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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: Tue, 21 Dec 2010 18:27:48 +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/21/t12929559841on31sm1n0zywdt.htm/, Retrieved Tue, 21 Dec 2010 19:26:28 +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/21/t12929559841on31sm1n0zywdt.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 «
807 213118 171986226 6282154 444 81767 36304548 4321023 412 153198 63117576 4111912 428 -26007 -11130996 223193 315 126942 39986730 1491348 168 157214 26411952 1629616 263 129352 34019576 1398893 267 234817 62696139 1926517 228 60448 13782144 983660 129 47818 6168522 1443586 104 245546 25536784 1073089 122 48020 5858440 984885 393 -1710 -672030 1405225 190 32648 6203120 227132 280 95350 26698000 929118 63 151352 9535176 1071292 102 288170 29393340 638830 265 114337 30299305 856956 234 37884 8864856 992426 277 122844 34027788 444477 73 82340 6010820 857217 67 79801 5346667 711969 103 165548 17051444 702380 290 116384 33751360 358589 83 134028 11124324 297978 56 63838 3574928 585715 236 74996 17699056 657954 73 31080 2268840 209458 34 32168 1093712 786690 139 49857 6930123 439798 26 87161 2266186 688779 70 106113 7427910 574339 40 80570 3222800 741409 42 102129 4289418 597793 12 301670 3620040 644190 211 102313 21588043 377934 74 88577 6554698 640273 80 112477 8998160 697458 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 time14 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk
R Framework
error message
The field 'Names of X columns' contains a hard return which cannot be interpreted.
Please, resubmit your request without hard returns in the 'Names of X columns'.


Multiple Linear Regression - Estimated Regression Equation
Wealth [t] = + 391670.712868058 + 843.172459312874Orders[t] -1.82322465724293Dividends[t] + 0.0305718053114561O_D[t] + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0		2-tail p-value1-tail p-value
(Intercept)391670.71286805833405.22016311.724800
Orders843.172459312874285.6765072.95150.0033370.001668
Dividends-1.823224657242930.448956-4.0615.8e-052.9e-05
O_D0.03057180531145610.00220213.88300


Multiple Linear Regression - Regression Statistics
Multiple R0.839477017094254
R-squared0.704721662229466
Adjusted R-squared0.702647107163163
F-TEST (value)339.69773744553
F-TEST (DF numerator)3
F-TEST (DF denominator)427
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation234757.882869973
Sum Squared Residuals23532509544215.8


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast		Residuals
Prediction Error
162821545941478.31255533340675.687444671
243210231726855.24763062594167.7523694
341119122389361.640267691722550.35973231
4223193459670.486480288-236477.486480288
514913481648292.77771364-156944.77771364
616296161054148.29920835575467.700791647
713988931417627.16805394-18734.1680539389
819265172105407.77045277-178890.770452769
9983660895048.77265282588611.2273471755
101443586601839.85710281841746.14289719
111073089812380.71567793260708.28432207
12984885586089.591972269398795.408027731
131405225705610.033218444699614.966781556
14227132681989.418491436-454857.418491436
159291181270120.5886128-341002.588612803
161071292460349.423764205610942.576235795
17638830850883.12217371-212053.12217371
188569561332953.83048321-475997.830483212
19992426790916.677178372201509.322821628
204444771441548.18421887-997071.184218874
21857217486859.602922721370357.397077279
22711969466125.379358564245843.620641436
23702380697979.7068672274400.29313277334
243585891455836.5544771-1097247.5544771
25297978557381.540179629-259403.540179629
26585715431789.357738978153925.642261022
27657954995016.951099863-337062.951099863
28209458465919.014813631-256461.014813631
29786690395125.836041308391564.163958692
30439798629837.54411683-190039.54411683
31688779323960.509651789364818.490348211
32574339484309.56535695790029.4346430425
33741409377027.21476427364381.78523573
34597793372015.097135091225777.902864909
35644190-37552.241870979681742.241870979
363779341043025.96507792-665091.96507792
