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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 16:48:21 +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/t1291308422uporlt5cd5ygyd8.htm/, Retrieved Thu, 02 Dec 2010 17:47:02 +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/t1291308422uporlt5cd5ygyd8.htm/},
    year = {2010},
}
@Manual{R,
    title = {R: A Language and Environment for Statistical Computing},
    author = {{R Development Core Team}},
    organization = {R Foundation for Statistical Computing},
    address = {Vienna, Austria},
    year = {2010},
    note = {{ISBN} 3-900051-07-0},
    url = {http://www.R-project.org},
}
 
Original text written by user:
 
IsPrivate?
No (this computation is public)
 
User-defined keywords:
 
Dataseries X:
» Textbox « » Textfile « » CSV «
1 162556 1081 213118 6282929 1 29790 309 81767 4324047 1 87550 458 153198 4108272 0 84738 588 -26007 -1212617 1 54660 299 126942 1485329 1 42634 156 157214 1779876 0 40949 481 129352 1367203 1 42312 323 234817 2519076 1 37704 452 60448 912684 1 16275 109 47818 1443586 0 25830 115 245546 1220017 0 12679 110 48020 984885 1 18014 239 -1710 1457425 0 43556 247 32648 -572920 1 24524 497 95350 929144 0 6532 103 151352 1151176 0 7123 109 288170 790090 1 20813 502 114337 774497 1 37597 248 37884 990576 0 17821 373 122844 454195 1 12988 119 82340 876607 1 22330 84 79801 711969 0 13326 102 165548 702380 0 16189 295 116384 264449 0 7146 105 134028 450033 0 15824 64 63838 541063 1 26088 267 74996 588864 0 11326 129 31080 -37216 0 8568 37 32168 783310 0 14416 361 49857 467359 1 3369 28 87161 688779 1 11819 85 106113 608419 1 6620 44 80570 696348 1 4519 49 102129 597793 0 2220 22 301670 821730 0 18562 155 102313 377934 0 10327 91 88577 651939 1 5336 81 112477 697458 1 2365 79 191778 70 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 time18 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24
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] = + 61717.3599305791 + 79750.7841883978Group[t] + 26.2815436219015Costs[t] -455.229985043956Trades[t] + 3.55237329156021Dividends[t] + 44851.7697638657M1[t] + 30297.9091810057M2[t] + 13057.1953704482M3[t] -135104.900329877M4[t] -40495.2398170421M5[t] -27870.9586201965M6[t] -13703.6963798287M7[t] -35442.1668144452M8[t] + 15124.118591117M9[t] -13400.7521437974M10[t] -64055.2437346312M11[t] + 33.2798030790441t + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0		2-tail p-value1-tail p-value
(Intercept)61717.359930579173262.520630.84240.4000430.200021
Group79750.784188397833589.3019272.37430.0180380.009019
Costs26.28154362190151.93467813.584500
Trades-455.229985043956213.770506-2.12950.03380.0169
Dividends3.552373291560210.5183486.853300
M144851.769763865771628.6150490.62620.5315480.265774
M230297.909181005771255.740160.42520.6709120.335456
M313057.195370448271497.4040280.18260.8551820.427591
M4-135104.90032987771521.572063-1.8890.0595890.029795
M5-40495.239817042171573.811093-0.56580.5718480.285924
M6-27870.958620196571502.988464-0.38980.6968940.348447
M7-13703.696379828771285.763609-0.19220.8476520.423826
M8-35442.166814445271560.39752-0.49530.6206680.310334
M915124.11859111771232.5689160.21230.8319620.415981
M10-13400.752143797471659.210408-0.1870.8517470.425873
M11-64055.243734631271790.94144-0.89220.3727790.186389
t33.2798030790441135.9949110.24470.8067990.4034


Multiple Linear Regression - Regression Statistics
Multiple R0.753065489427061
R-squared0.567107631366019
Adjusted R-squared0.55037749151543
F-TEST (value)33.8973634668132
F-TEST (DF numerator)16
F-TEST (DF denominator)414
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation300010.442841773
Sum Squared Residuals37262594047044.3


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast		Residuals
Prediction Error
162829294723546.876005951559382.12399405
243240471104560.638955013219486.36104499
341082722791295.473366451316976.52663355
4-12126171793729.21884625-3006346.21884625
514853291852520.08253956-367191.082539559
617798761721751.1320858958124.8679141072
713672031364990.519149302212.48085069837
825190761905435.24349416613640.756505844
99126841156781.00914634-244097.009146343
