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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, 01 Dec 2010 17:48:52 +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/01/t1291225796cd5giiixgjs5rfz.htm/, Retrieved Wed, 01 Dec 2010 18:50:07 +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/01/t1291225796cd5giiixgjs5rfz.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 «
162556 1081 807 213118 29790 309 444 81767 87550 458 412 153198 84738 588 428 -26007 54660 302 315 126942 42634 156 168 157214 40949 481 263 129352 45187 353 267 234817 37704 452 228 60448 16275 109 129 47818 25830 115 104 245546 12679 110 122 48020 18014 239 393 -1710 43556 247 190 32648 24811 505 280 95350 6575 159 63 151352 7123 109 102 288170 21950 519 265 114337 37597 248 234 37884 17821 373 277 122844 12988 119 73 82340 22330 84 67 79801 13326 102 103 165548 16189 295 290 116384 7146 105 83 134028 15824 64 56 63838 27664 282 236 74996 11920 182 73 31080 8568 37 34 32168 14416 361 139 49857 3369 28 26 87161 11819 85 70 106113 6984 45 40 80570 4519 49 42 102129 2220 22 12 301670 18562 155 211 102313 10327 91 74 88577 5336 81 80 112477 2365 79 83 191778 4069 145 131 79804 8636 855 203 128294 13718 61 56 96448 4525 226 89 93811 6869 105 88 117520 4628 62 39 69159 3689 25 25 101792 4891 217 49 210568 7489 322 149 136996 4901 84 58 121920 2284 33 41 76403 3160 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 time26 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135


Multiple Linear Regression - Estimated Regression Equation
Costs[t] = -893.592565761601 -2.56981865272106Trades[t] + 143.195500150592Orders[t] -0.00389442142546176Dividends[t] + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0		2-tail p-value1-tail p-value
(Intercept)-893.592565761601686.541643-1.30160.193760.09688
Trades-2.569818652721064.816867-0.53350.5939620.296981
Orders143.1955001505927.38172519.398600
Dividends-0.003894421425461760.009254-0.42080.6740920.337046


Multiple Linear Regression - Regression Statistics
Multiple R0.877324834981777
R-squared0.769698866075802
Adjusted R-squared0.768080825322236
F-TEST (value)475.698071497619
F-TEST (DF numerator)3
F-TEST (DF denominator)427
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation5692.02501260112
Sum Squared Residuals13834436513.7208


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast		Residuals
Prediction Error
1162556111057.23078682351498.769213177
22979061572.7003807152-31782.7003807152
38755056329.358979798631220.6410202014
48473858984.31034890425753.6896510959
55466042942.539103962211717.4608960378
64263422150.102179730820483.8978202692
74094935026.99000165895922.00999834107
84518735517.98363417339669.01636582675
93770430358.01345121717345.98654878286
101627517112.2932767955-837.293276795463
112583012746.950701500613083.0492984994
121267916106.5682839607-3427.56828396065
131801454774.7117960584-36760.7117960584
144355625551.662184930318004.3378150697
152481137532.0559738622-12721.0559738622
1665757129.69430635651-554.694306356512
17712312309.9827942768-5186.98279427681
182195035274.20263086-13324.20263086
193759731829.30318232005767.69681768005
201782137334.6123128980-19513.6123128980
21129888933.203865385274054.79613461473
22223308173.8624533262114156.1375466738
231332612948.7087690295377.291230970543
241618939421.7576321765-23232.7576321765
25714610199.84147339-3053.84147339001
26158246712.274973938779111.72502606123
272766431883.7905804869-4219.79058048687
28119208970.933332533022949.06666746698
2985683754.695400793594813.30459920641
301441617888.7132525291-3472.71325252912
3133692418.09385001291950.90614998709
32118198498.40911857853320.59088142149
3369844404.812066640162579.18793335984