37640273492958.655523994147314.344476006
38697458529143.665521706168314.334478294
39550608598628.622032986-48020.6220329865
40207393676233.242482312-468840.242482312
413016071125128.31362972-823521.313629719
42345783428163.009653854-82380.0096538542
43501749550924.008324784-49175.0083247844
44379983567770.800866205-187787.800866205
45387475380920.3485688616554.6514311393
46377305304959.47019740172345.5298025993
47370837364508.1448883716328.85511162942
48430866891572.96518881-460706.96518881
49469107434471.40650436434635.5934956356
50194493382707.833502212-188214.833502212
51530670567893.173206487-37223.1732064869
52518365820942.559776654-302577.559776654
53491303689196.823439255-197893.823439255
54527021459821.44770278867199.5522972123
55233773748068.784736907-514295.784736907
56405972489158.777605645-83186.7776056446
57652925314166.128516344338758.871483656
58446211397409.21333269748801.7866673035
59341340408401.185638777-67061.1856387765
60387699531123.210722517-143424.210722517
61493408379934.681761339113473.318238661
62146494367681.172164238-221187.172164238
63414462312501.16627058101960.83372942
64364304500346.540927252-136042.540927252
65355178427030.612714022-71852.6127140219
663577601134683.76042607-776923.760426066
67261216294067.057318205-32851.0573182051
68397144380761.55713438116382.442865619
69374943506785.434479665-131842.434479665
70424898541086.828228384-116188.828228384
71202055424098.278010882-222043.278010882
72378525397887.12181489-19362.1218148897
73310768340674.740829622-29906.7408296222
74325738276519.86830943749218.1316905629
75394510327161.6367728667348.3632271402
76247060314471.49935897-67411.4993589704
77368078308626.15033324559451.8496667549
78236761290890.130786066-54129.1307860656
79312378419296.243646882-106918.243646883
80339836234575.373277886105260.626722114
81347385359004.393253736-11619.393253736
82426280464851.880979517-38571.8809795168
83352850306323.66392964146526.3360703586
84301881350244.139496497-48363.1394964965
85377516264134.877351761113381.122648239
86357312465429.661040083-108117.661040083
87458343587367.283889549-129024.283889548
88354228254406.70291447799821.2970855231
89308636381905.752726495-73269.752726495
90386212259286.180174441126925.819825559
91393343352975.9786744440367.0213255602
92378509375626.5925105882882.40748941223
93452469465264.50590494-12795.5059049405
94364839297253.43948766167585.5605123393
95358649408839.506836845-50190.5068368454
96376641362377.85736050814263.142639492
97429112224334.145127221204777.854872779
98330546329463.6424765461082.35752345365
99403560246010.212822832157549.787177168
100317892285907.4157842831984.5842157198
101307528351171.35161913-43643.3516191297
102235133295215.137095451-60082.1370954509
103299243422665.548298189-123422.548298189
104314073218827.2654622495245.7345377597
105368186348835.8013297819350.19867022
106269661349095.65432807-79434.65432807
107125390410856.437259881-285466.437259881
108510834274568.794870568236265.205129432
109321896392092.653630251-70196.6536302511
110249898320129.340103654-70231.3401036539
111408881332046.84036772476834.159632276
112158492380388.444279265-221896.444279265
113292154387603.626613669-95449.6266136692
114289513297094.891089005-7581.8910890052
115378049302392.40885015875656.5911498423
116343466378727.73757329-35261.7375732897
117332743264246.61079084968496.3892091506
118442882290527.228244438152354.771755562
119214215286154.243451834-71939.2434518337
120315688337013.634238411-21325.6342384106
121375195578380.255442361-203185.255442361
122334280304212.46181494730067.5381850533
123355864635140.54024786-279276.54024786
124480382298833.56289842181548.43710158
125353058323988.17507599729069.8249240026
126217193326126.29345291-108933.29345291
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129318056346172.242351427-28116.2423514265
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134312846334751.992548738-21905.9925487375
135312075291762.48159156520312.5184084349
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137318903307617.99747258311285.0025274169