101443586676379.630138452767206.369861548
1112200171496800.06975292-276783.069752921
12984885515850.076255503469034.923744497
131457425545313.75337373912111.24662627
14-5729201240736.17726723-1813656.17726723
15929144912022.60310254317121.3968974570
161151176589586.09335292561589.90664708
177900901183058.6550438-392968.655043799
18774497838836.241901893-64339.2419018926
199905761138185.03303685-147609.033036847
20454195761891.138270648-307696.138270648
21876607736965.875742847139641.124257153
22711969960910.039016083-248941.039016083
23702380890310.237168951-187930.237168951
24264449767134.552476416-502685.552476416
25450033723527.374585145-273494.374585145
26541063706401.377408417-165338.377408417
27588864985924.185547839-397060.185547839
28-37216276892.150979592-314108.150979592
29783310344796.734751564438513.265248436
30467359426492.17885253540866.8211474649
31688779514220.610981233174558.389018767
32608419755970.933428907-147551.933428907
33696348597858.91174776298489.0882522378
34597793588459.2635338399333.7364661615
358217301118801.32733834-297071.327338337
36377934843646.766448746-465712.766448746
37651939652442.623799275-503.623799274778
38697458675955.6645097121502.3354902902
39700368863282.978765666-162914.978765666
40225986252368.503049678-26382.503049678
41348695309497.80463619639197.1953638039
42373683710624.638581665-336941.638581665
43501709398738.394206874102970.605793126
44413743577943.188384993-164200.188384994
45379825417424.3789407-37599.3789407004
46336260576282.404221064-240022.404221064
47636765848403.363456873-211638.363456873
48481231679964.93111762-198733.93111762
49469107631871.718299586-162764.718299586
50211928410095.691986584-198167.691986584
51563925574097.687484827-10172.6874848269
52511939527591.97422087-15652.9742208698
53521016912793.731567473-391777.731567473
54543856590864.120953932-47008.1209539317
55329304736418.005907029-407114.005907029
56423262264567.750224546158694.249775454
57509665352006.578156749157658.421843251
58455881472974.013281360-17093.0132813595
59367772338109.86613608529662.1338639149
60406339653159.581950657-246820.581950657
61493408648395.144754644-154987.144754643
62232942331238.547311742-98296.5473117418
63416002559498.306291492-143496.306291492
64337430455360.25568077-117930.255680770
65361517267375.68223179894141.3177682024
66360962275907.88379715685054.1162028436
67235561326683.940449508-91122.9404495077
68408247494857.806820692-86610.8068206916
69450296539544.060953815-89248.0609538145
70418799563982.716762388-145183.716762388
71247405230486.08965743916918.9103425611
72378519315023.55921484963495.4407851509
73326638510825.044019074-184187.044019074
74328233385680.336291835-57447.336291835
75386225535553.228982642-149328.228982642
76283662310697.536185903-27035.5361859031
77370225436684.555724704-66459.5557247037
78269236301084.296102227-31848.2961022269
79365732277786.84627811687945.153721884
80420383467062.229663435-46679.2296634354
81345811320600.52122410525210.4787758955
82431809538848.857070788-107039.857070788
83418876490265.271648115-71389.2716481146
84297476218474.69184472979001.3081552713
85416776480995.722977684-64219.722977684
86357257519647.011614015-162390.011614015
87458343454881.8193688973461.18063110331
88388386306664.62342746881721.3765725317
89358934428936.332593655-70002.3325936554
90407560413855.706801921-6295.70680192093
91392558419392.355577952-26834.3555779522
92373177462429.964932205-89252.964932205
93428370319987.124199028108382.875800972
94369419719582.463500102-350163.463500102
95358649163294.096575631195354.903424369
96376641419398.065319212-42757.0653192119
97467427514704.430657763-47277.4306577634
98364885371373.806739256-6488.80673925615
99436230597745.934145087-161515.934145087
100329118301139.3938719427978.6061280599
101317365392837.942127499-75472.9421274991
102286849374005.7201779-87156.7201779
103376685488844.662590856-112159.662590856
104407198440801.860052959-33603.8600529594
105377772345946.94987098831825.0501290116
106271483315191.393916428-43708.393916428
107153661350092.773859614-196431.773859614
108513294537445.341368252-24151.341368252
109324881587780.467530443-262899.467530443
