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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: Fri, 03 Dec 2010 16:36:11 +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/03/t1291394102a7s80b1qspnm35f.htm/, Retrieved Fri, 03 Dec 2010 17:35:13 +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/03/t1291394102a7s80b1qspnm35f.htm/},
    year = {2010},
}
@Manual{R,
    title = {R: A Language and Environment for Statistical Computing},
    author = {{R Development Core Team}},
    organization = {R Foundation for Statistical Computing},
    address = {Vienna, Austria},
    year = {2010},
    note = {{ISBN} 3-900051-07-0},
    url = {http://www.R-project.org},
}
 
Original text written by user:
 
IsPrivate?
No (this computation is public)
 
User-defined keywords:
 
Dataseries X:
» Textbox « » Textfile « » CSV «
1 162556 1081 807 213118 230380558 6282154 1 29790 309 444 81767 25266003 4321023 1 87550 458 412 153198 70164684 4111912 0 84738 588 428 -26007 -15292116 223193 1 54660 302 315 126942 37955658 1491348 1 42634 156 168 157214 24525384 1629616 0 40949 481 263 129352 62218312 1398893 1 45187 353 267 234817 75845891 1926517 1 37704 452 228 60448 27322496 983660 1 16275 109 129 47818 5212162 1443586 0 25830 115 104 245546 28237790 1073089 0 12679 110 122 48020 5282200 984885 1 18014 239 393 -1710 -408690 1405225 0 43556 247 190 32648 8064056 227132 1 24811 505 280 95350 47388950 929118 0 6575 159 63 151352 15589256 1071292 0 7123 109 102 288170 31410530 638830 1 21950 519 265 114337 57397174 856956 1 37597 248 234 37884 9395232 992426 0 17821 373 277 122844 45820812 444477 1 12988 119 73 82340 9798460 857217 1 22330 84 67 79801 6703284 711969 0 13326 102 103 165548 16885896 702380 0 16189 295 290 116384 34333280 358589 0 7146 105 83 134028 14072940 297978 0 15824 64 56 63838 4085632 585715 etc...
 
Output produced by software:

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


Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time28 seconds
R Server'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
Wealth [t] = + 321668.340252006 + 42164.0413336462Group[t] + 14.0798850142469Costs[t] -2725.3358023804Trades[t] + 3064.97433667866Orders[t] -0.585580804767308Dividends[t] + 0.0177762922190464TrDiv[t] + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0		2-tail p-value1-tail p-value
(Intercept)321668.34025200629929.45230910.747600
Group42164.041333646223695.6859291.77940.0758910.037945
Costs14.07988501424691.939637.259100
Trades-2725.3358023804227.721757-11.967800
Orders3064.97433667866386.6900627.926200
Dividends-0.5855808047673080.401065-1.46010.1450130.072506
TrDiv0.01777629221904640.00155711.416400


Multiple Linear Regression - Regression Statistics
Multiple R0.86961701117919
R-squared0.756233746132227
Adjusted R-squared0.752784223671834
F-TEST (value)219.228532301271
F-TEST (DF numerator)6
F-TEST (DF denominator)424
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation214053.430005554
Sum Squared Residuals19427201260388.4


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast		Residuals
Prediction Error
162821546150462.76793263131691.232067365
243210231703246.665581742617776.33441826
341119122768650.061916661343261.93808334
4223193967473.278214078-744280.278214078
514913481876230.46965469-384882.46965469
616296161397786.39480137231829.605198630
713988931423692.12853147-24799.1285314737
819265172067119.14957425-140602.149574247
9983660811958.216812763171701.783187237
101443586755954.20904725687631.79095275
1110730891048871.6662835124217.3337164876
12984885640105.473675116344779.526324884
1314052251164383.43808724240841.561912762
14227132968349.96652624-741217.96652624
15929118981631.336161272-52513.3361612715
161071292362498.919023334708793.080976666
17638830827141.080615577-188311.080615577
188569561024010.16052956-167054.160529563
199924261079342.78054869-86916.7805486893
204444771147622.66350815-703145.663508153
