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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: Wed, 24 Nov 2010 09:26:31 +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/Nov/24/t1290590839obzh0zfzzpmrqsk.htm/, Retrieved Wed, 24 Nov 2010 10:27:19 +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/Nov/24/t1290590839obzh0zfzzpmrqsk.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 12988 12988 119 119 82340 82340 9798460 876607 1 22330 22330 84 84 79801 79801 6703284 711969 0 13326 0 102 0 165548 0 16885896 702380 0 16189 0 295 0 116384 0 34333280 264449 0 7146 0 105 0 134028 0 14072940 450033 0 15824 0 64 0 63838 0 4085632 541063 1 26088 26088 267 267 74996 74996 20023932 588864 0 11326 0 129 0 31080 0 4009320 -37216 0 8568 0 37 0 32168 0 1190216 783310 0 14416 0 361 0 49857 0 17998377 467359 1 3369 3369 28 28 87161 87161 2440508 688779 1 11819 11819 85 85 106113 106113 9019605 608419 1 6620 6620 44 44 80570 80570 3545080 696348 1 4519 4519 49 49 102129 102129 5004321 597793 0 2220 0 22 0 301670 0 6636740 821730 0 18562 0 155 0 102313 0 15858515 377934 0 10327 0 91 0 88577 0 8060507 651939 1 5336 5336 81 81 112477 112477 9110637 697458 1 2365 2365 79 79 191778 191778 15150462 700368 0 4069 0 145 0 79804 0 11571580 225986 0 7710 0 816 0 128294 0 104687904 348695 0 13718 0 61 0 96448 0 5883328 373683 0 4525 0 226 0 93811 0 21201286 501709 0 6869 0 105 0 117520 0 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 time20 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24


Multiple Linear Regression - Estimated Regression Equation
Wealth[t] = + 226349.138797431 -50821.1974975865Group[t] + 6.20346656275413Costs[t] + 9.17566214553181GrCosts[t] + 38.3006672833682Trades[t] -183.754063543057GrTrades[t] + 1.62413093912172Dividends[t] + 0.661264008469915GrDiv[t] -0.00180664113731287TrDiv[t] + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0		2-tail p-value1-tail p-value
(Intercept)226349.13879743113699.46111716.522500
Group-50821.197497586521765.013359-2.3350.0200620.010031
Costs6.203466562754131.7938723.45810.0006050.000303
GrCosts9.175662145531812.642123.47280.0005740.000287
Trades38.3006672833682189.5504880.20210.8399770.419989
GrTrades-183.754063543057163.342466-1.1250.2613130.130657
Dividends1.624130939121720.1987058.173600
GrDiv0.6612640084699150.298872.21250.0275210.013761
TrDiv-0.001806641137312870.001754-1.02980.3037550.151878


Multiple Linear Regression - Regression Statistics
Multiple R0.69231711498078
R-squared0.47930298769531
Adjusted R-squared0.468369717095737
F-TEST (value)43.8389394399519
F-TEST (DF numerator)8
F-TEST (DF denominator)381
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation63840.9831089392
Sum Squared Residuals1552830698364.34


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast		Residuals
Prediction Error
1876607528440.229874541348166.770125459
2711969676992.17365332534976.8263466748
3702380551288.076631332151091.923368668
4264449465070.695022312-200621.695022312
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6541063423264.036441119117798.963558881
7588864673122.014447898-84258.0144478984
8-37216344784.974309991-382000.974309991
9783310331012.315858373452297.684141627
10467359378062.54159411789296.4584058834
11688779418055.717701082270723.282298918
12608419571145.24945948137273.7505405189
13696348448667.407477664247680.592522336
14597793462263.095935532135529.904064468
15821730718924.822150179102805.177849821
16377934484953.551762863-107019.551762863
17651939423195.901374566228743.098625434
18697458486403.962919163211054.037080837
19700368611325.78675115989042.2132488413
20225986365851.094011329-139865.094011329
21348695324663.99125771524031.0087422848
22373683459799.752236885-86116.7522368849
23501709377134.007878347124574.992121653
24413743441556.959669342-27813.9596693416
25379825362010.07438638917814.9256136109
26336260456438.300714644-120178.300714644
