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*The author of this computation has been verified*
R Software Module: /rwasp_multipleregression.wasp (opens new window with default values)
Title produced by software: Multiple Regression
Date of computation: Thu, 02 Dec 2010 13:45:59 +0000
 
Cite this page as follows:
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/02/t12912976049ct3t1e2mx2udl0.htm/, Retrieved Thu, 02 Dec 2010 14:46:55 +0100
 
BibTeX entries for LaTeX users:
@Manual{KEY,
    author = {{YOUR NAME}},
    publisher = {Office for Research Development and Education},
    title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2010/Dec/02/t12912976049ct3t1e2mx2udl0.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 213118 29790 309 81767 87550 458 153198 84738 588 -26007 54660 302 126942 42634 156 157214 40949 481 129352 45187 353 234817 37704 452 60448 16275 109 47818 25830 115 245546 12679 110 48020 18014 239 -1710 43556 247 32648 24811 505 95350 6575 159 151352 7123 109 288170 21950 519 114337 37597 248 37884 17821 373 122844 12988 119 82340 22330 84 79801 13326 102 165548 16189 295 116384 7146 105 134028 15824 64 63838 27664 282 74996 11920 182 31080 8568 37 32168 14416 361 49857 3369 28 87161 11819 85 106113 6984 45 80570 4519 49 102129 2220 22 301670 18562 155 102313 10327 91 88577 5336 81 112477 2365 79 191778 4069 145 79804 8636 855 128294 13718 61 96448 4525 226 93811 6869 105 117520 4628 62 69159 3689 25 101792 4891 217 210568 7489 322 136996 4901 84 121920 2284 33 76403 3160 108 108094 4150 150 134759 7285 115 188873 1134 162 146216 4658 158 156608 2384 97 61348 3748 9 50350 5371 66 87720 1285 107 99489 9327 101 87419 5565 47 94355 1528 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 time24 seconds
R Server'George Udny Yule' @ 72.249.76.132


Multiple Linear Regression - Estimated Regression Equation
Costs[t] = -1896.32015960522 + 76.1189716416966Trades[t] + 0.0230891638690773Dividends[t] + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0		2-tail p-value1-tail p-value
(Intercept)-1896.32015960522937.889069-2.02190.0438080.021904
Trades76.11897164169663.55876621.389100
Dividends0.02308916386907730.0125341.84210.0661510.033076


Multiple Linear Regression - Regression Statistics
Multiple R0.752820382867361
R-squared0.56673852886056
Adjusted R-squared0.564713942546824
F-TEST (value)279.928064817761
F-TEST (DF numerator)2
F-TEST (DF denominator)428
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation7798.04702343797
Sum Squared Residuals26026481998.5329


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast		Residuals
Prediction Error
116255685309.00461051877246.995389482
22979023512.37373976106277.62626023903
38755036503.382578706851046.6174212932
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64263413608.179225012529025.8207749875
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84518730395.405022158714791.5949778413
93770433905.14879999943798.85120000055
10162757504.72538723128770.2746127688
112583012526.813410586413303.1865894136
12126797585.508369974445093.49163002556
131801416256.63159254401757.36840745597
144355617658.880857891425897.1191421086
152481138745.3122943679-13934.3122943679
16657513701.1874613371-7126.18746133709
17712313054.2521014917-5931.25210149175
182195040249.3718517338-18299.3718517338
193759717855.894691551519741.1053084485
201782129332.4215090804-11511.4215090804
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22223306340.211824213515989.7881757865
23133269690.179848045833635.82015195417
241618923245.9857224339-7056.98572243387
2571469190.7663178176-2044.76631781759
26158244449.2600685374911374.7399314625
272766421300.82477687846363.17522312157
281192012674.9438922344-754.943892234397
2985681662.814014478006905.185985522
