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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 19:17:31 +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/t1291317371xtdyw78s6qflt7r.htm/, Retrieved Thu, 02 Dec 2010 20:16:11 +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/t1291317371xtdyw78s6qflt7r.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
Trades[t] = -6.39506766242515 + 1.94624800291167Group[t] + 0.00679068305600395Costs[t] + 0.000398000520557039Dividends[t] + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0		2-tail p-value1-tail p-value
(Intercept)-6.395067662425158.572689-0.7460.4560890.228045
Group1.946248002911677.7200910.25210.8010840.400542
Costs0.006790683056003950.00030622.165500
Dividends0.0003980005205570390.0001123.5590.0004140.000207


Multiple Linear Regression - Regression Statistics
Multiple R0.772359513708112
R-squared0.596539218415432
Adjusted R-squared0.593704599341067
F-TEST (value)210.447754271582
F-TEST (DF numerator)3
F-TEST (DF denominator)427
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation70.2894212212756
Sum Squared Residuals2109637.36811056


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast		Residuals
Prediction Error
110811184.23853013234-103.238530132339
2309230.38893714323178.6110628567686
3458651.048365641929-193.048365641929
4588558.6830335991129.3169664008897
5299417.252898262214-118.252898262214
6156347.636415589013-191.636415589013
7481323.158776132974157.841223867025
8323376.335850041768-53.3358500417677
9452275.645429750691176.354570249309
10109125.101135968947-16.1011359689472
11115266.735711494855-151.735711494855
1211098.815987801797911.1840121982021
13239117.197964021189121.802035978811
14247302.373844520029-55.3738445200289
15497200.035241241041296.964758758959
1610398.19984884674164.80015115325844
17109156.666777754413-47.6667777544128
18502182.391852304027319.608147695973
19248265.93834291785-17.9383429178498
20373163.51367102593209.48632897407
21119116.5199347345322.48006526546765
2284178.947972522027-94.9479725220269
23102149.98576491906-47.9857649190601
24295149.860192915733145.139807084267
2510595.47436722499799.52563277500214
2664126.468258247102-62.4682582471015
27267202.55496694521364.4450330547868
2812982.886064808788346.1139351912117
293764.5903855066955-27.5903855066955
30361111.34253122634249.65746877366
312853.1191149284359-25.1191149284359
3285118.043292617266-33.0432926172662
334472.5724041125133-28.5724041125133
344966.8856722345382-17.8856722345382
3522128.745065758346-106.745065758346
36155160.374218482872-5.37421848287242
379198.9860083663084-7.98600836630843
388176.55216967801764.44783032198237
397987.9388895993237-8.93888959932366
4014552.998255234988892.0017447650112
4181697.02217748371718.97782251629
4261125.145876706522-64.1458767065223
4322661.6695999999691164.330400000031
4410587.023155425129217.9768445748708
456252.55753152196549.44246847803464
462460.870814532611-36.870814532611
472687.947568018986-61.9475680189861
48322100.931085061132221.068914938868
498475.41029346136448.58970653863564
503339.5232862096073-6.52328620960731
5110860.031207066551547.9687929334485
5215077.366667172648972.6333328273511
53115120.192858722645-5.19285872264487
5416261.445859039763100.554140960237
5515889.512247538749668.4877524612504
569734.210456678221562.7895433217785
57939.0957386415246-30.0957386415246
586664.99029669463551.00970330536451
5910741.927633854239265.0723661457608
6010193.68068871041117.3193112895889
614770.8946706643079-23.8946706643079
623827.990875450272810.0091245497272
633454.4304021224657-20.4304021224657
648478.04380116818135.95619883181868
657935.258806234100243.7411937658998
66947119.751844160471827.24815583953
677431.735593483182142.2644065168179
685349.46085893036213.53914106963787
699455.459101262681238.5408987373188
706362.86549135025220.134508649747836
715827.106164472842430.8938355271576
724943.90398122328535.09601877671471
