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*The author of this computation has been verified*
R Software Module: /rwasp_multipleregression.wasp (opens new window with default values)
Title produced by software: Multiple Regression
Date of computation: Fri, 03 Dec 2010 14:09:33 +0000
 
Cite this page as follows:
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/03/t1291385488qhr56ckszbzvhoo.htm/, Retrieved Fri, 03 Dec 2010 15:11:40 +0100
 
BibTeX entries for LaTeX users:
@Manual{KEY,
    author = {{YOUR NAME}},
    publisher = {Office for Research Development and Education},
    title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2010/Dec/03/t1291385488qhr56ckszbzvhoo.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 162556 213118 213118 6282929 1 29790 29790 81767 81767 4324047 1 87550 87550 153198 153198 4108272 0 84738 0 -26007 0 -1212617 1 54660 54660 126942 126942 1485329 1 42634 42634 157214 157214 1779876 0 40949 0 129352 0 1367203 1 42312 42312 234817 234817 2519076 1 37704 37704 60448 60448 912684 1 16275 16275 47818 47818 1443586 0 25830 0 245546 0 1220017 0 12679 0 48020 0 984885 1 18014 18014 -1710 -1710 1457425 0 43556 0 32648 0 -572920 1 24524 24524 95350 95350 929144 0 6532 0 151352 0 1151176 0 7123 0 288170 0 790090 1 20813 20813 114337 114337 774497 1 37597 37597 37884 37884 990576 0 17821 0 122844 0 454195 1 12988 12988 82340 82340 876607 1 22330 22330 79801 79801 711969 0 13326 0 165548 0 702380 0 16189 0 116384 0 264449 0 7146 0 134028 0 450033 0 15824 0 63838 0 541063 1 26088 26088 74996 74996 588864 0 11326 0 31080 0 -37216 0 8568 0 32168 0 783310 0 14416 0 49857 0 467359 1 3369 3369 87161 87161 688779 1 11819 11819 106113 106113 608419 1 6620 6620 80570 80570 etc...
 
Output produced by software:

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


Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time37 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135


Multiple Linear Regression - Estimated Regression Equation
Wealth[t] = + 117378.942798075 + 45851.7248741234Group[t] -7.64971774851714Costs[t] + 43.284843657262GrCosts[t] + 3.42410064392434Dividends[t] -1.61331277750999GrDiv[t] + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0		2-tail p-value1-tail p-value
(Intercept)117378.94279807531052.1760383.78010.0001799e-05
Group45851.724874123455610.0300350.82450.4101050.205053
Costs-7.649717748517141.720886-4.44521.1e-056e-06
GrCosts43.2848436572622.06466320.964600
Dividends3.424100643924340.416838.214600
GrDiv-1.613312777509990.700046-2.30460.0216710.010836


Multiple Linear Regression - Regression Statistics
Multiple R0.884401241167263
R-squared0.782165555378196
Adjusted R-squared0.779602797206175
F-TEST (value)305.204589304386
F-TEST (DF numerator)5
F-TEST (DF denominator)425
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation210046.470857090
Sum Squared Residuals18750795965795.4


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast		Residuals
Prediction Error
162829296341845.68340867-58916.6834086667
243240471372863.759966842951183.24003316
341082723560495.02054174547776.979458262
4-1212617-619893.425222303-592723.574777697
514853292340911.68318257-855582.683182568
617798761967179.82929611-187303.829296107
71367203247044.9172069471120158.08279305
825190762096227.88955083422848.110449168
99126841616275.95988453-703591.95988453
101443586829780.596033225613805.403966775
111220017760560.95006692459456.04993308
12984885184813.484385875800071.515614125
131457425802065.378540761655359.621459239
14-572920-104022.125633494-468897.874366506
159291441209805.11852087-280661.118520868
161151176585655.467123997565520.532876003
177900901049613.08583506-259523.08583506
187744971111944.59549313-337447.595493126
199905761571604.38399452-581028.38399452
20454195401683.54230399352511.4576960074
21876607775159.955895538101447.044104462
227119691103465.71174221-391496.711742205
23702380582291.817481721120088.182518279
24264449392048.191509821-127599.191509821
25450033521639.420871063-71606.4208710627
26541063214917.546052383326145.453947617
275888641228681.67920915-639817.679209147
28-37216137159.287591541-174375.287591541