110264512468974.335567092-204462.335567092
111420968330755.92777689190212.0722231089
112129302249616.508072666-120314.508072666
113191521433410.425756866-241889.425756866
114268673436961.39436216-168288.394362160
115353179368367.654782122-15188.6547821224
116354624252108.809125806102515.190874194
117363713381380.622456508-17667.6224565079
118456657416232.92093294240424.0790670578
119211742407045.703749825-195303.703749825
120338381273923.21193112564457.7880688755
121418530738606.022637776-320076.022637776
122351483350707.546500311775.453499689494
123372928399364.437043739-26436.4370437386
124485538423043.01225953462494.9877404665
125279268381371.943712331-102103.943712331
126219060463275.127166866-244215.127166866
127325560267940.30480532557619.6951946752
128325314245778.29262922279535.7073707777
129322046285285.69159264536760.3084073549
130325560268343.08845059357216.9115494068
131325599214653.895669391110945.104330609
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133325560326695.449767493-1135.44976749345
134323850312532.53174801311317.4682519870
135325560294967.43498023430592.565019766
136331514150282.756744427181231.243255573
137325632239385.2311004586246.76889955
138325560254139.12039882671420.8796011735
139325560268339.66244227357220.3375577267
140325560246634.47181073678925.5281892642
141322265294938.73190328227326.2680967177
142325560268742.44608754256817.5539124582
143325906223523.969265779102382.030734221
144325985282408.31640548543576.6835945147
145346145341684.3999584944460.60004150556
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148325356145151.653630799180204.346369201
149325560241880.91703585083679.0829641497
150325930255502.69215573970427.3078442605
151318020270499.71019864147520.2898013586
152326389259213.47730753467175.5226924663
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154302925268728.99882201934196.0011779809
155325540218454.950231602107085.049768398
156325560282609.11547444642950.8845255543
157325560327494.165041391-1934.16504139052
158326736317374.0430009699361.95699903066
159340580303667.61218713936912.3878128614
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164331828248226.72411989683601.2758801039
165323299295774.4243942327524.5756057697
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168387722240858.508971897146863.491028103
169325560327893.522678339-2333.52267833903
170325560313372.94189855812187.0581014419
171325560296165.50789108029394.4921089204
172324598150160.110682123174437.889317877
173325560242679.63230974782880.3676902526
174328726260902.06746864367823.9325313572
175325560269537.73535311956022.2646468811
176325043247376.64199755177666.3580024486
177325560298432.10993022327127.8900697773
178325806351190.872131185-25384.8721311855
179325560219319.307210633106240.692789367
180325560283407.83074834342152.1692516572
181387732377159.74231470210572.2576852980
182349729441721.752253824-91992.7522538237
183332202277634.08286317854567.9171368224
184305442270691.83013450934750.1698654909
185329537327676.7047031911860.29529680927
186327055344638.40952313-17583.4095231302
187356245375528.002689321-19283.0026893208
188328451254564.38755112573886.6124488754
189307062320345.622290591-13283.6222905913
190325560270339.87663533655220.1233646641
191331345220791.273987725110553.726012275
192325560283807.18838529141752.8116147087
193331824332899.21538798-1075.21538798025
194325560314171.65717245511388.3428275449
195325685297393.54987586728291.4501241328
196325560228586.19145612896973.8085438718
197404480541818.036069996-137338.036069996
198325560335886.692771967-10326.6927719673
199325560350087.234815414-24527.2348154141
200318314400331.946931936-82017.9469319358
201325560378981.609392518-53421.6093925178
202325560350490.018460683-24930.0184606825
203325560299868.80667292825691.1933270723
204311807321775.940410586-9968.94041058597
205337724508880.911354209-171156.911354209
206326431396999.175864833-70568.175864833
207327556394597.372810798-67041.3728107981
208325560228985.54909307796574.4509069234
209356850295585.11403161361264.8859683871
210325560336286.050408916-10726.0504089157
211325560270735.80826396554824.1917360355
212325560249030.61763242776529.382367573