733445.8626854304556-11.8626854304556
741128.9224420229659-17.9224420229659
753554.331231257524-19.331231257524
761735.1779931577066-18.1779931577066
774746.15482733354110.84517266645891
784328.563394141967314.4366058580327
7911729.944112809754687.0558871902454
8017146.9856986133228124.014301386677
812627.2469426994696-1.24694269946964
827362.714832780879210.2851672191208
835954.86410103696664.13589896303344
841814.90331897223473.09668102776527
851537.9799469025827-22.9799469025827
867259.770903735324612.2290962646754
878654.260923014060731.7390769859393
881438.6480353049267-24.6480353049267
896450.289809569233613.7101904307664
901138.5866134272963-27.5866134272963
915245.22243687238446.77756312761562
924148.5723418283823-7.57234182838234
939934.214388366535564.7856116334645
947590.4249588092541-15.4249588092541
954521.368298165310323.6317018346897
964340.27505443857852.72494556142151
97840.4240669491505-32.4240669491505
9819833.0864747164513164.913525283549
992262.812031438462-40.812031438462
1001134.0846911226469-23.0846911226469
1013334.4076432957860-1.40764329578596
1022336.2584274452897-13.2584274452897
1038059.637069973591220.3629300264089
1041842.7933029969224-24.7933029969224
1052829.8146081689023-1.81460816890235
1062327.1520971489361-4.15209714893606
1076041.039809800699318.9601901993007
1082048.3983981473431-28.3983981473431
1095971.1869942619573-12.1869942619573
1103637.7065099814044-1.70650998140437
1113027.00076904411922.99923095588079
1124738.00353900216228.9964609978378
1137162.72014992361838.27985007638173
1141441.28844615736-27.28844615736
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1163926.244230311425712.7557696885743
1172630.1608511682312-4.16085116823117
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1191641.4472064746028-25.4472064746027
1206923.671041945815545.3289580541845
12192109.346607809167-17.346607809167
1221426.2128148888999-12.2128148888999
12310340.131385664040162.8686143359599
1242949.6326255303616-20.6326255303616
1253738.5683111431778-1.56831114317785
1262348.1008658018449-25.1008658018449
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128718.4389021910633-11.4389021910633
1292819.52876074568068.47123925431944
130017.7715239457983-17.7715239457983
131817.9665871228523-9.96658712285226
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1371318.6420026143640-5.64200261436404
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1411419.7245587540201-5.72455875402011
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1431522.9957263013028-7.99572630130277
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1451521.9403875185428-6.94038751854285
1461118.2042128315723-7.20421283157226
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148617.8784101531663-11.8784101531663
149017.7715239457983-17.7715239457983
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1511020.4788180573672-10.4788180573672
1527329.651634075904143.3483659240959
153017.7715239457983-17.7715239457983
1541120.0478456948811-9.04784569488107
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163017.7715239457983-17.7715239457983
1642721.09520391910945.90479608089058
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1841026.0784350593317-16.0784350593317
185520.6042886142202-15.6042886142202
1861423.9109275562455-9.91092755624548
1871626.1173555667301-10.1173555667301
188519.3090944087987-14.3090944087987
189521.3061709322543-16.3061709322543
190017.7715239457983-17.7715239457983
191419.1534011511198-15.1534011511198
192017.7715239457983-17.7715239457983
193619.0911907304017-13.0911907304017
194017.7715239457983-17.7715239457983
195218.0293231598611-16.0293231598611
196019.7177719487099-19.7177719487099
1978058.157490156348321.8425098436517
198019.7177719487099-19.7177719487099
199019.7177719487099-19.7177719487099
2002030.6143344109086-10.6143344109086
201019.7177719487099-19.7177719487099
202019.7177719487099-19.7177719487099
