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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 16:12:01 +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/t1291306374shf4xt8o4m8xiby.htm/, Retrieved Thu, 02 Dec 2010 17:13:06 +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/t1291306374shf4xt8o4m8xiby.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 «
6282929 1 162556 1081 213118 4324047 1 29790 309 81767 4108272 1 87550 458 153198 -1212617 0 84738 588 -26007 1485329 1 54660 299 126942 1779876 1 42634 156 157214 1367203 0 40949 481 129352 2519076 1 42312 323 234817 912684 1 37704 452 60448 1443586 1 16275 109 47818 1220017 0 25830 115 245546 984885 0 12679 110 48020 1457425 1 18014 239 -1710 -572920 0 43556 247 32648 929144 1 24524 497 95350 1151176 0 6532 103 151352 790090 0 7123 109 288170 774497 1 20813 502 114337 990576 1 37597 248 37884 454195 0 17821 373 122844 876607 1 12988 119 82340 711969 1 22330 84 79801 702380 0 13326 102 165548 264449 0 16189 295 116384 450033 0 7146 105 134028 541063 0 15824 64 63838 588864 1 26088 267 74996 -37216 0 11326 129 31080 783310 0 8568 37 32168 467359 0 14416 361 49857 688779 1 3369 28 87161 608419 1 11819 85 106113 696348 1 6620 44 80570 597793 1 4519 49 102129 821730 0 2220 22 301670 377934 0 18562 155 102313 651939 0 10327 91 88577 697458 1 5336 81 112477 700368 1 2365 79 19 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 time37 seconds
R Server'George Udny Yule' @ 72.249.76.132
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] = + 72181.4498121003 + 78702.9051010799Group[t] + 26.2814924515352Costs[t] -466.247947109258Trades[t] + 3.51295882947254`Dividends `[t] + 45311.4814373017M1[t] + 30258.9310141834M2[t] + 13636.4022027240M3[t] -134925.814792819M4[t] -39765.0881503493M5[t] -27177.4771094453M6[t] -13411.2690128487M7[t] -34722.6176943436M8[t] + 15125.0384876994M9[t] -13111.3793857858M10[t] -63422.662398434M11[t] + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0		2-tail p-value1-tail p-value
(Intercept)72181.449812100359421.5001421.21470.2251570.112579
Group78702.905101079933277.4822912.3650.0184870.009243
Costs26.28149245153521.93248513.599800
Trades-466.247947109258208.738468-2.23360.0260390.013019
`Dividends `3.512958829472540.4921327.138200
M145311.481437301771522.8270310.63350.526740.26337
M230258.931014183471174.8074110.42510.6709580.335479
M313636.402202724071377.2319180.1910.8485820.424291
M4-134925.81479281971436.775994-1.88870.0596230.029812
M5-39765.088150349371430.548405-0.55670.5780350.289018
M6-27177.477109445371365.838508-0.38080.7035320.351766
M7-13411.269012848771194.969472-0.18840.8506760.425338
M8-34722.617694343671418.931248-0.48620.6270950.313547
M915125.038487699471151.840150.21260.8317640.415882
M10-13111.379385785871568.252049-0.18320.854730.427365
M11-63422.66239843471663.078643-0.8850.3766630.188331


Multiple Linear Regression - Regression Statistics
Multiple R0.753023913205486
R-squared0.567045013859303
Adjusted R-squared0.551396038456627
F-TEST (value)36.2352805387083
F-TEST (DF numerator)15
F-TEST (DF denominator)415
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation299670.437651961
Sum Squared Residuals37267984049044.9


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast		Residuals
Prediction Error
162829294713070.85229671569858.14770330
243240471107242.435011323216804.56498868
341082722790102.128229271318169.87177073
4-12126171798781.42919913-3011398.42919913
514853291854199.52770898-368870.52770898
617798761723743.6566501356132.3433498682
713672031365114.003147542088.99685245694
825190761902488.61237215616587.387627845
99126841158534.04802413-245850.048024135
101443586682665.904248938760920.095751062
1112200171496584.21226092-276567.21226092
12984885522809.501414369462075.498585631