301441626733.7850460677-12317.7850460677
3133692247.485658354921121.51434164508
32118197023.852875578374795.14712442163
3369843389.327497202673594.67250279733
3445194191.58266762290327.417332377103
3522206743.60528089672-4523.60528089672
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353587393.106220872789193.893779127211
354135-311.053260787553446.053260787553
3550-494.346129474854494.346129474854
3560-494.346129474854494.346129474854
3575143880.83069536889-3366.83069536889
3580-494.346129474854494.346129474854
3590-494.346129474854494.346129474854
3600-494.346129474854494.346129474854
3611-189.824064580330190.824064580330
3620-494.346129474854494.346129474854
3630-494.346129474854494.346129474854
36417631352.82765413064410.172345869356
365180317.910815785856-137.910815785856
3660-494.346129474854494.346129474854
3670-494.346129474854494.346129474854
3680-494.346129474854494.346129474854
3690-494.346129474854494.346129474854
3702181104.15227500077-886.152275000768
3710-494.346129474854494.346129474854
3724482528.73201131993-2080.73201131993
373227558.396460751604-331.396460751604
374174-323.561585969939497.561585969939
3750-494.346129474854494.346129474854
3760-494.346129474854494.346129474854
3771211227.63820763250-1106.63820763250
378607336.405236044987270.594763955013
3792212571.3194735088941640.68052649111
3800-494.346129474854494.346129474854
3810-494.346129474854494.346129474854
3825304366.3247092945-3836.3247092945
3835715150.86682152818-4579.86682152818
3840-494.346129474854494.346129474854
38578769.273961253061-691.273961253061
38624892713.97637304154-224.976373041541
387131-62.0837241620297193.083724162030
38892366.1183995336537856.881600466346
38972-273.423925315609345.423925315609
390572674.14660611246-102.146606112460
391397312.79102304157484.2089769584263
39245082.3962600613536367.603739938646
39362243.7971797069081578.202820293092
394694284.080106457747409.919893542253
3953425947.823382827382477.17661717262
396562442.926634867605119.073365132395
39749172520.038482435852396.96151756415
39814429883.50174762265-8441.50174762265
399529263.455481488007265.544518511993
40021269092.99345736333-6966.99345736333
4011061110.098172444335950.901827555665
402776271.767580480875504.232419519125
40361179.2792229390284531.720777060972
40415261607.91073492156-81.9107349215615
405592120.453203752246471.546796247754
4061182725.491822297377456.508177702623
407621891.761975578517-270.761975578517
408989301.632955258156687.367044741844
409438287.548565298018150.451434701982
410726-52.1835571221068778.183557122107
41113034360.01536592359-3057.01536592359
41274191771.635078542455647.36492145755
4131164721.173231279118442.826768720882
41433102352.60370244144957.396297558562
41519201079.20580950234840.794190497659
41696528.8594080583557936.140591941644
41732563941.42499513169-685.424995131688
4181135835.810929889089299.189070110911
41912701680.68177780224-410.681777802241
420661-145.925562430562806.925562430562
4211013-133.1512531763101146.15125317631
42228444881.84063788457-2037.84063788457
423115283096.175966837758431.82403316225
42465261371.841121889465154.15887811054
42522641204.456687107951059.54331289205
42651097035.07145709451-1926.07145709451
42739991570.614816263612428.38518373639
4283562418709.628031493816914.3719685062
42992523593.209898426535658.79010157347
430152366742.412138168798493.58786183121
4311807312435.05948290405637.94051709601


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
60.9999981030249563.79395008777382e-061.89697504388691e-06
711.24808873743519e-166.24044368717594e-17
811.29221269601118e-196.46106348005588e-20
913.41440657643226e-251.70720328821613e-25
1013.25492766882052e-251.62746383441026e-25
1116.76816636172821e-263.38408318086411e-26
1211.75374453515586e-258.76872267577929e-26
1311.02434892893421e-255.12174464467103e-26
