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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 10:14:59 +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/t1291284876zugr5sovbyzq9se.htm/, Retrieved Thu, 02 Dec 2010 11:14:51 +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/t1291284876zugr5sovbyzq9se.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 «
0 162556 0 807 0 213118 0 6282154 0 29790 0 444 0 81767 0 4321023 0 87550 0 412 0 153198 0 4111912 1 84738 254214 428 2140 -26007 -52014 223193 0 54660 0 315 0 126942 0 1491348 0 42634 0 168 0 157214 0 1629616 1 40949 122847 263 1315 129352 258704 1398893 0 45187 0 267 0 234817 0 1926517 0 37704 0 228 0 60448 0 983660 0 16275 0 129 0 47818 0 1443586 1 25830 77490 104 520 245546 491092 1073089 1 12679 38037 122 610 48020 96040 984885 0 18014 0 393 0 -1710 0 1405225 1 43556 130668 190 950 32648 65296 227132 0 24811 0 280 0 95350 0 929118 1 6575 19725 63 315 151352 302704 1071292 1 7123 21369 102 510 288170 576340 638830 0 21950 0 265 0 114337 0 856956 0 37597 0 234 0 37884 0 992426 1 17821 53463 277 1385 122844 245688 444477 0 12988 0 73 0 82340 0 857217 0 22330 0 67 0 79801 0 711969 1 13326 39978 103 515 165548 331096 702380 1 16189 48567 290 1450 116384 232768 358589 1 7146 21438 83 415 134028 268056 297978 1 15824 47472 56 280 63838 127676 585715 0 27664 0 236 0 74996 0 657954 1 11 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 time36 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135
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] = + 209117.470913630 -13727.2209540091Group[t] + 23.2184021409993Costs[t] -6.05588147089353Costs_p[t] + 2548.98649987378Orders[t] -547.096167988767Orders_p[t] + 0.156743460828242Dividends[t] + 0.871018482536596Dividends_p[t] + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0		2-tail p-value1-tail p-value
(Intercept)209117.47091363041111.1401025.08661e-060
Group-13727.220954009149618.718749-0.27670.7821810.39109
Costs23.21840214099931.9923811.653600
Costs_p-6.055881470893531.160388-5.218800
Orders2548.98649987378333.6150737.640500
Orders_p-547.096167988767106.495262-5.137300
Dividends0.1567434608282420.5031290.31150.7555460.377773
Dividends_p0.8710184825365960.3181212.7380.0064420.003221


Multiple Linear Regression - Regression Statistics
Multiple R0.903579223349187
R-squared0.81645541286832
Adjusted R-squared0.8134180319938
F-TEST (value)268.802447436716
F-TEST (DF numerator)7
F-TEST (DF denominator)423
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation185959.742030785
Sum Squared Residuals14627773852554


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast		Residuals
Prediction Error
162821546073845.00762885208308.992371147
243210232045360.119199492275662.88080051
341119123316083.80101808795828.198981922
4223193494180.198255523-270987.198255523
514913482301063.40780534-809715.407805342
616296161651882.82622244-22266.8262224437
71398893598776.762389312800116.237610688
819265171975672.83316656-49155.8331665618
99836601675187.85592924-691527.855929236
101443586923311.383051997520274.616948003
111073089772693.849173201300395.150826799
12984885327855.933760219657029.066239781
1314052251628857.43021397-223632.430213974
14227132441938.512305798-214806.512305798
159291181513850.95538859-584732.955388595
161071292504234.053619937567057.946380063
17638830759515.929903304-120685.929903304
188569561412164.39745583-555208.397455834
199924261684460.64644926-692034.646449264
20444477466994.653876026-22517.6538760264
21857217709660.348976312147556.651023688
22711969910874.771131242-198905.771131242
23702380557827.032367113144552.967632887
24358589444061.269291177-85472.2692911769
25297978470493.677383091-172515.677383091
26585715386084.102037312199630.897962688
276579541464747.29430072-806793.294300722
28209458300995.290893086-91537.2908930863
29786690293404.303353874493285.696646126
30439798336946.755795499102851.244204501
31688779367275.833512625321503.166487375
32574339678597.339668131-104258.339668131
33741409485863.072100251255545.927899749
34597793437106.916094431160686.083905569