138314887283664.00415809231222.9958419084
139314913291762.48159156523150.5184084349
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141325506305291.51637438320214.4836256173
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143298568316562.06008764-17994.0600876396
144315834291466.51847770224367.4815222984
145329784317873.33430893311910.6656910673
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151291650303192.048606568-11542.0486065684
152305959405258.737555036-99299.7375550358
153315380294461.9740693920918.0259306105
154297765303232.27915707-5467.27915706995
155315245285979.36296775329265.6370322471
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158315236285006.69423001930229.3057699813
159336425294253.17836555442171.8216344461
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174309596303374.384477996221.6155220102
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176315547302195.78330325513351.2166967445
177313267586007.161674434-272740.161674434
178316176280918.93106383635257.0689361639
179315380280964.51168026734415.4883197329
180315380280964.51168026734415.4883197329
181359335318685.80894714840649.1910528522
182330068294420.11399845735647.8860015431
183314289353670.228322401-39381.228322401
184297413309277.444237447-11864.4442374472
185314806291396.85313708123409.1468629186
186333210311179.35611592222030.6438840776
187352108338401.17494024513706.8250597546
188313332294995.29890389518336.7010961053
189291787286068.3867751945718.61322480584
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191318745301824.20988951516920.7901104849
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193315366298396.56698678116969.4330132186
194315380280964.51168026734415.4883197329
195315688288768.63254271826919.3674572819
196315380280964.51168026734415.4883197329
197409642568617.005489829-158975.005489829
198315380280964.51168026734415.4883197329
199315380280964.51168026734415.4883197329
200269587308246.254872947-38659.2548729466
201315380280964.51168026734415.4883197329
202315380280964.51168026734415.4883197329
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204300962327799.716857761-26837.7168577611
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209343613363695.223561835-20082.2235618353
210306948289062.98911374117885.0108862594
211315380280964.51168026734415.4883197329
212315380280964.51168026734415.4883197329
213330059315238.68811669314820.3118833074
214288985306051.930657123-17066.9306571226
215304485291288.27937108713196.7206289132
216315380286363.49663591629016.5033640839
217315688296979.44943259718708.5505674025
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219315380286363.49663591629016.5033640839
220322331360897.92847716-38566.9284771598
221296656289426.6060544157229.39394558461
222315380280964.51168026734415.4883197329
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224312161334954.361236757-22793.3612367568
225315576283511.62866567732064.3713343226
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230315380280964.51168026734415.4883197329
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232321376305259.94398068716116.0560193125
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250315380280964.51168026734415.4883197329
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252315380280964.51168026734415.4883197329
253307322277344.90285503329977.0971449668
254304376375417.423804804-71041.4238048044
255253588433060.71673643-179472.71673643
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260315380280964.51168026734415.4883197329
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270331420341796.345932641-10376.345932641
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275315380280964.51168026734415.4883197329
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286315380280964.51168026734415.4883197329
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307315380280964.51168026734415.4883197329
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309309836334725.13725175-24889.1372517495
