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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: Thu, 02 Dec 2010 18:51:48 +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/02/t12913158370m1zcsyy52v2cb6.htm/, Retrieved Thu, 02 Dec 2010 19:50:48 +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/02/t12913158370m1zcsyy52v2cb6.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 213118 1 29790 309 81767 1 87550 458 153198 0 84738 588 -26007 1 54660 299 126942 1 42634 156 157214 0 40949 481 129352 1 42312 323 234817 1 37704 452 60448 1 16275 109 47818 0 25830 115 245546 0 12679 110 48020 1 18014 239 -1710 0 43556 247 32648 1 24524 497 95350 0 6532 103 151352 0 7123 109 288170 1 20813 502 114337 1 37597 248 37884 0 17821 373 122844 1 12988 119 82340 1 22330 84 79801 0 13326 102 165548 0 16189 295 116384 0 7146 105 134028 0 15824 64 63838 1 26088 267 74996 0 11326 129 31080 0 8568 37 32168 0 14416 361 49857 1 3369 28 87161 1 11819 85 106113 1 6620 44 80570 1 4519 49 102129 0 2220 22 301670 0 18562 155 102313 0 10327 91 88577 1 5336 81 112477 1 2365 79 191778 0 4069 145 79804 0 7710 816 128294 0 13718 61 96448 0 4525 226 93811 0 6869 105 117520 0 4628 62 69159 1 3653 24 101792 1 1265 26 210568 1 7489 322 136996 0 4901 84 121920 0 2284 33 76403 1 3160 108 108094 1 4150 150 134759 1 7285 115 188873 1 1134 162 146216 1 4658 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 time25 seconds
R Server'George Udny Yule' @ 72.249.76.132
R Framework
error message
Warning: there are blank lines in the 'Data X' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.


Multiple Linear Regression - Estimated Regression Equation
Trades[t] = -6.39506766242525 + 1.94624800291199Group[t] + 0.00679068305600392Costs[t] + 0.000398000520557041`Dividends `[t] + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)-6.395067662425258.572689-0.7460.4560890.228045
Group1.946248002911997.7200910.25210.8010840.400542
Costs0.006790683056003920.00030622.165500
`Dividends `0.0003980005205570410.0001123.5590.0004140.000207


Multiple Linear Regression - Regression Statistics
Multiple R0.772359513708112
R-squared0.596539218415431
Adjusted R-squared0.593704599341067
F-TEST (value)210.447754271582
F-TEST (DF numerator)3
F-TEST (DF denominator)427
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation70.2894212212757
Sum Squared Residuals2109637.36811056


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
110811184.23853013234-103.238530132338
2309230.38893714322978.6110628567706
3458651.048365641933-193.048365641933
4588558.6830335991129.3169664008899
5299417.252898262214-118.252898262214
6156347.636415589013-191.636415589013
7481323.158776132974157.841223867026
8323376.335850041768-53.3358500417677
9452275.645429750691176.354570249309
10109125.101135968947-16.1011359689472
11115266.735711494856-151.735711494856
1211098.815987801797811.1840121982022
13239117.197964021189121.802035978811
14247302.373844520029-55.3738445200287
15497200.035241241041296.964758758959
1610398.19984884674174.80015115325833
17109156.666777754413-47.6667777544131
18502182.391852304027319.608147695973
19248265.938342917850-17.9383429178496
20373163.51367102593209.48632897407
21119116.5199347345322.48006526546764
2284178.947972522027-94.9479725220268
23102149.985764919060-47.9857649190602
24295149.860192915733145.139807084267
2510595.4743672249989.52563277500207
2664126.468258247101-62.4682582471015
27267202.55496694521364.4450330547869
2812982.886064808788246.1139351912118
293764.5903855066954-27.5903855066954
30361111.34253122634249.65746877366
312853.1191149284359-25.1191149284359
3285118.043292617266-33.0432926172663
334472.5724041125133-28.5724041125133
344966.8856722345382-17.8856722345382
3522128.745065758346-106.745065758346
36155160.374218482872-5.37421848287241
379198.9860083663084-7.98600836630844
388176.55216967801774.44783032198229
397987.9388895993238-8.93888959932384
4014552.998255234988992.0017447650111