35644190777170.09111733-132980.091117329
36377934444062.030873151-66128.0308731507
37640273401937.117639858238335.882360142
38697458554559.818971482142898.181028518
39550608505654.81889733244953.1811026682
40207393343041.297715615-135648.297715615
41301607444752.378627764-143145.378627764
42345783437366.435950117-91583.4359501172
43501749379773.42294827121975.577051730
44379983436817.078521216-56834.0785212159
45387475342809.63293846744665.3670615331
46377305374450.0492732482854.95072675165
47370837480584.171338749-109747.171338749
48430866784272.300188391-353406.300188391
49469107440826.65138795228280.3486120483
50194493344352.433548378-149859.433548378
51530670528839.4343225951830.56567740514
52518365673258.595819362-154893.595819362
53491303655119.828675575-163816.828675575
54527021418951.690302031108069.309697969
55233773632400.528985402-398627.528985402
56405972309557.57376674396414.4262332573
57652925308805.118329078344119.881670922
58446211380313.65469520465897.3453047964
59341340381277.028089447-39937.0280894469
60387699656041.716774145-268342.716774145
61493408462723.82756931230684.1724306883
62146494311685.816859182-165191.816859182
63414462360168.88833128354293.1116687167
64364304593863.349750774-229559.349750774
65355178310890.65691451844287.3430854821
66357760387982.190079653-30222.1900796535
67261216350441.871048494-89225.8710484942
68397144384680.90507030112463.0949296985
69374943437928.936462126-62985.9364621265
70424898535207.304517761-110309.304517761
71202055409001.642711226-206946.642711226
72378525288284.78289499190240.217105009
73310768399041.728188869-88273.7281888687
74325738347054.726748075-21316.726748075
75394510424753.604722257-30243.6047222574
76247060313244.57834984-66184.5783498398
77368078413012.512838504-44934.5128385041
78236761337968.159201884-101207.159201884
79312378324056.296453471-11678.2964534713
80339836276192.94622225763643.0537777429
81347385312743.38769499234641.6123050079
82426280500070.491586663-73790.491586663
83352850457535.815075265-104685.815075265
84301881271943.32602576829937.6739742323
85377516390241.143581651-12725.1435816511
86357312524676.741071761-167364.741071761
87458343366523.3944018791819.6055981296
88354228393090.445788716-38862.4457887157
89308636400030.425113988-91394.4251139883
90386212391872.571945381-5660.57194538094
91393343380213.38840677413129.6115932263
92378509392542.501955432-14033.5019554316
93452469314837.135621112137631.864378888
94364839454616.213210828-89777.2132108284
95358649268167.40772820890481.5922717916
96376641365962.60773511610678.3922648843
97429112409638.30122582619473.6987741743
98330546309026.87759299621519.1224070044
99403560451904.284940512-48344.2849405116
100317892275646.31251880142245.6874811993
101307528329344.829286998-21816.8292869980
102235133368675.533361962-133542.533361962
103299243408111.713590652-108868.713590652
104314073412814.691721545-98741.691721545
105368186329122.60610533139063.3938946689
106269661329628.405420849-59967.4054208491
107125390414960.080546456-289570.080546456
108510834312726.50467043198107.495329570
109321896408114.572944106-86218.5729441064
110249898316390.21628878-66492.2162887798
111408881325016.12706710583864.872932895
112158492380562.808043974-222070.808043974
113292154376605.818155342-84451.8181553418
114289513309510.956314471-19997.9563144708
115378049265679.20178817112369.798211830
116343466303477.09684834239988.9031516575
117332743357306.048243208-24563.0482432082
118442882371741.45066274471140.5493372556
119214215301126.827971174-86911.827971174
120315688312024.4394883283663.56051167228
121375195441117.306681823-65922.3066818232
122334280324790.0194264569489.98057354361
123355864359282.893742161-3418.89374216084
124480382328223.453847911152158.546152089
125353058323771.65043402329286.3495659773
126217193356111.747184706-138918.747184706
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140315380310684.1974203574695.80257964306
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170315380310684.1974203574695.80257964306
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173315380310684.1974203574695.80257964306