1413.65804206610188e-331.82902103305094e-33
1518.4813164405847e-514.24065822029235e-51
1611.15668251279407e-525.78341256397036e-53
1711.05540019344865e-535.27700096724324e-54
1812.64857208335632e-681.32428604167816e-68
1911.49225872067432e-797.4612936033716e-80
2015.43389493069784e-852.71694746534892e-85
2112.40692061727082e-851.20346030863541e-85
2215.95123848257729e-922.97561924128864e-92
2313.04697645461517e-921.52348822730759e-92
2415.30181025644618e-952.65090512822309e-95
2511.98230928532818e-949.9115464266409e-95
2616.35430490656446e-983.17715245328223e-98
2713.73265808968127e-1061.86632904484064e-106
2813.76006815744361e-1071.88003407872181e-107
2913.14101140482839e-1081.57050570241420e-108
3012.07397454697080e-1131.03698727348540e-113
3111.1896076344999e-1125.9480381724995e-113
3219.77602768465458e-1144.88801384232729e-114
3311.15924868983055e-1135.79624344915275e-114
3416.28792978503892e-1133.14396489251946e-113
3516.52433172718832e-1133.26216586359416e-113
3611.27955571835965e-1176.39777859179826e-118
3711.97865971636292e-1189.8932985818146e-119
3818.88556931783261e-1184.44278465891631e-118
3911.23644985722213e-1176.18224928611067e-118
4011.41252977632691e-1177.06264888163453e-118
4112.84411942035661e-1571.42205971017831e-157
4218.61474984733362e-1614.30737492366681e-161
4312.12217777307652e-1611.06108888653826e-161
4417.39479771873703e-1613.69739885936851e-161
4513.46007065559043e-1601.73003532779521e-160
4612.33848000535507e-1591.16924000267753e-159
4711.86525890150187e-1609.32629450750936e-161
4814.81833071955822e-1622.40916535977911e-162
4913.28851338336105e-1611.64425669168052e-161
5012.67574100573452e-1601.33787050286726e-160
5111.26367111787767e-1596.31835558938837e-160
5213.13947015458666e-1591.56973507729333e-159
5311.99216624205254e-1589.9608312102627e-159
5412.71720550757095e-1591.35860275378547e-159
5516.02490554814751e-1593.01245277407376e-159
5613.59027961479785e-1581.79513980739893e-158
5719.24811792680958e-1584.62405896340479e-158
5814.03416602347487e-1572.01708301173744e-157
5919.85555727802222e-1574.92777863901111e-157
6013.92783945029003e-1571.96391972514502e-157
6111.28969396946738e-1566.44846984733691e-157
6211.0001393748611e-1555.0006968743055e-156
6317.1691104048086e-1553.5845552024043e-155
6418.33953102888808e-1554.16976551444404e-155
6515.46242849294645e-1542.73121424647322e-154
6612.12303930557323e-1761.06151965278661e-176
6718.29190867811625e-1764.14595433905813e-176
6816.23981001574817e-1753.11990500787409e-175
6918.75430045125036e-1754.37715022562518e-175
7017.1183274954065e-1743.55916374770325e-174
7114.70772626195457e-1732.35386313097729e-173
7219.79311959653247e-1734.89655979826623e-173
7317.10857121391562e-1723.55428560695781e-172
7415.89823996422372e-1712.94911998211186e-171
7514.39783372143193e-1702.19891686071597e-170
7613.59129178386545e-1691.79564589193273e-169
7711.59235047683164e-1687.96175238415818e-169
7811.06081750538504e-1675.30408752692521e-168
7911.77578799143434e-1678.87893995717171e-168
8011.06193940386239e-1695.30969701931193e-170
8118.69659183288653e-1694.34829591644327e-169
8216.63561619119118e-1683.31780809559559e-168
8317.80752177384468e-1683.90376088692234e-168
8415.91150360341402e-1672.95575180170701e-167
8513.55878722449291e-1661.77939361224645e-166
8611.33979318926359e-1656.69896594631793e-166
8719.177386465212e-1654.588693232606e-165
8815.36115223313567e-1642.68057611656784e-164
8912.32464657376396e-1631.16232328688198e-163
9011.37556260651621e-1626.87781303258107e-163
9118.1637421194611e-1624.08187105973055e-162
9216.230477567183e-1613.1152387835915e-161
9312.92514709022981e-1601.46257354511490e-160
9412.09992406787892e-1591.04996203393946e-159
9511.41657355887579e-1587.08286779437896e-159
9618.85688771395168e-1584.42844385697584e-158