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325315380280964.51168026734415.4883197329
326312502283660.41885238828841.5811476123
327315380280964.51168026734415.4883197329
328315380280964.51168026734415.4883197329
329315380280964.51168026734415.4883197329
330315380280964.51168026734415.4883197329
331315380280964.51168026734415.4883197329
332315380280964.51168026734415.4883197329
333315380280964.51168026734415.4883197329
334313729292342.5012572421386.4987427599
335315388283651.45558812831736.5444118719
336315371291762.48159156523608.5184084349
337296139334705.944583799-38566.944583799
338315380280964.51168026734415.4883197329
339313880283348.49725615230531.5027438483
340317698309455.6979701838242.30202981745
341295580310083.061041767-14503.0610417672
342315380280964.51168026734415.4883197329
343315380280964.51168026734415.4883197329
344315380280964.51168026734415.4883197329
345308256316057.913891985-7801.91389198542
346315380280964.51168026734415.4883197329
347303677291836.86691831711840.1330816831
348315380280964.51168026734415.4883197329
349315380280964.51168026734415.4883197329
350319369307959.43645851211409.563541488
351318690292737.25172379725952.7482762026
352314049299210.83332893314838.1666710668
353325699309666.63138815616032.3686118436
354314210281252.88607224432957.1139277562
355315380280964.51168026734415.4883197329
356315380280964.51168026734415.4883197329
357322378296811.36359670125566.6364032995
358315380280964.51168026734415.4883197329
359315380280964.51168026734415.4883197329
360315380280964.51168026734415.4883197329
361315398291759.07971669323638.9202833069
362315380280964.51168026734415.4883197329
363315380280964.51168026734415.4883197329
364308336355699.152643853-47363.1526438532
365316386306939.609054939446.3909450703
366315380280964.51168026734415.4883197329
367315380280964.51168026734415.4883197329
368315380280964.51168026734415.4883197329
369315380280964.51168026734415.4883197329
370315553299860.95902503915692.0409749615
371315380280964.51168026734415.4883197329
372323361301372.01850187721988.9814981226
373336639274235.70757755962403.2924224405
374307424281963.80122437525460.1987756245
375315380280964.51168026734415.4883197329
376315380280964.51168026734415.4883197329
377295370317412.586792563-22042.5867925629
378322340300317.97807873622022.0219212637
379319864307959.43645851211904.563541488
380315380280964.51168026734415.4883197329
381315380280964.51168026734415.4883197329
382317291313372.589710223918.41028977976
383280398345605.612954619-65207.6129546187
384315380280964.51168026734415.4883197329
385317330310474.822687026855.17731297986
386238125352614.619461233-114489.619461233
387327071290896.65740028636174.3425997137
388309038300605.03358058432.96641950014
389314210289620.53508944224589.4649105581
390307930305938.7629624311991.23703756925
391322327304939.59831629717387.4016837035
392292136299448.978933611-7312.97893361104
393263276302197.36195347-38921.3619534702
394367655285125.37986896782529.6201310325
395283910269808.94840451614101.0515954845
396283587306134.51558906-22547.5155890599
397243650359284.597304422-115634.597304422
3984384931257633.41948795-819140.419487947
399296261294791.9096618411469.09033815911
400230621414274.820490308-183653.820490308
401304252272276.00701925431975.9929807459
402333505297019.38924908636485.610750914
403296919299670.351100037-2751.35110003655
404278990327458.771982424-48468.7719824243
405276898294148.220853816-17250.2208538158
406327007295828.24125293731178.7587470634
407317046299826.60892695517219.3910730448
408304555315965.311172536-11410.3111725357
409298096308975.332163343-10879.3321633431
410231861273029.213539223-41168.2135392233
411309422434098.366784961-124676.366784961
412286963334659.469264226-47696.4692642259
413269753326096.700611376-56343.7006113761
414448243355088.38183627193154.618163729
415165404282853.24819846-117449.24819846
416204325263861.721670578-59536.7216705785
417407159371581.10142070435577.8985792964
418290476333057.91215442-42581.9121544202
419275311336506.822863644-61195.8228636436