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175315380310684.1974203574695.80257964306
176315547310267.2564519485279.74354805187
177313267291630.64008377121636.3599162287
178316176220287.35899365395888.6410063471
179315380310684.1974203574695.80257964306
180315380310684.1974203574695.80257964306
181359335332788.62128264726546.3787173526
182330068260714.55222630869353.4477736917
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184297413269943.43368101627469.5663189835
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186333210261432.26570840071777.7342915995
187352108331314.90386933620793.0961306639
188313332312826.083224072505.916775927928
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190315380310684.1974203574695.80257964306
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192315380310684.1974203574695.80257964306
193315366311818.784067133547.21593287003
194315380310684.1974203574695.80257964306
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196315380218634.93385512196745.0661448789
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198315380218634.93385512196745.0661448789
199315380218634.93385512196745.0661448789
200269587281053.83054378-11466.8305437798
201315380218634.93385512196745.0661448789
202315380218634.93385512196745.0661448789
203315380218634.93385512196745.0661448789
204300962252381.83933065748580.1606693431
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208315380218634.93385512196745.0661448789
209343613309372.73094883234240.2690511678
210306948232434.76992210774513.2300778927
211315380310684.1974203574695.80257964306
212315380310684.1974203574695.80257964306
213330059304133.06828127125925.9317187286
214288985313600.080178238-24615.0801782378
215304485316056.513156142-11571.5131561417
216315380310311.2087402175068.79125978311
217315688309851.7573731375836.2426268634
218317736311243.3781064936492.62189350736
219315380310311.2087402175068.79125978311
220322331306352.05180501215978.9481949879
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222315380310684.1974203574695.80257964306
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224312161309318.0652358102842.93476419045
225315576310760.1145710554815.88542894507
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228315380310684.1974203574695.80257964306
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230315380310684.1974203574695.80257964306
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233315380310684.1974203574695.80257964306
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235315380310684.1974203574695.80257964306
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256315380310684.1974203574695.80257964306
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294315380310684.1974203574695.80257964306
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297315380310684.1974203574695.80257964306
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318297141309661.744313356-12520.7443133556
319315372309754.8776973095617.12230269072
320315380310684.1974203574695.80257964306
321315380310684.1974203574695.80257964306
322315380310684.1974203574695.80257964306
323315380310684.1974203574695.80257964306
324315380218634.93385512196745.0661448789
325315380310684.1974203574695.80257964306
326312502310612.6173111621889.38268883825
327315380218634.93385512196745.0661448789
328315380218634.93385512196745.0661448789
329315380310684.1974203574695.80257964306
330315380310684.1974203574695.80257964306
331315380310684.1974203574695.80257964306
332315380310684.1974203574695.80257964306
333315380310684.1974203574695.80257964306
334313729309775.6086767633953.39132323697
335315388310516.0453009974871.95469900341
336315371311524.1579867693846.84201323106
337296139311606.400128967-15467.4001289672
338315380310684.1974203574695.80257964306
339313880310963.2081361822916.79186381816
340317698307578.40123575810119.5987642423
341295580314252.052866778-18672.0528667778
342315380310684.1974203574695.80257964306
343315380310684.1974203574695.80257964306
344315380310684.1974203574695.80257964306
345308256311396.291548733-3140.29154873252