131457425552190.222414929905234.777585071
14-5729201246684.90297398-1819604.90297398
15929144912283.4726742616860.5273257396
161151176592596.149918787558579.850081213
177900901181127.75204823-391037.752048232
18774497838308.284434094-63811.284434094
199905761143033.79901334-152457.799013341
20454195763456.739272539-309261.739272539
21876607741126.941674188135480.058325813
22711969965811.501963737-253842.501963737
23702380892991.973519201-190611.973519201
24264449768961.587122106-504512.587122106
25450033727179.287858149-277146.287858149
26541063712739.114520252-171676.114520253
27588864989121.990688506-400257.990688506
28-37216283956.593768282-321172.593768282
29783310353349.874569936429960.125430064
30467359430708.04733855836650.9526614418
31688779519153.495986154169625.504013846
32608419759922.221271066-151503.221271066
33696348602517.0566478493830.94335216
34597793592467.8628027335325.13719726716
358217301116600.53590666-294870.535906655
36377934847171.437615386-469237.437615386
37651939657640.694847655-5701.69484765475
38697458678742.31619549218715.6838045080
39700368863551.117340743-163183.117340743
40225986256937.241900964-30951.2419009641
41348695305279.88369028943415.116309711
42373683715910.214564118-342227.214564118
43501709401876.07884740799832.9211525925
44413743581873.290960495-168130.290960495
45379825422982.582332223-43157.5823322232
46336260580180.421891903-243920.421891903
47636765848302.048645476-211537.048645476
48481231678835.920715971-197604.920715971
49469107635433.638686494-166326.638686494
50211928415481.720779178-203553.720779178
51563925576945.266687964-13020.2666879644
52511939528492.360628737-16553.3606287371
53521016912464.498353671-391448.498353671
54543856591628.711022237-47772.7110222375
55329304736382.55846236-407078.55846236
56423262270400.857523103152861.142476897
57509665358490.767548114151174.232451886
58455881477612.350395632-21731.3503956323
59367772342142.73585859525629.2641414049
60406339656020.140264277-249681.140264277
61493408652003.918684026-158595.918684025
62232942336803.833648841-103861.833648841
63416002563290.958734052-147288.958734052
64337430458651.024350343-121221.024350343
65361517273210.0573869688306.94261304
66360962270854.3237725590107.6762274498
67235561331211.002862436-95650.0028624364
68408247498188.364557173-89941.3645571725
69450296541509.136407639-91213.1364076393
70418799566712.327266293-147913.327266293
71247405236455.62090682210949.3790931779
72378519321012.66000693657506.3399930639
73326638514731.92123401-188093.92123401
74328233390396.541020965-62163.5410209654
75386225539029.18006431-152804.18006431
76283662314516.727532328-30854.7275323282
77370225440274.837449477-70049.8374494771
78269236306254.967626113-37018.967626113
79365732281887.16641474783844.8335852535
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81345811325679.75659697420131.2434030265
82431809541468.484864286-109659.484864286
83418876492472.147412396-73596.1474123963
84297476224383.11523753673092.8847624644
85416776484876.594920422-68100.5949204223
86357257522836.651016125-165579.651016125
87458343458524.413937772-181.413937772435
88388386310127.36959554878258.630404452
89358934432261.399471431-73327.3994714309
90407560417823.581736316-10263.5817363158
91392558422781.283060025-30223.2830600255
92373177465784.5184667-92607.5184667
93428370323759.734871941104610.265128059
94369419720330.974728443-350911.974728443
95358649169254.175028318189394.824971682
96376641422770.883226158-46129.8832261581
97467427517858.296555599-50431.2965555987
98364885372541.725213907-7656.72521390677
99436230600122.605891716-163892.605891716
100329118304399.47521544524718.5247845555
101317365396259.394836088-78894.3948360884
102286849377946.939726858-91097.9397268583
103376685491016.109484733-114331.109484733