29783310161982.630642541621327.369357459
30467359177815.997539590289543.00246041
31688779441115.488083306247663.511916694
32608419776550.353656484-168131.353656484
33696348545030.379585098151317.620414902
34597793509199.75566285388593.2443371474
358217301133345.01064902-311615.010649018
36377934325714.89113193152219.1088680687
37651939341676.870346026310262.129653974
38697458557051.686371953140406.313628047
39700368594777.015891598105590.984108402
40225986359509.169067098-133523.169067098
41348695497691.186968637-148996.186968637
42373683342687.77362913230995.2263708677
43501709403982.27549322297726.724506778
44413743467233.339257499-53490.3392574994
45379825318783.42549110361041.5745088973
46336260477729.501114898-141469.501114898
47636765589603.08140190547161.9185980948
48481231678172.820150094-196941.820150094
49469107497354.026619848-28247.0266198481
50211928361518.548958215-149590.548958215
51563925471572.9691760392352.0308239699
52511939555136.402283627-43197.4022836267
53521016764841.496610689-243825.496610689
54543856468407.05912836275448.940871638
55329304612802.950338557-283498.950338557
56423262309203.741989082114058.258010918
57509665261111.268098225248553.731901775
58455881376654.41725583479226.5827441664
59367772448209.40445462-80437.4044546199
60406339653896.751517142-247557.751517142
61493408532397.032489894-38989.0324898943
62232942312252.469523722-79310.4695237223
63416002445910.818072751-29908.8180727515
64337430573227.073835692-235797.073835692
65361517298996.09552327662520.9044767238
66360962327004.87086398233957.1291360179
67235561387283.706302673-151722.706302673
68408247418234.331071785-9987.33107178523
69450296555440.12475297-105144.124752970
70418799488619.924417398-69820.924417398
71247405321228.458453434-73823.4584534344
72378519211893.502681580166625.497318420
73326638472417.19402580-145779.194025801
74328233384620.818718939-56387.8187189391
75386225509331.258895123-123106.258895123
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80420383400399.41655382119983.5834461786
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82431809490645.449047491-58836.4490474913
83418876586528.480637183-167652.480637183
84297476246832.06056628650643.9394337136
85416776465187.726522466-48411.7265224657
86357257482389.00609537-125132.006095370
87458343398584.84307987559758.1569201247
88388386469217.598156251-80831.5981562507
89358934466368.978993356-107434.978993356
90407560466905.233881027-59345.2338810273
91392558429248.098210908-36690.0982109077
92373177418438.400466441-45261.4004664406
93428370317892.960959748110477.039040252
94369419625842.033360679-256423.033360679
95358649231424.850835677127224.149164323
96376641381190.513911284-4549.5139112838
97467427502204.471830709-34777.4718307095
98364885340707.07132359324177.9286764068
99436230543377.524291191-107147.524291191
100329118345101.745170722-15983.7451707225
101317365345992.869107392-28627.8691073925
102286849419917.995690318-133068.995690318
103376685463073.006608835-86388.0066088353
104407198502501.818728406-95303.8187284063
105377772342610.42925354035161.5707464604
106271483356704.319537552-85221.3195375524
107153661385319.238408354-231658.238408353
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109324881422962.596135533-98081.5961355332
110264512364181.948934291-99669.9489342907
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113191521372980.971579404-181459.971579403
114268673382682.582347455-114009.582347455
115353179316902.48351426736276.5164857329
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117363713405318.069990302-41605.0699903019
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119211742382632.362239527-170890.362239527
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320325560325290.333897163269.666102837287
321325560325290.333897163269.666102837287
322325560325290.333897163269.666102837287
323325560325290.333897163269.666102837287
324325560273181.70692088352378.2930791175
325325560325290.333897163269.666102837287
326322649325128.888307983-2479.88830798322
327325560273181.70692088352378.2930791175
328325560273181.70692088352378.2930791175
329325560325290.333897163269.666102837287