346315380310684.1974203574695.80257964306
347303677307683.908327523-4006.90832752273
348315380310684.1974203574695.80257964306
349315380310684.1974203574695.80257964306
350319369316875.2125963252493.78740367496
351318690307671.33874762011018.6612523805
352314049310448.889795633600.11020436996
353325699309647.92082704116051.0791729593
354314210313733.415046447476.58495355267
355315380310684.1974203574695.80257964306
356315380310684.1974203574695.80257964306
357322378344774.846283442-22396.8462834419
358315380310684.1974203574695.80257964306
359315380310684.1974203574695.80257964306
360315380310684.1974203574695.80257964306
361315398309947.0683786575450.931621343
362315380310684.1974203574695.80257964306
363315380310684.1974203574695.80257964306
364308336331078.533071698-22742.5330716977
365316386307854.7079887218531.292011279
366315380310684.1974203574695.80257964306
367315380310684.1974203574695.80257964306
368315380310684.1974203574695.80257964306
369315380310684.1974203574695.80257964306
370315553310479.802224645073.19777535972
371315380310684.1974203574695.80257964306
372323361309858.52168223213502.4783177679
373336639340761.438546249-4122.43854624918
374307424318788.54599107-11364.5459910701
375315380310684.1974203574695.80257964306
376315380310684.1974203574695.80257964306
377295370300619.640670269-5249.64067026902
378322340311905.2933410434.7066599998
379319864319991.530114698-127.53011469768
380315380310684.1974203574695.80257964306
381315380310684.1974203574695.80257964306
382317291334143.39644959-16852.39644959
383280398274419.0275866265978.97241337432
384315380310684.1974203574695.80257964306
385317330312599.809685614730.19031438973
386238125331298.158081197-93173.158081197
387327071308775.55519152718295.4448084729
388309038310239.641868782-1201.64186878201
389314210309876.9616594464333.0383405544
390307930308017.886008966-87.8860089660466
391322327314602.9778853437724.02211465694
392292136309189.273663548-17053.2736635477
393263276312770.533504768-49494.5335047683
394367655327007.50556950640647.4944304937
395283910324688.264939874-40778.2649398738
396283587307731.929658871-24144.9296588711
397243650315652.465940225-72002.4659402251
398438493870799.255649724-432306.255649724
399296261318031.746219737-21770.7462197368
400230621366280.009781075-135659.009781075
401304252333892.244579007-29640.2445790072
402333505319776.34999188613728.6500081140
403296919309746.110300310-12827.1103003104
404278990308947.784830044-29957.7848300438
405276898319109.456126981-42211.4561269815
406327007333541.1912824-6534.19128240004
407317046325601.895631564-8555.89563156436
408304555310042.64777046-5487.64777046026
409298096306660.907222567-8564.90722256695
410231861331374.271254753-99513.2712547533
411309422323995.706790381-14573.7067903813
412286963444818.320509744-157855.320509744
413269753283363.023678535-13610.0236785352
414448243379329.76055440768913.2394455928
415165404353837.408482315-188433.408482315
416204325339432.615986806-135107.615986806
417407159274478.157314443132680.842685557
418290476296212.853798827-5736.85379882712
419275311328735.84626784-53424.8462678404
420246541323709.912153393-77168.912153393
421253468332798.083513482-79330.0835134816
422240897333963.081469572-93066.0814695719
423-83265647830.459148743-731095.459148743
424-42143330630.519271307-372773.519271307
425272713307858.589873821-35145.5898738207
426215362547264.948568649-331902.948568649
42742754308988.143361998-266234.143361998
428306275628450.212121085-322175.212121085
429253537387124.073243208-133587.073243208
430372631403346.63764407-30715.6376440703
431-7170325610.81005899-332780.81005899


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
1111.85927032486326e-539.2963516243163e-54
1211.00263392570402e-575.01316962852008e-58
1311.10601980009968e-885.53009900049838e-89
1418.16263892189514e-884.08131946094757e-88
1511.05770912546627e-965.28854562733133e-97
1615.74131520617973e-1052.87065760308987e-105
1711.54640562325853e-1117.73202811629266e-112
1815.95794639828989e-1172.97897319914495e-117
1913.57188793742699e-1181.78594396871349e-118