104407198443842.218121503-36644.2181215027
105377772349901.39467189327870.6053281073
106271483319343.207807534-47860.2078075338
107153661353561.179319666-199900.179319666
108513294539188.587851455-25894.5878514555
109324881590426.61150072-265545.61150072
110264512471418.60169314-206906.60169314
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112129302253073.685071086-123771.685071086
113191521436667.492950533-245146.492950533
114268673440205.356508096-171532.356508096
115353179371882.368851090-18703.3688510895
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117363713384315.572557349-20602.5725573491
118456657419336.14783898237320.8521610179
119211742409915.001133012-198173.001133012
120338381277218.83445464661162.1655453536
121418530740141.00428043-321611.00428043
122351483354277.45703651-2794.45703651011
123372928401509.949497529-28581.9494975293
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125279268384470.572789418-105202.572789418
126219060465949.105112144-246889.105112144
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128325314250228.86289856375085.1371014371
129322046288865.60538078233180.3946192183
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184305442271220.61296373634221.3870362639
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193331824334904.786662809-3080.78666280884
194325560315747.2409518599812.75904814104
195325685299525.30103583426159.6989641655
196325560229265.40024593796294.599754063
197404480540052.339905286-135572.339905286
198325560337013.737929311-11453.7379293112
199325560350779.946025908-25219.9460259080
200318314400436.43221891-82122.4322189096
201325560379316.253526455-53756.2535264553
202325560351079.835652971-25519.8356529709
203325560300768.55264032324791.4473596774
204311807322103.163681419-10296.1636814193
205337724508302.713613196-170578.713613196
206326431397068.594547623-70637.5945476233
207327556395070.73894231-67514.7389423102
208325560229265.40024593796294.599754063
209356850296510.89620394960339.1037960507
210325560337013.737929311-11453.7379293112
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216325560285488.30993767640071.690062324
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218326960312866.09198267814093.9080173217
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297325560300613.34842537424946.6515746259
298325560351079.835652971-25519.8356529709
299325560222065.647539242103494.352460758
300325560285488.30993767640071.690062324
301324047408700.160249867-84653.1602498669
302311464315656.367327704-4192.3673277036
303325560299124.71214040026435.2878596003
304325560229265.40024593796294.599754063
305353417234453.206034264118963.793965736
306325590254219.85867159271370.1413284081
307325560350779.946025908-25219.9460259080
308328576340478.918256305-11902.9182563053
309326126279240.25423683446885.7457631658
310325560351079.835652971-25519.8356529709
311325560300768.55264032324791.4473596774
312369376349377.52120621519998.4787937847
313325560409502.696476059-83942.6964760592
314332013403906.347161615-71893.347161615
315325871297482.59614132628388.4038586743
316342165166043.755412701176121.244587299
317324967243526.49573549281440.5042645076
318314832261626.49954631253205.5004536881
319325557269302.32177579356254.6782242066
320325560250765.69224333274794.3077566681
321325560300613.34842537424946.6515746259
322325560272376.93055189053183.0694481103
323325560222065.647539242103494.352460758
324325560364191.215038757-38631.2150387571
325325560330799.791374978-5239.79137497793
326322649315399.9638092337249.03619076684
327325560377827.617241481-52267.617241481
328325560229265.40024593796294.599754063
329325560245723.22178732779836.7782126735
330325560258310.8328282367249.16717177
331325560272077.04092482753482.9590751731
332325560250765.69224333274794.3077566681