213322741281138.68572870441602.3142712961
214310902278956.77711262631945.2228873737
215324295238114.6237742386180.3762257698
216325560284605.90365918840954.0963408116
217326156326637.649935473-481.649935473209
218326960312394.83005944114565.1699405591
219325560297762.93843887427797.0615611263
220333411152446.322678022180964.677321978
221297761249279.22908924648481.7709107544
222325560256934.62385746668625.3761425338
223325536270225.39834927755310.6016507235
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229318521349300.060014659-30779.0600146592
230325560315369.73008330110190.2699166993
231319775313746.3082051046028.69179489576
232325560150033.480178576175526.519821424
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250325560352087.449008477-26527.4490084766
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252325560365554.760758432-39994.7607584321
253317967346689.699804498-28722.6998044981
254331488342931.787215212-11443.787215212
255335452361720.469620189-26268.4696201892
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257334184230467.056889824103716.943110176
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260325560250628.04818022174931.9518197788
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270336704291743.46734814244960.5326518579
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272325560330778.190005568-5218.19000556787
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278325560316967.1606310958592.83936890518
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285327748340707.091768415-12959.0917684154
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287325560302664.31013156722895.6898684326
288328157290676.47046067837480.5295393219
289325560411637.883236222-86077.8832362222
290311594272961.83161106138632.1683889391
291325560379909.868448963-54349.8684489631
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297325560302425.68629970823134.3137002920
298325560353684.879556271-28124.8795562707
299325560223312.883580118102247.116419882
300325560287401.40711782838158.5928821719
301324047411281.852358394-87234.8523583938
302311464317620.983132544-6156.98313254424
303325560300558.44189751325001.5581024866
304325560232180.41018866593379.5898113351
305353417236429.404215685116987.595784315
306325590255738.90613732769851.0938626725
307325560353681.453547951-28121.4535479509
308328576343259.738096802-14683.7380968015
309326126281456.41945535144669.5805446493
310325560354084.237193219-28524.2371932193
311325560303463.02540546422096.9745945355
312369376353647.86519230415728.1348076957
313325560412436.598510119-86876.5985101194
314332013407593.861825974-75580.8618259743
315325871299361.37153010626509.6284698942
316342165168672.216394835173492.783605165
317324967245257.36611456579709.6338854354
318314832263650.09412149451181.9058785057
319325557271621.37625656853935.6237434321
320325560252624.83636496472935.1636350362
321325560303224.40157360522335.598426395
322325560274732.81064177050827.1893582303
323325560224111.598854015101448.401145985
324325560367950.906580123-42390.9065801233
325325560333085.17195867-7525.1719586699
326322649318239.4299150664409.57008493401
327325560381107.941359809-55547.9413598086
328325560232979.12546256292580.874537438
329325560247871.28159007877688.7184099217
330325560260528.84259000365031.1574099971
331325560274729.3846334550830.6153665502
332325560253024.19400191272535.8059980877
333325560303623.75921055421936.2407894464
334324598274167.68724877950430.312751221
335325567223651.644677538101915.355322462
336325560288599.48002867436960.5199713263
337324005333154.961258455-9149.96125845461
338325560318963.9488158376596.05118416253
339325748302609.82265679923138.1773432009
340323385147492.261992800175892.738007200
341315409257421.06624514457987.9337548555
342325560260928.20022695164631.7997730486
343325560275128.74227039850431.2577296017
344325560253423.55163886172136.4483611391
345325560304023.11684750221536.8831524979
346325560275531.52591566750028.4740843333
347312275219615.53589557592659.464104425
348325560288998.83766562236561.1623343778
349325560333883.887232567-8323.88723256697
350325560319363.3064527866196.693547214