2014.81151002330728e-1192.40575501165364e-119
2114.32343253742901e-1252.16171626871450e-125
2211.33820754234338e-1256.69103771171691e-126
2313.73877916456415e-1271.86938958228208e-127
2411.76526389973073e-1268.82631949865365e-127
2511.11917598573361e-1275.59587992866805e-128
2613.84502639572784e-1291.92251319786392e-129
2711.19201406009164e-1335.9600703004582e-134
2811.64622315941015e-1338.23111579705076e-134
2914.15078246893061e-1432.07539123446531e-143
3013.0235520742886e-1431.5117760371443e-143
3117.80637193659206e-1503.90318596829603e-150
3212.75673353957666e-1501.37836676978833e-150
3311.60273719431388e-1598.01368597156939e-160
3417.72881202109097e-1623.86440601054549e-162
3516.5602516782433e-1623.28012583912165e-162
3613.38842884629296e-1611.69421442314648e-161
3711.88045575240592e-1669.40227876202958e-167
3818.57464565786632e-1724.28732282893316e-172
3913.99812383163870e-1711.99906191581935e-171
4014.76769051238941e-1722.38384525619470e-172
4114.08358264230029e-1722.04179132115015e-172
4215.36396813898536e-1722.68198406949268e-172
4312.23313651114129e-1721.11656825557065e-172
4411.30425897067191e-1716.52129485335953e-172
4513.58343019484389e-1711.79171509742194e-171
4612.67216180413449e-1701.33608090206724e-170
4711.52157373288246e-1727.60786866441231e-173
4814.46986581333046e-1732.23493290666523e-173
4915.12991292282028e-1732.56495646141014e-173
5017.75230366952277e-1743.87615183476139e-174
5113.05009996174234e-1741.52504998087117e-174
5213.62171938597877e-1741.81085969298938e-174
5311.51516660281995e-1737.57583301409973e-174
5418.02064360485733e-1734.01032180242866e-173
5511.11802051604757e-1785.59010258023784e-179
5614.26535138412529e-1782.13267569206264e-178
5713.03937414880191e-1901.51968707440095e-190
5816.00621628804024e-1913.00310814402012e-191
5914.02158432243403e-1902.01079216121702e-190
6017.90582968942764e-1903.95291484471382e-190
6113.54666355024842e-1911.77333177512421e-191
6211.17162029398835e-1935.85810146994177e-194
6313.56497220529520e-1931.78248610264760e-193
6416.99321194136122e-1933.49660597068061e-193
6515.06603030653215e-1922.53301515326607e-192
6614.54134302736908e-1912.27067151368454e-191
6718.52480977484419e-1914.26240488742210e-191
6816.71230100295128e-1903.35615050147564e-190
6913.76716970034061e-1891.88358485017030e-189
7011.54463685424325e-1887.72318427121623e-189
7111.51359929300224e-1877.56799646501121e-188
7215.22765856624472e-1882.61382928312236e-188
7311.50065496475774e-1877.5032748237887e-188
7411.26096886107949e-1866.30484430539744e-187
7519.8629483628287e-1864.93147418141435e-186
7611.17408219985596e-1855.8704109992798e-186
7719.39384606153418e-1854.69692303076709e-185
7819.11019429152653e-1854.55509714576326e-185
7916.6536590976493e-1843.32682954882465e-184
8011.16262912013419e-1845.81314560067096e-185
8118.52335816589898e-1844.26167908294949e-184
8218.74369353770654e-1844.37184676885327e-184
8312.14334602462914e-1831.07167301231457e-183
8411.85875807371538e-1829.29379036857691e-183
8511.58861920325587e-1817.94309601627934e-182
8614.93458899228244e-1822.46729449614122e-182
8716.13365977922844e-1823.06682988961422e-182
8814.97014475280725e-1812.48507237640363e-181
8911.15032019670813e-1805.75160098354067e-181
9019.29086501497091e-1804.64543250748546e-180
9115.6841530946992e-1792.8420765473496e-179
9212.29082129388273e-1781.14541064694137e-178
9312.40004654105295e-1791.20002327052647e-179
9411.37768371543217e-1786.88841857716085e-179
9512.03086227951445e-1781.01543113975723e-178
9614.71313837069165e-1792.35656918534582e-179
9712.22632040224501e-1781.11316020112250e-178
9811.38428720512410e-1776.92143602562049e-178
9919.86038628114063e-1774.93019314057031e-177
10015.38539277285717e-1762.69269638642859e-176
10113.41424291595361e-1751.70712145797680e-175
10215.07370711128198e-1762.53685355564099e-176
10317.42638123564957e-1763.71319061782479e-176
10417.19810894496526e-1763.59905447248263e-176
10513.06571344043440e-1751.53285672021720e-175
10617.3860301278347e-1753.69301506391735e-175
10711.17440049735034e-1765.8720024867517e-177
10811.92678176251205e-1789.63390881256027e-179