4181697.02217748371718.97782251629
4261125.145876706522-64.1458767065223
4322661.6695999999692164.330400000031
4410587.023155425129217.9768445748708
456252.55753152196549.44246847803462
462460.8708145326111-36.8708145326111
472687.9475680189863-61.9475680189863
48322100.931085061132221.068914938868
498475.41029346136448.58970653863555
503339.5232862096073-6.52328620960734
5110860.031207066551647.9687929334484
5215077.36666717264972.633332827351
53115120.192858722645-5.19285872264503
5416261.4458590397631100.554140960237
5515889.512247538749868.4877524612502
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5910741.927633854239265.0723661457608
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633454.4304021224658-20.4304021224658
648478.04380116818145.95619883181864
657935.258806234100243.7411937658998
66947119.751844160470827.24815583953
677431.735593483182142.2644065168179
685349.46085893036223.53914106963778
699455.459101262681338.5408987373187
706362.86549135025220.134508649747755
715827.106164472842430.8938355271576
724943.90398122328535.09601877671473
733445.8626854304557-11.8626854304557
741128.9224420229659-17.9224420229659
753554.3312312575241-19.3312312575241
761735.1779931577067-18.1779931577067
774746.15482733354120.845172666458822
784328.563394141967314.4366058580327
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878654.260923014060731.7390769859393
881438.6480353049268-24.6480353049268
896450.289809569233713.7101904307663
901138.5866134272963-27.5866134272963
915245.22243687238446.77756312761557
924148.5723418283824-7.5723418283824
939934.214388366535564.7856116334645
947590.4249588092542-15.4249588092542
954521.368298165310323.6317018346897
964340.27505443857852.72494556142147
97840.4240669491506-32.4240669491506
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992262.8120314384621-40.8120314384621
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1013334.407643295786-1.407643295786
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1041842.7933029969225-24.7933029969225
1052829.8146081689024-1.81460816890238
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1076041.039809800699318.9601901993007
1082048.3983981473432-28.3983981473432
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1103637.7065099814044-1.70650998140440
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1124738.00353900216228.99646099783778
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1253738.5683111431779-1.56831114317788
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190017.7715239457983-17.7715239457983
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203019.71777194871-19.71777194871
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349017.7715239457983-17.7715239457983
350017.7715239457983-17.7715239457983
3511419.0456599546495-5.04565995464947
3521018.3397571394636-8.33975713946356
3531221.3099043140459-9.30990431404593
354219.2235768585080-17.2235768585080
355017.7715239457983-17.7715239457983
356017.7715239457983-17.7715239457983
3575228.449824437844423.5501755621556
358017.7715239457983-17.7715239457983
359017.7715239457983-17.7715239457983
360017.7715239457983-17.7715239457983
361417.7791106298954-13.7791106298954
362017.7715239457983-17.7715239457983
363017.7715239457983-17.7715239457983
364320.4618720240484-17.4618720240484
3651118.5620163310746-7.56201633107461
366017.7715239457983-17.7715239457983
367017.7715239457983-17.7715239457983
368017.7715239457983-17.7715239457983
369017.7715239457983-17.7715239457983
370017.7715239457983-17.7715239457983
371017.7715239457983-17.7715239457983
3724020.44002746608519.559972533915
373925.6507692888615-16.6507692888615
374120.5849049318268-19.5849049318268
375017.7715239457983-17.7715239457983
376017.7715239457983-17.7715239457983
3772416.78547823120477.21452176879532
3781121.7804364129545-10.7804364129545
379017.7715239457983-17.7715239457983
380017.7715239457983-17.7715239457983
381017.7715239457983-17.7715239457983