3445194596.96396081892-77.9639608189245
352220-406.6126857335032626.61268573350
361856228523.8861355383-9961.8861355383
37103279124.064781381451202.93521861855
3853369915.85929674367-4579.85929674367
39236510041.7539210403-7676.75392104033
40406917181.6038418839-13112.6038418839
41863625478.2681143738-16842.2681143738
42137186592.987347212617125.01265278739
43452510904.6883637821-6379.6883637821
44686910980.1080830345-4111.1080830345
4546284262.36889227926365.631107720742
4636892225.628525944551463.37147405545
4748914745.29576326022145.704236739779
48748919081.5351928978-11592.5351928978
4949016721.07381595184-1820.07381595184
5022844595.07344470331-2311.07344470331
51316011295.4984437339-8135.49844373393
52415017670.7143199369-13520.7143199369
53728511965.2907458916-4680.29074589162
5411347141.98659883952-6007.98659883952
55465814414.7655536772-9756.76555367722
5623849644.27357091081-7260.27357091081
573748-253.6320515045514001.63205150455
5853715325.3692627951145.63073720489
5912855746.95525287965-4461.95525287965
60932710678.0268365214-1351.02683652144
6155654775.5743304365789.425669563497
6215283356.07546334153-1828.07546334153
6331222230.23622746219891.763772537805
6475619587.88903705356-2026.88903705356
6526756406.11169953892-3731.11169953892
661325332261.1333042568-19008.1333042568
67880749.539154811411130.460845188589
6820534879.71956946106-2826.71956946106
6914248807.49503225496-7383.49503225496
70403610725.6366300077-6689.63663000766
7130455867.50292220172-2822.50292220172
7251194269.88100794896849.118992051042
7314313614.6208712561-2183.6208712561
7455458.1297276960383495.870272303962
7519753422.13807303294-1447.13807303294
7617651616.62438988718148.375610112819
7710122691.34050377025-1679.34050377025
78810282.810132022330527.18986797767
7912805981.3786753811-4701.3786753811
8066669.4783875829821596.521612417018
8113802954.7720462673-1574.7720462673
8246778013.56594772509-3336.56594772509
838763139.02799877951-2263.02799877951
848141053.76675176437-239.766751764370
85514815.738215775877-301.738215775877
8656928408.5007635325-2716.5007635325
87364212853.4347784586-9211.43477845856
88540527.10742366696612.8925763330335
8920994970.54838465096-2871.54838465096
90567680.407448952384-113.407448952384
9120013755.6990080939-1754.69900809390
9229494406.00565606544-1457.00565606544
9322538341.63145614987-6088.63145614987
9465332572.099516546103960.9004834539
9518895002.02614850810-3113.02614850810
9630553057.14302906935-2.14302906934699
97272-65.4417625981243337.441762598124
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9925641263.765922430151300.23407756985
100138381.74549922004081301.25450077996
10112613164.24393098935-1903.24393098935
1029751415.43855875428-440.438558754285
10333666354.11150849058-2988.11150849058
104576-237.318576087833813.318576087833
10516862745.5575181026-1059.55751810260
1067462921.2824179655-2175.2824179655
10731925592.59519399674-2400.59519399674
1082045964.914150254971080.08584974503
10957025284.62722282293417.372777177068
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123158514506.7661149745-12921.7661149745
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1920-1130.061834715661130.06183471566
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1940-1130.061834715661130.06183471566
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1960-1130.061834715661130.06183471566
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1980-1130.061834715661130.06183471566
1990-1130.061834715661130.06183471566
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2010-1130.061834715661130.06183471566
2020-1130.061834715661130.06183471566
2030-1130.061834715661130.06183471566
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336314-570.128927376893884.128927376893