10911.17542987875773e-1775.87714939378865e-178
11012.28916063880622e-1771.14458031940311e-177
11111.74172386865147e-1778.70861934325737e-178
11211.88685228460149e-1779.43426142300747e-178
11311.02325633370572e-1765.11628166852861e-177
11416.17435331543795e-1763.08717665771898e-176
11511.90702213358440e-1769.53511066792202e-177
11618.8896623715193e-1764.44483118575965e-176
11716.43214450192252e-1753.21607225096126e-175
11812.46399655687712e-1751.23199827843856e-175
11912.19618857556726e-1761.09809428778363e-176
12011.95177340434017e-1759.75886702170084e-176
12117.60814250956217e-1753.80407125478109e-175
12216.03864280822308e-1743.01932140411154e-174
12313.22780794004437e-1731.61390397002218e-173
12413.11101556703738e-1731.55550778351869e-173
12514.2164917148216e-1732.1082458574108e-173
12611.74158839430896e-1738.7079419715448e-174
12711.5221297980169e-1727.6106489900845e-173
12811.34299643374706e-1716.71498216873528e-172
12911.15853699812060e-1705.79268499060301e-171
13019.95592924131067e-1704.97796462065534e-170
13118.62085850947875e-1694.31042925473938e-169
13211.01348220169109e-1685.06741100845543e-169
13318.61461503210483e-1684.30730751605241e-168
13417.36999371242966e-1673.68499685621483e-167
13516.13076139228586e-1663.06538069614293e-166
13615.08585021067055e-1652.54292510533528e-165
13714.23782978621246e-1642.11891489310623e-164
13813.51823785854405e-1631.75911892927202e-163
13912.75014811998908e-1621.37507405999454e-162
14012.24979146101824e-1611.12489573050912e-161
14111.60872142825878e-1608.04360714129391e-161
14211.30186173172046e-1596.50930865860231e-160
14311.05744693057903e-1585.28723465289513e-159
14418.5163727495299e-1584.25818637476495e-158
14516.39807615792e-1573.19903807896e-157
14614.94161722676044e-1562.47080861338022e-156
14713.89319248767404e-1551.94659624383702e-155
14813.09262929501123e-1541.54631464750562e-154
14912.17479510878376e-1531.08739755439188e-153
15011.68510827723966e-1528.42554138619832e-153
15111.26090355720990e-1516.30451778604948e-152
15219.80214937630494e-1514.90107468815247e-151
15317.55707434782078e-1503.77853717391039e-150
15415.76076687826886e-1492.88038343913443e-149
15514.37779119715765e-1482.18889559857883e-148
15613.29165784725305e-1471.64582892362652e-147
15712.46197614950572e-1461.23098807475286e-146
15811.84250735086166e-1459.21253675430831e-146
15911.02925123899621e-1445.14625619498107e-145
16017.58124316518984e-1443.79062158259492e-144
16115.55505253931185e-1432.77752626965592e-143
16214.04919843910575e-1422.02459921955288e-142
16312.93621219295623e-1411.46810609647811e-141
16412.15328461655818e-1401.07664230827909e-140
16511.44461689564268e-1397.2230844782134e-140
16611.03460864942656e-1385.1730432471328e-139
16717.35516499365963e-1383.67758249682982e-138
16811.57630227803385e-1387.88151139016923e-139
16913.48093749026165e-1381.74046874513082e-138
17012.48028202264977e-1371.24014101132489e-137
17111.75824861791513e-1368.79124308957566e-137
17211.26275945533789e-1356.31379727668946e-136
17318.86163674442926e-1354.43081837221463e-135
17416.3115520333515e-1343.15577601667575e-134
17514.38539192464811e-1332.19269596232405e-133
17613.05834879558309e-1321.52917439779154e-132
17711.36345135324053e-1316.81725676620264e-132
17816.3260542358449e-1313.16302711792245e-131
17914.30630631357201e-1302.15315315678600e-130
18012.91651132115008e-1291.45825566057504e-129
18111.43400967259585e-1287.17004836297923e-129
18217.65952689049695e-1283.82976344524848e-128
18313.89809575869056e-1271.94904787934528e-127
18411.37358620997936e-1266.86793104989678e-127
18517.05271278247476e-1263.52635639123738e-126
18613.12553353317110e-1251.56276676658555e-125
18717.53331389610405e-1253.76665694805203e-125
18815.08973009227886e-1242.54486504613943e-124
18912.82312754884196e-1231.41156377442098e-123
19011.84884410035076e-1229.2442205017538e-123
19111.16143311118551e-1215.80716555592757e-122
19217.53084517948316e-1213.76542258974158e-121
19314.94583155734074e-1202.47291577867037e-120
19413.17537711416801e-1191.58768855708400e-119
19512.04284745848886e-1181.02142372924443e-118
19611.01389527679053e-1175.06947638395263e-118