9713.83090696796933e-1571.91545348398467e-157
9815.8883591321205e-1592.94417956606025e-159
9913.60941551825807e-1581.80470775912904e-158
10012.66588909390383e-1571.33294454695191e-157
10111.84880537506247e-1569.24402687531234e-157
10211.13343913457185e-1555.66719567285927e-156
10314.73299195609955e-1552.36649597804978e-155
10411.52394126669761e-1547.61970633348804e-155
10511.09135570933234e-1535.45677854666172e-154
10617.43994161141067e-1533.71997080570533e-153
10715.05998026572264e-1522.52999013286132e-152
10813.43839202373878e-1511.71919601186939e-151
10912.18019860673946e-1501.09009930336973e-150
11011.53861018184493e-1497.69305090922467e-150
11111.02907668995556e-1485.14538344977781e-149
11214.51676860605187e-1482.25838430302593e-148
11312.90979101676093e-1471.45489550838046e-147
11411.74422802931535e-1468.72114014657677e-147
11511.03372102894252e-1455.16860514471258e-146
11617.04744401151587e-1453.52372200575793e-145
11713.26084121597011e-1441.63042060798505e-144
11812.20234014719525e-1431.10117007359763e-143
11911.39930964482756e-1426.99654822413778e-143
12015.67305893875674e-1422.83652946937837e-142
12115.57436083807542e-1422.78718041903771e-142
12213.72204283286901e-1411.86102141643450e-141
12312.67110538243585e-1411.33555269121793e-141
12411.19272826327829e-1405.96364131639146e-141
12517.16213790601807e-1403.58106895300904e-140
12613.64544101823701e-1391.82272050911851e-139
12712.38382146423757e-1381.19191073211879e-138
12811.54762694552606e-1377.7381347276303e-138
12919.62677891576734e-1374.81338945788367e-137
13016.18988425086438e-1363.09494212543219e-136
13113.93405088241693e-1351.96702544120846e-135
13212.26664928559683e-1341.13332464279842e-134
13311.4334712445832e-1337.167356222916e-134
13419.02033736543251e-1334.51016868271626e-133
13515.53011977677604e-1322.76505988838802e-132
13613.4480642740888e-1311.7240321370444e-131
13712.0986139627099e-1301.04930698135495e-130
13811.29220767215811e-1296.46103836079056e-130
13917.52853543354487e-1293.76426771677243e-129
14014.58584779409391e-1282.29292389704695e-128
14112.78256413691849e-1271.39128206845924e-127
14211.67692700166026e-1268.3846350083013e-127
14319.74863578275524e-1264.87431789137762e-126
14415.81546991111998e-1252.90773495555999e-125
14513.42747548722315e-1241.71373774361157e-124
14612.0265519936622e-1231.0132759968311e-123
14711.18970328998441e-1225.94851644992204e-123
14816.92092663077232e-1223.46046331538616e-122
14914.00568753418138e-1212.00284376709069e-121
15012.31584158397976e-1201.15792079198988e-120
15111.32836082706858e-1196.64180413534291e-120
15216.19236157768109e-1193.09618078884054e-119
15313.52642928850577e-1181.76321464425289e-118
15412.00000819816739e-1171.00000409908370e-117
15511.12720844789739e-1165.63604223948695e-117
15616.32182960878953e-1163.16091480439476e-116
15713.52765969148102e-1151.76382984574051e-115
15811.95928318471673e-1149.79641592358367e-115
15911.08239361196776e-1135.41196805983881e-114
16015.94936610520438e-1132.97468305260219e-113
16113.25374294029086e-1121.62687147014543e-112
16211.77063059027170e-1118.8531529513585e-112
16319.58759926967782e-1114.79379963483891e-111
16414.95424970522694e-1102.47712485261347e-110
16511.90234957759758e-1099.5117478879879e-110
16611.01642434057194e-1085.08212170285971e-109
16715.40253484830872e-1082.70126742415436e-108
16812.73511636559894e-1071.36755818279947e-107
16911.39853885854242e-1176.9926942927121e-118
17018.09364374813117e-1174.04682187406558e-117
17114.66112192850856e-1162.33056096425428e-116
17212.69228792107335e-1151.34614396053667e-115
17311.53546065623846e-1147.67730328119232e-115
17418.76418155119286e-1144.38209077559643e-114
17514.95026907499937e-1132.47513453749968e-113
17612.78620884292877e-1121.39310442146439e-112
17718.82600662259119e-1164.41300331129559e-116
17815.10217878944861e-1152.55108939472430e-115
