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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 19:10:25 +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/t1291316912ozfkt1q6u1vkpie.htm/, Retrieved Thu, 02 Dec 2010 20:08:32 +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/t1291316912ozfkt1q6u1vkpie.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 1 29790 309 81767 1 87550 458 153198 0 84738 588 -26007 1 54660 299 126942 1 42634 156 157214 0 40949 481 129352 1 42312 323 234817 1 37704 452 60448 1 16275 109 47818 0 25830 115 245546 0 12679 110 48020 1 18014 239 -1710 0 43556 247 32648 1 24524 497 95350 0 6532 103 151352 0 7123 109 288170 1 20813 502 114337 1 37597 248 37884 0 17821 373 122844 1 12988 119 82340 1 22330 84 79801 0 13326 102 165548 0 16189 295 116384 0 7146 105 134028 0 15824 64 63838 1 26088 267 74996 0 11326 129 31080 0 8568 37 32168 0 14416 361 49857 1 3369 28 87161 1 11819 85 106113 1 6620 44 80570 1 4519 49 102129 0 2220 22 301670 0 18562 155 102313 0 10327 91 88577 1 5336 81 112477 1 2365 79 191778 0 4069 145 79804 0 7710 816 128294 0 13718 61 96448 0 4525 226 93811 0 6869 105 117520 0 4628 62 69159 1 3653 24 101792 1 1265 26 210568 1 7489 322 136996 0 4901 84 121920 0 2284 33 76403 1 3160 108 108094 1 4150 150 134759 1 7285 115 188873 1 1134 162 146216 1 4658 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 time15 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24


Multiple Linear Regression - Estimated Regression Equation
Dividends[t] = + 66154.6383459376 + 6264.73118174127Group[t] + 0.301540016695731Costs[t] + 72.3841726028555Trades[t] + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0		2-tail p-value1-tail p-value
(Intercept)66154.63834593761770.29028737.369400
Group6264.731181741273278.5805271.91080.0566990.028349
Costs0.3015400166957310.1910441.57840.1152190.05761
Trades72.384172602855520.3384753.5590.0004140.000207


Multiple Linear Regression - Regression Statistics
Multiple R0.366491770557242
R-squared0.134316217886182
Adjusted R-squared0.128234130424024
F-TEST (value)22.0839010819693
F-TEST (DF numerator)3
F-TEST (DF denominator)427
p-value2.59792187762287e-13
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation29975.7428495171
Sum Squared Residuals383678783055.42


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast		Residuals
Prediction Error
1213118199683.79906535713434.2009346431
281767103768.955959327-22001.9559593270
3153198131971.14904149821226.8509585021
4-26007134268.429771180-160275.429771180
5126942110544.41444852116397.5855514787
615721496567.157525530160646.8424744699
7129352113319.18751158516032.8124884154
8234817108558.218464831126258.781535169
960448116506.280333665-56058.2803336654
104781885216.8081131131-37398.8081131131
1124554682267.5968265167163278.403173483
124802077940.1232039369-29920.1232039369
13-171095151.1286405182-96861.1286405182
143264897167.4059460422-64519.4059460422
1595350115789.270680744-20439.2706807441
1615135275579.867513088275772.1324869118
1728817076192.3826985725211977.617301427
18114337115032.176541801-695.176541800566
1937884101707.644340896-63823.6443408964
2012284498527.679364337324316.3206356627
218234084949.4878042628-2609.48780426282
227980185233.0285991344-5432.0285991344
2316554877556.146213916187991.8537860839
2411638492389.600594067123994.3994059329
2513402875909.781428545158118.2185714549
266383875558.7946167136-11720.7946167136
277499699612.5195681995-24616.5195681995
283108078907.4388408018-47827.4388408018
293216871416.4475952923-39248.4475952923
304985796632.325536254-46775.3255362541
318716175462.014676806711698.9853231933
3210611382135.925656248423977.0743437516
338057077600.46803273022969.53196726976
3410212977328.853320666824800.1466793332
3530167068416.508980265233253.491019735
3610231382971.370889286419341.6291107137
378857775855.601805214212721.3981947858
3811247779891.505037598632585.4949624014
3919177878850.8613027898112927.138697210
407980477877.30970128661926.69029871344
41128294127544.996718592749.003281408244
429644874706.598823743821741.4011762562
439381183877.92992973119933.0700702689
4411752075826.254843920441693.7451560796
456915972037.9842445825-2878.98424458247
4610179275258.115351136926533.8846488631
4721056874682.8061364733135885.193863527
4813699697985.306290832739010.6937091673
4912192073712.756466403248207.2435335968
507640369232.03343996497170.96656003514
5110809481189.726621545826904.2733784542
5213475984528.386487394550230.6135126055
5318887382940.2683986356105932.731601364
5414621684487.551868274461728.4481317256
5515660885260.642196698771347.3578033013
566134873894.7744882172-12546.7744882172
575035067936.2678819389-17586.2678819389
588772072551.565167398815168.4348326012
599948974287.223735897125201.7762641029
608741982542.63469628844876.36530371165
619435577499.495832924816855.5041670752
626032669365.9900503572-9039.99005035717
639467075821.839328318848.1606717
648242580706.00832848141718.99167151862