3378441532.60395699172-688.603956991717
3380-1130.061834715661130.06183471566
33926-990.1215713886661016.12157138867
340125272.325423830397-147.325423830397
341304540.97833351477-236.978333514770
3420-1130.061834715661130.06183471566
3430-1130.061834715661130.06183471566
3440-1130.061834715661130.06183471566
345621608.12837191142712.8716280885733
3460-1130.061834715661130.06183471566
347119-709.655383056616828.655383056616
3480-1130.061834715661130.06183471566
3490-1130.061834715661130.06183471566
3501595258.2062496940081336.79375030599
351312-728.1888331371461040.18883313715
35260-154.964866444609214.964866444609
353587275.436567061258311.563432938742
354135-997.2439686877521132.24396868775
3550-1130.061834715661130.06183471566
3560-1130.061834715661130.06183471566
357514813.906846657881-299.906846657881
3580-1130.061834715661130.06183471566
3590-1130.061834715661130.06183471566
3600-1130.061834715661130.06183471566
3611-567.566897567023568.566897567023
3620-1130.061834715661130.06183471566
3630-1130.061834715661130.06183471566
36417632814.30943098121-1051.30943098121
365180134.65510870636845.3448912936319
3660-1130.061834715661130.06183471566
3670-1130.061834715661130.06183471566
3680-1130.061834715661130.06183471566
3690-1130.061834715661130.06183471566
370218-181.659525368655399.659525368655
3710-1130.061834715661130.06183471566
372448-226.829218051849674.829218051849
373227-212.836468315058439.836468315058
374174-719.012280760994893.012280760994
3750-1130.061834715661130.06183471566
3760-1130.061834715661130.06183471566
377121401.101481389999-280.101481389999
378607-154.855323156611761.855323156611
3792212265.9157056521701946.08429434783
3800-1130.061834715661130.06183471566
3810-1130.061834715661130.06183471566
3825301243.75826924983-713.758269249834
383571744.030026665108-173.030026665108
3840-1130.061834715661130.06183471566
38578539.456114225498-461.456114225498
38624892892.2268421647-403.226842164702
387131-711.770053890642842.770053890642
388923-283.2690980404021206.26909804040
38972-706.930786523044778.930786523044
390572-17.2808701039676589.280870103968
391397268.445081626386128.554918373614
392450-286.014665145352736.014665145352
393622-3.38228100782135625.382281007821
394694-320.0324362967641014.03243629676
395342538.67759216393923386.32240783606
396562-9.08850588904647571.088505889046
39749172515.889764839432401.11023516057
398144232554.9946418214-31112.9946418214
399529-163.089129026206692.089129026206
40021264541.00122198103-2415.00122198103
4011061-751.080843247341812.08084324734
402776-21.2956205887799797.29562058878
403611-285.488918252915896.488918252915
40415261779.18545080559-253.185450805592
405592-159.507260290948751.507260290948
4061182372.838065157925809.161934842075
407621375.600708412830245.399291587170
408989566.987176263097422.012823736903
409438139.776272880851298.223727119149
410726-744.2471326218221470.24713262182
41113036839.71604095912-5536.71604095912
41274191792.646569204325626.35343079568
4131164987.424783293541176.575216706459
41433103310.88209968005-0.882099680046394
4151920333.7157064939011586.2842935061
416965-901.1120519757861866.11205197579
41732562093.017551374891162.98244862511
41811351684.06648166908-549.066481669083
41912702206.76682371134-936.76682371134
420661-1014.826781935631675.82678193563
4211013-1027.250485770942040.25048577094
42228449247.63836318306-6403.63836318306
423115288720.458498421542807.54150157846
42465261686.076604095954839.92339590405
42522641693.77098185649570.229018143506
426510910338.0918137529-5229.09181375289
42739991836.821490921422162.17850907858
4283562432860.53309847232763.46690152771
42992523255.666696188255996.33330381175