203019.7177719487099-19.7177719487099
2042717.14970744723519.85029255276487
2051733.7006246277441-16.7006246277441
206220.1582072665114-18.1582072665114
207422.1228515673655-18.1228515673655
208019.7177719487099-19.7177719487099
2093222.57717755057569.42282244942435
210019.7177719487099-19.7177719487099
211017.7715239457983-17.7715239457983
212017.7715239457983-17.7715239457983
2133218.358794718435613.6412052815644
2142021.4905943686843-1.49059436868432
215722.1539496867627-15.1539496867627
216017.7715239457983-17.7715239457983
217817.9175622494201-9.91756224942014
2182820.43797308051067.5620269194894
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2202023.1874263283146-3.18742632831456
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222017.7715239457983-17.7715239457983
223217.783139983514-15.783139983514
224017.7715239457983-17.7715239457983
225217.9411676511657-15.9411676511657
2262619.93156619142846.06843380857164
227017.7715239457983-17.7715239457983
228017.7715239457983-17.7715239457983
229420.8886254642089-16.8886254642089
230017.7715239457983-17.7715239457983
231921.1957821377312-12.1957821377312
232017.7715239457983-17.7715239457983
233017.7715239457983-17.7715239457983
2341720.6549638132658-3.6549638132658
235017.7715239457983-17.7715239457983
236117.7942593238831-16.7942593238831
237017.7715239457983-17.7715239457983
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239017.7715239457983-17.7715239457983
240017.7715239457983-17.7715239457983
241017.7715239457983-17.7715239457983
242318.6645684862191-15.6645684862191
243017.7715239457983-17.7715239457983
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245438.3674830582616-34.3674830582616
246019.7177719487099-19.7177719487099
247019.7177719487099-19.7177719487099
2481119.0941279925008-8.09412799250084
249019.7177719487099-19.7177719487099
250019.7177719487099-19.7177719487099
251916.141620693896-7.141620693896
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256017.7715239457983-17.7715239457983
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267019.7177719487099-19.7177719487099
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270622.3292489430342-16.3292489430342
271019.7177719487099-19.7177719487099
272019.7177719487099-19.7177719487099
273019.7177719487099-19.7177719487099
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278017.7715239457983-17.7715239457983
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2802821.91825602410596.08174397589406
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2851324.0490446563886-11.0490446563886
286017.7715239457983-17.7715239457983
287019.7177719487099-19.7177719487099
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289019.7177719487099-19.7177719487099
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344017.7715239457983-17.7715239457983
345017.7715239457983-17.7715239457983
346017.7715239457983-17.7715239457983
347617.9420183955303-11.9420183955303
348017.7715239457983-17.7715239457983
349017.7715239457983-17.7715239457983
350017.7715239457983-17.7715239457983
3511419.0456599546494-5.04565995464944
3521018.3397571394635-8.33975713946354
3531221.3099043140459-9.3099043140459
354219.223576858508-17.223576858508
355017.7715239457983-17.7715239457983
356017.7715239457983-17.7715239457983
3575228.449824437844423.5501755621556
358017.7715239457983-17.7715239457983
359017.7715239457983-17.7715239457983
360017.7715239457983-17.7715239457983
361417.7791106298954-13.7791106298954
362017.7715239457983-17.7715239457983
363017.7715239457983-17.7715239457983
364320.4618720240484-17.4618720240484
3651118.5620163310746-7.56201633107458
366017.7715239457983-17.7715239457983
367017.7715239457983-17.7715239457983
368017.7715239457983-17.7715239457983
369017.7715239457983-17.7715239457983
370017.7715239457983-17.7715239457983
371017.7715239457983-17.7715239457983
3724020.440027466085019.5599725339150
373925.6507692888614-16.6507692888614