330325560325290.333897163269.666102837287
331325560325290.333897163269.666102837287
332325560325290.333897163269.666102837287
333325560325290.333897163269.666102837287
334324598323388.3426737271209.65732627314
335325567325306.652883922260.347116078348
336325560325290.333897163269.666102837287
337324005325372.647391537-1367.64739153727
338325560325290.333897163269.666102837287
339325748325694.08294903253.9170509680662
340323385320957.9559436892427.04405631133
341315409330665.622049799-15256.6220497993
342325560325290.333897163269.666102837287
343325560325290.333897163269.666102837287
344325560325290.333897163269.666102837287
345325560325290.333897163269.666102837287
346325560325290.333897163269.666102837287
347312275318894.608253522-6619.60825352243
348325560325290.333897163269.666102837287
349325560325290.333897163269.666102837287
350325560325290.333897163269.666102837287
351320576315637.6803932184938.31960678204
352325246326214.687492397-968.687492397123
353332961316947.83635436816013.1636456317
354323010328863.037367191-5853.03736719108
355325560325290.333897163269.666102837287
356325560325290.333897163269.666102837287
357345253383197.636603698-37944.636603698
358325560325290.333897163269.666102837287
359325560325290.333897163269.666102837287
360325560325290.333897163269.666102837287
361325559325289.532380702269.467619297950
362325560325290.333897163269.666102837287
363325560325290.333897163269.666102837287
364319634276842.03754603442791.9624539657
365319951320198.235503772-247.235503771724
366325560325290.333897163269.666102837287
367325560325290.333897163269.666102837287
368325560325290.333897163269.666102837287
369325560325290.333897163269.666102837287
370325560325290.333897163269.666102837287
371325560325290.333897163269.666102837287
372318519318648.029841182-129.029841182088
373343222378079.2266221-34857.2266221001
374317234337998.095649010-20764.0956490104
375325560325290.333897163269.666102837287
376325560325290.333897163269.666102837287
377314025308812.4529248885212.54707511214
378320249319674.510640938574.489359061681
379325560325290.333897163269.666102837287
380325560325290.333897163269.666102837287
381325560325290.333897163269.666102837287
382349365364766.574976658-15401.5749766584
383289197255032.37637172434164.6236282761
384325560325290.333897163269.666102837287
385329245331473.375187749-2228.37518774851
386240869330506.515382663-89637.5153826634
387327182320662.0982901916519.9017098089
388322876311039.0330630411836.9669369596
389323117323636.993811926-519.993811925833
390306351313587.119967013-7236.11996701289
391335137329067.3562324116069.6437675892
392308271317071.340512056-8800.34051205557
393301731321319.752605688-19588.7526056876
394382409345114.32850609637294.6714939037
395279230436699.055299222-157469.055299222
396298731313239.028664651-14508.0286646514
397243650260595.459734906-16945.4597349065
398532682434035.11736964098646.8826303597
399319771332029.550236559-12258.5502365587
400171493277019.301336761-105526.301336761
401347262350370.639108832-3108.63910883223
402343945331372.74618448812572.2538155123
403311874315377.482367615-3503.48236761452
404302211343189.819132649-40978.8191326494
405316708332917.258275972-16209.2582759719
406333463350400.347340917-16937.3473409166
407344282345484.432366322-1202.43236632216
408319635311595.6228912558039.37710874529
409301186313721.915977894-12535.9159778938
410300381351443.810774478-51062.8107744784
411318765346629.303858245-27864.3038582449
412286146503734.387549593-217588.387549593
413306844308504.314732853-1660.31473285256
414307705417408.5056205-109703.505620500
415312448378871.501494073-66423.5014940729
416299715361634.121492757-61919.1214927571
417373399213171.009507239160227.990492761
418299446316461.457838246-17015.4578382464
419325586344632.110420888-19046.1104208877
420291221338039.193813799-46818.1938137993
421261173348529.28064543-87356.2806454298
422255027344497.052623647-89470.0526236465
423-78375547694.489631214-626069.489631214
424-58143258624.42372155-316767.42372155
425227033288981.310743316-61948.3107433156
426235098443590.561339799-208492.561339799
42721267262279.727724167-241012.727724167