655901772679.6075262243-13662.6075262242
6690829138698.759642110-47869.7596421102
678079171776.42233324119014.57766675887
6810042376874.792329906523548.2076700935
6913111673388.143554380757727.8564456193
7010026978196.587909042722072.4120909573
712733077535.840889483-50205.840889483
723903971245.046148943-32206.0461489430
7310688569047.203978326337837.7960216737
747928567117.917413818412167.0825861816
7511888169283.625920011649597.3740799884
767762374037.68092339813585.31907660189
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8011786984997.888693886532871.1113061135
816098268452.752056652-7470.75205665193
829013179092.910524621211038.0894753788
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843962567703.0070263793-28078.0070263793
8510272567395.39250356235329.607496438
866423979347.3957301166-15108.3957301166
879026273477.88593058916784.114069411
8810396067330.848371393336629.1516286067
8910661171420.157887564735190.8421124353
9010334567121.837434035536223.1625659645
919555170521.996894694225029.0031053058
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936359374000.0410912358-10407.0410912358
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953752769981.5352046043-32454.5352046043
966024776453.0937006071-16206.0937006071
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987018487177.813286652-16993.813286652
9913014068520.238746008361619.7612539917
1007322173632.6252694005-411.625269400463
1017611475188.2891846264925.710815373595
1029053468113.475832081622420.5241679184
10310847972960.355850363835518.6441496361
10411376167631.240502405746129.7594975943
1056869668575.2064406222120.793559377837
1067156168044.42316825833516.57683174172
1075983177724.935617143-17893.9356171430
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3276072072419.3695276788-11699.3695276789
3286072072419.3695276788-11699.3695276789
3296072066154.6383459376-5434.63834593758
3306072066154.6383459376-5434.63834593758
3316072066154.6383459376-5434.63834593758
3326072066154.6383459376-5434.63834593758
3336072066154.6383459376-5434.63834593758
3346037966545.5070505546-6166.50705055465
3356072766299.70823116-5572.70823115999
3366072066154.6383459376-5434.63834593758
3376092566685.7522955099-5760.75229550992
3386072066154.6383459376-5434.63834593758
3396089666234.8625589745-5338.86255897453
3405973467133.3250918617-7399.32509186167
3416296967332.0691000559-4363.06910005592
3426072066154.6383459376-5434.63834593758
3436072066154.6383459376-5434.63834593758
3446072066154.6383459376-5434.63834593758
3456072066154.6383459376-5434.63834593758
3466072066154.6383459376-5434.63834593758
3475911866624.8266435415-7506.8266435415
3486072066154.6383459376-5434.63834593758
3496072066154.6383459376-5434.63834593758
3506072066154.6383459376-5434.63834593758
3515859867262.0972475866-8664.09724758663
3526112466896.5724729679-5772.57247296788
3535959567200.2524069722-7605.25240697224
3546206566340.1145933972-4275.11459339721
3556072066154.6383459376-5434.63834593758
3566072066154.6383459376-5434.63834593758
3577878070073.60688986778706.39311013233
3586072066154.6383459376-5434.63834593758
3596072066154.6383459376-5434.63834593758
3606072066154.6383459376-5434.63834593758
3616072266444.4765763657-5722.4765763657
3626072066154.6383459376-5434.63834593758
3636072066154.6383459376-5434.63834593758
3646160072654.0113664558-11054.0113664558
3655963567005.1414475742-7370.14144757422
3666072066154.6383459376-5434.63834593758
3676072066154.6383459376-5434.63834593758
3686072066154.6383459376-5434.63834593758
3696072066154.6383459376-5434.63834593758
3706072066154.6383459376-5434.63834593758
3716072066154.6383459376-5434.63834593758
3725978169185.0951775315-9404.09517753149
3737664466874.54548315329769.45451684679
3746482066279.4904814455-1459.49048144550
3756072066154.6383459376-5434.63834593758
3766072066154.6383459376-5434.63834593758
3775617867928.3448304263-11750.3448304263
3786043667133.8990347033-6697.8990347033
3796072066154.6383459376-5434.63834593758
3806072066154.6383459376-5434.63834593758
3816072066154.6383459376-5434.63834593758
3827343370657.50491095772775.49508904235
3834147772117.5515036993-30640.5515036993
3846072066154.6383459376-5434.63834593758
3856270067336.3052288855-4636.30522888554
3866780469800.5383516075-1996.53835160748
3875966166628.4451237419-6967.44512374185
3885862067012.0331621706-8392.03316217058
3896039866393.5017449482-5995.50174494824
3905858067485.2659971332-8905.26599713323
3916271066998.1914585943-4288.19145859434
3925932566869.4047342735-7544.4047342735
3936095066848.8854445423-5898.88544454231
3946806066942.98049834731117.01950165273
3958362074320.7541560969299.245843904
3965845667265.0980791577-8809.0980791577
3975281170677.4458573504-17866.4458573504
39812117381395.52259889139777.4774011090
3996387066965.6105681953-3095.61056819532
4002100183049.459422368-62048.459422368
4017041566836.4931666663578.50683333397
4026423067040.0909523192-2810.09095231917