27636765662540.853051506-25775.8530515057
28481231477260.3686632073970.63133679304
29469107439481.31082427329625.6891757274
30211928361315.172095964-149387.172095964
31563925434363.499440509129561.500559491
32511939488991.68078930722947.3192106925
33521016663246.194180634-142230.194180634
34543856460771.83655162983084.163448371
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311325560324966.369420902593.630579097941
312325560324966.369420902593.630579097941
313325560324966.369420902593.630579097941
314324598324654.160970954-56.1609709537216
315325567324841.119345914725.880654085796
316325560324966.369420902593.630579097941
317324005325299.414446953-1294.41444695317
318325560324966.369420902593.630579097941
319325748325341.790045405406.209954595350
320323385323235.385587905149.614412095111
321315409329372.967960683-13963.9679606828
322325560324966.369420902593.630579097941
323325560324966.369420902593.630579097941
324325560324966.369420902593.630579097941
325325560324966.369420902593.630579097941
326325560324966.369420902593.630579097941
327312275322691.698116563-10416.6981165630
328325560324966.369420902593.630579097941
329325560324966.369420902593.630579097941
330325560324966.369420902593.630579097941
331320576322509.536674533-1933.53667453259
332325246325273.441658135-27.4416581350516
333332961325948.2636511897012.7363488107
334323010327840.636490185-4830.63649018467
335325560324966.369420902593.630579097941
336325560324966.369420902593.630579097941
337345253352077.376875961-6824.37687596067
338325560324966.369420902593.630579097941
339325560324966.369420902593.630579097941
340325560324966.369420902593.630579097941
341325559324690.212365917868.787634083122
342325560324966.369420902593.630579097941
343325560324966.369420902593.630579097941
344319634316430.0320656163203.96793438445
345319951323556.989186908-3605.98918690761
346325560324966.369420902593.630579097941
347325560324966.369420902593.630579097941
348325560324966.369420902593.630579097941
349325560324966.369420902593.630579097941
350325560324966.369420902593.630579097941
351325560324966.369420902593.630579097941
352318519323432.377627327-4913.37762732732
353343222351335.709580818-8113.70958081795
354317234332625.903641983-15391.9036419831
355325560324966.369420902593.630579097941
356325560324966.369420902593.630579097941
357314025316823.558504818-2798.55850481820
358320249327490.879976379-7241.87997637926
359325560324966.369420902593.630579097941
360325560324966.369420902593.630579097941
361325560324966.369420902593.630579097941
362349365343239.7986470416125.2013529595
363289197294324.726193199-5127.72619319882
364325560324966.369420902593.630579097941
365329245327466.4073598401778.59264016049
366240869348544.268132696-107675.268132696
367327182323642.1567784343539.84322156618
368322876326740.656996681-3864.65699668122
369323117324677.598318639-1560.59831863900
370306351323958.59415643-17607.5941564302
371335137329911.2282307925225.77176920755
372308271324941.240168565-16670.2401685649
373301731328695.776968682-26964.7769686822
374382409340515.42168043041893.5783195703
375279230415747.885905395-136517.885905395
376298731323900.676671486-25169.6766714862
377243650340224.948884041-96574.9488840415
378532682431637.203192341101044.796807659
379319771332670.210171421-12899.2101714212
380171493230911.084211786-59418.084211786
381347262346849.627056767412.372943233327
382343945334781.3000332209163.69996677964
383311874325722.691780815-13848.6917808152
384302211350722.27257478-48511.2725747797
385316708333859.801349653-17151.8013496525
386333463347335.514608266-13872.5146082657
387344282339297.5566357214984.44336427939
388319635327444.591826115-7809.59182611475
389301186323047.884439204-21861.8844392043
390300381344245.154403211-43864.1544032113


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
1215.14868987337839e-302.57434493668919e-30
1315.87001697382171e-332.93500848691085e-33