21857217572093.659037064285123.340962936
22711969727090.888521325-15121.8885213253
23702380750231.88339577-47851.8833957707
243585891176642.27641854-818053.276418545
25297978562196.278977956-264218.278977956
26585715576930.5931358618784.40686413918
276579541020162.61637665-362208.616376654
28209458270303.572673638-60845.5726736384
29786690447997.161905104338692.838094896
30439798257578.277593679182219.722406321
31688779406990.819332243281788.180667757
32574339611334.601178308-36995.6011783082
33741409477963.293464977263445.706535023
34597793451800.340232729145992.659767271
35644190271072.457619091373117.542380909
363779341029294.76947866-651360.769478664
37640273537290.792613534102982.207386466
38697458559497.368398999137960.631601001
39550608593240.175389518-42632.1753895179
40207393544265.436107146-336872.436107146
41301607521126.176082234-219519.176082234
42345783568314.942076547-222531.942076547
43501749364182.979047457137566.020952543
44379983552475.43208254-172492.43208254
45387475373117.26140569914357.7385943014
46377305408084.223583261-30779.2235832613
47370837-34500.5305277161405337.530527716
48430866752337.919412714-321471.919412714
49469107450172.13509408518934.8649059146
50194493389633.881518772-195140.881518772
51530670534061.607725717-3391.60772571722
52518365710715.064628349-192350.064628349
53491303725800.922592825-234497.922592825
54527021466833.56304929960187.4369507009
55233773696371.577265067-462598.577265067
56405972396738.4035887089233.59641129162
57652925346872.906383080306052.093616920
58446211413022.08466414333188.9153358568
59341340335439.2765398655900.72346013532
60387699586181.037958025-198482.037958025
61493408469469.83508084323938.1649191565
62146494343123.234176081-196629.234176081
63414462393533.76281766720928.2371823335
64364304544000.417899602-179696.417899602
65355178357859.067696187-2681.06769618697
66357760172525.786209405185234.213790595
67261216237324.91336612423891.0866338757
68397144418961.55310666-21817.5531066596
69374943451591.739943903-76648.739943903
70424898563061.75466189-138163.754661890
71202055410993.885867035-208938.885867035
72378525387814.818004804-9289.81800480397
73310768358440.181682975-47672.1816829747
74325738296150.22426230629587.775737694
75394510362648.27470259931861.7252974010
76247060373479.045738935-126419.045738935
77368078325391.74589028342686.2541097174
78236761262832.189599290-26071.1895992905
79312378284002.72535840528375.2746415953
80339836236291.822971720103544.177028280
81347385351599.097991788-4214.09799178796
82426280491753.375886691-65473.375886691
83352850338725.86752753514124.1324724647
84301881319523.238297268-17642.2382972676
85377516301237.23526710676278.7647328943
86357312500771.08787393-143459.087873930
87458343530199.178728837-71856.1787288373
88354228295956.78958687758271.2104131227
89308636373584.508063003-64948.5080630026
90386212302273.73378687683938.2662131243
91393343350835.18297259542507.8170274053
92378509428089.788711853-49580.7887118532
93452469366675.81888752385793.1811124768
94364839435183.474449800-70344.4744497996
95358649365463.028868168-6814.0288681682
96376641392378.370082163-15737.3700821628
97429112281181.505666595147930.494333405
98330546117482.91836373213063.08163627
99403560330733.75096715272826.249032848
100317892352351.702476693-34459.7024766926
101307528386744.157469742-79216.1574697419
102235133314948.297818700-79815.2978187004
103299243410353.089706899-111110.089706899
104314073275026.32436401939046.6756359809
105368186316178.30152134852007.6984786517
106269661345726.771503819-76065.7715038193
107125390421152.509824314-295762.509824314
108510834364638.539706816146195.460293184
109321896426768.227563526-104872.227563526
110249898358188.313661803-108290.313661803
111408881316963.80517786991917.1948221312
112158492397279.251303925-238787.251303925
113292154393529.445674119-101375.445674119
114289513374348.356040178-84835.3560401778