374120.5849049318268-19.5849049318268
375017.7715239457983-17.7715239457983
376017.7715239457983-17.7715239457983
3772416.78547823120477.21452176879535
3781121.7804364129545-10.7804364129545
379017.7715239457983-17.7715239457983
380017.7715239457983-17.7715239457983
381017.7715239457983-17.7715239457983
3826026.43036658332233.569633416678
3838013.990279953697466.0097200463026
384017.7715239457983-17.7715239457983
3851619.0892382548695-3.08923825486949
3864037.49296975981812.50703024018185
387618.2396208748649-12.2396208748649
388823.2035233133201-15.2035233133201
389318.1322969582112-15.1322969582112
3901620.8040735398404-4.80407353984045
3911021.2594461549403-11.2594461549403
392820.2721205948230-12.2721205948230
393722.0868689263608-15.0868689263608
394825.4055818075537-17.4055818075537
3951252.0900733362796-40.0900733362796
3961320.6868146447313-7.68681464473133
3974248.013526415084-6.01352641508404
39811853.570262384702364.4297376152977
399922.617496922179-13.6174969221790
40013818.3465814497693119.653418550231
401528.8350537150189-23.8350537150189
402924.4380758244125-15.4380758244125
403821.3116904965644-13.3116904965644
4042533.5154967850998-8.51549678509976
405723.2045101629301-16.2045101629301
4061329.7677685100308-16.7677685100308
4071624.8879719158347-8.88797191583473
4081123.7750885563891-12.7750885563891
4091119.7906418749911-8.7906418749911
410326.3870446648153-23.3870446648153
4116130.258702727224430.7412972727756
4122463.786424526443-39.786424526443
4131726.2689252560046-9.26892525600459
4143347.9699204173656-14.9699204173656
415734.4902067347163-27.4902067347163
416329.4069997423555-26.4069997423555
4176629.744914717559336.2550852824407
4181728.0480680319462-11.0480680319462
4192629.7731238443703-3.7731238443703
420324.3297681527135-21.3297681527135
421228.2523905925715-26.2523905925715
4226741.845506784497325.1544932155027
4237068.04525703859791.95474296140212
4242660.1412990237561-34.1412990237561
4252430.9383194975819-6.93831949758185
4269452.525576350422941.4744236495771
4273041.159196558124-11.1591965581240
428223298.112951396829-75.1129513968294
4294888.0773533612135-40.0773533612135
43090127.888939690788-37.8889396907881
431180127.19199341161252.8080065883876


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
70.9891981553794040.02160368924119140.0108018446205957
80.9774970536558870.04500589268822630.0225029463441132
90.9990876127298650.001824774540270290.000912387270135145
100.9983065722330060.003386855533988930.00169342776699446
110.9993477548975460.001304490204907450.000652245102453727
120.99902962592360.001940748152801580.000970374076400788
130.998442611371310.003114777257379130.00155738862868956
140.999065787569020.001868424861959910.000934212430979953
150.9999980935192263.81296154716379e-061.90648077358190e-06
160.9999959139197838.17216043469173e-064.08608021734586e-06
170.9999937083218961.25833562086883e-056.29167810434415e-06
180.9999999880635732.38728547938146e-081.19364273969073e-08
190.999999992073151.58537010648380e-087.92685053241901e-09
200.9999999993454251.30914958472870e-096.54574792364349e-10
210.9999999992045441.59091216115954e-097.95456080579769e-10
220.9999999998812432.37513969426359e-101.18756984713179e-10
230.999999999843533.12941739222954e-101.56470869611477e-10
240.9999999998791822.41636250954574e-101.20818125477287e-10
250.9999999997565884.86823973310768e-102.43411986655384e-10
260.9999999999009241.98150974725969e-109.90754873629847e-11
270.9999999997941274.11745993419116e-102.05872996709558e-10
280.9999999995909048.18191082218446e-104.09095541109223e-10
290.9999999996455687.08864075001065e-103.54432037500533e-10
300.9999999999826753.46496779508075e-111.73248389754037e-11
310.9999999999819313.61376897378359e-111.80688448689180e-11
320.9999999999784924.30157773814543e-112.15078886907272e-11
330.9999999999745375.09250509159841e-112.54625254579920e-11
340.9999999999590238.19543109227067e-114.09771554613533e-11