1411.10048750195115e-335.50243750975577e-34
1517.00288559491852e-343.50144279745926e-34
1614.72521363196048e-342.36260681598024e-34
1711.90405326400681e-379.52026632003407e-38
1819.29304580100652e-424.64652290050326e-42
1913.68613699489582e-421.84306849744791e-42
2012.04450287282015e-451.02225143641007e-45
2115.71569740505251e-482.85784870252625e-48
2211.80816066601193e-489.04080333005966e-49
2313.08735242320048e-491.54367621160024e-49
2413.16617563248049e-491.58308781624025e-49
2517.02787389461666e-493.51393694730833e-49
2612.27806769813302e-551.13903384906651e-55
2711.07469038994387e-545.37345194971935e-55
2817.81420633706183e-553.90710316853092e-55
2911.31091057723304e-546.55455288616522e-55
3011.52341842151951e-587.61709210759754e-59
3114.06251876337762e-602.03125938168881e-60
3213.66042474776181e-601.83021237388091e-60
3314.73287699362921e-602.36643849681461e-60
3415.38410497026049e-602.69205248513025e-60
3511.1698502645266e-645.849251322633e-65
3614.85537528983474e-652.42768764491737e-65
3711.50550322680677e-697.52751613403387e-70
3814.93067862123758e-702.46533931061879e-70
3911.24354880662289e-696.21774403311444e-70
4011.68440086105082e-728.4220043052541e-73
4112.01307504049094e-751.00653752024547e-75
4212.14102414386271e-771.07051207193136e-77
4312.56087773892131e-781.28043886946066e-78
4419.3712954404448e-814.6856477202224e-81
4513.45979904728816e-801.72989952364408e-80
4617.6119879799562e-803.8059939899781e-80
4717.13048861846496e-833.56524430923248e-83
4819.25251744477447e-834.62625872238723e-83
4913.03541523551418e-821.51770761775709e-82
5011.60361109394265e-828.01805546971327e-83
5111.0016148058393e-835.0080740291965e-84
5212.54686945007059e-841.27343472503529e-84
5318.92780235498139e-854.46390117749069e-85
5412.96265184634708e-841.48132592317354e-84
5519.69361578281448e-844.84680789140724e-84
5613.99814750556632e-851.99907375278316e-85
5719.57099571309068e-854.78549785654534e-85
5811.33788101393042e-856.68940506965208e-86
5915.88035345917322e-852.94017672958661e-85
6012.926588776258e-851.463294388129e-85
6111.18815051254790e-845.94075256273951e-85
6213.03877842238935e-861.51938921119467e-86
6319.09881863436432e-864.54940931718216e-86
6414.54006972238557e-852.27003486119278e-85
6511.43878375883359e-847.19391879416797e-85
6611.62589805860887e-898.12949029304434e-90
6713.71265258953453e-911.85632629476726e-91
6811.88651360605629e-909.43256803028146e-91
6914.36465951142591e-902.18232975571295e-90
7011.82164490976629e-899.10822454883147e-90
7117.52449586992497e-893.76224793496248e-89
7213.47227375186423e-891.73613687593211e-89
7312.94685638781279e-911.47342819390640e-91
7412.41373197359306e-921.20686598679653e-92
7512.64453652623780e-931.32226826311890e-93
7613.26395078698845e-991.63197539349422e-99
7711.09996145422930e-995.49980727114649e-100
7815.0955758450064e-992.5477879225032e-99
7911.61291236066089e-988.06456180330447e-99
8014.28892955706617e-982.14446477853309e-98
8118.9009456708871e-984.45047283544355e-98
8211.95825240835079e-999.79126204175394e-100
8318.60096241319428e-994.30048120659714e-99
8414.54394298975436e-982.27197149487718e-98
8514.8681763534383e-982.43408817671915e-98
8613.74467114827631e-991.87233557413816e-99
8714.15501589704461e-1022.07750794852231e-102
8814.60883731721625e-1102.30441865860813e-110
8912.58228177735566e-1101.29114088867783e-110
9011.18212159759029e-1105.91060798795144e-111
9111.63384906371792e-1138.16924531858962e-114
9211.72368498324296e-1168.6184249162148e-117
9312.75451119336814e-1311.37725559668407e-131
9414.73039628792045e-1312.36519814396022e-131
9517.8769744505231e-1343.93848722526155e-134
9615.47783006326282e-1342.73891503163141e-134
9713.95472539056333e-1331.97736269528166e-133
9812.69970671785501e-1391.34985335892751e-139
9913.77515126121657e-1451.88757563060829e-145
10012.27519335212856e-1441.13759667606428e-144
10119.52113815957434e-1464.76056907978717e-146