428238675383401.098800031-144726.098800031
429197687318853.99638722-121166.996387220
430418341265990.19704717152350.80295283
431-29770672548.755897959-370254.755897959


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
913.92833764380399e-861.96416882190199e-86
1017.94029038552048e-923.97014519276024e-92
1111.74208604088542e-948.71043020442709e-95
1211.3827434295842e-1056.913717147921e-106
1312.44895699319538e-1201.22447849659769e-120
1413.57720897299937e-1291.78860448649968e-129
1511.42652836228758e-1327.1326418114379e-133
1612.81312699785080e-1431.40656349892540e-143
1718.84725154668854e-1484.42362577334427e-148
1811.49639738546778e-1497.48198692733888e-150
1913.04628553497649e-1551.52314276748824e-155
2016.49594255389204e-1553.24797127694602e-155
2114.10829470806273e-1592.05414735403137e-159
2211.39063052020980e-1616.95315260104901e-162
2311.04723017877108e-1625.23615089385538e-163
2416.33840705783347e-1633.16920352891674e-163
2511.27048585632586e-1626.3524292816293e-163
2611.95961922902115e-1649.79809614510577e-165
2711.17359963400185e-1675.86799817000925e-168
2819.01065542797597e-1704.50532771398799e-170
2911.83476575941465e-1829.17382879707324e-183
3011.40518216935902e-1847.02591084679509e-185
3113.35945039652713e-1881.67972519826357e-188
3211.03415139656564e-1895.17075698282818e-190
3315.41673588023668e-1962.70836794011834e-196
3412.34589563788228e-1971.17294781894114e-197
3511.13054926493599e-1975.65274632467995e-198
3612.42128394667476e-1971.21064197333738e-197
3711.79295746875151e-2048.96478734375753e-205
3812.21354424462557e-2091.10677212231279e-209
3911.27677148309385e-2086.38385741546925e-209
4014.13845490643105e-2092.06922745321552e-209
4111.02531976733122e-2085.12659883665611e-209
4211.99133053214681e-2089.95665266073403e-209
4314.28917590770755e-2092.14458795385378e-209
4412.47312744567090e-2081.23656372283545e-208
4517.9435015672914e-2083.9717507836457e-208
4613.09518759971784e-2071.54759379985892e-207
4712.24946700599617e-2061.12473350299808e-206
4819.18808320712711e-2064.59404160356356e-206
4913.33063409294644e-2051.66531704647322e-205
5019.45654825592594e-2064.72827412796297e-206
5111.35795577224985e-2066.78977886124923e-207
5218.64376872547342e-2064.32188436273671e-206
5313.85181575694426e-2051.92590787847213e-205
5414.0924627653063e-2042.04623138265315e-204
5518.49543691754488e-2074.24771845877244e-207
5616.14482363869259e-2073.07241181934630e-207
5714.07678096509960e-2112.03839048254980e-211
5811.22919064623945e-2116.14595323119723e-212
5917.84221651520046e-2113.92110825760023e-211
6012.66236318044644e-2111.33118159022322e-211
6112.67289035616298e-2121.33644517808149e-212
6215.68903875654441e-2122.84451937827220e-212
6314.34462305324357e-2112.17231152662178e-211
6411.04355652697190e-2105.21778263485948e-211
6514.10300227066453e-2102.05150113533227e-210
6611.92298478539255e-2109.61492392696277e-211
6713.73583766899738e-2111.86791883449869e-211
6814.2475570907537e-2102.12377854537685e-210
6913.21674578521865e-2091.60837289260932e-209
7011.92292033921847e-2089.61460169609233e-209
7117.49586818391606e-2083.74793409195803e-208
7211.91994672506728e-2099.59973362533642e-210
7312.19257505909180e-2091.09628752954590e-209
7411.56689888182729e-2087.83449440913646e-209
7516.52326861652502e-2083.26163430826251e-208
7612.36897880092744e-2071.18448940046372e-207
7715.07772655061936e-2072.53886327530968e-207
7819.8153832724462e-2074.9076916362231e-207
7917.87103879481652e-2063.93551939740826e-206
8014.15404253470707e-2052.07702126735353e-205
8113.18050061446333e-2041.59025030723166e-204
8212.82882190668061e-2041.41441095334031e-204
8312.17222379092400e-2041.08611189546200e-204
8411.60165498505322e-2038.00827492526611e-204
8511.50296333137186e-2027.51481665685932e-203
8612.54678697779299e-2031.27339348889650e-203
8711.84528092230125e-2039.22640461150623e-204
8811.05118463601952e-2025.25592318009758e-203
8913.33244811237200e-2021.66622405618600e-202
9012.67388767329107e-2011.33694383664553e-201
9112.67214640140270e-2001.33607320070135e-200
9211.67545265067596e-1998.3772632533798e-200
9312.69408192890323e-2001.34704096445162e-200
9411.58380011190825e-1997.91900055954124e-200