17912.93539105391816e-1141.46769552695908e-114
18011.68068704776021e-1138.40343523880106e-114
18117.65807757574183e-1133.82903878787092e-113
18214.37450718723749e-1122.18725359361874e-112
18312.22268125626048e-1111.11134062813024e-111
18413.62144453370311e-1111.81072226685155e-111
18512.06120482624057e-1101.03060241312028e-110
18611.168632840027e-1095.843164200135e-110
18716.4579809329986e-1093.2289904664993e-109
18813.6243672310101e-1081.81218361550505e-108
18912.02504754097099e-1071.01252377048549e-107
19011.11389227458672e-1065.56946137293358e-107
19116.0828911195569e-1063.04144555977845e-106
19213.31442567361854e-1051.65721283680927e-105
19311.81772762575235e-1049.08863812876175e-105
19419.81158533237376e-1044.90579266618688e-104
19515.30679149696409e-1032.65339574848205e-103
19612.83756939556544e-1021.41878469778272e-102
19715.57172384724214e-1022.78586192362107e-102
19812.96370381712229e-1011.48185190856114e-101
19911.56904760412998e-1007.84523802064988e-101
20016.8227579894619e-1003.41137899473095e-100
20113.58292600087922e-991.79146300043961e-99
20211.87273295436392e-989.36366477181959e-99
20319.74259830050557e-984.87129915025279e-98
20414.59614452140225e-972.29807226070113e-97
20511.91978835717625e-969.59894178588124e-97
20619.95242800911025e-964.97621400455513e-96
20715.14116668399564e-952.57058334199782e-95
20812.61856070086627e-941.30928035043314e-94
20911.32778343470900e-936.63891717354498e-94
21015.16868801971169e-932.58434400985585e-93
21112.60041128071694e-921.30020564035847e-92
21211.30218529159416e-916.5109264579708e-92
21315.09729405944832e-912.54864702972416e-91
21412.43773087771222e-901.21886543885611e-90
21511.20912196821582e-896.04560984107908e-90
21615.95434065628871e-892.97717032814435e-89
21712.93001984759824e-881.46500992379912e-88
21811.22362523690272e-876.11812618451358e-88
21915.94925857343597e-872.97462928671799e-87
22012.88625480984617e-861.44312740492308e-86
22111.38954071713219e-856.94770358566097e-86
22216.66200835536846e-853.33100417768423e-85
22313.20037556968772e-841.60018778484386e-84
22411.45970093458572e-837.29850467292858e-84
22516.94624379075495e-833.47312189537747e-83
22612.80812460773505e-821.40406230386753e-82
22711.27930015640291e-816.39650078201455e-82
22815.97556913717999e-812.98778456858999e-81
22912.80215429232649e-801.40107714616325e-80
23011.29670472947443e-796.48352364737217e-80
23116.01325841338265e-793.00662920669133e-79
23212.75414399419639e-781.37707199709819e-78
23311.25677881808636e-776.2838940904318e-78
23415.58384260527911e-772.79192130263956e-77
23512.52503262463517e-761.26251631231758e-76
23611.14048449911413e-755.70242249557063e-76
23715.10889137303626e-752.55444568651813e-75
23812.29749249005505e-741.14874624502753e-74
23911.01955915268977e-735.09779576344883e-74
24014.5031265462095e-732.25156327310475e-73
24111.97950585095728e-729.8975292547864e-73
24218.71529568448863e-724.35764784224432e-72
24313.79493877519335e-711.89746938759667e-71
24411.65394350487551e-708.26971752437756e-71
24515.27928461043877e-702.63964230521938e-70
24612.26935706443769e-691.13467853221885e-69
24719.70854642898564e-694.85427321449282e-69
24814.12454283673457e-682.06227141836728e-68
24911.74811241840731e-678.74056209203657e-68
25017.37356022736592e-673.68678011368296e-67
25113.11622035276570e-661.55811017638285e-66
25211.30184914074014e-656.50924570370068e-66
25315.44100161982364e-652.72050080991182e-65
25413.26083257824243e-651.63041628912121e-65
25511.34493239917264e-656.7246619958632e-66
25615.65630463452592e-652.82815231726296e-65
25712.36625197705689e-641.18312598852844e-64
25818.47505476927672e-644.23752738463836e-64
25913.51750559532702e-631.75875279766351e-63
26011.45279650384451e-627.26398251922257e-63
26115.97101137424284e-622.98550568712142e-62