10212.01225277305565e-1451.00612638652782e-145
10311.32307166715681e-1446.61535833578404e-145
10419.32289665077705e-1564.66144832538853e-156
10515.65925547492358e-1552.82962773746179e-155
10619.36568139184236e-1594.68284069592118e-159
10718.43008569595122e-1584.21504284797561e-158
10817.53252628458549e-1573.76626314229274e-157
10916.69948062446007e-1563.34974031223004e-156
11015.90675534649729e-1552.95337767324864e-155
11115.1635669450927e-1542.58178347254635e-154
11215.06026274571263e-1592.53013137285631e-159
11314.59410785899881e-1582.29705392949941e-158
11414.06465343897707e-1572.03232671948854e-157
11513.64148775137202e-1561.82074387568601e-156
11612.78135265485192e-1551.39067632742596e-155
11712.47199441156243e-1541.23599720578121e-154
11812.17335600075367e-1531.08667800037684e-153
11911.89838652149364e-1529.49193260746818e-153
12011.64748876828547e-1518.23744384142734e-152
12111.42722072169124e-1507.1361036084562e-151
12211.22285632796853e-1496.11428163984265e-150
12317.26385441584577e-1493.63192720792289e-149
12416.18075534382638e-1483.09037767191319e-148
12511.45516220394293e-1477.27581101971466e-148
12611.16322387285576e-1465.81611936427882e-147
12719.73205754295385e-1464.86602877147693e-146
12818.06951560048882e-1454.03475780024441e-145
12916.6678902642658e-1443.3339451321329e-144
13015.48907574959031e-1432.74453787479515e-143
13114.39857550204102e-1422.19928775102051e-142
13211.57693008997973e-1417.88465044989863e-142
13311.27458316078377e-1406.37291580391883e-141
13414.11585658913569e-1402.05792829456785e-140
13513.29933515479562e-1391.64966757739781e-139
13612.62729382365211e-1381.31364691182605e-138
13712.07954865928326e-1371.03977432964163e-137
13811.64833050516598e-1368.24165252582992e-137
13915.70073637763127e-1362.85036818881563e-136
14014.45144823397382e-1352.22572411698691e-135
14113.45533165152786e-1341.72766582576393e-134
14212.66627310326256e-1331.33313655163128e-133
14312.04528683582751e-1321.02264341791376e-132
14411.23793742523145e-1316.18968712615724e-132
14519.13704444493437e-1314.56852222246719e-131
14616.89743764644169e-1303.44871882322085e-130
14715.176508995528e-1292.588254497764e-129
14814.77419506834111e-1372.38709753417056e-137
14913.88857420814777e-1361.94428710407389e-136
15013.14906141743279e-1351.57453070871639e-135
15112.53558844259929e-1341.26779422129964e-134
15211.99931981085204e-1339.99659905426018e-134
15311.59155606657060e-1327.95778033285302e-133
15411.22835908631022e-1316.14179543155108e-132
15519.67103582295982e-1314.83551791147991e-131
15617.59099445160833e-1303.79549722580417e-130
15715.90936263239258e-1292.95468131619629e-129
15814.14999780067704e-1282.07499890033852e-128
15913.19605217783599e-1271.59802608891800e-127
16012.44758794231152e-1261.22379397115576e-126
16117.7795767853162e-1303.8897883926581e-130
16218.54565184752816e-1304.27282592376408e-130
16311.42941496104863e-1297.14707480524313e-130
16411.78692912341476e-1298.93464561707381e-130
16511.31141169796117e-1286.55705848980586e-129
16618.15787863294286e-1284.07893931647143e-128
16718.86412828651662e-1294.43206414325831e-129
16817.03595835912961e-1283.51797917956481e-128
16911.17087604134162e-1275.85438020670812e-128
17019.38608089728904e-1274.69304044864452e-127
17115.74342808415441e-1262.87171404207721e-126
17214.56295588125198e-1252.28147794062599e-125
17313.21014716389725e-1241.60507358194863e-124
17412.52524331083573e-1231.26262165541787e-123
17511.98288728706714e-1229.91443643533569e-123
17611.46395189273750e-1217.31975946368748e-122
17717.22719794102684e-1213.61359897051342e-121
17815.32013175981683e-1202.66006587990842e-120
17913.91761183164372e-1191.95880591582186e-119
18015.12470173256921e-1192.56235086628460e-119
18113.76960637172949e-1181.88480318586474e-118
18212.77030355052845e-1171.38515177526422e-117
18312.03290679441074e-1161.01645339720537e-116
18411.28358821805925e-1156.41794109029623e-116
18514.85751891536769e-1152.42875945768385e-115