115378049352766.73279308425282.2672069161
116343466349886.510890172-6420.51089017232
117332743270501.98923021662241.0107697841
118442882329259.947459511113622.052540489
119214215362146.62759379-147931.627593790
120315688249037.41721398466650.5827860159
121375195617672.77767204-242477.77767204
122334280310053.47862834824226.5213716521
123355864511594.533527866-155730.533527866
124480382377242.790191174103139.209808826
125353058356908.151355498-3850.15135549757
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186333210348048.018168774-14838.0181687743
187352108368138.627527349-16030.6275273487
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189291787293893.088586998-2106.08858699816
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193315366299240.38192043516125.6180795655
194315380286111.87378653729268.1262134632
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196315380328275.915120183-12895.9151201832
197409642553690.245886267-144048.245886267
198315380328275.915120183-12895.9151201832
199315380328275.915120183-12895.9151201832
200269587355791.134357537-86204.1343575371
201315380328275.915120183-12895.9151201832
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206316155339934.840561811-23779.8405618108
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209343613371493.486264074-27880.4862640735
210306948256716.59778520250231.402214798
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316339445275426.48909518564018.5109048149
317314964285332.10367133829631.8963286618
318297141324484.776869916-27343.7768699158
319315372291575.54824495623796.4517550437
320315380286111.87378653729268.1262134632
321315380286111.87378653729268.1262134632
322315380286111.87378653729268.1262134632
323315380286111.87378653729268.1262134632
324315380328275.915120183-12895.9151201832
325315380286111.87378653729268.1262134632
326312502286193.58685940826308.4131405916
327315380328275.915120183-12895.9151201832
328315380328275.915120183-12895.9151201832
329315380286111.87378653729268.1262134632
330315380286111.87378653729268.1262134632
331315380286111.87378653729268.1262134632
332315380286111.87378653729268.1262134632
333315380286111.87378653729268.1262134632
334313729291663.01787661222065.9821233882
335315388285895.15913300829492.8408669924
336315371289166.17601582326204.8239841771
337296139154179.691045603141959.308954397
338315380286111.87378653729268.1262134632
339313880287797.03220053826082.9677994625
340317698297473.65753502220224.3424649777
341295580301765.172776501-6185.17277650095
342315380286111.87378653729268.1262134632
343315380286111.87378653729268.1262134632
344315380286111.87378653729268.1262134632
345308256203884.030242947104371.969757053
346315380286111.87378653729268.1262134632
347303677287873.78180865715803.2181913435
348315380286111.87378653729268.1262134632
349315380286111.87378653729268.1262134632
350319369292888.3251105826480.6748894198
351318690277370.79455573241319.205444268
352314049291787.13543118222261.8645688179
353325699305693.79605101420005.2039489865
354314210287045.92596611627164.0740338838
355315380286111.87378653729268.1262134632
356315380286111.87378653729268.1262134632
357322378259852.14632901862525.853670982
358315380286111.87378653729268.1262134632
359315380286111.87378653729268.1262134632
360315380286111.87378653729268.1262134632
361315398291800.98471163423597.0152883658
362315380286111.87378653729268.1262134632
363315380286111.87378653729268.1262134632
364308336376279.722264057-67943.7222640572
365316386298548.66451750817837.3354824916
366315380286111.87378653729268.1262134632
367315380286111.87378653729268.1262134632
368315380286111.87378653729268.1262134632
369315380286111.87378653729268.1262134632
370315553253404.05722640562148.9427735953
371315380286111.87378653729268.1262134632
372323361247918.29191600375442.7080839969
373336639289172.03235251247466.9676474875
374307424293782.73894876413641.2610512360
375315380286111.87378653729268.1262134632
