0.24464038666036
35400.23630761049475-0.23630761049475
35500.234819885647591-0.234819885647591
35600.234819885647591-0.234819885647591
35700.254380059226622-0.254380059226622
35800.234819885647591-0.234819885647591
35900.234819885647591-0.234819885647591
36000.234819885647591-0.234819885647591
36100.239765198395283-0.239765198395283
36200.234819885647591-0.234819885647591
36300.234819885647591-0.234819885647591
36410.2651638664907820.734836133509218
36500.243682903066336-0.243682903066336
36600.234819885647591-0.234819885647591
36700.234819885647591-0.234819885647591
36800.234819885647591-0.234819885647591
36900.234819885647591-0.234819885647591
37000.237225400735265-0.237225400735265
37100.234819885647591-0.234819885647591
37200.229000518842225-0.229000518842225
37300.259040031716693-0.259040031716693
37400.241560771787857-0.241560771787857
37500.234819885647591-0.234819885647591
37600.234819885647591-0.234819885647591
37700.236334567441970-0.236334567441970
37800.240446131598954-0.240446131598954
37900.238817904855791-0.238817904855791
38000.234819885647591-0.234819885647591
38100.234819885647591-0.234819885647591
38200.250552160653057-0.250552160653057
38300.202309489047723-0.202309489047723
38400.234819885647591-0.234819885647591
38500.249856339765956-0.249856339765956
38600.255427149390891-0.255427149390891
38700.237320794432308-0.237320794432308
38800.235718863540557-0.235718863540557
38900.237856825214816-0.237856825214816
39000.236805601673896-0.236805601673896
39100.248515884184388-0.248515884184388
39200.235926274675976-0.235926274675976
39300.237090301366437-0.237090301366437
39400.252067807068005-0.252067807068005
39510.2506962294323810.749303770567619
39600.235030953269422-0.235030953269422
39700.228629391174365-0.228629391174365
39810.643422296341550.35657770365845
39900.241554722130148-0.241554722130148
40010.1936049188089610.806395081191039
40100.241795957752544-0.241795957752544
40200.247111516335894-0.247111516335894
40300.235836976746975-0.235836976746975
40410.2577510655351690.742248934464831
40500.2402125134058-0.2402125134058
40600.254235884273449-0.254235884273449
40700.251257187332973-0.251257187332973
40800.243859707196326-0.243859707196326
40900.239459306684565-0.239459306684565
41000.234723847426247-0.234723847426247
41100.307062986626482-0.307062986626482
41210.2320506536051560.767949346394844
41310.2402042858475220.759795714152478
41410.2920737672866280.707926232713372
41500.239862591991973-0.239862591991973
41600.232257040721491-0.232257040721491
41700.222982256436538-0.222982256436538
41810.2554661240740860.744533875925914
41900.262529478728334-0.262529478728334
42000.229691889546782-0.229691889546782
42100.233273275561566-0.233273275561566
42200.321813363592644-0.321813363592644
42310.1638124028702420.836187597129758
42400.188779025499767-0.188779025499767
42500.240341657020475-0.240341657020475
42610.3073032431566920.692696756843308
42700.203035898755305-0.203035898755305
42800.514448546801472-0.514448546801472
42900.247357952024666-0.247357952024666
43000.31129886350784-0.31129886350784
43100.147569368862861-0.147569368862861


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
90.7056360316927520.5887279366144960.294363968307248
100.5570342686979280.8859314626041430.442965731302072
110.7773858517466120.4452282965067760.222614148253388
120.8569902971356180.2860194057287650.143009702864382
130.8146466913489420.3707066173021170.185353308651058
140.7857492808732280.4285014382535450.214250719126772
150.7756331850832290.4487336298335420.224366814916771
160.7935155661770780.4129688676458450.206484433822922
170.7798064859278660.4403870281442670.220193514072134
180.7625889270233040.4748221459533920.237411072976696
190.7618082839666360.4763834320667270.238191716033363
200.7757835499747320.4484329000505370.224216450025268
210.7706984641928350.458603071614330.229301535807165
220.7650809360746110.4698381278507770.234919063925388
230.756827155781330.4863456884373390.243172844218669
240.7269606725834020.5460786548331960.273039327416598
250.705193483302050.58961303339590.29480651669795