18613.53273973674001e-1141.76636986837001e-114
18712.45836175566518e-1131.22918087783259e-113
18811.77622160569817e-1128.88110802849087e-113
18911.65349604500236e-1238.26748022501179e-124
19011.38664226728596e-1226.93321133642978e-123
19111.18213831647383e-1215.91069158236913e-122
19211.00239712195128e-1205.01198560975642e-121
19317.84906909984842e-1203.92453454992421e-120
19413.6137144452681e-1191.80685722263405e-119
19512.96119390817877e-1181.48059695408939e-118
19612.46712686272112e-1171.23356343136056e-117
19712.04591269597794e-1161.02295634798897e-116
19811.50359778530735e-1157.51798892653673e-116
19911.23359191157576e-1146.16795955787878e-115
20011.89029556112618e-1159.4514778056309e-116
20111.28443831671488e-1156.4221915835744e-116
20211.07549723883901e-1145.37748619419505e-115
20318.95556079434729e-1144.47778039717365e-114
20417.41840795827383e-1133.70920397913692e-113
20516.11821954085444e-1123.05910977042722e-112
20614.7666270843514e-1112.3833135421757e-111
20713.88664464789988e-1101.94332232394994e-110
20813.15205324360649e-1091.57602662180325e-109
20911.07324214646481e-1085.36621073232403e-109
21018.6506123155223e-1084.32530615776115e-108
21115.07659940459581e-1072.53829970229790e-107
21214.05429643834074e-1062.02714821917037e-106
21313.2203208932597e-1051.61016044662985e-105
21411.84639034523619e-1049.23195172618095e-105
21511.45407281158082e-1037.2703640579041e-104
21611.13784356873722e-1025.6892178436861e-103
21718.86360073259852e-1024.43180036629926e-102
21816.86482304374865e-1013.43241152187432e-101
21915.28997561541721e-1002.64498780770860e-100
22014.05415094816777e-992.02707547408389e-99
22113.0900425615297e-981.54502128076485e-98
22212.08388286792048e-971.04194143396024e-97
22311.57272770580504e-967.86363852902518e-97
22411.18297628839845e-955.91488144199227e-96
22514.1814713224685e-962.09073566123425e-96
22613.1186127660785e-951.55930638303925e-95
22712.31613094707011e-941.15806547353505e-94
22811.39341575262653e-936.96707876313263e-94
22911.02631935903414e-925.13159679517068e-93
23017.52558965487548e-923.76279482743774e-92
23115.44610999467807e-912.72305499733904e-91
23213.95404082508161e-901.97702041254080e-90
23311.55180287685341e-897.75901438426703e-90
23418.53770185934944e-894.26885092967472e-89
23511.67113962976412e-888.35569814882058e-89
23611.21810929952201e-876.09054649761007e-88
23718.24677592486772e-884.12338796243386e-88
23812.66442759882197e-871.33221379941099e-87
23911.93587064629506e-869.6793532314753e-87
24011.41422112516889e-857.07110562584445e-86
24111.01679466948114e-845.08397334740568e-85
24217.27417607677708e-843.63708803838854e-84
24315.1879465627498e-832.5939732813749e-83
24412.4515324161854e-821.2257662080927e-82
24511.73076850351599e-818.65384251757996e-82
24611.22619580939352e-806.1309790469676e-81
24718.56315155038882e-804.28157577519441e-80
24817.92982464601553e-813.96491232300777e-81
24915.66466405980828e-802.83233202990414e-80
25013.94359260772846e-791.97179630386423e-79
25112.78653345820859e-781.39326672910429e-78
25211.95834606225553e-779.79173031127766e-78
25311.36881209227834e-766.84406046139172e-77
25419.24656484081706e-764.62328242040853e-76
25516.43021874376486e-753.21510937188243e-75
25613.59345798500840e-741.79672899250420e-74
25711.78165209227370e-738.90826046136849e-74
25811.22255928410540e-726.11279642052699e-73
25911.50532820517700e-737.52664102588498e-74
26013.65366760933527e-731.82683380466763e-73
26112.55392236138256e-721.27696118069128e-72
26211.78559158559228e-718.9279579279614e-72
26311.21744137059403e-706.08720685297014e-71
26418.40866326033359e-704.20433163016679e-70
26513.20191619436521e-691.60095809718261e-69
26612.19535177036121e-681.09767588518060e-68
26711.48768916657256e-677.43844583286278e-68
26811.00799922122507e-665.03999610612536e-67
26916.74749957390574e-663.37374978695287e-66
27014.15254678561739e-652.07627339280870e-65
27112.74759924586826e-641.37379962293413e-64