350.99999999996227.55997511845707e-113.77998755922853e-11
360.999999999943881.12240096291775e-105.61200481458875e-11
370.9999999999152411.69518018823769e-108.47590094118846e-11
380.999999999838613.22779963438869e-101.61389981719435e-10
390.9999999997038845.92231694605797e-102.96115847302898e-10
400.9999999995544768.91048029402818e-104.45524014701409e-10
4115.47857247280237e-372.73928623640118e-37
4211.05162687458585e-375.25813437292923e-38
4312.09918480113953e-381.04959240056977e-38
4415.45546506926472e-382.72773253463236e-38
4519.7163151310864e-384.8581575655432e-38
4611.52050929430781e-377.60254647153906e-38
4712.07613038921895e-371.03806519460947e-37
4814.02562737835381e-402.01281368917691e-40
4919.99711485094232e-404.99855742547116e-40
5011.55945396760852e-397.79726983804258e-40
5114.06615500544651e-392.03307750272326e-39
5217.22186816972171e-393.61093408486086e-39
5311.90454402438518e-389.52272012192591e-39
5411.3173095058005e-386.5865475290025e-39
5512.29867551993445e-381.14933775996722e-38
5614.37679676345944e-382.18839838172972e-38
5713.51833628359198e-381.75916814179599e-38
5817.24435234138526e-383.62217617069263e-38
5911.29579431732077e-376.47897158660383e-38
6013.163700907876e-371.581850453938e-37
6115.29762602111342e-372.64881301055671e-37
6211.02906739049469e-365.14533695247344e-37
6311.93737880585915e-369.68689402929574e-37
6414.74474952945597e-362.37237476472798e-36
6511.02790421568145e-355.13952107840726e-36
6611.25070133687824e-1416.2535066843912e-142
6718.67209641444616e-1424.33604820722308e-142
6814.89713069706993e-1412.44856534853497e-141
6913.92132655563723e-1411.96066327781861e-141
7012.26819106324075e-1401.13409553162037e-140
7115.18276263913221e-1402.59138131956610e-140
7211.43366159291475e-1397.16830796457377e-140
7315.14631142310678e-1392.57315571155339e-139
7411.35958050845527e-1386.79790254227635e-139
7514.796381915069e-1382.3981909575345e-138
7612.0767952156123e-1371.03839760780615e-137
7718.88638717742404e-1374.44319358871202e-137
7812.68501098905435e-1361.34250549452717e-136
7917.39643465082588e-1393.69821732541294e-139
8016.40428061224597e-1463.20214030612299e-146
8112.43710308433517e-1451.21855154216759e-145
8211.01119139748242e-1445.05595698741208e-145
8312.94096805464651e-1441.47048402732326e-144
8411.09980516753739e-1435.49902583768697e-144
8514.04251364912564e-1432.02125682456282e-143
8611.7710389737729e-1428.8551948688645e-143
8711.53418833939405e-1427.67094169697024e-143
8815.63846934110887e-1422.81923467055444e-142
8911.26696674491739e-1416.33483372458696e-142
9014.42805519875108e-1412.21402759937554e-141
9111.48702310017062e-1407.43511550085311e-141
9218.2026973441194e-1404.1013486720597e-140
9312.39584748145593e-1411.19792374072797e-141
9411.39969051959488e-1406.99845259797442e-141
9513.60342803477473e-1401.80171401738737e-140
9611.88540140618659e-1399.42700703093297e-140
9716.29460376827909e-1393.14730188413955e-139
9814.32968094246673e-1542.16484047123336e-154
9911.27095123940024e-1536.3547561970012e-154
10015.75577909090105e-1532.87788954545053e-153
10113.05704621956482e-1521.52852310978241e-152
10211.57404893591752e-1517.87024467958758e-152
10311.45339590833967e-1517.26697954169837e-152
10417.2222235117546e-1513.6111117558773e-151
10513.56532659079235e-1501.78266329539617e-150
10611.80482986842009e-1499.02414934210046e-150
10714.09421388766382e-1492.04710694383191e-149
10812.00048753968988e-1481.00024376984494e-148
10911.08792316939498e-1475.43961584697488e-148
11015.7215628409632e-1472.8607814204816e-147
11112.56961236718856e-1461.28480618359428e-146
11211.13092732459713e-1455.65463662298563e-146
11313.53998879655240e-1451.76999439827620e-145
11411.46599811645882e-1447.32999058229412e-145
11517.13464184294122e-1443.56732092147061e-144
11612.41542904855643e-1431.20771452427822e-143
11711.17657768686398e-1425.88288843431989e-143
11815.37214387128865e-1422.68607193564433e-142
11912.47543666452037e-1411.23771833226018e-141