376315380286111.87378653729268.1262134632
377295370282749.18339760812620.8166023925
378322340298118.40343135824221.5965686421
379319864309751.62157151210112.3784284882
380315380286111.87378653729268.1262134632
381315380286111.87378653729268.1262134632
382317291256101.10198174761189.8980182532
383280398189287.17786843091110.8221315705
384315380286111.87378653729268.1262134632
385317330297058.15038041420271.8496195865
386238125345091.425539299-106966.425539299
387327071287782.68521188839288.3147881116
388309038305260.8569447713777.14305522924
389314210291554.0556219322655.9443780697
390307930292994.49596329914935.5040367013
391322327305080.18052925217246.8194707476
392292136298288.495153786-6152.49515378643
393263276307761.577832324-44485.5778323245
394367655297851.14606788769803.8539321128
395283910375807.902930630-91897.9029306302
396283587297949.655562456-14362.6555624563
397243650364628.174312124-120978.174312124
398438493978291.020238343-539798.020238343
399296261298860.697615658-2599.69761565779
400230621182554.18969947748066.8103005231
401304252297200.2579655887051.74203441161
402333505305250.18964792928254.8103520711
403296919300615.211654127-3696.2116541272
404278990371758.828778796-92768.828778796
405276898302743.199704562-25845.1997045615
406327007311535.8708268815471.1291731201
407317046300040.89912073317005.1008792670
408304555319409.193825272-14854.1938252723
409298096302694.179542505-4598.17954250458
410231861295662.262446096-63801.2624460961
411309422383318.263208845-73896.2632088451
412286963443566.402245594-156603.402245594
413269753363621.712612616-93868.7126126158
414448243418657.89963541329585.1003645874
415165404304912.124528758-139508.124528758
416204325294094.176360156-89769.1763601558
417407159278849.513124462128309.486875538
418290476377131.266879675-86655.2668796748
419275311333710.620325867-58399.6203258666
420246541290778.06407494-44237.0640749401
421253468295170.097570988-41702.0975709884
422240897449926.660327272-209029.660327272
423-83265534208.385639930-617473.38563993
424-42143397105.15965583-439248.15965583
425272713340666.731603923-67953.7316039226
426215362495499.256221562-280137.256221562
42742754357898.115881204-315144.115881204
4283062751494722.83074697-1188447.83074697
429253537440481.830604375-186944.830604375
430372631633043.307797887-260412.307797887
431-7170368381.404482379-375551.404482379


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
1013.90887342945695e-421.95443671472847e-42
1111.04494568487069e-435.22472842435345e-44
1212.14533834892267e-451.07266917446133e-45
1311.39036929347142e-776.95184646735712e-78
1419.21523992096204e-814.60761996048102e-81
1516.07429866142054e-833.03714933071027e-83
1612.63813657335478e-941.31906828667739e-94
1713.10218415102575e-971.55109207551287e-97
1811.05535637343905e-995.27678186719527e-100
1911.12248532136626e-1045.61242660683128e-105
2011.18905964724326e-1105.94529823621631e-111
2114.80775015928234e-1152.40387507964117e-115
2218.39060565165917e-1174.19530282582959e-117
2312.66018372395437e-1171.33009186197718e-117
2411.18642243891050e-1245.93211219455251e-125
2513.10409958423975e-1241.55204979211987e-124
2611.13822093107211e-1255.69110465536056e-126
2719.54532361047835e-1314.77266180523917e-131
2816.63755449303174e-1313.31877724651587e-131
2912.29462754203998e-1411.14731377101999e-141
3013.68427804135794e-1451.84213902067897e-145
3116.8228869032501e-1493.41144345162505e-149
3218.96663558940176e-1514.48331779470088e-151
3313.24750362794970e-1581.62375181397485e-158
3413.24331610664047e-1601.62165805332024e-160
3511.02612916752791e-1605.13064583763956e-161
3613.08987771132551e-1641.54493885566276e-164
3711.30176942266618e-1696.5088471133309e-170
3814.69580684925343e-1752.34790342462672e-175
3913.9845332875143e-1751.99226664375715e-175
4013.91948417758265e-1761.95974208879133e-176
4119.20301542941453e-1784.60150771470726e-178
4213.88109940939564e-1771.94054970469782e-177