9512.22216224262446e-2001.11108112131223e-200
9617.11429813632744e-2013.55714906816372e-201
9717.0867673184876e-2003.5433836592438e-200
9814.43736185881883e-1992.21868092940941e-199
9911.42696218889631e-1987.13481094448154e-199
10011.47026707243148e-1977.35133536215738e-198
10111.27979733938605e-1966.39898669693027e-197
10212.26493655111729e-1971.13246827555865e-197
10318.53578631477292e-1974.26789315738646e-197
10417.15905085322211e-1973.57952542661105e-197
10514.1777786137542e-1962.0888893068771e-196
10615.93846357288015e-1962.96923178644007e-196
10711.40975593034603e-1967.04877965173016e-197
10818.48537848853565e-1984.24268924426783e-198
10911.86757475252504e-1979.33787376262521e-198
11017.6531001465592e-1973.8265500732796e-197
11118.89445567306155e-1974.44722783653078e-197
11212.89208145251203e-1971.44604072625601e-197
11311.08578432015332e-1995.42892160076661e-200
11415.2699020370746e-1992.6349510185373e-199
11511.54451885505248e-1987.72259427526238e-199
11613.20614508883431e-1981.60307254441716e-198
11711.42660034654418e-1977.13300173272092e-198
11815.06990682949091e-1972.53495341474546e-197
11914.2545881430592e-1982.1272940715296e-198
12013.62987762187280e-1971.81493881093640e-197
12119.97685201330917e-1974.98842600665459e-197
12219.43263951720592e-1964.71631975860296e-196
12313.55134161372766e-1951.77567080686383e-195
12416.58501514631263e-1953.29250757315632e-195
12516.50245974529645e-1943.25122987264822e-194
12613.58392362142005e-1941.79196181071002e-194
12713.70806538826817e-1931.85403269413408e-193
12813.81015525100784e-1921.90507762550392e-192
12913.59994921617312e-1911.79997460808656e-191
13013.66313301757618e-1901.83156650878809e-190
13113.70214428100818e-1891.85107214050409e-189
13211.32966694814989e-1896.64833474074947e-190
13311.34476547358931e-1886.72382736794656e-189
13411.35395898902119e-1876.76979494510594e-188
13511.35442157300025e-1866.77210786500126e-187
13611.26422755259308e-1856.32113776296538e-186
13711.24882191654396e-1846.24410958271979e-185
13811.22908681988304e-1836.14543409941522e-184
13911.20312445093368e-1826.01562225466839e-183
14011.17136133765868e-1815.8568066882934e-182
14111.08462049021763e-1805.42310245108813e-181
14211.0447441885018e-1795.22372094250901e-180
14316.80547844434632e-1793.40273922217316e-179
14416.4891040712983e-1783.24455203564915e-178
14515.40475545020984e-1772.70237772510492e-177
14614.19196954598017e-1762.09598477299008e-176
14713.93875667972153e-1751.96937833986076e-175
14813.68420094769676e-1741.84210047384838e-174
14913.42538242972882e-1731.71269121486441e-173
15013.17086487691716e-1721.58543243845858e-172
15112.80237843586953e-1711.40118921793477e-171
15211.83895342020671e-1709.19476710103353e-171
15311.67608810549504e-1698.3804405274752e-170
15411.50893175701004e-1687.54465878505019e-169
15511.36255515087569e-1676.81277575437843e-168
15611.22291656986700e-1666.11458284933501e-167
15711.09194613376645e-1655.45973066883226e-166
15819.70564784747863e-1654.85282392373932e-165
15917.15710414942425e-1643.57855207471213e-164
16016.2958114895328e-1633.1479057447664e-163
16115.50997892599803e-1622.75498946299901e-162
16214.79774488040333e-1612.39887244020166e-161
16314.15641027765646e-1602.07820513882823e-160
16413.29873124339075e-1591.64936562169537e-159
16512.83048450888616e-1581.41524225444308e-158
16612.41577449011009e-1571.20788724505504e-157
16712.05147083472251e-1561.02573541736125e-156
16813.19761958519746e-1581.59880979259873e-158
16912.75068868644462e-1571.37534434322231e-157
17012.3544238317732e-1561.1772119158866e-156
17112.00521286770221e-1551.00260643385111e-155
17211.70796805799498e-1548.53984028997489e-155
17311.44029933043121e-1537.20149665215606e-154
17411.20386937176148e-1526.0193468588074e-153
17511.00517879480124e-1515.02589397400619e-152
17618.35232143937408e-1514.17616071968704e-151
17716.90524301616076e-1503.45262150808038e-150
17815.52265949235075e-1492.76132974617538e-149
17914.52179844345432e-1482.26089922172716e-148
18013.68417215047486e-1471.84208607523743e-147
18111.96925625371787e-1469.84628126858933e-147
18211.55445939980537e-1457.77229699902686e-146
18317.3988600103533e-1453.69943000517665e-145
18413.16339722505635e-1441.58169861252817e-144