3826026.430366583322033.569633416678
3838013.990279953697466.0097200463026
384017.7715239457983-17.7715239457983
3851619.0892382548695-3.08923825486953
3864037.49296975981822.50703024018184
387618.2396208748649-12.2396208748649
388823.2035233133201-15.2035233133201
389318.1322969582112-15.1322969582112
3901620.8040735398405-4.80407353984047
3911021.2594461549404-11.2594461549404
392820.2721205948230-12.2721205948230
393722.0868689263609-15.0868689263609
394825.4055818075537-17.4055818075537
3951252.0900733362797-40.0900733362797
3961320.6868146447314-7.68681464473135
3974248.013526415084-6.01352641508403
39811853.570262384702464.4297376152976
399922.6174969221790-13.6174969221790
40013818.3465814497692119.653418550231
401528.8350537150190-23.8350537150190
402924.4380758244125-15.4380758244125
403821.3116904965644-13.3116904965644
4042533.5154967850998-8.51549678509978
405723.2045101629301-16.2045101629301
4061329.7677685100309-16.7677685100309
4071624.8879719158348-8.88797191583476
4081123.7750885563891-12.7750885563891
4091119.7906418749911-8.7906418749911
410326.3870446648153-23.3870446648153
4116130.258702727224430.7412972727756
4122463.786424526443-39.7864245264431
4131726.2689252560046-9.26892525600463
4143347.9699204173657-14.9699204173657
415734.4902067347163-27.4902067347163
416329.4069997423555-26.4069997423555
4176629.744914717559336.2550852824407
4181728.0480680319462-11.0480680319462
4192629.7731238443703-3.77312384437032
420324.3297681527135-21.3297681527135
421228.2523905925715-26.2523905925715
4226741.845506784497425.1544932155026
4237068.04525703859781.95474296140222
4242660.1412990237561-34.1412990237561
4252430.9383194975819-6.93831949758186
4269452.525576350422941.4744236495771
4273041.159196558124-11.1591965581240
428223298.112951396829-75.1129513968294
4294888.0773533612135-40.0773533612135
43090127.888939690788-37.8889396907880
431180127.19199341161252.8080065883877


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
70.9891981553794040.02160368924119120.0108018446205956
80.9774970536558870.04500589268822630.0225029463441132
90.9990876127298650.001824774540270280.00091238727013514
100.9983065722330060.003386855533988970.00169342776699448
110.9993477548975460.001304490204907470.000652245102453733
120.99902962592360.001940748152801560.00097037407640078
130.998442611371310.003114777257379140.00155738862868957
140.999065787569020.001868424861959910.000934212430979954
150.9999980935192263.8129615471636e-061.9064807735818e-06
160.9999959139197838.17216043469153e-064.08608021734577e-06
170.9999937083218961.25833562086886e-056.2916781043443e-06
180.9999999880635732.38728547938149e-081.19364273969074e-08
190.999999992073151.58537010648383e-087.92685053241916e-09
200.9999999993454251.30914958472870e-096.54574792364349e-10
210.9999999992045441.5909121611595e-097.9545608057975e-10
220.9999999998812432.37513969426365e-101.18756984713182e-10
230.999999999843533.12941739222959e-101.56470869611480e-10
240.9999999998791822.41636250954578e-101.20818125477289e-10
250.9999999997565884.86823973310774e-102.43411986655387e-10
260.9999999999009251.98150974725971e-109.90754873629854e-11
270.9999999997941274.11745993419116e-102.05872996709558e-10
280.9999999995909048.18191082218456e-104.09095541109228e-10
290.9999999996455687.08864075001077e-103.54432037500539e-10
300.9999999999826753.46496779508082e-111.73248389754041e-11
310.999999999981933.61376897378354e-111.80688448689177e-11
320.9999999999784924.30157773814543e-112.15078886907271e-11
330.9999999999745375.09250509159837e-112.54625254579919e-11
340.9999999999590238.19543109227114e-114.09771554613557e-11
350.99999999996227.55997511845712e-113.77998755922856e-11
360.999999999943881.12240096291779e-105.61200481458895e-11
370.999999999915241.69518018823784e-108.4759009411892e-11
380.999999999838613.22779963438828e-101.61389981719414e-10
390.9999999997038845.9223169460568e-102.9611584730284e-10
400.9999999995544768.91048029402752e-104.45524014701376e-10