4314.15707009369007e-1782.07853504684503e-178
4413.56189247890488e-1771.78094623945244e-177
4519.17936964633066e-1774.58968482316533e-177
4612.85947809042611e-1761.42973904521306e-176
4719.8354077458548e-1774.9177038729274e-177
4812.38998976159632e-1771.19499488079816e-177
4916.6220245227294e-1773.3110122613647e-177
5012.78680490776657e-1771.39340245388329e-177
5114.73954910828606e-1782.36977455414303e-178
5217.22138962177848e-1793.61069481088924e-179
5313.63677725975679e-1791.81838862987840e-179
5411.00914730986334e-1785.04573654931669e-179
5511.07270444969467e-1835.36352224847334e-184
5612.44381858940570e-1831.22190929470285e-183
5718.31377505353253e-1964.15688752676626e-196
5812.98241137027424e-1961.49120568513712e-196
5912.09745336181468e-1951.04872668090734e-195
6011.06192223874994e-1955.30961119374971e-196
6112.56456637712028e-1971.28228318856014e-197
6216.16134195784157e-1993.08067097892079e-199
6311.76682532598677e-1988.83412662993384e-199
6412.4064120265702e-1981.2032060132851e-198
6511.27159925704577e-1976.35799628522887e-198
6611.19507590299232e-1985.97537951496162e-199
6712.6321981251214e-1981.3160990625607e-198
6811.91589672128086e-1979.5794836064043e-198
6918.40565642469633e-1974.20282821234817e-197
7011.53995114856040e-1967.69975574280202e-197
7113.86610731215059e-1961.93305365607530e-196
7214.16738970519825e-1972.08369485259913e-197
7311.30777806845163e-1966.53889034225816e-197
7411.11721907316351e-1955.58609536581755e-196
7511.03345416047865e-1945.16727080239323e-195
7611.56494176023628e-1947.8247088011814e-195
7711.07977824398060e-1935.39889121990301e-194
7811.30399429840434e-1936.51997149202169e-194
7911.01785951954661e-1925.08929759773307e-193
8018.12128934841567e-1934.06064467420783e-193
8115.12316442729918e-1922.56158221364959e-192
8215.73188989495926e-1922.86594494747963e-192
8313.13588181699741e-1921.56794090849870e-192
8412.38153809456228e-1911.19076904728114e-191
8511.89217519291616e-1909.46087596458082e-191
8612.07469441162370e-1901.03734720581185e-190
8711.23015811298496e-1906.15079056492478e-191
8818.27844249897984e-1904.13922124948992e-190
8911.17732505529433e-1895.88662527647167e-190
9019.18985773067056e-1894.59492886533528e-189
9116.99713771368795e-1883.49856885684398e-188
9213.13227650934948e-1871.56613825467474e-187
9311.74435849170668e-1888.72179245853338e-189
9411.20291233450037e-1876.01456167250186e-188
9514.9584191857402e-1882.4792095928701e-188
9614.37268966302159e-1882.18634483151080e-188
9712.43924143530818e-1871.21962071765409e-187
9816.15948003082505e-1873.07974001541253e-187
9914.68089577856884e-1862.34044788928442e-186
10014.14428299861416e-1852.07214149930708e-185
10112.72469981376771e-1841.36234990688385e-184
10212.51335188169913e-1851.25667594084956e-185
10319.71144466597536e-1864.85572233298768e-186
10411.86342065584052e-1869.31710327920258e-187
10516.93578645281782e-1863.46789322640891e-186
10612.34378005837816e-1851.17189002918908e-185
10713.87044024642494e-1881.93522012321247e-188
10818.91970765760588e-1904.45985382880294e-190
10915.93522188544745e-1892.96761094272372e-189
11017.44256738863504e-1893.72128369431752e-189
11115.30110285468853e-1892.65055142734427e-189
11211.18002806912066e-1895.90014034560332e-190
11316.49661817973533e-1893.24830908986767e-189
11414.54647991692659e-1882.27323995846330e-188
11513.63879844464388e-1881.81939922232194e-188
11611.37429167787537e-1876.87145838937684e-188
11717.32045448913524e-1873.66022724456762e-187
11812.7813331314197e-1871.39066656570985e-187
11912.65447732392418e-1881.32723866196209e-188
12012.06756175502514e-1871.03378087751257e-187
12115.75258657197685e-1872.87629328598843e-187
12214.71406003067903e-1862.35703001533952e-186
12312.20228099041546e-1851.10114049520773e-185
12411.74057026140711e-1858.70285130703554e-186
12515.71021464436666e-1852.85510732218333e-185
12611.81528495245382e-1859.07642476226911e-186
12711.62245047053386e-1848.11225235266928e-185