19713.93883089323433e-1171.96941544661716e-117
19811.97799534865936e-1169.88997674329678e-117
19911.00742001393125e-1155.03710006965623e-116
20016.37527194368656e-1163.18763597184328e-116
20113.3144753381993e-1151.65723766909965e-115
20211.74100974265868e-1148.7050487132934e-115
20319.22752669113695e-1144.61376334556847e-114
20415.26574520210492e-1132.63287260105246e-113
20511.18740995750436e-1125.93704978752182e-113
20616.59940720545123e-1123.29970360272561e-112
20713.44229613264762e-1111.72114806632381e-111
20811.86770497462773e-1109.33852487313864e-111
20911.85118277298906e-1109.2559138649453e-111
21011.05282137815071e-1095.26410689075355e-110
21116.4654972841309e-1093.23274864206545e-109
21213.9509332405338e-1081.9754666202669e-108
21311.97141947553336e-1079.85709737766678e-108
21411.09178920849209e-1065.45894604246045e-107
21516.73920220581848e-1063.36960110290924e-106
21614.0708127302541e-1052.03540636512705e-105
21712.46773603984625e-1041.23386801992313e-104
21811.43776948254073e-1037.18884741270367e-104
21918.5591805435647e-1034.27959027178235e-103
22013.89051309195638e-1021.94525654597819e-102
22112.30790196720206e-1011.15395098360103e-101
22211.34908176966683e-1006.74540884833413e-101
22317.86633908434119e-1003.93316954217059e-100
22414.6801738495267e-992.34008692476335e-99
22512.69991446279821e-981.34995723139910e-98
22611.59352102859257e-977.96760514296284e-98
22719.27730640205523e-974.63865320102762e-97
22815.26794185098845e-962.63397092549423e-96
22913.05651974165983e-951.52825987082991e-95
23011.7190124098595e-948.5950620492975e-95
23119.42344736051583e-944.71172368025792e-94
23214.8641291405366e-932.4320645702683e-93
23312.698320201889e-921.3491601009445e-92
23411.51589481910053e-917.57947409550264e-92
23518.33005970644572e-914.16502985322286e-91
23614.55240479978899e-902.27620239989450e-90
23712.47654479038478e-891.23827239519239e-89
23811.35013951653910e-886.75069758269548e-89
23917.27198419035278e-883.63599209517639e-88
24013.89696742115982e-871.94848371057991e-87
24112.07776014607354e-861.03888007303677e-86
24211.12383168777679e-855.61915843888397e-86
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35712.01085034395221e-181.00542517197611e-18
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36111.10894017502948e-165.5447008751474e-17
36212.93461523906691e-161.46730761953345e-16
36317.68860221185929e-163.84430110592964e-16
3640.9999999999999992.11451904870693e-151.05725952435346e-15
3650.9999999999999975.58167006473298e-152.79083503236649e-15
3660.9999999999999931.42206842936647e-147.11034214683234e-15
3670.9999999999999823.5849768828731e-141.79248844143655e-14
3680.9999999999999558.94079108878365e-144.47039554439183e-14
3690.999999999999892.20545632081745e-131.10272816040872e-13
3700.9999999999997245.52768641903523e-132.76384320951762e-13
3710.9999999999993331.33409522430457e-126.67047612152286e-13
3720.9999999999984643.07222715385955e-121.53611357692978e-12
3730.999999999996197.62204132455886e-123.81102066227943e-12
3740.9999999999905471.89064257496526e-119.45321287482632e-12
3750.9999999999782064.35872184273922e-112.17936092136961e-11
3760.999999999950399.92186944785046e-114.96093472392523e-11
3770.9999999998786332.42734951495783e-101.21367475747892e-10
3780.9999999997387345.22531621214260e-102.61265810607130e-10
3790.9999999995012249.97551152680611e-104.98775576340306e-10
3800.999999998919852.16030105071253e-091.08015052535626e-09
3810.9999999976943844.61123157175569e-092.30561578587785e-09
3820.9999999945795641.08408724356851e-085.42043621784255e-09
3830.999999987917622.41647612928940e-081.20823806464470e-08
3840.9999999751315234.97369546745484e-082.48684773372742e-08
3850.9999999456886141.08622771622541e-075.43113858112706e-08
3860.9999998963772632.07245473038382e-071.03622736519191e-07
3870.9999998047280293.90543941922233e-071.95271970961117e-07
3880.9999996181800827.63639835358217e-073.81819917679109e-07
3890.9999992458893631.50822127419361e-067.54110637096803e-07
3900.9999985091970322.98160593577661e-061.49080296788830e-06
3910.9999971257842165.74843156773614e-062.87421578386807e-06