260.7282005578811030.5435988842377950.271799442118897
270.7479357837673520.5041284324652960.252064216232648
280.757063099949840.485873800100320.24293690005016
290.7732054976876170.4535890046247650.226794502312383
300.7665526887820380.4668946224359250.233447311217962
310.7926679874873490.4146640250253030.207332012512651
320.8179267025401860.3641465949196290.182073297459814
330.8221741260576530.3556517478846940.177825873942347
340.8305459184748820.3389081630502370.169454081525118
350.8120178541858260.3759642916283480.187982145814174
360.8024679536323980.3950640927352050.197532046367602
370.8082405993874780.3835188012250440.191759400612522
380.8183566898882020.3632866202235960.181643310111798
390.8458853881047040.3082292237905920.154114611895296
400.8402686406465470.3194627187069060.159731359353453
410.8150961553409570.3698076893180860.184903844659043
420.8098223243282470.3803553513435060.190177675671753
430.8031963759792930.3936072480414130.196803624020707
440.7939970133993280.4120059732013440.206002986600672
450.7890946317728160.4218107364543680.210905368227184
460.8136760088871850.3726479822256310.186323991112815
470.8562820609229710.2874358781540580.143717939077029
480.8778355144295820.2443289711408370.122164485570419
490.875219850185130.2495602996297390.124780149814869
500.8684346389193290.2631307221613430.131565361080671
510.8786288626762550.242742274647490.121371137323745
520.8875958341634130.2248083316731740.112404165836587
530.897633359499050.2047332810019010.102366640500951
540.9057327013088580.1885345973822850.0942672986911423
550.9159304673352960.1681390653294070.0840695326647037
560.9160847129161540.1678305741676930.0839152870838465
570.916635963889460.1667280722210790.0833640361105395
580.9140688853901380.1718622292197240.085931114609862
590.9096541267392780.1806917465214450.0903458732607223
600.9194115131879270.1611769736241460.080588486812073
610.926958795476860.146082409046280.07304120452314
620.9218429937665530.1563140124668930.0781570062334467
630.9309053183138130.1381893633723750.0690946816861873
640.937990167696570.1240196646068590.0620098323034297
650.9359926329083370.1280147341833260.0640073670916632
660.9268462427238980.1463075145522040.0731537572761021
670.9221140399079230.1557719201841540.0778859600920768
680.9302614948283460.1394770103433090.0697385051716544
690.9295749833850890.1408500332298230.0704250166149113
700.934917475180440.130165049639120.06508252481956
710.9435287716578580.1129424566842840.056471228342142
720.941700096803530.1165998063929400.0582999031964698
730.9400332219969210.1199335560061570.0599667780030785
740.9372234722186240.1255530555627530.0627765277813763
750.9353104481228690.1293791037542620.0646895518771308
760.9449893181253140.1100213637493710.0550106818746856
770.9428549607254170.1142900785491660.0571450392745828
780.9386629297306820.1226741405386360.0613370702693182
790.9348330751300920.1303338497398160.0651669248699079
800.947349791585620.1053004168287600.0526502084143801
810.9445707869544570.1108584260910860.0554292130455429
820.9511335064077470.09773298718450550.0488664935922528
830.9488626705660560.1022746588678890.0511373294339444
840.9452035745053370.1095928509893260.0547964254946629
850.9421034614543170.1157930770913670.0578965385456834
860.9501881754157270.09962364916854520.0498118245842726
870.9495057266753510.1009885466492980.0504942733246488
880.9463901009710720.1072197980578560.0536098990289278
890.943218676000160.1135626479996800.0567813239998399
900.9397085125929070.1205829748141860.0602914874070932
910.9359873657422530.1280252685154930.0640126342577465
920.9458296352945230.1083407294109530.0541703647054766
930.9428503982136150.1142992035727690.0571496017863847
940.9528290980836440.09434180383271130.0471709019163557
950.9495013030151360.1009973939697280.0504986969848641
960.9584595969818110.08308080603637790.0415404030181889
970.9558094882037990.08838102359240280.0441905117962014
980.9668554302579620.0662891394840760.033144569742038
990.9646210960159740.07075780796805280.0353789039840264
1000.9713154586782720.05736908264345590.0286845413217279