12811.50989386989281e-1837.54946934946404e-184
12911.35431808092870e-1826.77159040464351e-183
13011.20063511778911e-1816.00317558894554e-182
13111.09044401337482e-1805.45222006687412e-181
13211.59994781177669e-1807.99973905888346e-181
13311.41886936054797e-1797.09434680273987e-180
13411.31732224522112e-1786.58661122610559e-179
13511.14565468464413e-1775.72827342322064e-178
13611.00275591942294e-1765.01377959711472e-177
13718.83119731980548e-1764.41559865990274e-176
13817.67888185058582e-1753.83944092529291e-175
13916.2378044747941e-1743.11890223739705e-174
14015.39274665962866e-1732.69637332981433e-173
14114.07608839521393e-1722.03804419760696e-172
14213.49975558289318e-1711.74987779144659e-171
14313.11076090486729e-1701.55538045243365e-170
14412.67397014539706e-1691.33698507269853e-169
14512.09860892844309e-1681.04930446422154e-168
14611.72458659307238e-1678.6229329653619e-168
14711.44968366510757e-1667.24841832553787e-167
14811.23871145954545e-1656.19355729772723e-166
14919.13156202605306e-1654.56578101302653e-165
15017.57307572788886e-1643.78653786394443e-164
15116.30273371010829e-1633.15136685505414e-163
15215.41204554213643e-1622.70602277106822e-162
15314.48336544630322e-1612.24168272315161e-161
15413.75566171902488e-1601.87783085951244e-160
15513.06790602656314e-1591.53395301328157e-159
15612.48012728123541e-1581.24006364061771e-158
15711.99650959057051e-1579.98254795285253e-158
15811.61286976887785e-1568.06434884438925e-157
15919.5535203078644e-1564.7767601539322e-156
16017.59741467731667e-1553.79870733865833e-155
16116.01565333072407e-1543.00782666536203e-154
16214.74246475345949e-1532.37123237672974e-153
16313.72237626133197e-1521.86118813066598e-152
16412.8579338261421e-1511.42896691307105e-151
16511.89319047956663e-1509.46595239783317e-151
16611.46225498727031e-1497.31127493635155e-150
16711.12928587579983e-1485.64642937899914e-149
16811.52101231143742e-1497.60506155718711e-150
16914.06660942577345e-1542.03330471288672e-154
17013.33243673909024e-1531.66621836954512e-153
17112.71857507412657e-1521.35928753706329e-152
17212.23830563112264e-1511.11915281556132e-151
17311.80957517557593e-1509.04787587787965e-151
17411.48749849821135e-1497.43749249105677e-150
17511.19156960564843e-1485.95784802824214e-149
17619.5346735038676e-1484.7673367519338e-148
17715.96866498700331e-1482.98433249350166e-148
17814.84468474380801e-1472.42234237190400e-147
17913.86034509399592e-1461.93017254699796e-146
18013.06213482345831e-1451.53106741172915e-145
18111.55245647149752e-1447.76228235748759e-145
18211.22456410059399e-1436.12282050296996e-144
18314.69163796701436e-1432.34581898350718e-143
18413.63154745815969e-1421.81577372907984e-142
18512.82477269447985e-1411.41238634723993e-141
18611.85918515497536e-1409.29592577487681e-141
18713.59078793686707e-1401.79539396843354e-140
18812.80997135008455e-1391.40498567504227e-139
18911.84523932437353e-1389.22619662186765e-139
19011.41421628473043e-1377.07108142365214e-138
19111.03055501305592e-1365.15277506527961e-137
19217.8265310947853e-1363.91326554739265e-136
19315.9490830920757e-1352.97454154603785e-135
19414.47673177039827e-1342.23836588519913e-134
19513.35843911328127e-1331.67921955664063e-133
19612.53345262864888e-1321.26672631432444e-132
19719.28147988600307e-1324.64073994300154e-132
19816.96823810454998e-1313.48411905227499e-131
19915.20791745239363e-1302.60395872619682e-130
20017.2817713305574e-1303.6408856652787e-130
20115.43285425067103e-1292.71642712533551e-129
20214.03467015085768e-1282.01733507542884e-128
20312.9824350214391e-1271.49121751071955e-127
20412.18467671374883e-1261.09233835687441e-126
20511.23117029033595e-1256.15585145167975e-126
20618.94106277066544e-1254.47053138533272e-125
20716.43292325197568e-1243.21646162598784e-124
20814.64764134165889e-1232.32382067082945e-123
20911.06069105966862e-1225.30345529834311e-123
21017.37744663535409e-1223.68872331767704e-122