18512.46881841025928e-1431.23440920512964e-143
18611.85812752355633e-1429.29063761778165e-143
18711.06114657499803e-1415.30573287499016e-142
18818.3843527896971e-1414.19217639484855e-141
18914.84931412598235e-1402.42465706299117e-140
19013.79923229017154e-1391.89961614508577e-139
19112.64295809611659e-1381.32147904805830e-138
19212.05116087895767e-1371.02558043947884e-137
19311.55277205659262e-1367.76386028296311e-137
19411.19350134434147e-1355.96750672170735e-136
19519.13310457855897e-1354.56655228927948e-135
19616.82827879974384e-1343.41413939987192e-134
19714.66167498612605e-1332.33083749306303e-133
19813.45844496776764e-1321.72922248388382e-132
19912.55723618731036e-1311.27861809365518e-131
20018.33268571773434e-1314.16634285886717e-131
20116.1351469212381e-1303.06757346061905e-130
20214.50109677768382e-1292.25054838884191e-129
20313.29025415777602e-1281.64512707888801e-128
20412.21159266857053e-1271.10579633428527e-127
20516.13575850540114e-1273.06787925270057e-127
20614.44629170065137e-1262.22314585032568e-126
20713.07386087145359e-1251.53693043572680e-125
20812.21298789364365e-1241.10649394682183e-124
20911.85155854867805e-1249.25779274339026e-125
21011.33685484882370e-1236.68427424411852e-124
21119.67499540896726e-1234.83749770448363e-123
21216.96860813015444e-1223.48430406507722e-122
21314.52372402654648e-1212.26186201327324e-121
21413.18990256392253e-1201.59495128196126e-120
21512.27037149971865e-1191.13518574985932e-119
21611.60521914088682e-1188.02609570443412e-119
21711.12831977285422e-1175.64159886427109e-118
21817.5889948654514e-1173.7944974327257e-117
21915.28965301909934e-1162.64482650954967e-116
22011.89971327182454e-1159.49856635912268e-116
22111.21558203552666e-1146.07791017763332e-115
22218.37983312479161e-1144.18991656239580e-114
22315.74721888387015e-1132.87360944193508e-113
22413.92423722311032e-1121.96211861155516e-112
22512.66541216429678e-1111.33270608214839e-111
22611.77431729403285e-1108.87158647016424e-111
22711.19424227519097e-1095.97121137595487e-110
22817.99966283748475e-1093.99983141874237e-109
22914.93072830693738e-1082.46536415346869e-108
23013.27423817028686e-1071.63711908514343e-107
23112.13414364888729e-1061.06707182444365e-106
23211.40414271001770e-1057.02071355008852e-106
23319.19410881245868e-1054.59705440622934e-105
23415.74195942376196e-1042.87097971188098e-104
23513.72391038182996e-1031.86195519091498e-103
23612.40448221491051e-1021.20224110745526e-102
23711.54443011882836e-1017.72215059414178e-102
23819.77509818225739e-1014.88754909112869e-101
23916.21817987987248e-1003.10908993993624e-100
24013.93641321774186e-991.96820660887093e-99
24112.47988032146665e-981.23994016073333e-98
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35815.21072562641593e-222.60536281320797e-22
35911.70269947431331e-218.51349737156654e-22
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3720.9999999999999983.50169380759046e-151.75084690379523e-15
3730.9999999999999968.91466492115593e-154.45733246057797e-15
3740.9999999999999872.55135678217259e-141.27567839108630e-14
3750.9999999999999647.1754771525139e-143.58773857625695e-14
3760.99999999999991.99564466313458e-139.97822331567288e-14
3770.9999999999997375.26376846402203e-132.63188423201102e-13
3780.9999999999992961.40863935595096e-127.0431967797548e-13
3790.9999999999981083.78499966539778e-121.89249983269889e-12
3800.9999999999949761.00488793155573e-115.02443965777863e-12
3810.9999999999868232.63543987456554e-111.31771993728277e-11
3820.9999999999654976.9005707828743e-113.45028539143715e-11
3830.9999999999454521.09095245481633e-105.45476227408165e-11
3840.9999999998609342.78131638779340e-101.39065819389670e-10
3850.9999999996458337.08333596106056e-103.54166798053028e-10
3860.9999999992681671.46366530417025e-097.31832652085124e-10
3870.9999999982355443.52891245574458e-091.76445622787229e-09
3880.999999996047977.90405959140312e-093.95202979570156e-09
3890.9999999904957041.90085916786386e-089.5042958393193e-09
3900.999999977539674.49206603206504e-082.24603301603252e-08
3910.9999999483337361.03332527936949e-075.16662639684747e-08
3920.999999880443422.39113160308251e-071.19556580154125e-07