4115.47857247280166e-372.73928623640083e-37
4211.05162687458587e-375.25813437292937e-38
4312.09918480113947e-381.04959240056974e-38
4415.45546506926487e-382.72773253463244e-38
4519.71631513108687e-384.85815756554343e-38
4611.52050929430785e-377.60254647153925e-38
4712.07613038921895e-371.03806519460947e-37
4814.02562737835402e-402.01281368917701e-40
4919.99711485094308e-404.99855742547154e-40
5011.55945396760864e-397.79726983804318e-40
5114.06615500544673e-392.03307750272336e-39
5217.22186816972113e-393.61093408486057e-39
5311.90454402438523e-389.52272012192614e-39
5411.31730950580054e-386.58654752900269e-39
5512.29867551993438e-381.14933775996719e-38
5614.37679676345945e-382.18839838172972e-38
5713.51833628359207e-381.75916814179604e-38
5817.24435234138452e-383.62217617069226e-38
5911.29579431732063e-376.47897158660316e-38
6013.16370090787591e-371.58185045393795e-37
6115.2976260211133e-372.64881301055665e-37
6211.02906739049415e-365.14533695247075e-37
6311.93737880585877e-369.68689402929386e-37
6414.74474952946187e-362.37237476473094e-36
6511.02790421568163e-355.13952107840816e-36
6611.25070133687803e-1416.25350668439016e-142
6718.67209641444665e-1424.33604820722333e-142
6814.89713069707047e-1412.44856534853523e-141
6913.92132655563702e-1411.96066327781851e-141
7012.26819106324074e-1401.13409553162037e-140
7115.18276263913221e-1402.59138131956610e-140
7211.43366159291475e-1397.16830796457377e-140
7315.1463114231068e-1392.5731557115534e-139
7411.35958050845527e-1386.79790254227635e-139
7514.79638191506848e-1382.39819095753424e-138
7612.07679521561265e-1371.03839760780632e-137
7718.88638717742256e-1374.44319358871128e-137
7812.68501098905315e-1361.34250549452657e-136
7917.39643465082463e-1393.69821732541231e-139
8016.40428061224564e-1463.20214030612282e-146
8112.43710308433503e-1451.21855154216752e-145
8211.01119139748230e-1445.05595698741151e-145
8312.94096805464651e-1441.47048402732325e-144
8411.09980516753733e-1435.49902583768665e-144
8514.04251364912633e-1432.02125682456317e-143
8611.771038973773e-1428.855194868865e-143
8711.53418833939422e-1427.6709416969711e-143
8815.63846934110887e-1422.81923467055444e-142
8911.26696674491754e-1416.33483372458768e-142
9014.42805519875083e-1412.21402759937541e-141
9111.48702310017045e-1407.43511550085227e-141
9218.20269734411939e-1404.10134867205970e-140
9312.39584748145593e-1411.19792374072797e-141
9411.39969051959520e-1406.99845259797602e-141
9513.60342803477391e-1401.80171401738696e-140
9611.88540140618659e-1399.42700703093297e-140
9716.29460376827802e-1393.14730188413901e-139
9814.32968094246649e-1542.16484047123324e-154
9911.27095123940024e-1536.3547561970012e-154
10015.75577909090105e-1532.87788954545053e-153
10113.05704621956482e-1521.52852310978241e-152
10211.57404893591752e-1517.87024467958758e-152
10311.45339590833967e-1517.26697954169837e-152
10417.22222351175378e-1513.61111175587689e-151
10513.56532659079235e-1501.78266329539617e-150
10611.80482986842020e-1499.02414934210098e-150
10714.09421388766382e-1492.04710694383191e-149
10812.00048753968965e-1481.00024376984483e-148
10911.08792316939510e-1475.43961584697549e-148
11015.7215628409632e-1472.8607814204816e-147
11112.56961236718856e-1461.28480618359428e-146
11211.13092732459732e-1455.6546366229866e-146
11313.53998879655240e-1451.76999439827620e-145
11411.46599811645882e-1447.32999058229412e-145
11517.13464184294122e-1443.56732092147061e-144
11612.41542904855657e-1431.20771452427828e-143
11711.17657768686404e-1425.88288843432022e-143
11815.37214387128896e-1422.68607193564448e-142
11912.47543666452093e-1411.23771833226047e-141
12013.33131157993651e-1421.66565578996825e-142
12111.86019236801361e-1419.30096184006806e-142
12219.54367813835706e-1414.77183906917853e-141
12318.77501619185288e-1444.38750809592644e-144
12415.2579248717242e-1432.6289624358621e-143
12512.92902549669949e-1421.46451274834974e-142
12611.42174252691256e-1417.1087126345628e-142
12716.3534446715286e-1413.1767223357643e-141