4035919066917.9526769615-7727.95267696152
4046935174689.123908228-5338.12390822793
4056427066839.8392440414-2569.83924404144
4067069467452.0528895093241.94711049094
4076800567500.0414579513504.958542048679
4085893067249.0873210811-8319.08732108107
4095832067082.9387718817-8762.93877188172
4106998066590.70891586723389.29108413275
4116986370962.9795164663-1099.97951646631
4126325576068.654916015-12813.6549160150
4135732074000.8930413612-16680.8930413612
4147523075806.144678836-576.144678835958
4157942067073.23121696412346.7687830361
4167349066662.77697985756827.22302014247
4173525071913.8080320873-36663.8080320873
4186228573992.148380877-11707.1483808771
4196920668419.5826548154786.417345184594
4206592066571.108814782-651.108814782028
4216977066604.86672805613165.13327194393
4227268371861.9577178116821.04228218844
423-1454580962.4149223471-95507.4149223471
4245583070004.4769825682-14174.4769825682
4255517468574.5450862053-13400.5450862052
4266703880568.651766827-13530.6517668269
4275125269532.0220507895-18280.0220507895
42815727893038.37039114364239.6296088569
4297951072418.92686534367091.07313465645
4307744077263.4775745707176.522425429261
4312728484633.5221361935-57349.5221361935


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
70.9998664604118340.0002670791763327790.000133539588166389
80.9999906030137891.87939724223185e-059.39698621115925e-06
90.99999989938622.01227599123323e-071.00613799561661e-07
100.9999999751391834.97216336217371e-082.48608168108686e-08
110.9999999999999686.3424876856279e-143.17124384281395e-14
120.999999999999983.88377264960096e-141.94188632480048e-14
1316.98141620269444e-163.49070810134722e-16
1414.14450051917899e-172.07225025958950e-17
1514.88609986191464e-172.44304993095732e-17
1613.68660732534439e-181.84330366267220e-18
1711.19585204134458e-295.97926020672291e-30
1812.15435708995585e-291.07717854497792e-29
1913.41483828410704e-311.70741914205352e-31
2011.14711757010621e-305.73558785053105e-31
2113.31793904938564e-301.65896952469282e-30
2216.7977233168448e-303.3988616584224e-30
2311.60259479959757e-308.01297399798787e-31
2415.47574274983702e-302.73787137491851e-30
2517.04408350077889e-303.52204175038945e-30
2612.46267275434326e-301.23133637717163e-30
2713.22395534020144e-301.61197767010072e-30
2819.70601344068731e-324.85300672034366e-32
2917.50570797610103e-333.75285398805052e-33
3011.87012176499562e-339.3506088249781e-34
3116.15346217651164e-333.07673108825582e-33
3211.85620213550425e-329.28101067752126e-33
3315.6273718502512e-322.8136859251256e-32
3411.45780932101762e-317.2890466050881e-32
3515.61775586893149e-512.80887793446575e-51
3611.92611135508902e-509.6305567754451e-51
3715.00720361760937e-502.50360180880468e-50
3811.00182343455198e-495.00911717275989e-50
3914.35534867831914e-552.17767433915957e-55
4011.14974151306219e-545.74870756531096e-55
4111.31260966527383e-546.56304832636916e-55
4214.01350544788632e-542.00675272394316e-54
4311.36390187402909e-536.81950937014546e-54
4411.86085850647150e-539.30429253235752e-54
4512.83558220023679e-531.41779110011839e-53
4616.40822517281648e-533.20411258640824e-53
4714.42922388483364e-622.21461194241682e-62
4813.15280189175142e-621.57640094587571e-62
4911.44606863843991e-627.23034319219955e-63
5012.94660172516343e-621.47330086258172e-62
5115.08944287297477e-622.54472143648739e-62
5218.8290307074512e-634.4145153537256e-63
5315.44985442381529e-692.72492721190764e-69
5412.87246606017250e-711.43623303008625e-71
5511.37204963050929e-746.86024815254646e-75
5611.52882492976425e-747.64412464882126e-75
5716.89512179068464e-753.44756089534232e-75
5811.89170817569506e-749.45854087847529e-75
5912.27530096341847e-741.13765048170923e-74
6015.83334486052494e-742.91667243026247e-74
6111.06670120553093e-735.33350602765467e-74
6211.56812748564965e-737.84063742824823e-74
6312.22359948294514e-731.11179974147257e-73
6415.37761737543487e-732.68880868771744e-73
6517.17676285726656e-733.58838142863328e-73
6619.63898095398554e-754.81949047699277e-75
6713.09713746203827e-741.54856873101913e-74
6813.36151512978024e-741.68075756489012e-74
6918.6778719722988e-764.3389359861494e-76
7011.04971890346499e-755.24859451732496e-76
7114.84564705245622e-782.42282352622811e-78
7214.52580357979258e-792.26290178989629e-79
7311.37554680645843e-796.87773403229217e-80
7413.27008263022395e-791.63504131511198e-79
7511.17966561883171e-805.89832809415854e-81
7612.48444440018079e-801.24222220009039e-80
7711.90657027775966e-819.53285138879831e-82
7815.60349217548953e-812.80174608774477e-81
7911.36305189395128e-806.8152594697564e-81
8015.29381250131751e-812.64690625065876e-81
8111.10584606555554e-805.52923032777771e-81
8212.43613806511576e-801.21806903255788e-80
8312.03808694207219e-841.01904347103609e-84
8414.66250004291649e-852.33125002145825e-85
8517.91270326579614e-863.95635163289807e-86
8611.12903481289797e-855.64517406448986e-86
8712.48818477205656e-851.24409238602828e-85
8812.89929897572164e-861.44964948786082e-86