4301523610888.35277325674347.64722674335
431180738418.074192967159654.92580703285


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
715.51448874002864e-262.75724437001432e-26
811.63594648564807e-298.17973242824035e-30
912.93616528145024e-331.46808264072512e-33
1013.72629610305727e-331.86314805152864e-33
1114.51940925380337e-352.25970462690169e-35
1212.24505428183278e-341.12252714091639e-34
1315.03388633767586e-412.51694316883793e-41
1416.58941519210736e-533.29470759605368e-53
1513.03942341479436e-701.51971170739718e-70
1611.33177525605379e-706.65887628026897e-71
1711.70226128965504e-728.51130644827521e-73
1814.78130962046475e-832.39065481023238e-83
1911.25353406416443e-906.26767032082214e-91
2014.66333282680614e-972.33166641340307e-97
2111.95598448850966e-989.7799224425483e-99
2211.33946522144874e-1096.69732610724371e-110
2317.81772018112434e-1103.90886009056217e-110
2411.19866662136187e-1155.99333310680937e-116
2518.55852907588612e-1154.27926453794306e-115
2612.6595128289281e-1201.32975641446405e-120
2712.53367681123682e-1231.26683840561841e-123
2813.10638875680774e-1241.55319437840387e-124
2917.4519378686168e-1263.7259689343084e-126
3011.7665853502917e-1278.8329267514585e-128
3117.0602100722195e-1273.53010503610975e-127
3213.40616715552267e-1281.70308357776134e-128
3312.48369102436619e-1281.24184551218310e-128
3411.41255925069816e-1277.0627962534908e-128
3515.98863057954535e-1272.99431528977267e-127
3613.53611920468212e-1271.76805960234106e-127
3711.14246772763709e-1275.71233863818545e-128
3817.35395505287439e-1273.67697752643720e-127
3915.99009318249919e-1272.99504659124960e-127
4015.38787782830932e-1282.69393891415466e-128
4118.84487697245172e-1394.42243848622586e-139
4212.63013614919809e-1431.31506807459905e-143
4311.01260504256487e-1425.06302521282437e-143
4415.97384188473017e-1422.98692094236508e-142
4512.19825487285307e-1411.09912743642653e-141
4617.43707399276034e-1413.71853699638017e-141
4712.66407292050152e-1401.33203646025076e-140
4815.7696845012686e-1412.8848422506343e-141
4913.60181321701114e-1401.80090660850557e-140
5012.57359735711936e-1391.28679867855968e-139
5114.35971081869945e-1392.17985540934972e-139
5211.30651503983936e-1406.53257519919682e-141
5315.17941394084959e-1402.58970697042479e-140
5411.04960938419799e-1395.24804692098994e-140
5516.66191518142337e-1403.33095759071169e-140
5611.49676747360101e-1397.48383736800506e-140
5716.81409176110217e-1403.40704588055109e-140
5812.36154287243652e-1391.18077143621826e-139
5919.29853039189155e-1394.64926519594577e-139
6011.57065119370660e-1387.85325596853302e-139
6113.65894535909479e-1381.82947267954740e-138
6212.18083743961068e-1371.09041871980534e-137
6318.62878779690871e-1374.31439389845435e-137
6413.11750076913482e-1361.55875038456741e-136
6511.87793785693e-1359.3896892846500e-136
6611.40814359151618e-1397.04071795758089e-140
6717.08586225412514e-1393.54293112706257e-139
6814.35966738588815e-1382.17983369294407e-138
6913.07895484627833e-1381.53947742313917e-138
7011.02678852032778e-1375.13394260163888e-138
7116.34278136863274e-1373.17139068431637e-137
7211.44313152895724e-1367.2156576447862e-137
7318.49050679312999e-1364.24525339656499e-136
7414.27073344275735e-1352.13536672137867e-135
7512.71156864192595e-1341.35578432096298e-134
7611.42256840704712e-1337.11284203523562e-134
7717.58328487046853e-1333.79164243523426e-133
7813.67031095411604e-1321.83515547705802e-132
7917.24475002260509e-1323.62237501130254e-132
8012.09226929399367e-1311.04613464699683e-131
8111.20044903800222e-1306.00224519001109e-131
8217.345730594594e-1303.672865297297e-130
8312.68695684325259e-1291.34347842162630e-129
8411.31983671427602e-1286.59918357138008e-129
8517.01083732736125e-1283.50541866368062e-128