333325560300613.34842537424946.6515746259
334324598271370.79513084153227.2048691593
335325567221184.023849281104382.976150719
336325560285488.30993767640071.690062324
337324005330385.013193829-6380.01319382933
338325560315747.2409518599812.75904814104
339325748299960.06375101825787.9362489825
340323385144322.680983017179062.319016983
341315409254619.72069343860789.2793065619
342325560258310.8328282367249.16717177
343325560272077.04092482753482.9590751731
344325560250765.69224333274794.3077566681
345325560300613.34842537424946.6515746259
346325560272376.93055189053183.0694481103
347312275216767.89741350495507.1025864963
348325560285488.30993767640071.690062324
349325560330799.791374978-5239.79137497793
350325560315747.2409518599812.75904814104
351320576293342.56788960827233.4321103916
352325246148896.140587962176349.859412038
353332961251603.4038079181357.59619209
354323010265651.26804060957358.7319593907
355325560272077.04092482753482.9590751731
356325560250765.69224333274794.3077566681
357345253353321.178756056-8068.17875605596
358325560272376.93055189053183.0694481103
359325560222065.647539242103494.352460758
360325560285488.30993767640071.690062324
361325559328968.106996651-3409.10699665139
362325560315747.2409518599812.75904814104
363325560299124.71214040026435.2878596003
364319634232482.38673673487151.6132632658
365319951241513.60268042378437.3973195766
366325560258310.8328282367249.16717177
367325560272077.04092482753482.9590751731
368325560250765.69224333274794.3077566681
369325560300613.34842537424946.6515746259
370325560272376.93055189053183.0694481103
371325560222065.647539242103494.352460758
372318519275313.83233071943205.1676692812
373343222388509.815038014-45287.8150380139
374317234334257.103892154-17023.1038921542
375325560299124.71214040026435.2878596003
376325560150562.495144856174997.504855144
377314025221757.47263987692267.5273601241
378320249268137.2910205452111.7089794602
379325560272077.04092482753482.9590751731
380325560250765.69224333274794.3077566681
381325560300613.34842537424946.6515746259
382349365302991.49032373246373.5096762675
383289197132172.677204788157024.322795212
384325560285488.30993767640071.690062324
385329245332345.439114805-3100.43911480518
386240869387397.758127343-146528.758127343
387327182296049.87656848431132.1234315162
388322876163713.115558856159162.884441144
389323117245085.57265941978031.4273405808
390306351258366.14746168947984.8525383112
391335137284839.10202764450297.8979723558
392308271253961.80270253454309.1972974656
393301731314504.681631243-12773.6816312428
394382409312671.42054471069737.5794552905
395279230465634.44611644-186404.446116440
396298731286243.94659309212487.0534069075
397243650412659.484598289-169009.484598289
398532682589699.700527265-57017.7005272655
399319771319897.210436117-126.210436116904
40017149381266.424749003690226.5752509964
401347262305334.78139459541927.2186054048
402343945286839.52493808757105.4750619135
403311874279030.22222674832843.7777732522
404302211388238.303804902-86027.3038049017
405316708325379.260171546-8671.26017154554
406333463332418.6826823431044.31731765697
407344282256518.39227060487763.6077293958
408319635300063.78224928619571.2177507136
409301186328751.256459814-27565.2564598143
410300381365958.859391261-65577.8593912614
411318765337047.354608953-18282.3546089529
412286146393631.743783211-107485.743783211
413306844335147.508980931-28303.5089809308
414307705459592.328304933-151887.328304933
415312448370406.154094996-57958.1540949955
416299715319589.0728701-19874.0728700998
417373399265938.461951696107460.538048304
418299446378480.895052731-79034.8950527305
419325586273131.66495475452454.3350452455
420291221319729.01852007-28508.0185200701
421261173388282.724740891-127109.724740891
422255027401278.719504685-146251.719504685