12013.33131157993613e-1421.66565578996807e-142
12111.86019236801382e-1419.30096184006912e-142
12219.54367813835706e-1414.77183906917853e-141
12318.77501619185288e-1444.38750809592644e-144
12415.2579248717245e-1432.62896243586225e-143
12512.92902549669916e-1421.46451274834958e-142
12611.42174252691248e-1417.1087126345624e-142
12716.3534446715286e-1413.1767223357643e-141
12813.30136192524862e-1401.65068096262431e-140
12911.30597112075892e-1396.52985560379461e-140
13015.95702916553855e-1392.97851458276927e-139
13113.18549911205113e-1381.59274955602556e-138
13211.28667768075168e-1386.4333884037584e-139
13315.9883417817787e-1382.99417089088935e-138
13413.00749829299624e-1371.50374914649812e-137
13511.41315361776883e-1367.06576808884417e-137
13617.65600982468983e-1363.82800491234492e-136
13714.20047275388725e-1352.10023637694363e-135
13811.99277344214401e-1349.96386721072004e-135
13919.48254166547708e-1344.74127083273854e-134
14014.52408200096878e-1332.26204100048439e-133
14112.50642590379006e-1321.25321295189503e-132
14211.19999353678304e-1315.99996768391519e-132
14316.66120168919014e-1313.33060084459507e-131
14413.42038357866602e-1301.71019178933301e-130
14511.88994038284898e-1299.44970191424491e-130
14611.04827600925887e-1285.24138004629436e-129
14715.03801819493345e-1282.51900909746672e-128
14812.72137377053175e-1271.36068688526588e-127
14911.30829436718951e-1266.54147183594755e-127
15016.43561177587396e-1263.21780588793698e-126
15113.50433326976010e-1251.75216663488005e-125
15215.07182585650349e-1262.53591292825175e-126
15312.46328322641595e-1251.23164161320797e-125
15411.36316373447947e-1246.81581867239733e-125
15517.05996455488912e-1243.52998227744456e-124
15613.42040109986703e-1231.71020054993351e-123
15711.65546377238429e-1228.27731886192146e-123
15818.25686440291655e-1224.12843220145828e-122
15914.36047378738292e-1212.18023689369146e-121
16012.10191988048301e-1201.05095994024151e-120
16111.01165621074739e-1195.05828105373693e-120
16214.8610561603557e-1192.43052808017785e-119
16312.33162262430887e-1181.16581131215443e-118
16419.76036576163147e-1184.88018288081574e-118
16517.40598844777612e-1183.70299422388806e-118
16613.56635881667578e-1171.78317940833789e-117
16711.71388524736623e-1168.56942623683117e-117
16818.90087580808878e-1164.45043790404439e-116
16914.26120478263941e-1152.13060239131971e-115
17012.03534370416067e-1141.01767185208034e-114
17119.69864907065295e-1144.84932453532648e-114
17214.97116795694016e-1132.48558397847008e-113
17312.3569257746653e-1121.17846288733265e-112
17411.25147538963918e-1116.2573769481959e-112
17515.90265190038582e-1112.95132595019291e-111
17613.11475458741537e-1101.55737729370768e-110
17711.46110986166774e-1097.3055493083387e-110
17816.66264983668358e-1093.33132491834179e-109
17913.10743400848407e-1081.55371700424204e-108
18011.44504812491831e-1077.22524062459157e-108
18115.2629083905402e-1072.6314541952701e-107
18212.60205714741713e-1061.30102857370857e-106
18316.02167394683706e-1063.01083697341853e-106
18413.03022999383301e-1051.51511499691651e-105
18511.48624992703929e-1047.43124963519645e-105
18617.65287825403076e-1043.82643912701538e-104
18713.92760048864002e-1031.96380024432001e-103
18811.92676032069166e-1029.63380160345831e-103
18919.26411861812751e-1024.63205930906375e-102
19014.20073914977857e-1012.10036957488929e-101
19111.99397072391064e-1009.9698536195532e-101
19218.98354134415069e-1004.49177067207534e-100
19314.39800891791977e-992.19900445895989e-99
19411.96854500001389e-989.84272500006947e-99
19519.12443925678105e-984.56221962839052e-98
19613.91920754678397e-971.95960377339199e-97
19711.09092326974143e-975.45461634870716e-98
19814.77938008572897e-972.38969004286449e-97
19912.08453203358549e-961.04226601679275e-96
20019.8196807152364e-964.9098403576182e-96
20114.26533754033741e-952.13266877016870e-95
20211.84297452258304e-949.21487261291519e-95
20317.91845461546308e-943.95922730773154e-94
20412.92888411184438e-931.46444205592219e-93