351320576296444.35814003524131.6418599654
352325246152486.808124726172759.191875274
353332961254638.08319649978322.9168035012
354323010268743.04835991754266.9516400827
355325560275528.09990734750031.9000926532
356325560253822.90927580971737.0907241906
357345253358415.0903294-13162.0903293997
358325560275930.88355261549629.1164473847
359325560225309.671764861100250.328235139
360325560289398.19530257136161.8046974293
361325559332495.711219545-6936.7112195447
362325560319762.6640897355797.33591026546
363325560302555.23008225623004.7699177439
364319634237461.92644491982172.073555081
365319951244938.1774960475012.8225039602
366325560261726.91550084863833.0844991515
367325560275927.45754429549632.5424557046
368325560254222.26691275871337.7330872421
369325560304821.83212139920738.1678786008
370325560276330.24118956449229.7588104362
371325560225709.02940180999850.970598191
372318519280026.80655959838492.1934404021
373343222393119.435338045-49897.4353380448
374317234338844.510827247-21610.5108272468
375325560302954.58771920522605.4122807954
376325560154825.771821958170734.228178042
377314025225588.37978480188436.620215199
378320249272062.76626600548186.2337339953
379325560276326.81518124449233.1848187561
380325560254621.62454970670938.3754502936
381325560305221.18975834820338.8102416523
382349365308506.33949908840858.6605009122
383289197136338.430393854152858.569606146
384325560290196.91057646835363.0894235322
385329245336881.939902507-7636.9399025068
386240869392931.954434199-152062.954434199
387327182300303.48434459626878.5156554037
388322876168381.170429294154494.829570706
389323117249250.78676058473866.2132394164
390306351262672.91512183143678.0848781689
391335137289676.86863585345460.1313641474
392308271258250.27619443350020.7238055675
393301731319598.10348987-17867.1034898701
394382409317800.92781676164608.0721832391
395279230472159.404325318-192929.404325318
396298731291405.9327912617325.06720873876
397243650417492.288034455-173842.288034455
398532682599643.991451262-66961.9914512626
399319771324749.145572107-4978.1455721066
40017149387331.380320869784161.6196791303
401347262310316.25433106336945.7456689366
402343945291691.22665027052253.7733497296
403311874284106.58259168427767.4174083159
404302211394556.543832380-92345.5438323805
405316708331002.894146142-14294.8941461416
406333463338106.480065947-4643.48006594709
407344282261823.30057016882458.6994298317
408319635305621.79446504914013.2055349508
409301186333858.765788474-32672.7657884744
410300381371969.782031745-71588.7820317448
411318765343107.831886442-24342.8318864416
412286146400505.643680729-114359.643680729
413306844341192.307075957-34348.3070759573
414307705466589.386579623-158884.386579623
415312448376668.247336475-64220.2473364751
416299715325179.504033779-25464.504033779
417373399271467.841953165101931.158046835
418299446385328.562392158-85882.5623921584
419325586278993.48049045546592.5195095448
420291221325873.734982372-34652.7349823716
421261173394141.755061776-132968.755061776
422255027408500.795024155-153473.795024155
423-78375388040.962586321-466415.962586321
424-58143298729.471039409-356872.471039409
425227033279940.575529604-52907.5755296037
426235098440368.729833237-205270.729833237
42721267335733.368797212-314466.368797212
4282386751433966.53870579-1195291.53870579
429197687594873.516762281-397186.516762281
430418341697177.610778528-278836.610778528
431-297706501973.604780658-799679.604780658


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
2011.26591730518362e-986.32958652591812e-99
2116.71616280895762e-1053.35808140447881e-105
2211.14436092666410e-1075.72180463332051e-108
2311.86322410321611e-1189.31612051608055e-119
2412.48947530377986e-1231.24473765188993e-123
2511.19050716926223e-1235.95253584631113e-124
2612.4840277790352e-1271.2420138895176e-127
2712.54573643829456e-1291.27286821914728e-129
2811.46898991464012e-1437.34494957320061e-144
2911.84136070830341e-1959.20680354151705e-196
3013.52605807509895e-2071.76302903754948e-207
3114.47295660229739e-2112.23647830114870e-211
3214.14618763195707e-2132.07309381597854e-213
3316.64130729235011e-2193.32065364617506e-219
3415.88055810950743e-2202.94027905475371e-220