420246541274342.209328048-27801.209328048
421253468267440.495848112-13972.4958481118
422240897485979.775978312-245082.775978312
423-83265445287.892979583-528552.892979583
424-42143340880.007251214-383023.007251214
425272713341674.940540679-68961.9405406794
426215362506642.280085952-291280.280085952
42742754348837.613862891-306083.613862891
4283062751483870.12986769-1177595.12986769
429253537351472.094758728-97935.0947587283
430372631526596.35879752-153965.35879752
431-7170457659.109404556-464829.109404556


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
70.999999999999882.41220497723694e-131.20610248861847e-13
811.76627368047406e-728.83136840237029e-73
914.41385352284742e-732.20692676142371e-73
1012.3079020140213e-871.15395100701065e-87
1118.96704077456703e-914.48352038728352e-91
1211.09796369110654e-935.4898184555327e-94
1316.20357247913331e-953.10178623956665e-95
1412.51495261646083e-1001.25747630823041e-100
1514.0475698926693e-1062.02378494633465e-106
1619.64827166421658e-1144.82413583210829e-114
1713.83003639254322e-1151.91501819627161e-115
1812.37506313993295e-1221.18753156996648e-122
1913.43109114579225e-1271.71554557289612e-127
2015.53062975607301e-1372.76531487803651e-137
2112.30057533347948e-1431.15028766673974e-143
2212.62389525158638e-1461.31194762579319e-146
2312.40323195662183e-1471.20161597831091e-147
2414.03900176542722e-1572.01950088271361e-157
2514.86621026674051e-1572.43310513337025e-157
2613.27171997681371e-1581.63585998840686e-158
2712.09620683720277e-1611.04810341860139e-161
2815.98231328311921e-1612.9911566415596e-161
2915.42894694179624e-1712.71447347089812e-171
3013.62038318020682e-1711.81019159010341e-171
3118.63979107248506e-1764.31989553624253e-176
3211.61797979488279e-1768.08989897441397e-177
3315.84959699700016e-1842.92479849850008e-184
3418.06296332810018e-1864.03148166405009e-186
3511.12870317592278e-1865.64351587961389e-187
3613.96510059816076e-1891.98255029908038e-189
3715.26384272267204e-1932.63192136133602e-193
3813.45176659076863e-1981.72588329538431e-198
3911.81311638299933e-1979.06558191499665e-198
4011.14176730558576e-1985.70883652792882e-199
4112.20697161753378e-2021.10348580876689e-202
4212.40005374406423e-2011.20002687203212e-201
4317.4484259446832e-2023.7242129723416e-202
4415.1980091391581e-2012.59900456957905e-201
4512.8037667165859e-2001.40188335829295e-200
4612.91767131933999e-1991.45883565966999e-199
4719.88378670452643e-2004.94189335226321e-200
4815.84579907765011e-2002.92289953882505e-200
4912.8387336722113e-1991.41936683610565e-199
5011.77190546573944e-1998.85952732869722e-200
5113.04028582470116e-2001.52014291235058e-200
5211.06764762584352e-2005.3382381292176e-201
5316.88382626630964e-2003.44191313315482e-200
5411.1911281759573e-1995.95564087978648e-200
5518.53431166231296e-2034.26715583115648e-203
5619.29926849793954e-2034.64963424896977e-203
5711.79621961391072e-2128.98109806955362e-213
5812.20881878017452e-2121.10440939008726e-212
5912.42132232515249e-2111.21066116257625e-211
6011.1672549742578e-2105.83627487128899e-211
6111.82976754458544e-2119.14883772292719e-212
6211.44085041943165e-2127.20425209715825e-213
6316.28102379075332e-2123.14051189537666e-212
6414.10722263545506e-2112.05361131772753e-211
6511.82612293490272e-2109.13061467451359e-211
6614.7835150860519e-2132.39175754302595e-213
6711.83670593311841e-2129.18352966559204e-213
6811.41426018265321e-2117.07130091326607e-212
6911.24469127478666e-2106.22345637393329e-211
7013.00351118642898e-2101.50175559321449e-210
7112.10889709575453e-2091.05444854787726e-209
7211.15087924516323e-2095.75439622581616e-210
7316.60055576747241e-2093.30027788373621e-209
7416.42488769637264e-2083.21244384818632e-208
7516.36958551692552e-2073.18479275846276e-207
7611.76758230148045e-2068.83791150740224e-207
7711.68879638813174e-2058.44398194065868e-206
7813.26239916692527e-2051.63119958346263e-205
7913.24661579939151e-2041.62330789969575e-204
8011.51304161501964e-2037.5652080750982e-204
8119.34302039773237e-2034.67151019886619e-203
8211.3532971924683e-2026.7664859623415e-203