423-78375383760.459624878-462135.459624878
424-58143292774.699582612-350917.699582612
425227033274551.700298725-47518.700298725
426235098432623.042611947-197525.042611947
42721267329928.596627792-308661.596627792
4282386751422248.56578766-1183573.56578766
429197687587398.311531521-389711.311531521
430418341689576.105932425-271235.105932426
431-297706495667.138713925-793373.138713925


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
1912.9418053273637e-691.47090266368185e-69
2012.80149488330554e-1061.40074744165277e-106
2111.40111559383752e-1107.00557796918759e-111
2212.9756970701775e-1201.48784853508875e-120
2312.95400880129629e-1231.47700440064815e-123
2411.56891054480042e-1357.84455272400209e-136
2518.41370922795199e-1374.20685461397599e-137
2611.09916738845668e-1375.49583694228342e-138
2713.86919268621552e-1431.93459634310776e-143
2812.34484087190937e-1471.17242043595468e-147
2911.27889335061614e-1916.39446675308072e-192
3011.57706629923997e-2027.88533149619986e-203
3111.94366234250857e-2079.71831171254285e-208
3212.37551685593203e-2101.18775842796602e-210
3312.33079552757646e-2161.16539776378823e-216
3412.25667228880967e-2181.12833614440484e-218
3513.22151009825424e-2181.61075504912712e-218
3614.89857500853003e-2182.44928750426502e-218
3714.74291449055019e-2252.37145724527509e-225
3811.94874412359031e-2369.74372061795157e-237
3911.09205152762531e-2375.46025763812656e-238
4012.27528900128768e-2381.13764450064384e-238
4113.01527898681152e-2381.50763949340576e-238
4211.05112318876393e-2385.25561594381965e-239
4311.29481358228960e-2396.47406791144801e-240
4416.67902510827616e-2393.33951255413808e-239
4512.20144114339031e-2391.10072057169516e-239
4614.10736383801031e-2392.05368191900516e-239
4711.10158872001055e-2385.50794360005273e-239
4812.79367705109993e-2391.39683852554996e-239
4915.25667877503968e-2392.62833938751984e-239
5014.47559686000717e-2392.23779843000358e-239
5116.48553748185504e-2403.24276874092752e-240
5213.92177301129768e-2391.96088650564884e-239
5311.86902878983449e-2399.34514394917244e-240
5411.15307853054840e-2385.76539265274198e-239
5512.10260222221807e-2411.05130111110904e-241
5614.32871499672738e-2422.16435749836369e-242
5714.3400023885019e-2472.17000119425095e-247
5812.92583334148386e-2471.46291667074193e-247
5916.75872352442189e-2473.37936176221094e-247
6018.0127925724473e-2474.00639628622365e-247
6114.3441854394041e-2492.17209271970205e-249
6212.00369110571757e-2481.00184555285878e-248
6311.62841392925972e-2478.1420696462986e-248
6419.0025960142378e-2474.5012980071189e-247
6516.58627038541416e-2473.29313519270708e-247
6615.50179672195044e-2462.75089836097522e-246
6712.02265597621424e-2461.01132798810712e-246
6812.49442227148836e-2451.24721113574418e-245
6913.00656708905114e-2441.50328354452557e-244
7012.15790176430432e-2431.07895088215216e-243
7111.23378638358421e-2426.16893191792107e-243
7211.93449717210688e-2449.67248586053442e-245
7312.38117936828986e-2441.19058968414493e-244
7412.65489076909882e-2431.32744538454941e-243
7511.52905661872742e-2427.64528309363712e-243
7617.37884606848016e-2423.68942303424008e-242
7712.11842521708076e-2411.05921260854038e-241
7815.50491383176794e-2412.75245691588397e-241
7913.28503430334934e-2401.64251715167467e-240
8011.82852178972365e-2399.14260894861824e-240
8111.74293267034982e-2388.71466335174908e-239
8214.38638377996691e-2382.19319188998345e-238
8316.64418380086491e-2383.32209190043245e-238
8413.53264788006689e-2371.76632394003345e-237
8514.48194882166801e-2362.24097441083401e-236
8611.34384467899917e-2366.71922339499586e-237
8711.26099394219326e-2366.3049697109663e-237
8812.04924199923667e-2361.02462099961833e-236
8919.5028935453229e-2364.75144677266145e-236
9011.00428318288947e-2345.02141591444735e-235
9111.32140495849308e-2336.60702479246542e-234