21115.21708572201768e-1212.60854286100884e-121
21213.67279177386238e-1201.83639588693119e-120
21312.16285973797844e-1191.08142986898922e-119
21411.34667435550895e-1186.73337177754476e-119
21519.4783936646018e-1184.7391968323009e-118
21616.57232407120153e-1173.28616203560077e-117
21714.54483504452416e-1162.27241752226208e-116
21813.05821415627913e-1151.52910707813956e-115
21912.09173112517942e-1141.04586556258971e-114
22017.03312948918035e-1143.51656474459018e-114
22114.70288486226668e-1132.35144243113334e-113
22213.17836827351263e-1121.58918413675631e-112
22312.13950481458625e-1111.06975240729313e-111
22411.22084369151476e-1106.10421845757381e-111
22518.14087441870958e-1104.07043720935479e-110
22615.41902296329194e-1092.70951148164597e-109
22713.36631429252575e-1081.68315714626288e-108
22812.21446410249322e-1071.10723205124661e-107
22911.46114719005776e-1067.30573595028882e-107
23019.52452895528808e-1064.76226447764404e-106
23115.98826011988173e-1052.99413005994087e-105
23213.13010658430776e-1041.56505329215388e-104
23312.01439208018730e-1031.00719604009365e-103
23411.30392039542495e-1026.51960197712474e-103
23518.31391215190742e-1024.15695607595371e-102
23615.27547032331704e-1012.63773516165852e-101
23713.33232685665470e-1001.66616342832735e-100
23812.08762877173623e-991.04381438586811e-99
23911.30623916682333e-986.53119583411667e-99
24018.1346628828815e-984.06733144144075e-98
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34914.84394260966262e-262.42197130483131e-26
35011.27706149645395e-256.38530748226975e-26
35114.30573105973399e-252.15286552986699e-25
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35411.50322713805263e-237.51613569026316e-24
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35611.61681562855705e-228.08407814278524e-23
35714.36758391716914e-222.18379195858457e-22
35811.40727178824976e-217.03635894124878e-22
35914.49272136677173e-212.24636068338587e-21
36011.4209386820277e-207.1046934101385e-21
36114.46153588359542e-202.23076794179771e-20
36211.38438398301495e-196.92191991507477e-20
36314.25369098997758e-192.12684549498879e-19
36411.1835082527733e-185.9175412638665e-19
36513.54646022449137e-181.77323011224568e-18
36611.06054611504323e-175.30273057521613e-18
36713.13853572073892e-171.56926786036946e-17
36819.18967652891838e-174.59483826445919e-17
36912.66168153542862e-161.33084076771431e-16
37017.33285289352427e-163.66642644676213e-16
3710.9999999999999992.08012949903217e-151.04006474951608e-15
3720.9999999999999976.04905104881178e-153.02452552440589e-15
3730.9999999999999911.72490265110914e-148.62451325554568e-15
3740.9999999999999754.90820331471660e-142.45410165735830e-14
3750.9999999999999331.33367342500157e-136.66836712500785e-14
3760.9999999999998213.57947687026383e-131.78973843513191e-13
3770.99999999999951.00016972566662e-125.00084862833312e-13
3780.999999999998752.49874639054768e-121.24937319527384e-12
3790.9999999999975564.88741227971374e-122.44370613985687e-12
3800.9999999999937391.25227160801317e-116.26135804006585e-12
3810.9999999999841823.16368202844163e-111.58184101422081e-11
3820.9999999999627827.4435118990833e-113.72175594954165e-11
3830.9999999999043121.91375522178973e-109.56877610894867e-11
3840.9999999997649644.70072586255686e-102.35036293127843e-10
3850.999999999412031.17593933461631e-095.87969667308156e-10
3860.9999999987230072.55398646338279e-091.27699323169139e-09
3870.9999999971155525.76889598278615e-092.88444799139308e-09
3880.9999999934493081.31013841230591e-086.55069206152954e-09
3890.9999999849174173.01651662267787e-081.50825831133894e-08
3900.999999964993167.00136801124073e-083.50068400562036e-08
3910.9999999239360061.52127987879577e-077.60639939397884e-08
3920.9999998235918243.52816351846330e-071.76408175923165e-07
3930.9999995868864738.26227054863263e-074.13113527431631e-07
3940.9999993260972151.34780557084576e-066.73902785422878e-07
3950.999998542870282.9142594388082e-061.4571297194041e-06