12813.30136192524862e-1401.65068096262431e-140
12911.30597112075892e-1396.52985560379461e-140
13015.95702916553888e-1392.97851458276944e-139
13113.18549911205095e-1381.59274955602547e-138
13211.28667768075175e-1386.43338840375877e-139
13315.98834178177904e-1382.99417089088952e-138
13413.00749829299624e-1371.50374914649812e-137
13511.41315361776883e-1367.06576808884417e-137
13617.65600982468983e-1363.82800491234492e-136
13714.20047275388725e-1352.10023637694363e-135
13811.99277344214412e-1349.96386721072061e-135
13919.48254166547761e-1344.74127083273881e-134
14014.52408200096904e-1332.26204100048452e-133
14112.50642590379006e-1321.25321295189503e-132
14211.19999353678311e-1315.99996768391554e-132
14316.66120168919015e-1313.33060084459507e-131
14413.42038357866602e-1301.71019178933301e-130
14511.88994038284909e-1299.44970191424545e-130
14611.04827600925881e-1285.24138004629407e-129
14715.03801819493344e-1282.51900909746672e-128
14812.72137377053191e-1271.36068688526595e-127
14911.30829436718936e-1266.5414718359468e-127
15016.43561177587433e-1263.21780588793716e-126
15113.50433326975971e-1251.75216663487985e-125
15215.07182585650349e-1262.53591292825175e-126
15312.46328322641609e-1251.23164161320804e-125
15411.36316373447947e-1246.81581867239733e-125
15517.05996455488912e-1243.52998227744456e-124
15613.42040109986703e-1231.71020054993351e-123
15711.65546377238439e-1228.27731886192193e-123
15818.25686440291608e-1224.12843220145804e-122
15914.36047378738292e-1212.18023689369146e-121
16012.10191988048301e-1201.05095994024151e-120
16111.01165621074727e-1195.05828105373635e-120
16214.8610561603557e-1192.43052808017785e-119
16312.33162262430887e-1181.16581131215443e-118
16419.76036576163147e-1184.88018288081573e-118
16517.40598844777612e-1183.70299422388806e-118
16613.56635881667558e-1171.78317940833779e-117
16711.71388524736643e-1168.56942623683215e-117
16818.90087580808928e-1164.45043790404464e-116
16914.26120478263941e-1152.13060239131971e-115
17012.03534370416067e-1141.01767185208034e-114
17119.69864907065295e-1144.84932453532648e-114
17214.97116795694044e-1132.48558397847022e-113
17312.35692577466523e-1121.17846288733262e-112
17411.25147538963904e-1116.2573769481952e-112
17515.90265190038549e-1112.95132595019274e-111
17613.11475458741546e-1101.55737729370773e-110
17711.46110986166770e-1097.30554930833849e-110
17816.66264983668358e-1093.33132491834179e-109
17913.10743400848354e-1081.55371700424177e-108
18011.44504812491844e-1077.22524062459218e-108
18115.2629083905405e-1072.63145419527025e-107
18212.60205714741698e-1061.30102857370849e-106
18316.02167394683706e-1063.01083697341853e-106
18413.03022999383267e-1051.51511499691634e-105
18511.48624992703929e-1047.43124963519645e-105
18617.6528782540299e-1043.82643912701495e-104
18713.92760048864014e-1031.96380024432007e-103
18811.92676032069166e-1029.63380160345831e-103
18919.26411861812698e-1024.63205930906349e-102
19014.20073914977869e-1012.10036957488935e-101
19111.99397072391052e-1009.96985361955262e-101
19218.98354134415043e-1004.49177067207522e-100
19314.39800891791927e-992.19900445895964e-99
19411.96854500001412e-989.84272500007058e-99
19519.12443925678105e-984.56221962839052e-98
19613.91920754678342e-971.95960377339171e-97
19711.09092326974149e-975.45461634870747e-98
19814.77938008572911e-972.38969004286455e-97
19912.08453203358549e-961.04226601679275e-96
20019.81968071523668e-964.90984035761834e-96
20114.26533754033716e-952.13266877016858e-95
20211.84297452258298e-949.21487261291492e-95
20317.9184546154642e-943.9592273077321e-94
20412.92888411184430e-931.46444205592215e-93
20511.40322704573136e-927.01613522865678e-93
20616.28518903754327e-923.14259451877164e-92
20712.87488719902922e-911.43744359951461e-91
20811.21931269467493e-906.09656347337467e-91
20914.65003138336578e-902.32501569168289e-90
21011.96747815369951e-899.83739076849754e-90
21118.4005867231166e-894.2002933615583e-89
21213.57422625542495e-881.78711312771247e-88
21311.01703135742562e-875.08515678712809e-88