9211.48725557098846e-2327.4362778549423e-233
9314.27486063757389e-2332.13743031878694e-233
9419.84527451617237e-2334.92263725808619e-233
9511.36655757780558e-2346.83278788902789e-235
9612.55156363640492e-2341.27578181820246e-234
9713.34856068964714e-2331.67428034482357e-233
9811.62922630363943e-2328.14613151819717e-233
9917.75950288145214e-2323.87975144072607e-232
10017.58076959035752e-2313.79038479517876e-231
10118.44027872022598e-2304.22013936011299e-230
10214.10145227613127e-2302.05072613806563e-230
10313.60850783095706e-2291.80425391547853e-229
10416.44798862432655e-2293.22399431216328e-229
10514.95268277249955e-2282.47634138624978e-228
10615.5438445695157e-2282.77192228475785e-228
10713.80779427463899e-2281.90389713731949e-228
10814.14583839724894e-2282.07291919862447e-228
10911.60616690752361e-2278.03083453761803e-228
11013.87749657849999e-2271.93874828925000e-227
11114.1757746657362e-2272.0878873328681e-227
11213.52873579139346e-2271.76436789569673e-227
11318.10749664132428e-2294.05374832066214e-229
11413.52188562116869e-2281.76094281058435e-228
11511.11376674194036e-2275.56883370970179e-228
11613.04705824532858e-2271.52352912266429e-227
11712.71374707297800e-2261.35687353648900e-226
11819.42015888455859e-2264.71007944227929e-226
11919.62158638657848e-2274.81079319328924e-227
12019.0924701438917e-2264.54623507194585e-226
12115.91160211085417e-2262.95580105542709e-226
12216.78346588683921e-2253.39173294341960e-225
12316.42690195978676e-2243.21345097989338e-224
12413.50081105903976e-2231.75040552951988e-223
12514.50570732594739e-2222.25285366297369e-222
12611.21272710413987e-2226.06363552069935e-223
12711.32072477737777e-2216.60362388688887e-222
12811.45048863258757e-2207.25244316293784e-221
12911.86563942188847e-2199.32819710944233e-220
13011.93337832390166e-2189.6668916195083e-219
13111.44155161833054e-2177.20775809165271e-218
13211.10200661642484e-2175.51003308212422e-218
13311.49450088098293e-2167.47250440491467e-217
13411.99175842687311e-2159.95879213436553e-216
13512.46368413978534e-2141.23184206989267e-214
13617.972679869941e-2143.9863399349705e-214
13717.3397057329924e-2133.6698528664962e-213
13817.35122916730636e-2123.67561458365318e-212
13918.3842240275961e-2114.19211201379805e-211
14019.74584082990053e-2104.87292041495026e-210
14111.24615187690014e-2086.23075938450068e-209
14211.35992539495169e-2076.79962697475844e-208
14317.53641479431508e-2073.76820739715754e-207
14418.59228657347514e-2064.29614328673757e-206
14518.97604424914196e-2054.48802212457098e-205
14619.18288988842131e-2044.59144494421065e-204
14711.12726121365252e-2025.63630606826259e-203
14815.46702134644101e-2022.73351067322051e-202
14915.40952559980273e-2012.70476279990136e-201
15015.70069589359509e-2002.85034794679754e-200
15116.14255423416537e-1993.07127711708269e-199
15215.33850732430989e-1982.66925366215494e-198
15316.58617659523653e-1973.29308829761827e-197
15416.70256924535226e-1963.35128462267613e-196
15516.18577565187077e-1953.09288782593539e-195
15616.92706291130107e-1943.46353145565053e-194
15718.3509145087889e-1934.17545725439445e-193
15819.97135322577074e-1924.98567661288537e-192
15911.00464484425916e-1905.0232242212958e-191
16015.77049145440475e-1902.88524572720238e-190
16115.81047303117834e-1892.90523651558917e-189
16216.12335562673151e-1883.06167781336575e-188
16316.68597771706232e-1873.34298885853116e-187
16416.97667759866467e-1863.48833879933233e-186
16518.16782427494308e-1854.08391213747154e-185
16618.58586086081224e-1844.29293043040612e-184
16717.97100488706866e-1833.98550244353433e-183
16817.1264978974871e-1843.56324894874355e-184
16918.24274300366999e-1834.12137150183499e-183
17019.4667269896191e-1824.73336349480955e-182
17111.09038963831471e-1805.45194819157356e-181
17217.2319172088552e-1803.6159586044276e-180