8914.72310575637925e-872.36155287818963e-87
9014.68127517442247e-882.34063758721124e-88
9113.11423689073734e-881.55711844536867e-88
9216.66557655553885e-883.33278827776942e-88
9311.50259029240456e-877.51295146202278e-88
9415.55834522275687e-902.77917261137843e-90
9515.25286017446349e-912.62643008723175e-91
9617.80790176477366e-913.90395088238683e-91
9713.27642657279362e-931.63821328639681e-93
9817.40350518584647e-933.70175259292324e-93
9911.09064807794920e-975.45324038974598e-98
10012.68990281235354e-971.34495140617677e-97
10116.66631071010473e-973.33315535505236e-97
10213.5610083192062e-971.7805041596031e-97
10311.45814722341576e-987.2907361170788e-99
10411.05161639940005e-1015.25808199700024e-102
10513.34192547361221e-1011.67096273680611e-101
10619.76424301281477e-1014.88212150640738e-101
10711.56250021574134e-1007.81250107870671e-101
10811.82643436098466e-1019.1321718049233e-102
10912.46595406204240e-1021.23297703102120e-102
11017.07874474847892e-1023.53937237423946e-102
11112.29580489807309e-1011.14790244903655e-101
11217.65169726640384e-1023.82584863320192e-102
11311.37354177715719e-1016.86770888578593e-102
11413.83361511024974e-1011.91680755512487e-101
11517.9082359252403e-1013.95411796262015e-101
11611.55364116578447e-1007.76820582892237e-101
11711.17627334359481e-1005.88136671797406e-101
11816.07042114098422e-1013.03521057049211e-101
11911.41572886254853e-1007.07864431274265e-101
12013.98947713653411e-1001.99473856826706e-100
12111.52420565386771e-1017.62102826933855e-102
12215.07791323755548e-1012.53895661877774e-101
12311.50527417304191e-1017.52637086520954e-102
12413.20058038145943e-1041.60029019072972e-104
12519.48459996403987e-1044.74229998201993e-104
12612.47997002844039e-1031.23998501422019e-103
12718.07757043202867e-1034.03878521601434e-103
12812.65559282283238e-1021.32779641141619e-102
12917.47619133097397e-1023.73809566548699e-102
13012.52172166308808e-1011.26086083154404e-101
13118.51924794636202e-1014.25962397318101e-101
13211.76450801899824e-1008.8225400949912e-101
13316.12881089315306e-1003.06440544657653e-100
13412.14870676559554e-991.07435338279777e-99
13517.56782404303044e-993.78391202151522e-99
13612.63926946786677e-981.31963473393339e-98
13719.36793295458625e-984.68396647729313e-98
13813.3551142117717e-971.67755710588585e-97
13911.20720199047219e-966.03600995236095e-97
14014.36183775516997e-962.18091887758499e-96
14111.46290197935726e-957.31450989678628e-96
14215.32767743254489e-952.66383871627245e-95
14311.55120865538512e-947.7560432769256e-95
14415.70076687075598e-942.85038343537799e-94
14512.15707774918194e-931.07853887459097e-93
14616.52859661383247e-933.26429830691623e-93
14712.41251798279999e-921.20625899139999e-92
14818.91243530622135e-924.45621765311068e-92
14913.30192453185967e-911.65096226592984e-91
15011.23023390073197e-906.15116950365984e-91
15114.1966790466993e-902.09833952334965e-90
15211.34899726625029e-896.74498633125144e-90
15315.01655101448796e-892.50827550724398e-89
15411.71636656106460e-888.58183280532302e-89
15516.39926394149906e-883.19963197074953e-88
15612.38076775953580e-871.19038387976790e-87
15718.85358432891025e-874.42679216445513e-87
15813.32327165736282e-861.66163582868141e-86
15911.22697635510095e-856.13488177550476e-86
16014.5522994964701e-852.27614974823505e-85
16111.68729624935830e-848.43648124679152e-85
16216.24686755550808e-843.12343377775404e-84
16312.30988798900409e-831.15494399450204e-83
16418.32178086226718e-834.16089043113359e-83
16513.08639510595293e-821.54319755297646e-82
16611.13597247946669e-815.67986239733343e-82
16714.17408811610426e-812.08704405805213e-81
16814.08063988559535e-812.04031994279767e-81
16911.50531688335368e-807.52658441676839e-81
17015.54190648707241e-802.77095324353621e-80
17112.03603951013347e-791.01801975506674e-79
17217.52630949057581e-793.76315474528791e-79
17312.7526384512427e-781.37631922562135e-78
17411.01379610873720e-775.06898054368601e-78
17513.6899662683696e-771.8449831341848e-77
17611.33696541054523e-766.68482705272617e-77
17714.84222635159467e-762.42111317579733e-76
17811.42190552492914e-757.10952762464569e-76
17915.12476455165734e-752.56238227582867e-75
18011.84216462021742e-749.21082310108709e-75
18115.5511487301754e-742.7755743650877e-74
18211.41323007106697e-737.06615035533486e-74
18313.85221169377157e-731.92610584688579e-73
18419.45218850984506e-734.72609425492253e-73
18512.88500280830639e-721.44250140415320e-72
18618.39932158063667e-724.19966079031834e-72
18712.62067036270234e-711.31033518135117e-71
18819.33084286914441e-714.66542143457221e-71
18913.21540667058162e-701.60770333529081e-70
19011.12692632212161e-695.63463161060806e-70
19113.82845888453343e-691.91422944226672e-69
19211.33403082862195e-686.67015414310976e-69
19314.66138459455268e-682.33069229727634e-68
19411.61412832694830e-678.07064163474148e-68
19515.57604035108655e-672.78802017554327e-67
19611.65852099920693e-668.29260499603464e-67
19711.82352988798999e-699.11764943994997e-70
19815.61771155081457e-692.80885577540728e-69