8613.89710680133712e-1271.94855340066856e-127
8712.47123981317533e-1271.23561990658767e-127
8811.28158251669838e-1266.4079125834919e-127
8915.5005001669876e-1262.7502500834938e-126
9012.83074666761415e-1251.41537333380707e-125
9111.46426085963047e-1247.32130429815237e-125
9218.41597576139609e-1244.20798788069804e-124
9311.45006055854793e-1237.25030279273966e-124
9411.21483544487695e-1236.07417722438474e-124
9516.00114814445292e-1233.00057407222646e-123
9612.76953979645215e-1221.38476989822608e-122
9711.40522913048150e-1217.02614565240752e-122
9813.24816239599919e-1211.62408119799960e-121
9911.47952454402748e-1207.3976227201374e-121
10016.01919599492095e-1203.00959799746048e-120
10112.96442485883425e-1191.48221242941712e-119
10211.51736253192665e-1187.58681265963326e-119
10316.97698167110946e-1183.48849083555473e-118
10413.38512163198507e-1171.69256081599254e-117
10511.72386697252378e-1168.61933486261892e-117
10617.71810371641929e-1163.85905185820964e-116
10714.07502784417777e-1152.03751392208889e-115
10811.78883770173802e-1148.94418850869009e-115
10915.81302279399136e-1142.90651139699568e-114
11012.70520907979945e-1131.35260453989972e-113
11111.28902587690337e-1126.44512938451684e-113
11215.49111138499343e-1122.74555569249671e-112
11312.06403500158195e-1111.03201750079098e-111
11416.54409322292506e-1113.27204661146253e-111
11512.28887295723216e-1101.14443647861608e-110
11611.04073676754421e-1095.20368383772105e-110
11714.7145921273541e-1092.35729606367705e-109
11811.89892956664519e-1089.49464783322596e-109
11916.0786695836227e-1083.03933479181135e-108
12012.44750942174652e-1071.22375471087326e-107
12112.19683931541198e-1071.09841965770599e-107
12211.00029205334535e-1065.00146026672676e-107
12314.94324681910785e-1092.47162340955392e-109
12412.48605033917023e-1081.24302516958512e-108
12518.74493909521672e-1084.37246954760836e-108
12612.7683446355875e-1071.38417231779375e-107
12711.16899337645586e-1065.84496688227929e-107
12815.32611112206463e-1062.66305556103231e-106
12912.15672901483472e-1051.07836450741736e-105
13019.07461039394123e-1054.53730519697062e-105
13114.04958413174077e-1042.02479206587038e-104
13211.79022864516459e-1038.95114322582296e-104
13317.50801140840214e-1033.75400570420107e-103
13413.10613355173646e-1021.55306677586823e-102
13511.2665345333418e-1016.332672666709e-102
13615.40060520681174e-1012.70030260340587e-101
13712.36815742169543e-1001.18407871084771e-100
13819.97902761597272e-1004.98951380798636e-100
13913.84573746558329e-991.92286873279165e-99
14011.59883713747417e-987.99418568737086e-99
14116.95334772490969e-983.47667386245485e-98
14212.88122388694328e-971.44061194347164e-97
14311.23401296913429e-966.17006484567144e-97
14415.2816285529275e-962.64081427646375e-96
14512.2957194078563e-951.14785970392815e-95
14619.8785165651408e-954.9392582825704e-95
14714.04347824011970e-942.02173912005985e-94
14811.7218030478802e-938.609015239401e-94
14916.99539548553686e-933.49769774276843e-93
15012.84008187068460e-921.42004093534230e-92
15111.18649809594738e-915.93249047973689e-92
15213.18541150596183e-911.59270575298091e-91
15311.33500949492474e-906.6750474746237e-91
15415.53541606161428e-902.76770803080714e-90
15512.25607240582611e-891.12803620291306e-89
15619.012816972671e-894.5064084863355e-89
15713.59157778265093e-881.79578889132546e-88
15811.44580303546363e-877.22901517731814e-88
15915.83437627492638e-872.91718813746319e-87
16012.30551572473220e-861.15275786236610e-86
16119.08542837416556e-864.54271418708278e-86
16213.570260477721e-851.7851302388605e-85
16311.39896326572555e-846.99481632862777e-85
16415.56378951495491e-842.78189475747746e-84
16511.7541418331998e-838.770709165999e-84
16616.84482366590856e-833.42241183295428e-83
16712.64781383999823e-821.32390691999911e-82