17317.35943648623753e-1793.67971824311877e-179
17417.75388233853609e-1783.87694116926805e-178
17518.26584900774816e-1774.13292450387408e-177
17619.09659635243805e-1764.54829817621903e-176
17711.02688383081100e-1745.13441915405502e-175
17811.10457931925959e-1735.52289659629794e-174
17911.02882787849794e-1725.14413939248972e-173
18011.10554419275905e-1715.52772096379524e-172
18115.53540783065233e-1712.76770391532617e-171
18215.54317865151531e-1702.77158932575765e-170
18313.88707423249871e-1691.94353711624935e-169
18412.19913345991018e-1681.09956672995509e-168
18512.39313301116024e-1671.19656650558012e-167
18612.50645339791909e-1661.25322669895954e-166
18711.74812555527678e-1658.74062777638389e-166
18811.84781025373103e-1649.23905126865514e-165
18911.38129243461675e-1636.90646217308376e-164
19011.35447171945447e-1626.77235859727234e-163
19111.02689348210533e-1615.13446741052664e-162
19211.06202046753641e-1605.31010233768206e-161
19311.04076087281271e-1595.20380436406355e-160
19411.07706033120419e-1585.38530165602095e-159
19511.12306060058447e-1575.61530300292234e-158
19611.02001551501686e-1565.10007757508432e-157
19713.06949808035283e-1561.53474904017642e-156
19813.20121390136649e-1551.60060695068324e-155
19913.18462623657012e-1541.59231311828506e-154
20017.8714637960053e-1543.93573189800265e-154
20117.69379608910717e-1533.84689804455359e-153
20217.31939755515405e-1523.65969877757703e-152
20317.18223665502935e-1513.59111832751467e-151
20416.13024086465782e-1503.06512043232891e-150
20511.35770049387569e-1496.78850246937847e-150
20611.30797837326691e-1486.53989186633457e-149
20711.19550485611991e-1475.97752428059953e-148
20811.06357152158510e-1465.31785760792549e-147
20911.15951676143839e-1465.79758380719195e-147
21011.17145699752461e-1455.85728498762307e-146
21111.08369616023436e-1445.4184808011718e-145
21211.05978779446679e-1435.29893897233394e-144
21311.01263274890504e-1425.06316374452518e-143
21418.28605618465663e-1424.14302809232831e-142
21517.17780739821749e-1413.58890369910874e-141
21616.86989523743773e-1403.43494761871886e-140
21716.54034485048588e-1393.27017242524294e-139
21815.61260939690305e-1382.80630469845153e-138
21915.39851502514865e-1372.69925751257433e-137
22011.83484214685929e-1369.17421073429643e-137
22111.43686346218545e-1357.18431731092725e-136
22211.31119702439784e-1346.5559851219892e-135
22311.15411751668505e-1335.77058758342526e-134
22411.08023195984757e-1325.40115979923784e-133
22511.01848768360689e-1315.09243841803445e-132
22619.17505154516403e-1314.58752577258202e-131
22717.49519310544869e-1303.74759655272434e-130
22816.85296505553796e-1293.42648252776898e-129
22916.10100993033222e-1283.05050496516611e-128
23015.39779277467371e-1272.69889638733685e-127
23114.86874357971435e-1262.43437178985718e-126
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34611.45212385604088e-337.26061928020439e-34
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34813.03342868221522e-321.51671434110761e-32
34911.41998202264935e-317.09991011324674e-32
35015.8553678152957e-312.92768390764785e-31
35112.79611808563198e-301.39805904281599e-30
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36815.50747525171532e-202.75373762585766e-20
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3800.9999999999998992.01803961927193e-131.00901980963596e-13
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3830.9999999999985962.80785994517181e-121.40392997258590e-12
3840.999999999995059.89895282987843e-124.94947641493921e-12
3850.9999999999829163.41687528889987e-111.70843764444993e-11
3860.999999999942111.15780069512129e-105.78900347560644e-11
3870.9999999998042233.91553715830091e-101.95776857915046e-10
3880.9999999995851578.29685551727754e-104.14842775863877e-10
3890.9999999986471842.70563115210740e-091.35281557605370e-09