19911.73955148756994e-688.69775743784972e-69
20011.78647143605441e-688.93235718027204e-69
20115.57643672961522e-682.78821836480761e-68
20211.74729837024229e-678.73649185121147e-68
20315.49317032705846e-672.74658516352923e-67
20411.01252174565647e-665.06260872828233e-67
20513.01632384923802e-671.50816192461901e-67
20619.66177559213099e-674.83088779606549e-67
20712.89963830473178e-661.44981915236589e-66
20819.2859982072801e-664.64299910364005e-66
20911.32976071560854e-656.64880357804269e-66
21014.30556946853059e-652.15278473426529e-65
21111.50253562306761e-647.51267811533804e-65
21215.22580858150912e-642.61290429075456e-64
21311.61975985862275e-638.09879929311374e-64
21415.61192767024013e-632.80596383512007e-63
21511.95404209621654e-629.7702104810827e-63
21616.70713964289538e-623.35356982144769e-62
21712.28868206508875e-611.14434103254438e-61
21817.64962394705616e-613.82481197352808e-61
21912.59822423213653e-601.29911211606827e-60
22017.22817173702026e-603.61408586851013e-60
22112.42155353517682e-591.21077676758841e-59
22218.14534520613498e-594.07267260306749e-59
22312.72651839984562e-581.36325919992281e-58
22419.10321524589924e-584.55160762294962e-58
22513.02801943453041e-571.51400971726521e-57
22619.98375754096375e-574.99187877048187e-57
22713.29591152463786e-561.64795576231893e-56
22811.08391007738066e-555.41955038690331e-56
22913.50130474158674e-551.75065237079337e-55
23011.14268633227186e-545.71343166135931e-55
23113.73221974470614e-541.86610987235307e-54
23211.20854262820883e-536.04271314104415e-54
23313.89806148351688e-531.94903074175844e-53
23411.25366657915638e-526.26833289578192e-53
23514.01169527961318e-522.00584763980659e-52
23611.27843141130582e-516.3921570565291e-52
23714.05830771925526e-512.02915385962763e-51
23811.27346291126682e-506.3673145563341e-51
23914.01015350896328e-502.00507675448164e-50
24011.25766542812616e-496.28832714063081e-50
24113.92816860152164e-491.96408430076082e-49
24211.22711159757603e-486.13555798788016e-49
24313.80117463982632e-481.90058731991316e-48
24411.15398681714136e-475.76993408570679e-48
24512.93728899154356e-471.46864449577178e-47
24618.38769219309783e-474.19384609654891e-47
24712.39347611619112e-461.19673805809556e-46
24817.30618069104575e-463.65309034552287e-46
24912.07466691070594e-451.03733345535297e-45
25015.88450985888392e-452.94225492944196e-45
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25812.82836566194613e-421.41418283097306e-42
25917.91666589556333e-423.95833294778167e-42
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26313.8759363181397e-401.93796815906985e-40
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29313.14756280285831e-281.57378140142916e-28
29418.08380714549918e-284.04190357274959e-28
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29711.26070198285059e-266.30350991425296e-27
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31511.55175779749416e-207.75878898747078e-21
31613.48170522252487e-201.74085261126243e-20
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32112.17638286996591e-181.08819143498296e-18
32214.89477431958019e-182.44738715979009e-18
32311.09427985249764e-175.47139926248819e-18
32412.37929897790324e-171.18964948895162e-17
32515.25669087474746e-172.62834543737373e-17
32611.15418666641774e-165.7709333320887e-17
32712.46393874912511e-161.23196937456255e-16
32815.22192991862113e-162.61096495931056e-16
32911.12626873685827e-155.63134368429133e-16
3300.9999999999999992.41390664025862e-151.20695332012931e-15
3310.9999999999999975.14097858647593e-152.57048929323796e-15
3320.9999999999999951.08792022870916e-145.43960114354581e-15
3330.9999999999999892.28745672805033e-141.14372836402517e-14
3340.9999999999999764.7695249720929e-142.38476248604645e-14
3350.999999999999959.8989499945548e-144.9494749972774e-14
3360.9999999999998982.04098016216738e-131.02049008108369e-13
3370.999999999999794.18146714888245e-132.09073357444122e-13
3380.9999999999995758.50726045525105e-134.25363022762553e-13
3390.999999999999141.72006320266275e-128.60031601331376e-13
3400.9999999999982823.43545702951877e-121.71772851475939e-12
3410.9999999999965786.84450765462902e-123.42225382731451e-12
3420.9999999999932241.35516034509691e-116.77580172548453e-12
3430.9999999999866782.66443679424914e-111.33221839712457e-11
3440.999999999973995.20187370322427e-112.60093685161213e-11
3450.999999999949581.00838560236946e-105.04192801184731e-11
3460.999999999902961.94078818770132e-109.70394093850662e-11
3470.9999999998162333.67534556917268e-101.83767278458634e-10
3480.999999999651386.97240985504926e-103.48620492752463e-10
3490.99999999934351.31300120304292e-096.56500601521462e-10
3500.9999999987728872.45422582987652e-091.22711291493826e-09
3510.9999999977529514.49409776797735e-092.24704888398867e-09
3520.9999999958583328.28333542493973e-094.14166771246986e-09
3530.9999999924922841.50154319988935e-087.50771599944676e-09
3540.9999999863509062.72981884441557e-081.36490942220778e-08