20511.40322704573144e-927.01613522865718e-93
20616.28518903754256e-923.14259451877128e-92
20712.87488719902955e-911.43744359951477e-91
20811.21931269467497e-906.09656347337484e-91
20914.65003138336617e-902.32501569168309e-90
21011.96747815369962e-899.8373907684981e-90
21118.40058672311684e-894.20029336155842e-89
21213.57422625542485e-881.78711312771242e-88
21311.01703135742562e-875.08515678712809e-88
21414.51545676754076e-872.25772838377038e-87
21512.03087317873615e-861.01543658936807e-86
21618.56663976768792e-864.28331988384396e-86
21713.99442762125164e-851.99721381062582e-85
21811.38836749275774e-846.9418374637887e-85
21915.81178108575549e-842.90589054287774e-84
22012.65577984853923e-831.32788992426962e-83
22111.15019151773356e-825.75095758866782e-83
22214.76475326562225e-822.38237663281112e-82
22312.04403722823103e-811.02201861411551e-81
22418.40316512661743e-814.20158256330871e-81
22513.56953299627724e-801.78476649813862e-80
22611.27420012991689e-796.37100064958444e-80
22715.19295625762315e-792.59647812881158e-79
22812.10803108687699e-781.05401554343850e-78
22918.9058345305361e-784.45291726526805e-78
23013.58686977662883e-771.79343488831442e-77
23111.57823429463334e-767.89117147316671e-77
23216.30711247457628e-763.15355623728814e-76
23312.51021959066297e-751.25510979533148e-75
23411.07786803170543e-745.38934015852717e-75
23514.25971538719589e-742.12985769359794e-74
23611.71001950675260e-738.55009753376302e-74
23716.70177345289429e-733.35088672644715e-73
23812.85025978612231e-721.42512989306116e-72
23911.10788588277901e-715.53942941389503e-72
24014.2879144626621e-712.14395723133105e-71
24111.65243617986281e-708.26218089931406e-71
24216.62296451012013e-703.31148225506007e-70
24312.53037807239126e-691.26518903619563e-69
24411.06669658414333e-685.33348292071664e-69
24512.67421574130872e-681.33710787065436e-68
24611.00085057957848e-675.00425289789239e-68
24713.71851694159768e-671.85925847079884e-67
24811.55405266651100e-667.77026333255498e-67
24915.70757072343236e-662.85378536171618e-66
25012.07940071727144e-651.03970035863572e-65
25118.5694701918847e-654.28473509594235e-65
25213.08386798342649e-641.54193399171324e-64
25311.15011101146924e-635.75055505734621e-64
25411.55530577120603e-647.77652885603015e-65
25514.02132635830802e-662.01066317915401e-66
25611.55133207130306e-657.75666035651531e-66
25716.47863321016124e-653.23931660508062e-65
25811.56250875393246e-647.8125437696623e-65
25915.69076296152512e-642.84538148076256e-64
26012.17343801633144e-631.08671900816572e-63
26117.8110676614427e-633.90553383072135e-63
26212.77777127212709e-621.38888563606355e-62
26311.14460847850604e-615.72304239253021e-62
26414.67538581505956e-612.33769290752978e-61
26511.63226971068939e-608.16134855344697e-61
26616.09987151812513e-603.04993575906257e-60
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36813.27933755334408e-161.63966877667204e-16
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3820.9999999999802243.95509587563111e-111.97754793781555e-11
3830.9999999999942641.14727308207416e-115.7363654103708e-12
3840.9999999999853262.93478193184905e-111.46739096592453e-11
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3860.9999999999099121.80175144669433e-109.00875723347165e-11
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3890.9999999985474912.90501700546783e-091.45250850273392e-09
3900.999999996350267.29947983602106e-093.64973991801053e-09
3910.9999999909646721.80706556737171e-089.03532783685856e-09
3920.999999978145274.37094588829378e-082.18547294414689e-08
3930.9999999484983841.03003231533285e-075.15016157666425e-08
3940.999999879809422.40381160531668e-071.20190580265834e-07
3950.9999998666722592.66655482699207e-071.33327741349604e-07
3960.999999683963726.32072559514831e-073.16036279757416e-07
3970.999999262585631.47482874034714e-067.3741437017357e-07
3980.9999999531822879.36354257377668e-084.68177128688834e-08
3990.9999998789418162.42116367073984e-071.21058183536992e-07