1010.9763222387401080.04735552251978310.0236777612598916
1020.9744470040003730.05110599199925470.0255529959996274
1030.9726582699857340.05468346002853270.0273417300142663
1040.9705641950783580.05887160984328410.0294358049216421
1050.9683734838900580.06325303221988380.0316265161099419
1060.9660286704020650.0679426591958710.0339713295979355
1070.9725127332698540.05497453346029130.0274872667301457
1080.9775028050229420.04499438995411530.0224971949770576
1090.9757839026571460.04843219468570830.0242160973428542
1100.9806600820533070.03867983589338510.0193399179466926
1110.9792964994381860.04140700112362830.0207035005618141
1120.9836416935507150.03271661289856940.0163583064492847
1130.9822635319648360.03547293607032870.0177364680351643
1140.9859130535345650.02817389293086990.0140869464654350
1150.9887382281012650.02252354379747010.0112617718987351
1160.9880046318841720.02399073623165630.0119953681158281
1170.9870155803147610.02596883937047740.0129844196852387
1180.9860996526618640.02780069467627190.0139003473381360
1190.9892762055068430.02144758898631450.0107237944931573
1200.988300217335840.02339956532832130.0116997826641606
1210.9875897771223370.02482044575532620.0124102228776631
1220.9865752033531820.02684959329363490.0134247966468175
1230.986152994254250.02769401149150100.0138470057457505
1240.9888309468284910.02233810634301700.0111690531715085
1250.9913585474851980.01728290502960490.00864145251480243
1260.9934247083080220.01315058338395600.00657529169197798
1270.9928675103679660.01426497926406770.00713248963203385
1280.9922767660680380.01544646786392480.00772323393196238
1290.991653822297460.01669235540508100.00834617770254049
1300.9908722343297460.01825553134050740.00912776567025370
1310.9900241413885050.01995171722298990.00997585861149495
1320.9891035684373930.0217928631252140.010896431562607
1330.9880163257144340.02396734857113230.0119836742855662
1340.9870065915390780.02598681692184390.0129934084609219
1350.985680240225620.0286395195487580.014319759774379
1360.984202353776180.03159529244763990.0157976462238200
1370.9826364070648730.03472718587025410.0173635929351270
1380.9808241232130750.03835175357384920.0191758767869246
1390.978818426492160.04236314701568220.0211815735078411
1400.9765939770881320.04681204582373670.0234060229118684
1410.9742172967060.05156540658800020.0257827032940001
1420.9715162235068440.05696755298631230.0284837764931562
1430.9686201194300140.06275976113997140.0313798805699857
1440.9654400905149280.06911981897014460.0345599094850723
1450.9621754628879960.07564907422400770.0378245371120038
1460.9584714838131820.0830570323736360.041528516186818
1470.954251028824510.091497942350980.04574897117549
1480.9498351811884180.1003296376231650.0501648188115823
1490.9449116506961620.1101766986076770.0550883493038384
1500.9394781246448870.1210437507102270.0605218753551135
1510.9336520491962650.1326959016074710.0663479508037354
1520.9283467836098630.1433064327802740.0716532163901368
1530.921849384461230.1563012310775400.0781506155387699
1540.914669603508840.1706607929823200.0853303964911599
1550.906922709619310.1861545807613810.0930772903806906
1560.8985544707236580.2028910585526840.101445529276342
1570.8896030825449760.2207938349100490.110396917455024
1580.880130316028220.2397393679435600.119869683971780
1590.8702814110570720.2594371778858560.129718588942928
1600.8595085046766830.2809829906466350.140491495323317
1610.8480976000465380.3038047999069240.151902399953462
1620.8360417512534110.3279164974931780.163958248746589
1630.823337330296530.3533253394069380.176662669703469
1640.8096826881699660.3806346236600680.190317311830034
1650.7963393565875710.4073212868248590.203660643412429
1660.7817053923059680.4365892153880630.218294607694032
1670.7664471185213070.4671057629573850.233552881478693
1680.7535767602088590.4928464795822830.246423239791142
1690.7330993825358580.5338012349282830.266900617464142
1700.7160969350327590.5678061299344820.283903064967241
1710.698560791196770.602878417606460.30143920880323
1720.6806757993897290.6386484012205430.319324200610271
1730.6621754656102590.6756490687794820.337824534389741