3930.9999997217727535.56454492998334e-072.78227246499167e-07
3940.9999994481187011.10376259744689e-065.51881298723443e-07
3950.9999989889295272.02214094585892e-061.01107047292946e-06
3960.9999977695600364.46087992878254e-062.23043996439127e-06
3970.9999959507713888.09845722335485e-064.04922861167742e-06
3980.999991588337481.68233250379194e-058.41166251895972e-06
3990.9999819929860863.60140278279708e-051.80070139139854e-05
4000.9999622261447877.55477104252666e-053.77738552126333e-05
4010.9999221609365550.0001556781268898897.78390634449444e-05
4020.9998525437029960.0002949125940075310.000147456297003765
4030.9997201319686340.0005597360627324910.000279868031366246
4040.9994491934083840.001101613183232250.000550806591616127
4050.998947619832030.00210476033594010.00105238016797005
4060.9980163293596060.003967341280787970.00198367064039398
4070.9964359616400430.00712807671991470.00356403835995735
4080.9942112143712010.01157757125759750.00578878562879876
4090.9902445419662060.01951091606758840.00975545803379418
4100.9830383310660230.03392333786795320.0169616689339766
4110.9715885698201570.05682286035968580.0284114301798429
4120.9566296104784570.08674077904308520.0433703895215426
4130.9306207648119990.1387584703760030.0693792351880013
4140.893387510640560.2132249787188800.106612489359440
4150.842503794508510.314992410982980.15749620549149
4160.7738484282860070.4523031434279860.226151571713993
4170.9108151391351060.1783697217297870.0891848608648935
4180.850871274351720.298257451296560.14912872564828
4190.7709301133691980.4581397732616030.229069886630802
4200.6587238687716490.6825522624567030.341276131228351
4210.5139630533789270.9720738932421460.486036946621073
4220.3521062745046260.7042125490092510.647893725495374


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level3990.963768115942029NOK
5% type I error level4020.971014492753623NOK
10% type I error level4040.97584541062802NOK
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Dec/03/t1291385488qhr56ckszbzvhoo/100grg1291385334.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/03/t1291385488qhr56ckszbzvhoo/100grg1291385334.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/03/t1291385488qhr56ckszbzvhoo/1txc41291385334.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/03/t1291385488qhr56ckszbzvhoo/1txc41291385334.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/03/t1291385488qhr56ckszbzvhoo/24ob71291385334.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/03/t1291385488qhr56ckszbzvhoo/24ob71291385334.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/03/t1291385488qhr56ckszbzvhoo/34ob71291385334.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/03/t1291385488qhr56ckszbzvhoo/34ob71291385334.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/03/t1291385488qhr56ckszbzvhoo/44ob71291385334.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/03/t1291385488qhr56ckszbzvhoo/44ob71291385334.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/03/t1291385488qhr56ckszbzvhoo/54ob71291385334.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/03/t1291385488qhr56ckszbzvhoo/54ob71291385334.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/03/t1291385488qhr56ckszbzvhoo/6egss1291385334.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/03/t1291385488qhr56ckszbzvhoo/6egss1291385334.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/03/t1291385488qhr56ckszbzvhoo/7779u1291385334.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/03/t1291385488qhr56ckszbzvhoo/7779u1291385334.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/03/t1291385488qhr56ckszbzvhoo/8779u1291385334.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/03/t1291385488qhr56ckszbzvhoo/8779u1291385334.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/03/t1291385488qhr56ckszbzvhoo/90grg1291385334.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/03/t1291385488qhr56ckszbzvhoo/90grg1291385334.ps (open in new window)


 
Parameters (Session):
par1 = 6 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;
 
Parameters (R input):
par1 = 6 ; 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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