3550.9999999754384394.91231227420859e-082.45615613710429e-08
3560.999999956149118.77017803313525e-084.38508901656763e-08
3570.9999999451488531.09702294245090e-075.48511471225448e-08
3580.9999999028701111.94259777224834e-079.7129888612417e-08
3590.99999982939983.41200400362666e-071.70600200181333e-07
3600.9999997028146295.9437074284276e-072.9718537142138e-07
3610.9999994864871411.02702571722821e-065.13512858614106e-07
3620.9999991203155051.75936899024407e-068.79684495122033e-07
3630.999998505817692.98836462086358e-061.49418231043179e-06
3640.9999975196958134.96060837458328e-062.48030418729164e-06
3650.999995871441348.2571173214392e-064.1285586607196e-06
3660.9999931647063121.36705873756175e-056.83529368780876e-06
3670.99998878386472.24322706013855e-051.12161353006928e-05
3680.9999817606009843.64787980325812e-051.82393990162906e-05
3690.9999706091706365.87816587275615e-052.93908293637808e-05
3700.9999530755805839.38488388345048e-054.69244194172524e-05
3710.999925779762460.0001484404750808137.42202375404065e-05
3720.9998839246449720.0002321507100554660.000116075355027733
3730.9998446558170350.0003106883659307590.000155344182965380
3740.9997607783002890.0004784433994227670.000239221699711383
3750.9996338873077770.0007322253844455650.000366112692222782
3760.9994452530838550.001109493832289950.000554746916144975
3770.99918038568780.001639228624401490.000819614312200745
3780.9987844159276730.002431168144653920.00121558407232696
3790.9982129423852520.003574115229496870.00178705761474844
3800.9974002872338910.005199425532217350.00259971276610867
3810.9962581610182110.007483677963577160.00374183898178858
3820.9951988503793320.009602299241336230.00480114962066812
3830.9941871224647340.01162575507053170.00581287753526586
3840.991810869600520.01637826079896150.00818913039948075
3850.9885910282594980.02281794348100420.0114089717405021
3860.9843821199588270.03123576008234650.0156178800411733
3870.978766015860850.04246796827830.02123398413915
3880.9716292174426540.05674156511469280.0283707825573464
3890.962264456088840.07547108782231820.0377355439111591
3900.950630511682340.09873897663531990.0493694883176599
3910.9357941343804210.1284117312391570.0642058656195787
3920.9178458322461050.1643083355077900.0821541677538948
3930.8958979948592530.2082040102814930.104102005140747
3940.8703765326341330.2592469347317340.129623467365867
3950.8599031001832870.2801937996334260.140096899816713
3960.8278128641858470.3443742716283060.172187135814153
3970.8011320080300550.397735983939890.198867991969945
3980.9685891294523880.06282174109522320.0314108705476116
3990.9564386675796070.08712266484078690.0435613324203934
4000.945358189391690.1092836212166220.0546418106083109
4010.9268207759214340.1463584481571310.0731792240785657
4020.9026469048699690.1947061902600620.0973530951300312
4030.8736412937942920.2527174124114150.126358706205708
4040.8569683696427870.2860632607144270.143031630357213
4050.8169043233386020.3661913533227960.183095676661398
4060.772412742828810.4551745143423810.227587257171190
4070.7212250175992420.5575499648015170.278774982400758
4080.6626293018164930.6747413963670130.337370698183507
4090.5983153819852460.8033692360295080.401684618014754
4100.5305418106078740.9389163787842520.469458189392126
4110.4810734906058170.9621469812116330.518926509394183
4120.4086395599249750.817279119849950.591360440075025
4130.3462798277888440.6925596555776880.653720172211156
4140.3512752048997790.7025504097995580.648724795100221
4150.2998120256519450.599624051303890.700187974348055
4160.2427526536944260.4855053073888510.757247346305574
4170.2094223579712110.4188447159424220.790577642028789
4180.2298523177181590.4597046354363190.77014768228184
4190.1711687471722990.3423374943445980.828831252827701
4200.1202381120521580.2404762241043150.879761887947842
4210.08520058382870810.1704011676574160.914799416171292
4220.06016729086291090.1203345817258220.93983270913709
4230.90334824598190.1933035080361990.0966517540180996
4240.8879237753156720.2241524493686560.112076224684328


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level3760.899521531100478NOK
5% type I error level3810.911483253588517NOK
10% type I error level3860.923444976076555NOK
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Dec/02/t1291316912ozfkt1q6u1vkpie/10pc7m1291317005.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/02/t1291316912ozfkt1q6u1vkpie/10pc7m1291317005.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/02/t1291316912ozfkt1q6u1vkpie/1ibba1291317005.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/02/t1291316912ozfkt1q6u1vkpie/1ibba1291317005.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/02/t1291316912ozfkt1q6u1vkpie/2ibba1291317005.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/02/t1291316912ozfkt1q6u1vkpie/2ibba1291317005.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/02/t1291316912ozfkt1q6u1vkpie/3tlav1291317005.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/02/t1291316912ozfkt1q6u1vkpie/3tlav1291317005.