21414.51545676754089e-872.25772838377044e-87
21512.03087317873603e-861.01543658936802e-86
21618.56663976768768e-864.28331988384384e-86
21713.99442762125153e-851.99721381062577e-85
21811.38836749275766e-846.9418374637883e-85
21915.81178108575549e-842.90589054287775e-84
22012.65577984853961e-831.32788992426980e-83
22111.15019151773360e-825.75095758866798e-83
22214.76475326562225e-822.38237663281112e-82
22312.04403722823091e-811.02201861411546e-81
22418.40316512661767e-814.20158256330883e-81
22513.56953299627734e-801.78476649813867e-80
22611.27420012991678e-796.3710006495839e-80
22715.1929562576233e-792.59647812881165e-79
22812.10803108687711e-781.05401554343856e-78
22918.90583453053584e-784.45291726526792e-78
23013.58686977662873e-771.79343488831437e-77
23111.57823429463334e-767.89117147316671e-77
23216.3071124745761e-763.15355623728805e-76
23312.51021959066283e-751.25510979533141e-75
23411.07786803170547e-745.38934015852733e-75
23514.25971538719625e-742.12985769359812e-74
23611.71001950675260e-738.55009753376302e-74
23716.7017734528943e-733.35088672644715e-73
23812.85025978612215e-721.42512989306107e-72
23911.10788588277910e-715.53942941389551e-72
24014.28791446266185e-712.14395723133093e-71
24111.65243617986291e-708.26218089931453e-71
24216.62296451011994e-703.31148225505997e-70
24312.53037807239112e-691.26518903619556e-69
24411.06669658414336e-685.33348292071679e-69
24512.67421574130856e-681.33710787065428e-68
24611.00085057957859e-675.00425289789295e-68
24713.718516941598e-671.859258470799e-67
24811.55405266651113e-667.77026333255565e-67
24915.7075707234322e-662.8537853617161e-66
25012.07940071727167e-651.03970035863584e-65
25118.56947019188421e-654.28473509594211e-65
25213.08386798342622e-641.54193399171311e-64
25311.15011101146931e-635.75055505734654e-64
25411.55530577120603e-647.77652885603015e-65
25514.02132635830837e-662.01066317915418e-66
25611.55133207130311e-657.75666035651553e-66
25716.47863321016161e-653.23931660508081e-65
25811.56250875393251e-647.81254376966253e-65
25915.69076296152512e-642.84538148076256e-64
26012.17343801633144e-631.08671900816572e-63
26117.81106766144226e-633.90553383072113e-63
26212.77777127212710e-621.38888563606355e-62
26311.14460847850617e-615.72304239253086e-62
26414.67538581505956e-612.33769290752978e-61
26511.63226971068949e-608.16134855344743e-61
26616.09987151812513e-603.04993575906256e-60
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36614.58917206281507e-172.29458603140753e-17
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36813.27933755334410e-161.63966877667205e-16
36918.63637017570787e-164.31818508785394e-16
3700.9999999999999992.25138964086226e-151.12569482043113e-15
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3790.9999999999961327.73562935367258e-123.86781467683629e-12
3800.9999999999907371.85253521291318e-119.2626760645659e-12
3810.9999999999780924.38150594932057e-112.19075297466029e-11
3820.9999999999802243.95509587563115e-111.97754793781557e-11
3830.9999999999942641.14727308207414e-115.73636541037068e-12
3840.9999999999853262.93478193184902e-111.46739096592451e-11
3850.999999999961437.71392808816143e-113.85696404408072e-11
3860.9999999999099131.80175144669434e-109.00875723347168e-11
3870.9999999997666384.66723830036795e-102.33361915018398e-10
3880.9999999994147161.17056740236002e-095.85283701180012e-10
3890.9999999985474912.90501700546785e-091.45250850273393e-09
3900.999999996350267.29947983602111e-093.64973991801056e-09
3910.9999999909646721.80706556737168e-089.0353278368584e-09
3920.9999999781452714.37094588829378e-082.18547294414689e-08
3930.9999999484983841.03003231533285e-075.15016157666427e-08
3940.999999879809422.40381160531661e-071.20190580265830e-07
3950.9999998666722592.66655482699204e-071.33327741349602e-07
3960.999999683963726.32072559514826e-073.16036279757413e-07
3970.999999262585631.47482874034712e-067.3741437017356e-07
3980.9999999531822879.3635425737764e-084.6817712868882e-08