4000.999999999339781.32044062884279e-096.60220314421396e-10
4010.999999998054793.89041996614763e-091.94520998307382e-09
4020.9999999939709581.20580838773750e-086.02904193868751e-09
4030.999999981876663.62466794022001e-081.81233397011001e-08
4040.9999999452798821.09440236126033e-075.47201180630167e-08
4050.9999998419534563.16093087544845e-071.58046543772422e-07
4060.9999995394857279.21028545489576e-074.60514272744788e-07
4070.9999986639500052.6720999907987e-061.33604999539935e-06
4080.999996378637147.24272572121318e-063.62136286060659e-06
4090.9999901513708761.96972582482762e-059.8486291241381e-06
4100.9999762319003164.75361993683548e-052.37680996841774e-05
4110.999976421687244.71566255215016e-052.35783127607508e-05
4120.999962226788587.55464228381152e-053.77732114190576e-05
4130.9998989430318470.0002021139363051340.000101056968152567
4140.9997311140655920.0005377718688150420.000268885934407521
4150.9993359660899310.001328067820137350.000664033910068675
4160.9984743642762950.003051271447410290.00152563572370515
4170.9975548699835740.004890260032851480.00244513001642574
4180.9946802958166330.01063940836673490.00531970418336744
4190.9876585977078140.0246828045843730.0123414022921865
4200.9734041101516350.05319177969672970.0265958898483648
4210.9482037879441670.1035924241116650.0517962120558325
4220.9274582663638270.1450834672723460.0725417336361731
4230.995951964243590.008096071512819040.00404803575640952
4240.9916996978389550.01660060432209000.00830030216104498


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level4100.980861244019139NOK
5% type I error level4150.992822966507177NOK
10% type I error level4160.995215311004785NOK
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Dec/02/t1291317371xtdyw78s6qflt7r/10h4x71291317431.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/02/t1291317371xtdyw78s6qflt7r/10h4x71291317431.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/02/t1291317371xtdyw78s6qflt7r/1b3iv1291317431.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/02/t1291317371xtdyw78s6qflt7r/1b3iv1291317431.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/02/t1291317371xtdyw78s6qflt7r/2b3iv1291317431.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/02/t1291317371xtdyw78s6qflt7r/2b3iv1291317431.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/02/t1291317371xtdyw78s6qflt7r/3lczy1291317431.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/02/t1291317371xtdyw78s6qflt7r/3lczy1291317431.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/02/t1291317371xtdyw78s6qflt7r/4lczy1291317431.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/02/t1291317371xtdyw78s6qflt7r/4lczy1291317431.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/02/t1291317371xtdyw78s6qflt7r/5lczy1291317431.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/02/t1291317371xtdyw78s6qflt7r/5lczy1291317431.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/02/t1291317371xtdyw78s6qflt7r/6emzj1291317431.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/02/t1291317371xtdyw78s6qflt7r/6emzj1291317431.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/02/t1291317371xtdyw78s6qflt7r/7emzj1291317431.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/02/t1291317371xtdyw78s6qflt7r/7emzj1291317431.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/02/t1291317371xtdyw78s6qflt7r/87vgm1291317431.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/02/t1291317371xtdyw78s6qflt7r/87vgm1291317431.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/02/t1291317371xtdyw78s6qflt7r/97vgm1291317431.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/02/t1291317371xtdyw78s6qflt7r/97vgm1291317431.ps (open in new window)


 
Parameters (Session):
par1 = 3 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;
 
Parameters (R input):
par1 = 3 ; 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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