8314.1432094251815e-2022.07160471259075e-202
8413.42289593142679e-2011.7114479657134e-201
8512.89194913703651e-2001.44597456851826e-200
8617.40619782253952e-2003.70309891126976e-200
8715.48629846424876e-2012.74314923212438e-201
8814.33501058379734e-2002.16750529189867e-200
8912.02923478500789e-1991.01461739250395e-199
9011.61087079269089e-1988.05435396345445e-199
9111.07038156383584e-1975.35190781917918e-198
9215.76322349616579e-1972.8816117480829e-197
9312.39777282741762e-1991.19888641370881e-199
9411.46457222150689e-1987.32286110753443e-199
9513.35911518657846e-1991.67955759328923e-199
9614.82163023661515e-1992.41081511830758e-199
9712.43294688445144e-1981.21647344222572e-198
9812.24275003497612e-1971.12137501748806e-197
9911.6236852653467e-1968.11842632673351e-197
10011.52918598481246e-1957.64592992406232e-196
10111.50103195928548e-1947.50515979642738e-195
10215.2543794488149e-1952.62718972440745e-195
10311.27874474862119e-1946.39372374310597e-195
10418.3446004515646e-1954.1723002257823e-195
10513.30568856546629e-1941.65284428273315e-194
10612.0152571056691e-1931.00762855283455e-193
10715.8487976480487e-1952.92439882402435e-195
10814.08860506810126e-1962.04430253405063e-196
10912.38724349974319e-1951.19362174987159e-195
11015.71481203683262e-1952.85740601841631e-195
11114.19678406805094e-1952.09839203402547e-195
11212.1030890245665e-1951.05154451228325e-195
11311.22065203833875e-1946.10326019169375e-195
11417.55410052597402e-1943.77705026298701e-194
11511.40883832731083e-1937.04419163655416e-194
11614.11894033872232e-1932.05947016936116e-193
11713.14184070129423e-1921.57092035064711e-192
11813.57649602433827e-1921.78824801216914e-192
11914.39104819346961e-1932.1955240967348e-193
12014.03286934732528e-1922.01643467366264e-192
12112.77142621297032e-1911.38571310648516e-191
12212.45199411154445e-1901.22599705577222e-190
12316.46226051647387e-1903.23113025823694e-190
12414.24114906190083e-1902.12057453095042e-190
12512.00162819557399e-1891.00081409778699e-189
12617.15240668619673e-1903.57620334309836e-190
12716.76190468085913e-1893.38095234042957e-189
12816.41839755694546e-1883.20919877847273e-188
12914.91006887345467e-1872.45503443672734e-187
13014.58416503784008e-1862.29208251892004e-186
13114.30721739167926e-1852.15360869583963e-185
13214.45213860842491e-1852.22606930421245e-185
13314.13626163614232e-1842.06813081807116e-184
13413.68649806693064e-1831.84324903346532e-183
13513.44455012486209e-1821.72227506243105e-182
13613.17525677920483e-1811.58762838960242e-181
13712.81534908657817e-1801.40767454328909e-180
13812.56684194624369e-1791.28342097312184e-179
13912.33714901434009e-1781.16857450717005e-178
14012.10630837544589e-1771.05315418772294e-177
14111.66782239910561e-1768.33911199552804e-177
14211.49081231598625e-1757.45406157993126e-176
14311.36550173580345e-1746.82750867901725e-175
14411.21194371244815e-1736.05971856224073e-174
14519.2616673638913e-1734.63083368194565e-173
14617.78961170488528e-1723.89480585244264e-172
14716.80698800535127e-1713.40349400267563e-171
14815.92833918014261e-1702.9641695900713e-170
14914.86665525017122e-1692.43332762508561e-169
15014.19452559113591e-1682.09726279556796e-168
15113.56116369290324e-1671.78058184645162e-167
15212.15814789133151e-1661.07907394566575e-166
15311.83758192054083e-1659.18790960270415e-166
15411.58118856083985e-1647.90594280419927e-165
15511.33654934908777e-1636.68274674543885e-164
15611.12164789090892e-1625.60823945454458e-163
15719.3720896118494e-1624.6860448059247e-162
15817.82419576685697e-1613.91209788342849e-161
15915.28885335548635e-1602.64442667774318e-160
16014.36416944405131e-1592.18208472202565e-159
16113.58530448277574e-1581.79265224138787e-158
16212.93244501567086e-1571.46622250783543e-157
16312.38785817009163e-1561.19392908504582e-156
16411.967429090389e-1559.83714545194498e-156
16511.5984826484107e-1547.99241324205351e-155
16611.28552394293172e-1536.42761971465858e-154
16711.02730145157881e-1525.13650725789407e-153
16812.31284327570894e-1531.15642163785447e-153
16913.35300245216343e-1531.67650122608171e-153