1740.6439955113164630.7120089773670740.356004488683537
1750.6246992979104280.7506014041791440.375300702089572
1760.6057609492575730.7884781014848540.394239050742427
1770.6005111758872620.7989776482254750.399488824112738
1780.6557532526308150.688493494738370.344246747369185
1790.6367193429124010.7265613141751980.363280657087599
1800.6173214925901620.7653570148196750.382678507409838
1810.5989702893095940.8020594213808130.401029710690406
1820.6512192169618940.6975615660762120.348780783038106
1830.6333420586645850.733315882670830.366657941335415
1840.6897730359827290.6204539280345420.310226964017271
1850.736733696693790.5265326066124190.263266303306210
1860.7770063265977860.4459873468044280.222993673402214
1870.8118353572434620.3763292855130760.188164642756538
1880.7986998631450270.4026002737099450.201300136854973
1890.7843672368835010.4312655262329980.215632763116499
1900.7696028121950440.4607943756099130.230397187804956
1910.7552403968039840.4895192063920310.244759603196016
1920.7393904494915590.5212191010168810.260609550508441
1930.7237352631952280.5525294736095440.276264736804772
1940.7068699500633670.5862600998732670.293130049936633
1950.6899229591348620.6201540817302760.310077040865138
1960.7376297159576770.5247405680846460.262370284042323
1970.7709096902247710.4581806195504580.229090309775229
1980.8109040109624940.3781919780750120.189095989037506
1990.8461403491074630.3077193017850740.153859650892537
2000.8799962037215340.2400075925569320.120003796278466
2010.9055043212007220.1889913575985560.094495678799278
2020.9267838497213940.1464323005572110.0732161502786056
2030.9442236209536620.1115527580926760.0557763790463378
2040.9567796691461760.08644066170764850.0432203308538243
2050.971156280250830.057687439498340.02884371974917
2060.9789800667615970.04203986647680590.0210199332384029
2070.9855775269221070.02884494615578560.0144224730778928
2080.9900881595661750.01982368086764940.00991184043382468
2090.9923014829928480.01539703401430380.00769851700715189
2100.9952107333399990.009578533320002320.00478926666000116
2110.9945227083073230.01095458338535410.00547729169267706
2120.9937452491999060.01250950160018730.00625475080009366
2130.9928845835974170.01423083280516630.00711541640258313
2140.9918733331084180.01625333378316370.00812666689158184
2150.990747753443020.01850449311395830.00925224655697916
2160.98953150900830.02093698198340180.0104684909917009
2170.988184533229170.02363093354166110.0118154667708305
2180.9865498780349270.02690024393014530.0134501219650727
2190.9848560858235220.03028782835295610.0151439141764780
2200.983495506769930.03300898646013880.0165044932300694
2210.9814097183473140.03718056330537110.0185902816526855
2220.9791089753116040.04178204937679150.0208910246883958
2230.976571984457480.04685603108504040.0234280155425202
2240.9741836971150.05163260577000140.0258163028850007
2250.9711429398920070.0577141202159860.028857060107993
2260.9682819806976460.06343603860470770.0317180193023539
2270.9648127143497070.0703745713005870.0351872856502935
2280.9608698253312690.07826034933746260.0391301746687313
2290.9563286478867150.08734270422657090.0436713521132854
2300.951623883044420.09675223391116130.0483761169555806
2310.9464043383708440.1071913232583110.0535956616291555
2320.941217619487520.1175647610249610.0587823805124806
2330.9352569632860530.1294860734278930.0647430367139466
2340.9291269489590650.1417461020818710.0708730510409355
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2360.9148009741622530.1703980516754950.0851990258377473
2370.9068880660073410.1862238679853170.0931119339926587
2380.898891493827380.2022170123452420.101108506172621
2390.8899279226603950.220144154679210.110072077339605
2400.8804071715262620.2391856569474760.119592828473738
2410.8703201360128630.2593597279742750.129679863987137
2420.859760718451590.2804785630968210.140239281548410
2430.8485276626971980.3029446746056050.151472337302802
2440.8374699848058170.3250600303883650.162530015194183
2450.823279037705550.3534419245889010.176720962294450
2460.8585538803239340.2828922393521330.141446119676066