3516.40156755342259e-2193.20078377671129e-219
3615.17042906730416e-2182.58521453365208e-218
3712.28022493199618e-2241.14011246599809e-224
3813.94418903753161e-2321.97209451876581e-232
3912.34179230688861e-2321.17089615344430e-232
4018.91133083099437e-2364.45566541549719e-236
4118.69084866641544e-2364.34542433320772e-236
4212.87626189196537e-2371.43813094598268e-237
4317.10142899861852e-2393.55071449930926e-239
4417.66697742760557e-2393.83348871380279e-239
4517.50390908803499e-2403.75195454401750e-240
4613.56075628512148e-2391.78037814256074e-239
4714.66494227857172e-2382.33247113928586e-238
4811.68428845104521e-2378.42144225522603e-238
4911.07470725080872e-2365.37353625404361e-237
5015.55042214846523e-2372.77521107423262e-237
5111.04836576566186e-2375.24182882830929e-238
5215.30287871646696e-2372.65143935823348e-237
5313.36043824551246e-2361.68021912275623e-236
5413.68575252506433e-2351.84287626253216e-235
5518.28788832429972e-2374.14394416214986e-237
5614.71382592907991e-2392.35691296453995e-239
5711.06962523362252e-2445.34812616811259e-245
5812.75140703527977e-2451.37570351763988e-245
5915.92861706469956e-2462.96430853234978e-246
6011.50689763792396e-2457.53448818961981e-246
6114.15805822053818e-2472.07902911026909e-247
6211.24898329156338e-2466.24491645781691e-247
6311.31218676707794e-2456.5609338353897e-246
6413.78517518448879e-2451.89258759224440e-245
6517.01936549643968e-2463.50968274821984e-246
6613.33226500205837e-2451.66613250102919e-245
6714.51017154184021e-2462.25508577092011e-246
6817.19221244155449e-2453.59610622077724e-245
6917.86818534373299e-2443.93409267186649e-244
7019.24116273087772e-2434.62058136543886e-243
7114.29966601258203e-2422.14983300629102e-242
7216.4998961214985e-2443.24994806074925e-244
7318.37535954365387e-2444.18767977182693e-244
7418.35776153687081e-2434.17888076843540e-243
7513.42593139961272e-2421.71296569980636e-242
7618.57359468013816e-2424.28679734006908e-242
7711.54570282602731e-2417.72851413013653e-242
7812.13941193258964e-2411.06970596629482e-241
7911.08083173125742e-2405.40415865628711e-241
8017.19812311747625e-2403.59906155873812e-240
8116.5763935388067e-2393.28819676940335e-239
8212.39721879820505e-2381.19860939910253e-238
8313.02789102666374e-2381.51394551333187e-238
8411.47280914338476e-2377.36404571692379e-238
8511.88560684223457e-2369.42803421117284e-237
8611.24323040741834e-2366.21615203709172e-237
8711.31803927705893e-2366.59019638529467e-237
8811.47241684068257e-2367.36208420341286e-237
8915.63043578372406e-2362.81521789186203e-236
9015.40474737107711e-2352.70237368553856e-235
9116.95540925853582e-2343.47770462926791e-234
9218.68838146941837e-2334.34419073470918e-233
9313.58805797579998e-2331.79402898789999e-233
9418.31326275320813e-2334.15663137660407e-233
9511.86513578685522e-2349.32567893427612e-235
9614.43171288509793e-2342.21585644254896e-234
9715.90456383244184e-2332.95228191622092e-233
9813.36760888578381e-2321.68380444289191e-232
9911.52583386480117e-2317.62916932400585e-232
10011.39073912765883e-2306.95369563829413e-231
10111.47962105110701e-2297.39810525553506e-230
10215.53537103892923e-2302.76768551946461e-230
10314.41576914297392e-2292.20788457148696e-229
10416.54216017561485e-2293.27108008780742e-229
10515.75203438238998e-2282.87601719119499e-228
10614.57010816030519e-2282.28505408015259e-228
10711.9639148056596e-2289.819574028298e-229
10812.827842472007e-2281.4139212360035e-228
10918.96889251840893e-2284.48444625920447e-228
11011.75881111379773e-2278.79405556898866e-228
11112.62679180435192e-2271.31339590217596e-227
11211.16780046864139e-2275.83900234320697e-228
11318.74754722867876e-2304.37377361433938e-230
11412.51166504760437e-2291.25583252380219e-229
11511.24734856839131e-2286.23674284195655e-229
11614.88797785035495e-2282.44398892517748e-228
11713.41601787537610e-2271.70800893768805e-227
11811.63012545737867e-2268.15062728689337e-227
11916.6308925048587e-2283.31544625242935e-228
12016.82500413219744e-2273.41250206609872e-227
12119.6601447378045e-2274.83007236890225e-227
12211.26602617041430e-2256.33013085207151e-226
12319.07161878793019e-2254.53580939396510e-225
12416.22639217154435e-2243.11319608577217e-224