3920.9999941885456311.16229087377648e-055.8114543688824e-06
3930.9999879583310762.40833378470815e-051.20416689235407e-05
3940.9999838149695233.23700609539259e-051.61850304769629e-05
3950.9999745708184255.08583631499282e-052.54291815749641e-05
3960.9999497945427980.0001004109144035385.0205457201769e-05
3970.9999032773256440.0001934453487130679.67226743565336e-05
3980.9998420529357220.0003158941285562050.000157947064278102
3990.9997055708603020.0005888582793964330.000294429139698216
4000.9996334911842790.000733017631441710.000366508815720855
4010.9993539493587360.001292101282528560.000646050641264280
4020.9990168733256970.001966253348606920.000983126674303462
4030.9983337838903490.003332432219302950.00166621610965148
4040.9971949951247310.005610009750538280.00280500487526914
4050.9950440560749670.009911887850066380.00495594392503319
4060.9925095067808420.01498098643831590.00749049321915797
4070.9883788202395760.02324235952084740.0116211797604237
4080.9825882209432890.03482355811342260.0174117790567113
4090.9739988349940780.05200233001184460.0260011650059223
4100.9571630321992030.08567393560159360.0428369678007968
4110.9313077057225510.1373845885548970.0686922942774486
4120.9152946397671770.1694107204656460.0847053602328229
4130.8692038141171940.2615923717656130.130796185882806
4140.8056023272812820.3887953454374370.194397672718718
4150.7418097033734410.5163805932531180.258190296626559
4160.646782639622490.7064347207550210.353217360377510
4170.7987506526268080.4024986947463840.201249347373192
4180.6871032085173780.6257935829652450.312896791482622
4190.5494810281469260.9010379437061470.450518971853074
4200.3868022377746790.7736044755493580.613197762225321


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level3950.963414634146341NOK
5% type I error level3980.970731707317073NOK
10% type I error level4000.97560975609756NOK
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Dec/02/t1291284876zugr5sovbyzq9se/10wpx81291284860.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/02/t1291284876zugr5sovbyzq9se/10wpx81291284860.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/02/t1291284876zugr5sovbyzq9se/1p6jf1291284860.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/02/t1291284876zugr5sovbyzq9se/1p6jf1291284860.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/02/t1291284876zugr5sovbyzq9se/2p6jf1291284860.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/02/t1291284876zugr5sovbyzq9se/2p6jf1291284860.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/02/t1291284876zugr5sovbyzq9se/3p6jf1291284860.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/02/t1291284876zugr5sovbyzq9se/3p6jf1291284860.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/02/t1291284876zugr5sovbyzq9se/40x0h1291284860.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/02/t1291284876zugr5sovbyzq9se/40x0h1291284860.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/02/t1291284876zugr5sovbyzq9se/50x0h1291284860.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/02/t1291284876zugr5sovbyzq9se/50x0h1291284860.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/02/t1291284876zugr5sovbyzq9se/6bphk1291284860.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/02/t1291284876zugr5sovbyzq9se/6bphk1291284860.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/02/t1291284876zugr5sovbyzq9se/73gg51291284860.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/02/t1291284876zugr5sovbyzq9se/73gg51291284860.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/02/t1291284876zugr5sovbyzq9se/83gg51291284860.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/02/t1291284876zugr5sovbyzq9se/83gg51291284860.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/02/t1291284876zugr5sovbyzq9se/93gg51291284860.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/02/t1291284876zugr5sovbyzq9se/93gg51291284860.ps (open in new window)


 
Parameters (Session):
par1 = 8 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;
 
Parameters (R input):
par1 = 8 ; 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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