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/02/t1291316912ozfkt1q6u1vkpie/4tlav1291317005.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/02/t1291316912ozfkt1q6u1vkpie/4tlav1291317005.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/02/t1291316912ozfkt1q6u1vkpie/5tlav1291317005.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/02/t1291316912ozfkt1q6u1vkpie/5tlav1291317005.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/02/t1291316912ozfkt1q6u1vkpie/6mu9y1291317005.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/02/t1291316912ozfkt1q6u1vkpie/6mu9y1291317005.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/02/t1291316912ozfkt1q6u1vkpie/7wl811291317005.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/02/t1291316912ozfkt1q6u1vkpie/7wl811291317005.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/02/t1291316912ozfkt1q6u1vkpie/8wl811291317005.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/02/t1291316912ozfkt1q6u1vkpie/8wl811291317005.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/02/t1291316912ozfkt1q6u1vkpie/9pc7m1291317005.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/02/t1291316912ozfkt1q6u1vkpie/9pc7m1291317005.ps (open in new window)


 
Parameters (Session):
par1 = 4 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;
 
Parameters (R input):
par1 = 4 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;
 
R code (references can be found in the software module):
library(lattice)
library(lmtest)
n25 <- 25 #minimum number of obs. for Goldfeld-Quandt test
par1 <- as.numeric(par1)
x <- t(y)
k <- length(x[1,])
n <- length(x[,1])
x1 <- cbind(x[,par1], x[,1:k!=par1])
mycolnames <- c(colnames(x)[par1], colnames(x)[1:k!=par1])
colnames(x1) <- mycolnames #colnames(x)[par1]
x <- x1
if (par3 == 'First Differences'){
x2 <- array(0, dim=c(n-1,k), dimnames=list(1:(n-1), paste('(1-B)',colnames(x),sep='')))
for (i in 1:n-1) {
for (j in 1:k) {
x2[i,j] <- x[i+1,j] - x[i,j]
}
}
x <- x2
}
if (par2 == 'Include Monthly Dummies'){
x2 <- array(0, dim=c(n,11), dimnames=list(1:n, paste('M', seq(1:11), sep ='')))
for (i in 1:11){
x2[seq(i,n,12),i] <- 1
}
x <- cbind(x, x2)
}
if (par2 == 'Include Quarterly Dummies'){
x2 <- array(0, dim=c(n,3), dimnames=list(1:n, paste('Q', seq(1:3), sep ='')))
for (i in 1:3){
x2[seq(i,n,4),i] <- 1
}
x <- cbind(x, x2)
}
k <- length(x[1,])
if (par3 == 'Linear Trend'){
x <- cbind(x, c(1:n))
colnames(x)[k+1] <- 't'
}
x
k <- length(x[1,])
df <- as.data.frame(x)
(mylm <- lm(df))
(mysum <- summary(mylm))
if (n > n25) {
kp3 <- k + 3
nmkm3 <- n - k - 3
gqarr <- array(NA, dim=c(nmkm3-kp3+1,3))
numgqtests <- 0
numsignificant1 <- 0
numsignificant5 <- 0
numsignificant10 <- 0
for (mypoint in kp3:nmkm3) {
j <- 0
numgqtests <- numgqtests + 1
for (myalt in c('greater', 'two.sided', 'less')) {
j <- j + 1
gqarr[mypoint-kp3+1,j] <- gqtest(mylm, point=mypoint, alternative=myalt)$p.value
}
if (gqarr[mypoint-kp3+1,2] < 0.01) numsignificant1 <- numsignificant1 + 1
if (gqarr[mypoint-kp3+1,2] < 0.05) numsignificant5 <- numsignificant5 + 1
if (gqarr[mypoint-kp3+1,2] < 0.10) numsignificant10 <- numsignificant10 + 1
}
gqarr
}
bitmap(file='test0.png')
plot(x[,1], type='l', main='Actuals and Interpolation', ylab='value of Actuals and Interpolation (dots)', xlab='time or index')
points(x[,1]-mysum$resid)
grid()
dev.off()
bitmap(file='test1.png')
plot(mysum$resid, type='b', pch=19, main='Residuals', ylab='value of Residuals', xlab='time or index')
grid()
dev.off()
bitmap(file='test2.png')
hist(mysum$resid, main='Residual Histogram', xlab='values of Residuals')
grid()
dev.off()
bitmap(file='test3.png')
densityplot(~mysum$resid,col='black',main='Residual Density Plot', xlab='values of Residuals')
dev.off()
bitmap(file='test4.png')
qqnorm(mysum$resid, main='Residual Normal Q-Q Plot')
qqline(mysum$resid)
grid()
dev.off()
(myerror <- as.ts(mysum$resid))
bitmap(file='test5.png')
dum <- cbind(lag(myerror,k=1),myerror)
dum
dum1 <- dum[2:length(myerror),]
dum1
z <- as.data.frame(dum1)
z
plot(z,main=paste('Residual Lag plot, lowess, and regression line'), ylab='values of Residuals', xlab='lagged values of Residuals')
lines(lowess(z))
abline(lm(z))
grid()
dev.off()
bitmap(file='test6.png')
acf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Autocorrelation Function')
grid()
dev.off()
bitmap(file='test7.png')
pacf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Partial Autocorrelation Function')
grid()
dev.off()
bitmap(file='test8.png')
opar <- par(mfrow = c(2,2), oma = c(0, 0, 1.1, 0))
plot(mylm, las = 1, sub='Residual Diagnostics')
par(opar)
dev.off()
if (n > n25) {
bitmap(file='test9.png')
plot(kp3:nmkm3,gqarr[,2], main='Goldfeld-Quandt test',ylab='2-sided p-value',xlab='breakpoint')
grid()
dev.off()
}
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Estimated Regression Equation', 1, TRUE)
a<-table.row.end(a)
myeq <- colnames(x)[1]
myeq <- paste(myeq, '[t] = ', sep='')
for (i in 1:k){