16811.04274723508694e-815.2137361754347e-82
16914.97212479567477e-832.48606239783739e-83
17011.93238669159086e-829.66193345795431e-83
17117.48651917061539e-823.74325958530770e-82
17212.95942392716844e-811.47971196358422e-81
17311.13892577846310e-805.69462889231548e-81
17414.53713224057991e-802.26856612028995e-80
17511.73366078529003e-798.66830392645014e-80
17616.80625421364949e-793.40312710682475e-79
17717.8750700194232e-843.9375350097116e-84
17813.11147984985643e-831.55573992492822e-83
17911.2326897874046e-826.163448937023e-83
18014.86739611309879e-822.43369805654940e-82
18111.84174374599811e-819.20871872999055e-82
18217.57650281754144e-813.78825140877072e-81
18312.94065764394425e-801.47032882197212e-80
18417.40655875115426e-803.70327937557713e-80
18512.97410631208998e-791.48705315604499e-79
18611.19597426834713e-785.97987134173567e-79
18714.75781145181125e-782.37890572590562e-78
18811.89083278626916e-779.45416393134578e-78
18917.43504658461061e-773.71752329230530e-77
19012.83173800479951e-761.41586900239976e-76
19111.11219105372891e-755.56095526864454e-76
19214.20448591320637e-752.10224295660319e-75
19311.64024207723134e-748.20121038615672e-75
19416.15427480438209e-743.07713740219104e-74
19512.35323297133457e-731.17661648566729e-73
19618.76400559600524e-734.38200279800262e-73
19711.16581122498964e-725.8290561249482e-73
19814.32509429305579e-722.16254714652790e-72
19911.59871561619735e-717.99357808098676e-72
20015.55617183829778e-712.77808591914889e-71
20112.03849537589357e-701.01924768794679e-70
20217.45130868534047e-703.72565434267024e-70
20312.71353229219011e-691.35676614609506e-69
20419.01870129153876e-694.50935064576938e-69
20513.28676824879006e-681.64338412439503e-68
20611.21980361003008e-676.09901805015039e-68
20714.44512947176338e-672.22256473588169e-67
20811.58824963364605e-667.94124816823026e-67
20915.27148121039196e-662.63574060519598e-66
21011.75234481363139e-658.76172406815693e-66
21116.19339083001487e-653.09669541500743e-65
21212.18053559585223e-641.09026779792612e-64
21316.76919521326956e-643.38459760663478e-64
21412.37203897476641e-631.18601948738320e-63
21518.30761921072405e-634.15380960536202e-63
21612.91970791036708e-621.45985395518354e-62
21711.02813646700479e-615.14068233502397e-62
21813.39357980654196e-611.69678990327098e-61
21911.17830930523451e-605.89154652617256e-61
22014.12804760735841e-602.06402380367920e-60
22111.41033369028350e-597.05166845141752e-60
22214.77468681591531e-592.38734340795766e-59
22311.62462040026555e-588.12310200132777e-59
22415.089110065302e-582.544555032651e-58
22511.71618410558901e-578.58092052794507e-58
22614.70772474339587e-572.35386237169793e-57
22711.54764923212536e-567.73824616062682e-57
22815.12105159800069e-562.56052579900035e-56
22911.69825963575999e-558.49129817879994e-56
23015.57368720102065e-552.78684360051032e-55
23111.86054668261718e-549.30273341308588e-55
23216.16012855070992e-543.08006427535496e-54
23311.99641904750623e-539.98209523753116e-54
23416.38066470669254e-533.19033235334627e-53
23512.05098406997538e-521.02549203498769e-52
23616.57535344288863e-523.28767672144432e-52
23712.09606557661065e-511.04803278830532e-51
23816.78308099090144e-513.39154049545072e-51
23912.14402712720240e-501.07201356360120e-50
24016.74847105939989e-503.37423552969995e-50
24112.11517224111762e-491.05758612055881e-49
24216.68924627504487e-493.34462313752244e-49
24312.07871352642272e-481.03935676321136e-48
24416.51777121295624e-483.25888560647812e-48
24511.20173389725506e-476.00866948627531e-48
24613.69739386694243e-471.84869693347122e-47
24711.13268259352777e-465.66341296763883e-47
24813.39112239564244e-461.69556119782122e-46
24911.03007461077388e-455.15037305386938e-46