17012.6968737889509e-1521.34843689447545e-152
17112.15953423147181e-1511.07976711573591e-151
17211.73515684107099e-1508.67578420535494e-151
17311.37699271776658e-1496.8849635888329e-150
17411.10246356947668e-1485.5123178473834e-149
17518.66900997131471e-1484.33450498565736e-148
17616.70090091889177e-1473.35045045944589e-147
17718.46511111340067e-1484.23255555670034e-148
17816.67416543741938e-1473.33708271870969e-147
17915.24520960878996e-1462.62260480439498e-146
18014.1039560011383e-1452.05197800056915e-145
18111.89897070068478e-1449.4948535034239e-145
18211.45914410590661e-1437.29572052953304e-144
18317.5521879292481e-1433.77609396462405e-143
18415.28577751958557e-1422.64288875979279e-142
18514.07685416043358e-1412.03842708021679e-141
18612.37614918319925e-1401.18807459159962e-140
18718.01195360991156e-1404.00597680495578e-140
18816.12396666461226e-1393.06198333230613e-139
18913.95515329657063e-1381.97757664828531e-138
19012.98416229404751e-1371.49208114702375e-137
19112.12532086284271e-1361.06266043142136e-136
19211.58949098432798e-1357.94745492163992e-136
19311.17432652092662e-1345.87163260463312e-135
19418.70401280512876e-1344.35200640256438e-134
19516.4085027214163e-1333.20425136070815e-133
19614.7075802045826e-1322.3537901022913e-132
19711.26367673460326e-1316.31838367301629e-132
19819.24157458508021e-1314.62078729254011e-131
19916.72854823996802e-1303.36427411998401e-130
20012.02690686597772e-1291.01345343298886e-129
20111.46809826209419e-1287.34049131047095e-129
20211.05862027157183e-1275.29310135785915e-128
20317.59953731412798e-1273.79976865706399e-127
20414.93084570479405e-1262.46542285239702e-126
20512.91863147723804e-1251.45931573861902e-125
20612.05990089591575e-1241.02995044795788e-124
20711.44866899820831e-1237.24334499104156e-124
20811.01793846521635e-1225.08969232608176e-123
20911.10016292925838e-1225.50081464629188e-123
21017.76512282189582e-1223.88256141094791e-122
21115.42882796892015e-1212.71441398446008e-121
21213.77846356627836e-1201.88923178313918e-120
21311.91848468275739e-1199.59242341378693e-120
21411.26724417927389e-1186.33622089636946e-119
21518.688477127228e-1184.344238563614e-118
21615.93989095694836e-1172.96994547847418e-117
21713.99212635698197e-1161.99606317849099e-116
21812.6204720484279e-1151.31023602421395e-115
21911.76710072859209e-1148.83550364296047e-115
22016.11743444217503e-1143.05871722108751e-114
22113.99450765442915e-1131.99725382721458e-113
22212.66963842174626e-1121.33481921087313e-112
22311.77536737447054e-1118.8768368723527e-112
22411.04266894302614e-1105.21334471513068e-111
22516.87240262361764e-1103.43620131180882e-110
22613.82578034197232e-1091.91289017098616e-109
22712.43300571160071e-1081.21650285580035e-108
22811.58396544099323e-1077.91982720496616e-108
22911.01576620483714e-1065.0788310241857e-107
23016.55375589190766e-1063.27687794595383e-106
23114.10361022436721e-1052.0518051121836e-105
23212.42843256995296e-1041.21421628497648e-104
23311.54612396081646e-1037.73061980408231e-104
23419.83976119905054e-1034.91988059952527e-103
23516.20667681684272e-1023.10333840842136e-102
23613.89660999651613e-1011.94830499825806e-101
23712.43539970340839e-1001.2176998517042e-100
23811.48450023685708e-997.42250118428539e-100
23919.1931547366489e-994.59657736832445e-99
24015.66684719854178e-982.83342359927089e-98
24113.4770223855803e-971.73851119279015e-97
24212.13014024146901e-961.0650701207345e-96
24311.29486631374375e-956.47433156871875e-96
24417.5945332779533e-953.79726663897665e-95
24514.43757574488882e-942.21878787244441e-94
24612.66094238920249e-931.33047119460125e-93
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3900.9999999913173091.73653824618733e-088.68269123093664e-09
3910.9999999817066983.65866038203296e-081.82933019101648e-08
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3930.9999999025906411.94818717114965e-079.74093585574823e-08
3940.9999998339088583.32182284677356e-071.66091142338678e-07
3950.9999996427312087.14537584234416e-073.57268792117208e-07
3960.9999992230457631.55390847487898e-067.76954237439488e-07