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2490.9078983484681480.1842033030637040.0921016515318522
2500.9305964492755750.138807101448850.0694035507244251
2510.9249311234000430.1501377531999140.0750688765999569
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2530.9382845951266450.1234308097467100.0617154048733549
2540.9315174031165760.1369651937668480.068482596883424
2550.92402585832850.1519482833429990.0759741416714997
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2570.909483116158020.1810337676839600.0905168838419802
2580.90487658267640.1902468346471990.0951234173235993
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2600.9215511544936480.1568976910127040.0784488455063521
2610.9424523861630110.1150952276739780.0575476138369888
2620.9590348638701040.08193027225979260.0409651361298963
2630.9541315087114950.09173698257700950.0458684912885047
2640.9494871012046710.1010257975906580.0505128987953288
2650.964632038004880.07073592399024070.0353679619951204
2660.9603074026592280.07938519468154430.0396925973407721
2670.972920856000260.05415828799948010.0270791439997400
2680.9691545755184210.0616908489631580.030845424481579
2690.9795437661977370.04091246760452620.0204562338022631
2700.9774015753995370.0451968492009260.022598424600463
2710.9855035882124810.02899282357503740.0144964117875187
2720.9911145601878050.01777087962439060.0088854398121953
2730.9948223599923120.01035528001537650.00517764000768826
2740.9941375546603160.01172489067936730.00586244533968365
2750.9931358618346880.01372827633062450.00686413816531227
2760.992022910205270.01595417958945930.00797708979472963
2770.9909244807495840.01815103850083290.00907551925041645
2780.9894509831458960.02109803370820870.0105490168541044
2790.9951806123554560.00963877528908860.0048193876445443
2800.9942177322710160.01156453545796800.00578226772898402
2810.9967782116342370.00644357673152620.0032217883657631
2820.9961847077747060.007630584450588310.00381529222529415
2830.9954829501713210.009034099657357090.00451704982867855
2840.9946779320433220.01064413591335690.00532206795667845
2850.9936685209428550.01266295811428970.00633147905714487
2860.9925819946294440.01483601074111180.00741800537055592
2870.9957549511558340.00849009768833240.0042450488441662
2880.99497965740640.01004068518719850.00502034259359924
2890.9973348567231720.00533028655365540.0026651432768277
2900.9967665382574040.006466923485191610.00323346174259581
2910.9983836815826560.00323263683468740.0016163184173437
2920.9980505573837630.003898885232473520.00194944261623676
2930.9976179057618180.004764188476364980.00238209423818249
2940.9971321529018170.005735694196366620.00286784709818331
2950.9966098214002050.006780357199589430.00339017859979472
2960.9982544773606420.003491045278715930.00174552263935797
2970.9978807671892220.004238465621556130.00211923281077807
2980.9990262559110010.001947488177996950.000973744088998475
2990.998801285714770.002397428570461480.00119871428523074
3000.9985720029793540.00285599404129290.00142799702064645
3010.9993598145652030.001280370869595020.00064018543479751
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3070.999772510019420.0004549799611610730.000227489980580537
3080.9999080584458940.0001838831082110629.19415541055308e-05
3090.9998878283742450.0002243432515090970.000112171625754548
3100.9999679207129256.41585741501903e-053.20792870750952e-05
3110.9999924405457631.51189084738074e-057.55945423690368e-06
3120.9999894639785652.10720428704611e-051.05360214352305e-05
3130.99999797405054.0518989994074e-062.0259494997037e-06
3140.999999609324437.81351138834986e-073.90675569417493e-07
3150.9999994472440471.10551190563063e-065.52755952815314e-07
3160.9999991911791621.61764167545624e-068.0882083772812e-07
3170.9999988343147462.33137050836487e-061.16568525418243e-06
3180.9999984380622953.12387540908825e-061.56193770454412e-06
3190.9999977918939634.41621207358561e-062.20810603679281e-06
3200.9999968512768346.29744633220404e-063.14872316610202e-06
3210.9999955295840418.94083191725198e-064.47041595862599e-06
3220.9999936811252211.26377495577614e-056.31887477888072e-06