12516.94740556920085e-2233.47370278460043e-223
12616.95067837249785e-2243.47533918624892e-224
12717.77803247461124e-2233.88901623730562e-223
12818.33780134107138e-2224.16890067053569e-222
12911.12870175822733e-2205.64350879113663e-221
13011.0635180085361e-2195.3175900426805e-220
13118.7274003193769e-2194.36370015968845e-219
13211.38888496882673e-2186.94442484413364e-219
13311.91702928449573e-2179.58514642247864e-218
13412.60872357501438e-2161.30436178750719e-216
13513.25357346816242e-2151.62678673408121e-215
13611.35739838659016e-2146.78699193295079e-215
13711.30426614165282e-2136.52133070826409e-214
13811.36472482692817e-2126.82362413464085e-213
13911.70156665678550e-2118.50783328392751e-212
14012.02484680809542e-2101.01242340404771e-210
14112.68476400318027e-2091.34238200159014e-209
14212.81326827497579e-2081.40663413748790e-208
14312.23697069741212e-2071.11848534870606e-207
14412.58788522522657e-2061.29394261261328e-206
14513.12658338975863e-2051.56329169487931e-205
14613.76793183031838e-2041.88396591515919e-204
14714.69721281043411e-2032.34860640521705e-203
14812.95676501937519e-2021.47838250968759e-202
14913.09384336854349e-2011.54692168427175e-201
15013.44455117147539e-2001.72227558573770e-200
15114.27223076558776e-1992.13611538279388e-199
15214.78235856958521e-1982.39117928479261e-198
15315.71361058611467e-1972.85680529305733e-197
15415.12536675860538e-1962.56268337930269e-196
15515.5854568625232e-1952.7927284312616e-195
15616.30848625200766e-1943.15424312600383e-194
15717.53419607211151e-1933.76709803605575e-193
15819.06407456494233e-1924.53203728247117e-192
15911.05697813682383e-1905.28489068411913e-191
16018.01686328713232e-1904.00843164356616e-190
16118.48797432117886e-1894.24398716058943e-189
16219.39894052126092e-1884.69947026063046e-188
16311.11896964424896e-1865.59484822124478e-187
16411.31874111448985e-1856.59370557244927e-186
16511.43083175768734e-1847.1541587884367e-185
16611.41508223492348e-1837.07541117461742e-184
16711.54448480963593e-1827.72242404817965e-183
16813.39723117395115e-1831.69861558697558e-183
16913.82810742347308e-1821.91405371173654e-182
17014.35831239620071e-1812.17915619810036e-181
17115.00380077080162e-1802.50190038540081e-180
17214.28671489015268e-1792.14335744507634e-179
17314.56331230130041e-1782.28165615065021e-178
17415.08996771990251e-1772.54498385995126e-177
17515.83313335177105e-1762.91656667588553e-176
17616.52792451606124e-1753.26396225803062e-175
17716.90133984068629e-1743.45066992034314e-174
17816.14191302432624e-1733.07095651216312e-173
17916.61435602133494e-1723.30717801066747e-172
18017.22260410936749e-1713.61130205468375e-171
18114.55846994083995e-1702.27923497041997e-170
18213.47606652054632e-1691.73803326027316e-169
18313.01928101868589e-1681.50964050934295e-168
18411.50956053292992e-1677.54780266464959e-168
18511.52400830503695e-1667.62004152518475e-167
18611.56559849610909e-1657.82799248054543e-166
18711.15665001845957e-1645.78325009229785e-165
18811.24039998077043e-1636.20199990385217e-164
18917.06850584475601e-1633.53425292237801e-163
19016.4964655962779e-1623.24823279813895e-162
19116.0846471693142e-1613.0423235846571e-161
19216.35375393530594e-1603.17687696765297e-160
19316.37829722423509e-1593.18914861211754e-159
19416.5762000395371e-1583.28810001976855e-158
19516.81473053062778e-1573.40736526531389e-157
19616.99073037735415e-1563.49536518867708e-156
19711.23369618822316e-1556.16848094111578e-156
19811.22084603954284e-1546.10423019771421e-155
19911.17199858098136e-1535.8599929049068e-154
20011.79717510733344e-1538.98587553666721e-154
20111.49459540917772e-1527.47297704588858e-153
20211.21574664952397e-1516.07873324761985e-152
20311.23468624825387e-1506.17343124126935e-151
20411.13906039750576e-1495.6953019875288e-150
20511.41339076102803e-1497.06695380514017e-150
20611.25541847383607e-1486.27709236918036e-149
20719.72705785434562e-1484.86352892717281e-148
20819.40962618728617e-1474.70481309364309e-147
20911.77453261121069e-1468.87266305605345e-147
21011.72642585874421e-1458.63212929372103e-146
21111.73883157949326e-1448.6941578974663e-145
21211.69531798448482e-1438.47658992242412e-144
21311.69216991000158e-1428.46084955000792e-143