27211.54501521346188e-637.72507606730941e-64
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3570.999999995845148.3097198849377e-094.15485994246885e-09
3580.9999999865222232.69555548802224e-081.34777774401112e-08
3590.999999956497038.70059388041772e-084.35029694020886e-08
3600.9999998628018522.74396296732014e-071.37198148366007e-07
3610.9999995776729118.44654177606847e-074.22327088803423e-07
3620.9999998364362973.27127405285515e-071.63563702642758e-07
3630.9999996136389457.72722111050408e-073.86361055525204e-07
3640.999998766605982.46678803867387e-061.23339401933694e-06
3650.999996067772147.86445571863287e-063.93222785931643e-06
3660.9999990455898331.90882033318555e-069.54410166592774e-07
3670.9999971272744885.74545102497988e-062.87272551248994e-06
3680.9999909232518261.81534963476663e-059.07674817383314e-06
3690.9999710139518845.79720962319169e-052.89860481159585e-05
3700.9999027603071950.0001944793856095059.72396928047526e-05
3710.999745458427720.0005090831445605220.000254541572280261
3720.9992019295551430.001596140889713230.000798070444856615
3730.9980719259770670.003856148045866800.00192807402293340
3740.9998162644334470.0003674711331056230.000183735566552811
3750.999181629909780.001636740180441110.000818370090220553
3760.9965771750271140.006845649945771820.00342282497288591
3770.987169862013670.02566027597265810.0128301379863290
3780.9529134922281470.09417301554370630.0470865077718532


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level3650.994550408719346NOK
5% type I error level3660.997275204359673NOK
10% type I error level3671NOK
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Nov/24/t1290590839obzh0zfzzpmrqsk/10y31m1290590765.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Nov/24/t1290590839obzh0zfzzpmrqsk/10y31m1290590765.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Nov/24/t1290590839obzh0zfzzpmrqsk/19kma1290590765.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Nov/24/t1290590839obzh0zfzzpmrqsk/19kma1290590765.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Nov/24/t1290590839obzh0zfzzpmrqsk/2kuld1290590765.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Nov/24/t1290590839obzh0zfzzpmrqsk/2kuld1290590765.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Nov/24/t1290590839obzh0zfzzpmrqsk/3kuld1290590765.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Nov/24/t1290590839obzh0zfzzpmrqsk/3kuld1290590765.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Nov/24/t1290590839obzh0zfzzpmrqsk/4kuld1290590765.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Nov/24/t1290590839obzh0zfzzpmrqsk/4kuld1290590765.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Nov/24/t1290590839obzh0zfzzpmrqsk/5c32g1290590765.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Nov/24/t1290590839obzh0zfzzpmrqsk/5c32g1290590765.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Nov/24/t1290590839obzh0zfzzpmrqsk/6c32g1290590765.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Nov/24/t1290590839obzh0zfzzpmrqsk/6c32g1290590765.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Nov/24/t1290590839obzh0zfzzpmrqsk/7nu2j1290590765.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Nov/24/t1290590839obzh0zfzzpmrqsk/7nu2j1290590765.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Nov/24/t1290590839obzh0zfzzpmrqsk/8nu2j1290590765.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Nov/24/t1290590839obzh0zfzzpmrqsk/8nu2j1290590765.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Nov/24/t1290590839obzh0zfzzpmrqsk/9y31m1290590765.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Nov/24/t1290590839obzh0zfzzpmrqsk/9y31m1290590765.ps (open in new window)


 
Parameters (Session):
par1 = 9 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;
 
Parameters (R input):
par1 = 9 ; 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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