3230.999991108204181.77835916419528e-058.89179582097642e-06
3240.9999986497890332.70042193490472e-061.35021096745236e-06
3250.9999980343796813.93124063739906e-061.96562031869953e-06
3260.9999971560249345.68795013227043e-062.84397506613522e-06
3270.9999996764663826.47067236758102e-073.23533618379051e-07
3280.9999999770184164.59631673402198e-082.29815836701099e-08
3290.9999999635871067.28257873943055e-083.64128936971527e-08
3300.9999999425905531.14818893647510e-075.74094468237551e-08
3310.9999999099388071.80122385016513e-079.00611925082567e-08
3320.9999998594304372.81139125414555e-071.40569562707278e-07
3330.9999997817183954.3656320975369e-072.18281604876845e-07
3340.9999996665172626.66965475860828e-073.33482737930414e-07
3350.9999994885004861.02299902808434e-065.11499514042169e-07
3360.9999992244068661.55118626753208e-067.75593133766038e-07
3370.9999988459911972.30801760680604e-061.15400880340302e-06
3380.999998252974943.49405011883926e-061.74702505941963e-06
3390.9999973743533875.25129322709201e-062.62564661354601e-06
3400.9999962009475837.59810483319915e-063.79905241659957e-06
3410.9999944785336691.10429326624314e-055.5214663312157e-06
3420.999991819599111.63608017816030e-058.18040089080151e-06
3430.9999879497477922.41005044165739e-051.20502522082869e-05
3440.999982352205613.52955887819806e-051.76477943909903e-05
3450.9999746921142935.06157714140915e-052.53078857070458e-05
3460.9999633480803097.3303839382178e-053.6651919691089e-05
3470.9999477684168210.000104463166358225.223158317911e-05
3480.9999252556037540.0001494887924925477.47443962462735e-05
3490.9998936944581750.0002126110836507510.000106305541825376
3500.9998515397656720.0002969204686563230.000148460234328161
3510.9997928590647330.0004142818705338320.000207140935266916
3520.999715171369180.0005696572616379180.000284828630818959
3530.9996156172377960.0007687655244077110.000384382762203856
3540.9994685279723620.001062944055276190.000531472027638095
3550.9992717476267430.001456504746513430.000728252373256715
3560.9990086753234450.001982649353109260.00099132467655463
3570.9986377087379820.002724582524036920.00136229126201846
3580.9981696994448580.003660601110284180.00183030055514209
3590.9975575564647070.004884887070586820.00244244353529341
3600.9967629621776970.006474075644606710.00323703782230335
3610.995777061563940.008445876872119210.00422293843605960
3620.994479755654870.01104048869025980.0055202443451299
3630.9928345976289120.01433080474217510.00716540237108756
3640.9971114104361180.005777179127764140.00288858956388207
3650.996228688736770.007542622526459770.00377131126322988
3660.9949957452773710.01000850944525760.00500425472262882
3670.993409942561880.01318011487623860.00659005743811932
3680.9913879059967540.01722418800649190.00861209400324596
3690.9888322520551320.02233549588973600.0111677479448680
3700.985722353776190.02855529244761950.0142776462238098
3710.9817657428753270.03646851424934630.0182342571246732
3720.9768954670173450.04620906596531000.0231045329826550
3730.9704871978871240.05902560422575250.0295128021128762
3740.9630149483498150.07397010330036960.0369850516501848
3750.9542156547283160.09156869054336770.0457843452716839
3760.9437835563752430.1124328872495130.0562164436247567
3770.9332732664546190.1334534670907620.0667267335453809
3780.9200213624132370.1599572751735270.0799786375867635
3790.904582228776490.1908355424470190.0954177712235096
3800.8864679450400480.2270641099199040.113532054959952
3810.866033766908030.267932466183940.13396623309197
3820.8408458332251560.3183083335496890.159154166774844
3830.8248153825948440.3503692348103130.175184617405156
3840.7973036467487340.4053927065025330.202696353251266
3850.7706138117040420.4587723765919170.229386188295958
3860.7408099277131130.5183801445737740.259190072286887
3870.7085939498923030.5828121002153950.291406050107697
3880.6752045728474280.6495908543051450.324795427152572
3890.639670671058560.720658657882880.36032932894144
3900.6057324648642760.7885350702714480.394267535135724
3910.5707725900518030.8584548198963950.429227409948197
3920.5345038824626070.9309922350747860.465496117537393
3930.4963203676963420.9926407353926840.503679632303658