25013.11531679623392e-451.55765839811696e-45
25119.5382734569077e-454.76913672845385e-45
25212.85943698378618e-441.42971849189309e-44
25318.51756719142715e-444.25878359571357e-44
25416.99889702108522e-443.49944851054261e-44
25514.39425349072734e-442.19712674536367e-44
25611.31790955521454e-436.5895477760727e-44
25714.00874305682888e-432.00437152841444e-43
25818.70159235782232e-434.35079617891116e-43
25912.58102225507609e-421.29051112753805e-42
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3370.9999999999999984.7730912724086e-152.3865456362043e-15
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3410.9999999999999519.79123072802334e-144.89561536401167e-14
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3510.9999999999596858.06303115299413e-114.03151557649706e-11
3520.9999999999204281.59144562242717e-107.95722811213585e-11
3530.9999999998426763.14649006459506e-101.57324503229753e-10
3540.9999999996930486.13903276892093e-103.06951638446046e-10
3550.999999999407251.18550167026274e-095.92750835131368e-10
3560.9999999988643762.27124826384776e-091.13562413192388e-09
3570.9999999990378021.9243967672894e-099.621983836447e-10
3580.9999999981550823.68983533296629e-091.84491766648314e-09
3590.9999999964914027.0171966698392e-093.5085983349196e-09
3600.9999999933824851.32350291639473e-086.61751458197363e-09
3610.9999999875329442.49341122956237e-081.24670561478119e-08
3620.9999999768778534.62442930360845e-082.31221465180422e-08
3630.999999957482098.50358199474684e-084.25179099737342e-08
3640.9999999220222421.55955515442420e-077.79777577212102e-08
3650.9999998587015282.82596943593111e-071.41298471796555e-07
3660.9999997468100345.06379932527751e-072.53189966263875e-07
3670.9999995503711788.99257644310168e-074.49628822155084e-07
3680.9999992087540231.58249195481383e-067.91245977406916e-07
3690.9999986203517652.75929647088951e-061.37964823544476e-06
3700.9999977235696624.55286067617927e-062.27643033808963e-06
3710.9999960966384717.8067230580307e-063.90336152901535e-06
3720.9999947677421881.04645156243621e-055.23225781218106e-06
3730.9999913515595281.72968809435445e-058.64844047177227e-06
3740.9999854292632762.91414734486143e-051.45707367243071e-05
3750.999975759348034.84813039406918e-052.42406519703459e-05
3760.9999600782853387.98434293231841e-053.99217146615921e-05
3770.9999384090932640.0001231818134728476.15909067364235e-05
3780.9999000543294810.0001998913410376789.9945670518839e-05
3790.99984525277950.0003094944409980840.000154747220499042
3800.9997548059328830.0004903881342341450.000245194067117072
3810.999615703027710.0007685939445816790.000384296972290839
3820.999709595688390.0005808086232216670.000290404311610833
3830.9998364753740580.0003270492518849130.000163524625942456
3840.999735479697050.0005290406059006390.000264520302950319
3850.9995924650054010.0008150699891971680.000407534994598584
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3880.9985325319560280.002934936087944160.00146746804397208
3890.9977507820260010.004498435947997830.00224921797399891
3900.9966325415013690.006734916997262650.00336745849863133
3910.9949827734906680.01003445301866350.00501722650933174
3920.9926023250117160.01479534997656840.00739767498828422
3930.9892443778446640.02151124431067120.0107556221553356
3940.9846078041679040.03078439166419110.0153921958320956
3950.978647361909960.04270527618007850.0213526380900393
3960.9702558007603680.05948839847926450.0297441992396323
3970.960008998370060.07998200325988050.0399910016299402
3980.9998924516439440.0002150967121114100.000107548356055705
3990.9997982909106860.0004034181786270990.000201709089313549
4000.9999634587370857.30825258290758e-053.65412629145379e-05
4010.9999286546987380.0001426906025247037.13453012623514e-05