3990.9999998789418172.42116367073988e-071.21058183536994e-07
4000.999999999339781.32044062884282e-096.6022031442141e-10
4010.999999998054793.89041996614763e-091.94520998307382e-09
4020.9999999939709581.20580838773750e-086.02904193868752e-09
4030.999999981876663.62466794022009e-081.81233397011004e-08
4040.9999999452798821.09440236126035e-075.47201180630173e-08
4050.9999998419534563.16093087544844e-071.58046543772422e-07
4060.9999995394857279.21028545489577e-074.60514272744789e-07
4070.9999986639500052.6720999907987e-061.33604999539935e-06
4080.999996378637147.24272572121309e-063.62136286060655e-06
4090.9999901513708761.96972582482763e-059.84862912413815e-06
4100.9999762319003164.75361993683547e-052.37680996841774e-05
4110.999976421687244.71566255215014e-052.35783127607507e-05
4120.9999622267885817.55464228381153e-053.77732114190576e-05
4130.9998989430318470.0002021139363051340.000101056968152567
4140.9997311140655920.0005377718688150460.000268885934407523
4150.9993359660899310.001328067820137350.000664033910068676
4160.9984743642762950.003051271447410270.00152563572370513
4170.9975548699835740.004890260032851430.00244513001642571
4180.9946802958166330.01063940836673480.0053197041833674
4190.9876585977078130.02468280458437310.0123414022921865
4200.9734041101516350.05319177969672960.0265958898483648
4210.9482037879441670.1035924241116650.0517962120558327
4220.9274582663638270.1450834672723460.0725417336361731
4230.995951964243590.008096071512819020.00404803575640951
4240.9916996978389550.01660060432209000.00830030216104499


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level4100.980861244019139NOK
5% type I error level4150.992822966507177NOK
10% type I error level4160.995215311004785NOK
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Dec/02/t12913158370m1zcsyy52v2cb6/106gqd1291315881.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/02/t12913158370m1zcsyy52v2cb6/106gqd1291315881.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/02/t12913158370m1zcsyy52v2cb6/1a7t41291315881.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/02/t12913158370m1zcsyy52v2cb6/1a7t41291315881.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/02/t12913158370m1zcsyy52v2cb6/2a7t41291315881.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/02/t12913158370m1zcsyy52v2cb6/2a7t41291315881.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/02/t12913158370m1zcsyy52v2cb6/3a7t41291315881.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/02/t12913158370m1zcsyy52v2cb6/3a7t41291315881.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/02/t12913158370m1zcsyy52v2cb6/42yr71291315881.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/02/t12913158370m1zcsyy52v2cb6/42yr71291315881.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/02/t12913158370m1zcsyy52v2cb6/52yr71291315881.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/02/t12913158370m1zcsyy52v2cb6/52yr71291315881.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/02/t12913158370m1zcsyy52v2cb6/62yr71291315881.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/02/t12913158370m1zcsyy52v2cb6/62yr71291315881.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/02/t12913158370m1zcsyy52v2cb6/7d79s1291315881.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/02/t12913158370m1zcsyy52v2cb6/7d79s1291315881.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/02/t12913158370m1zcsyy52v2cb6/8d79s1291315881.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/02/t12913158370m1zcsyy52v2cb6/8d79s1291315881.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/02/t12913158370m1zcsyy52v2cb6/96gqd1291315881.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/02/t12913158370m1zcsyy52v2cb6/96gqd1291315881.ps (open in new window)


 
Parameters (Session):
par1 = 3 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;
 
Parameters (R input):
par1 = 3 ; 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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