3940.4574908334376090.9149816668752180.542509166562391
3950.6799366906659830.6401266186680330.320063309334017
3960.6450562628685020.7098874742629960.354943737131498
3970.6157479680988840.7685040638022320.384252031901116
3980.5665790698948320.8668418602103360.433420930105168
3990.5230603650836940.9538792698326130.476939634916306
4000.5608803490467580.8782393019064850.439119650953242
4010.5083018611296810.9833962777406380.491698138870319
4020.469063895338170.938127790676340.53093610466183
4030.4340420450693440.8680840901386890.565957954930656
4040.5860884339629070.8278231320741870.413911566037093
4050.5373235227815620.9253529544368760.462676477218438
4060.4847728434489970.9695456868979930.515227156551003
4070.4331903066222360.8663806132444720.566809693377764
4080.4096763905859420.8193527811718830.590323609414058
4090.3860032003180780.7720064006361560.613996799681922
4100.3293755911486840.6587511822973690.670624408851316
4110.3119450585663180.6238901171326360.688054941433682
4120.4577870434226580.9155740868453160.542212956577342
4130.5692825410357140.8614349179285710.430717458964286
4140.78211145324330.43577709351340.2178885467567
4150.7060239870707370.5879520258585270.293976012929263
4160.6156868732572490.7686262534855020.384313126742751
4170.5786609770662460.8426780458675090.421339022933754
4180.8528957860837670.2942084278324670.147104213916233
4190.7727166393627940.4545667212744120.227283360637206
4200.6577748677998010.6844502644003970.342225132200199
4210.5233202400965990.9533595198068020.476679759903401
4220.733053634768950.5338927304620990.266946365231049


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level810.195652173913043NOK
5% type I error level1560.376811594202899NOK
10% type I error level1950.471014492753623NOK
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Dec/01/t1291208166s09stulgq5bmt68/10iwpa1291208184.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/01/t1291208166s09stulgq5bmt68/10iwpa1291208184.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/01/t1291208166s09stulgq5bmt68/1bvag1291208184.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/01/t1291208166s09stulgq5bmt68/1bvag1291208184.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/01/t1291208166s09stulgq5bmt68/2bvag1291208184.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/01/t1291208166s09stulgq5bmt68/2bvag1291208184.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/01/t1291208166s09stulgq5bmt68/3m4r11291208184.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/01/t1291208166s09stulgq5bmt68/3m4r11291208184.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/01/t1291208166s09stulgq5bmt68/4m4r11291208184.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/01/t1291208166s09stulgq5bmt68/4m4r11291208184.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/01/t1291208166s09stulgq5bmt68/5m4r11291208184.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/01/t1291208166s09stulgq5bmt68/5m4r11291208184.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/01/t1291208166s09stulgq5bmt68/6kzgs1291208184.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/01/t1291208166s09stulgq5bmt68/6kzgs1291208184.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/01/t1291208166s09stulgq5bmt68/775q71291208184.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/01/t1291208166s09stulgq5bmt68/775q71291208184.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/01/t1291208166s09stulgq5bmt68/875q71291208184.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/01/t1291208166s09stulgq5bmt68/875q71291208184.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/01/t1291208166s09stulgq5bmt68/9iwpa1291208184.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/01/t1291208166s09stulgq5bmt68/9iwpa1291208184.ps (open in new window)


 
Parameters (Session):
par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;
 
Parameters (R input):
par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No 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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