3900.9999999958920528.21589617148636e-094.10794808574318e-09
3910.999999990762091.84758196940454e-089.23790984702269e-09
3920.9999999723399745.53200529113121e-082.76600264556560e-08
3930.9999999192649361.6147012790237e-078.0735063951185e-08
3940.9999997545845944.90830811845005e-072.45415405922503e-07
3950.999999289335241.42132952025296e-067.1066476012648e-07
3960.9999979135659274.1728681461461e-062.08643407307305e-06
3970.9999946400102031.07199795932365e-055.35998979661825e-06
3980.999985233842152.95323157022318e-051.47661578511159e-05
3990.9999598446382648.0310723471536e-054.0155361735768e-05
4000.9999400203515390.0001199592969223595.99796484611795e-05
4010.9998402201000950.0003195597998107270.000159779899905364
4020.9996486183592120.0007027632815751560.000351381640787578
4030.999405926569810.001188146860379780.00059407343018989
4040.9985228061440770.002954387711847120.00147719385592356
4050.9967882459363850.006423508127230930.00321175406361547
4060.9932632782018680.01347344359626480.00673672179813238
4070.986464558378250.02707088324350120.0135354416217506
4080.971011095043290.05797780991342030.0289889049567101
4090.9422910705722180.1154178588555630.0577089294277816
4100.8841625915382020.2316748169235960.115837408461798
4110.8113008732357570.3773982535284860.188699126764243
4120.8270984707626320.3458030584747360.172901529237368


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level3870.98223350253807NOK
5% type I error level3890.987309644670051NOK
10% type I error level3900.98984771573604NOK
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Dec/02/t1291306374shf4xt8o4m8xiby/10sgu91291306282.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/02/t1291306374shf4xt8o4m8xiby/10sgu91291306282.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/02/t1291306374shf4xt8o4m8xiby/13xff1291306282.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/02/t1291306374shf4xt8o4m8xiby/13xff1291306282.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/02/t1291306374shf4xt8o4m8xiby/23xff1291306282.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/02/t1291306374shf4xt8o4m8xiby/23xff1291306282.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/02/t1291306374shf4xt8o4m8xiby/3eow01291306282.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/02/t1291306374shf4xt8o4m8xiby/3eow01291306282.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/02/t1291306374shf4xt8o4m8xiby/4eow01291306282.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/02/t1291306374shf4xt8o4m8xiby/4eow01291306282.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/02/t1291306374shf4xt8o4m8xiby/5eow01291306282.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/02/t1291306374shf4xt8o4m8xiby/5eow01291306282.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/02/t1291306374shf4xt8o4m8xiby/6ofel1291306282.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/02/t1291306374shf4xt8o4m8xiby/6ofel1291306282.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/02/t1291306374shf4xt8o4m8xiby/7ofel1291306282.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/02/t1291306374shf4xt8o4m8xiby/7ofel1291306282.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/02/t1291306374shf4xt8o4m8xiby/8zovo1291306282.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/02/t1291306374shf4xt8o4m8xiby/8zovo1291306282.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/02/t1291306374shf4xt8o4m8xiby/9zovo1291306282.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/02/t1291306374shf4xt8o4m8xiby/9zovo1291306282.ps (open in new window)


 
Parameters (Session):
par1 = 1 ; par2 = Include Monthly Dummies ; par3 = No Linear Trend ;
 
Parameters (R input):
par1 = 1 ; par2 = Include Monthly 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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