3970.9999982923655173.41526896575485e-061.70763448287743e-06
3980.9999988943735072.21125298533679e-061.1056264926684e-06
3990.9999975207430984.95851380436677e-062.47925690218339e-06
4000.9999968570690586.28586188463569e-063.14293094231785e-06
4010.999992882921461.42341570819097e-057.11707854095487e-06
4020.9999865233301782.69533396447177e-051.34766698223588e-05
4030.999972968890355.40622193011506e-052.70311096505753e-05
4040.9999414607350550.0001170785298902515.85392649451255e-05
4050.9998766263644450.0002467472711102910.000123373635555145
4060.9997595139498230.0004809721003539210.000240486050176961
4070.9995423271111580.0009153457776843110.000457672888842155
4080.999214301435350.001571397129298460.000785698564649232
4090.998671230369990.002657539260022350.00132876963001118
4100.99747996031480.005040079370399560.00252003968519978
4110.995640706696530.008718586606939510.00435929330346976
4120.9923942026773910.0152115946452180.00760579732260901
4130.9872296288501020.02554074229979570.0127703711498978
4140.9889947114506330.02201057709873470.0110052885493674
4150.984360693531930.03127861293614010.0156393064680701
4160.9739276696042360.05214466079152810.026072330395764
4170.9976556638590510.004688672281897070.00234433614094853
4180.9963847449571350.007230510085730890.00361525504286545
4190.9920131509456230.01597369810875430.00798684905437713
4200.9844017211221760.03119655775564740.0155982788778237
4210.9707689297630320.05846214047393670.0292310702369684
4220.9348680583416070.1302638833167860.0651319416583929
4230.885544336538190.2289113269236210.11445566346181
4240.8880028804667210.2239942390665580.111997119533279


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level4070.973684210526316NOK
5% type I error level4130.988038277511962NOK
10% type I error level4150.992822966507177NOK
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Dec/21/t12929559841on31sm1n0zywdt/10jljo1292956049.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/21/t12929559841on31sm1n0zywdt/10jljo1292956049.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/21/t12929559841on31sm1n0zywdt/1nb4g1292956049.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/21/t12929559841on31sm1n0zywdt/1nb4g1292956049.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/21/t12929559841on31sm1n0zywdt/2nb4g1292956049.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/21/t12929559841on31sm1n0zywdt/2nb4g1292956049.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/21/t12929559841on31sm1n0zywdt/3nb4g1292956049.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/21/t12929559841on31sm1n0zywdt/3nb4g1292956049.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/21/t12929559841on31sm1n0zywdt/4xk311292956049.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/21/t12929559841on31sm1n0zywdt/4xk311292956049.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/21/t12929559841on31sm1n0zywdt/5xk311292956049.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/21/t12929559841on31sm1n0zywdt/5xk311292956049.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/21/t12929559841on31sm1n0zywdt/68u241292956049.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/21/t12929559841on31sm1n0zywdt/68u241292956049.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/21/t12929559841on31sm1n0zywdt/7jljo1292956049.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/21/t12929559841on31sm1n0zywdt/7jljo1292956049.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/21/t12929559841on31sm1n0zywdt/8jljo1292956049.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/21/t12929559841on31sm1n0zywdt/8jljo1292956049.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/21/t12929559841on31sm1n0zywdt/9jljo1292956049.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/21/t12929559841on31sm1n0zywdt/9jljo1292956049.ps (open in new window)


 
Parameters (Session):
par1 = 4 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;
 
Parameters (R input):
par1 = 4 ; 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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