3960.9999967523150876.49536982586689e-063.24768491293344e-06
3970.9999932187413231.3562517353289e-056.7812586766445e-06
3980.9999881063092752.37873814492624e-051.18936907246312e-05
3990.9999747454768685.05090462631309e-052.52545231315654e-05
4000.9999476191025480.0001047617949042435.23808974521216e-05
4010.9998930754116110.0002138491767772800.000106924588388640
4020.999815084194780.0003698316104387620.000184915805219381
4030.999651849694490.0006963006110187270.000348150305509363
4040.9993570313072970.001285937385404960.000642968692702482
4050.99875315668950.002493686620997890.00124684331049894
4060.9978237660885240.004352467822952640.00217623391147632
4070.9961316615660930.007736676867814720.00386833843390736
4080.9939038549679360.01219229006412830.00609614503206413
4090.9902458618772940.01950827624541150.00975413812270577
4100.9827844956044220.03443100879115650.0172155043955783
4110.970939168108690.05812166378261950.0290608318913097
4120.9537907882573850.09241842348522980.0462092117426149
4130.9250909812245530.1498180375508930.0749090187754467
4140.9238617884805580.1522764230388830.0761382115194415
4150.8936620474858070.2126759050283860.106337952514193
4160.8401800095062540.3196399809874920.159819990493746
4170.969602922197700.06079415560460210.0303970778023011
4180.9434310548530650.113137890293870.056568945146935
4190.8923107379805760.2153785240388470.107689262019423
4200.814893976217910.3702120475641790.185106023782090
4210.6874003286427720.6251993427144570.312599671357228


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level3980.966019417475728NOK
5% type I error level4010.973300970873786NOK
10% type I error level4040.980582524271845NOK
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Dec/03/t1291394102a7s80b1qspnm35f/10absh1291394141.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/03/t1291394102a7s80b1qspnm35f/10absh1291394141.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/03/t1291394102a7s80b1qspnm35f/1lsvn1291394141.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/03/t1291394102a7s80b1qspnm35f/1lsvn1291394141.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/03/t1291394102a7s80b1qspnm35f/2lsvn1291394141.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/03/t1291394102a7s80b1qspnm35f/2lsvn1291394141.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/03/t1291394102a7s80b1qspnm35f/3w1u81291394141.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/03/t1291394102a7s80b1qspnm35f/3w1u81291394141.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/03/t1291394102a7s80b1qspnm35f/4w1u81291394141.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/03/t1291394102a7s80b1qspnm35f/4w1u81291394141.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/03/t1291394102a7s80b1qspnm35f/5w1u81291394141.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/03/t1291394102a7s80b1qspnm35f/5w1u81291394141.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/03/t1291394102a7s80b1qspnm35f/66tbb1291394141.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/03/t1291394102a7s80b1qspnm35f/66tbb1291394141.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/03/t1291394102a7s80b1qspnm35f/7h2ae1291394141.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/03/t1291394102a7s80b1qspnm35f/7h2ae1291394141.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/03/t1291394102a7s80b1qspnm35f/8h2ae1291394141.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/03/t1291394102a7s80b1qspnm35f/8h2ae1291394141.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/03/t1291394102a7s80b1qspnm35f/9h2ae1291394141.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/03/t1291394102a7s80b1qspnm35f/9h2ae1291394141.ps (open in new window)


 
Parameters (Session):
par1 = 7 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;
 
Parameters (R input):
par1 = 7 ; 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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