21411.15024185255968e-1415.7512092627984e-142
21511.11802529228045e-1405.59012646140224e-141
21611.08629951823157e-1395.43149759115784e-140
21711.04824574035593e-1385.24122870177964e-139
21819.87838860271e-1384.939194301355e-138
21919.4748961768108e-1374.7374480884054e-137
22014.90468344494452e-1362.45234172247226e-136
22113.33456824665253e-1351.66728412332627e-135
22213.10904488513382e-1341.55452244256691e-134
22312.97326500032252e-1331.48663250016126e-133
22412.75653856478257e-1321.37826928239129e-132
22512.45739901803019e-1311.22869950901510e-131
22612.0646273635217e-1301.03231368176085e-130
22711.89556014863017e-1299.47780074315086e-130
22811.74884491961174e-1288.74422459805868e-129
22911.34892230902430e-1276.74461154512148e-128
23011.23314157571278e-1266.16570787856391e-127
23111.00698743040684e-1255.03493715203422e-126
23218.19108158196425e-1254.09554079098213e-125
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3950.9999994637848191.07243036207590e-065.36215181037951e-07
3960.9999985559556582.88808868397187e-061.44404434198594e-06
3970.9999958467041888.30659162438917e-064.15329581219458e-06
3980.99998908742222.18251555993409e-051.09125777996704e-05
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4000.9999294581036640.0001410837926719597.05418963359793e-05
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4020.9995081103880140.0009837792239719310.000491889611985966
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4080.9689985663654880.06200286726902420.0310014336345121
4090.9318242666973390.1363514666053220.0681757333026612
4100.8780504596255260.2438990807489480.121949540374474
4110.8272068467415860.3455863065168280.172793153258414


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level3860.98469387755102NOK
5% type I error level3880.989795918367347NOK
10% type I error level3890.99234693877551NOK
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Dec/02/t1291308422uporlt5cd5ygyd8/10so6u1291308478.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/02/t1291308422uporlt5cd5ygyd8/10so6u1291308478.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/02/t1291308422uporlt5cd5ygyd8/1lnrj1291308478.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/02/t1291308422uporlt5cd5ygyd8/1lnrj1291308478.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/02/t1291308422uporlt5cd5ygyd8/2ew8m1291308478.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/02/t1291308422uporlt5cd5ygyd8/2ew8m1291308478.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/02/t1291308422uporlt5cd5ygyd8/3ew8m1291308478.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/02/t1291308422uporlt5cd5ygyd8/3ew8m1291308478.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/02/t1291308422uporlt5cd5ygyd8/4ew8m1291308478.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/02/t1291308422uporlt5cd5ygyd8/4ew8m1291308478.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/02/t1291308422uporlt5cd5ygyd8/57oq71291308478.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/02/t1291308422uporlt5cd5ygyd8/57oq71291308478.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/02/t1291308422uporlt5cd5ygyd8/67oq71291308478.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/02/t1291308422uporlt5cd5ygyd8/67oq71291308478.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/02/t1291308422uporlt5cd5ygyd8/7zfp91291308478.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/02/t1291308422uporlt5cd5ygyd8/7zfp91291308478.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/02/t1291308422uporlt5cd5ygyd8/8zfp91291308478.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/02/t1291308422uporlt5cd5ygyd8/8zfp91291308478.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/02/t1291308422uporlt5cd5ygyd8/9so6u1291308478.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/02/t1291308422uporlt5cd5ygyd8/9so6u1291308478.ps (open in new window)


 
Parameters (Session):
par1 = 5 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;
 
Parameters (R input):
par1 = 5 ; par2 = Include Monthly Dummies ; par3 = 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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