4020.9998576590538260.0002846818923485010.000142340946174251
4030.9997218601900570.0005562796198859060.000278139809942953
4040.9994941151315150.001011769736969880.000505884868484941
4050.9990464003309840.001907199338031860.000953599669015932
4060.9982400858473020.003519828305396990.00175991415269850
4070.9968912680324610.006217463935077230.00310873196753862
4080.9945079612020940.01098407759581140.00549203879790571
4090.9905791024442620.01884179511147670.00942089755573836
4100.9843283946461850.03134321070763070.0156716053538153
4110.9919916108851640.01601677822967210.00800838911483603
4120.9917428934570380.01651421308592500.00825710654296249
4130.9852470158603630.02950596827927410.0147529841396371
4140.9748434051427480.05031318971450350.0251565948572518
4150.9573731039408030.08525379211839380.0426268960591969
4160.9315500094926770.1368999810146450.0684499905073226
4170.9051178808464430.1897642383071140.0948821191535569
4180.8555785899454260.2888428201091480.144421410054574
4190.7989746015460450.4020507969079090.201025398453955
4200.7079228573611660.5841542852776690.292077142638834
4210.5974764886272790.8050470227454410.402523511372721
4220.7235574182478650.552885163504270.276442581752135
4230.7483434347202050.503313130559590.251656565279795
4240.6650532554023990.6698934891952030.334946744597601


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level3940.942583732057416NOK
5% type I error level4050.9688995215311NOK
10% type I error level4090.978468899521531NOK
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Dec/01/t1291225796cd5giiixgjs5rfz/10lzsv1291225705.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/01/t1291225796cd5giiixgjs5rfz/10lzsv1291225705.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/01/t1291225796cd5giiixgjs5rfz/1p7cn1291225705.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/01/t1291225796cd5giiixgjs5rfz/1p7cn1291225705.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/01/t1291225796cd5giiixgjs5rfz/2p7cn1291225705.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/01/t1291225796cd5giiixgjs5rfz/2p7cn1291225705.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/01/t1291225796cd5giiixgjs5rfz/3p7cn1291225705.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/01/t1291225796cd5giiixgjs5rfz/3p7cn1291225705.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/01/t1291225796cd5giiixgjs5rfz/40gtp1291225705.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/01/t1291225796cd5giiixgjs5rfz/40gtp1291225705.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/01/t1291225796cd5giiixgjs5rfz/50gtp1291225705.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/01/t1291225796cd5giiixgjs5rfz/50gtp1291225705.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/01/t1291225796cd5giiixgjs5rfz/60gtp1291225705.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/01/t1291225796cd5giiixgjs5rfz/60gtp1291225705.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/01/t1291225796cd5giiixgjs5rfz/7a7aa1291225705.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/01/t1291225796cd5giiixgjs5rfz/7a7aa1291225705.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/01/t1291225796cd5giiixgjs5rfz/8lzsv1291225705.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/01/t1291225796cd5giiixgjs5rfz/8lzsv1291225705.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/01/t1291225796cd5giiixgjs5rfz/9lzsv1291225705.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/01/t1291225796cd5giiixgjs5rfz/9lzsv1291225705.ps (open in new window)


 
Parameters (Session):
par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;
 
Parameters (R input):
par1 = 1 ; 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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