if (mysum$coefficients[i,1] > 0) myeq <- paste(myeq, '+', '')
myeq <- paste(myeq, mysum$coefficients[i,1], sep=' ')
if (rownames(mysum$coefficients)[i] != '(Intercept)') {
myeq <- paste(myeq, rownames(mysum$coefficients)[i], sep='')
if (rownames(mysum$coefficients)[i] != 't') myeq <- paste(myeq, '[t]', sep='')
}
}
myeq <- paste(myeq, ' + e[t]')
a<-table.row.start(a)
a<-table.element(a, myeq)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,hyperlink('http://www.xycoon.com/ols1.htm','Multiple Linear Regression - Ordinary Least Squares',''), 6, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Variable',header=TRUE)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'S.D.',header=TRUE)
a<-table.element(a,'T-STAT<br />H0: parameter = 0',header=TRUE)
a<-table.element(a,'2-tail p-value',header=TRUE)
a<-table.element(a,'1-tail p-value',header=TRUE)
a<-table.row.end(a)
for (i in 1:k){
a<-table.row.start(a)
a<-table.element(a,rownames(mysum$coefficients)[i],header=TRUE)
a<-table.element(a,mysum$coefficients[i,1])
a<-table.element(a, round(mysum$coefficients[i,2],6))
a<-table.element(a, round(mysum$coefficients[i,3],4))
a<-table.element(a, round(mysum$coefficients[i,4],6))
a<-table.element(a, round(mysum$coefficients[i,4]/2,6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Regression Statistics', 2, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Multiple R',1,TRUE)
a<-table.element(a, sqrt(mysum$r.squared))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'R-squared',1,TRUE)
a<-table.element(a, mysum$r.squared)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Adjusted R-squared',1,TRUE)
a<-table.element(a, mysum$adj.r.squared)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (value)',1,TRUE)
a<-table.element(a, mysum$fstatistic[1])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (DF numerator)',1,TRUE)
a<-table.element(a, mysum$fstatistic[2])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (DF denominator)',1,TRUE)
a<-table.element(a, mysum$fstatistic[3])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'p-value',1,TRUE)
a<-table.element(a, 1-pf(mysum$fstatistic[1],mysum$fstatistic[2],mysum$fstatistic[3]))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Residual Statistics', 2, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Residual Standard Deviation',1,TRUE)
a<-table.element(a, mysum$sigma)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Sum Squared Residuals',1,TRUE)
a<-table.element(a, sum(myerror*myerror))
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable3.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Actuals, Interpolation, and Residuals', 4, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Time or Index', 1, TRUE)
a<-table.element(a, 'Actuals', 1, TRUE)
a<-table.element(a, 'Interpolation<br />Forecast', 1, TRUE)
a<-table.element(a, 'Residuals<br />Prediction Error', 1, TRUE)
a<-table.row.end(a)
for (i in 1:n) {
a<-table.row.start(a)
a<-table.element(a,i, 1, TRUE)
a<-table.element(a,x[i])
a<-table.element(a,x[i]-mysum$resid[i])
a<-table.element(a,mysum$resid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable4.tab')
if (n > n25) {
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Goldfeld-Quandt test for Heteroskedasticity',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'p-values',header=TRUE)
a<-table.element(a,'Alternative Hypothesis',3,header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'breakpoint index',header=TRUE)
a<-table.element(a,'greater',header=TRUE)
a<-table.element(a,'2-sided',header=TRUE)
a<-table.element(a,'less',header=TRUE)
a<-table.row.end(a)
for (mypoint in kp3:nmkm3) {
a<-table.row.start(a)
a<-table.element(a,mypoint,header=TRUE)
a<-table.element(a,gqarr[mypoint-kp3+1,1])
a<-table.element(a,gqarr[mypoint-kp3+1,2])
a<-table.element(a,gqarr[mypoint-kp3+1,3])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable5.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Description',header=TRUE)
a<-table.element(a,'# significant tests',header=TRUE)
a<-table.element(a,'% significant tests',header=TRUE)
a<-table.element(a,'OK/NOK',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'1% type I error level',header=TRUE)
a<-table.element(a,numsignificant1)
a<-table.element(a,numsignificant1/numgqtests)
if (numsignificant1/numgqtests < 0.01) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'5% type I error level',header=TRUE)
a<-table.element(a,numsignificant5)
a<-table.element(a,numsignificant5/numgqtests)
if (numsignificant5/numgqtests < 0.05) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'10% type I error level',header=TRUE)
a<-table.element(a,numsignificant10)
a<-table.element(a,numsignificant10/numgqtests)
if (numsignificant10/numgqtests < 0.1) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable6.tab')
}
 




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Software written by Ed van Stee & Patrick Wessa


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