26212.44207745845048e-611.22103872922524e-61
26319.48163254123945e-614.74081627061973e-61
26413.83202344655911e-601.91601172327955e-60
26511.54582808473045e-597.72914042365223e-60
26616.20503346803849e-593.10251673401925e-59
26712.47840157557188e-581.23920078778594e-58
26819.17458873106424e-584.58729436553212e-58
26913.63171675084242e-571.81585837542121e-57
27011.43012120661115e-567.15060603305577e-57
27115.60624656384409e-562.80312328192204e-56
27212.18670019481532e-551.09335009740766e-55
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36311.07342764889110e-155.36713824445551e-16
3640.9999999999999992.81652624333926e-151.40826312166963e-15
3650.9999999999999967.2822805875982e-153.6411402937991e-15
3660.999999999999991.86768135482161e-149.33840677410803e-15
3670.9999999999999764.74598513819037e-142.37299256909519e-14
3680.999999999999941.19477231651075e-135.97386158255374e-14
3690.9999999999998512.97936889143986e-131.48968444571993e-13
3700.9999999999996536.93019925927985e-133.46509962963992e-13
3710.999999999999151.69893785333375e-128.49468926666875e-13
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3760.9999999999512859.7430469696954e-114.8715234848477e-11
3770.9999999998949942.10012591623891e-101.05006295811945e-10
3780.9999999997568364.86327455989367e-102.43163727994684e-10
3790.9999999994681931.06361303356338e-095.31806516781691e-10
3800.999999998798352.40330061276402e-091.20165030638201e-09
3810.9999999973153815.36923750450049e-092.68461875225024e-09
3820.999999997466385.06724116696847e-092.53362058348424e-09
3830.9999999981492383.70152328068337e-091.85076164034169e-09
3840.9999999957772478.44550646586603e-094.22275323293302e-09
3850.9999999909320871.81358266140421e-089.06791330702106e-09
3860.9999999810495173.790096585814e-081.895048292907e-08
3870.9999999581313758.37372496550317e-084.18686248275159e-08
3880.9999999090684251.81863150598068e-079.09315752990338e-08
3890.999999803999413.92001179213096e-071.96000589606548e-07
3900.9999995884492258.2310154910655e-074.11550774553275e-07
3910.9999991410237931.71795241367527e-068.58976206837635e-07
3920.9999982223924713.55521505765816e-061.77760752882908e-06
3930.9999963739271237.25214575389923e-063.62607287694961e-06
3940.9999927155349041.45689301929621e-057.28446509648104e-06
3950.9999862959467142.74081065724835e-051.37040532862418e-05
3960.9999732979719355.3404056129612e-052.6702028064806e-05
3970.999950333405669.93331886790936e-054.96665943395468e-05
3980.9999991082166431.78356671380651e-068.91783356903255e-07
3990.9999979761934054.04761318908476e-062.02380659454238e-06
4000.9999999506465179.87069650051753e-084.93534825025876e-08
4010.9999998704447482.59110503937983e-071.29555251968992e-07
4020.9999996610792626.77841476616603e-073.38920738308302e-07
4030.9999991322544331.73549113400632e-068.67745567003158e-07
4040.999997979334794.04133041832992e-062.02066520916496e-06
4050.9999950016484029.99670319497184e-064.99835159748592e-06
4060.9999879501010772.40997978460377e-051.20498989230188e-05
4070.9999728462966555.43074066903233e-052.71537033451616e-05
4080.9999369907384150.0001260185231702836.30092615851416e-05
4090.9998578887541860.0002842224916269490.000142111245813475
4100.9996869167721060.0006261664557884970.000313083227894248
4110.9997924871282080.0004150257435846580.000207512871792329
4120.9997133417392440.0005733165215119810.000286658260755990
4130.9993443264533640.001311347093272630.000655673546636314
4140.9985892089608620.002821582078275960.00141079103913798
4150.9969676471728720.00606470565425550.00303235282712775
4160.993663307174190.01267338565162040.0063366928258102
4170.990656883124660.01868623375068160.0093431168753408
4180.9816336436521980.03673271269560440.0183663563478022
4190.9685004881253770.06299902374924630.0314995118746231
4200.941025901823690.1179481963526190.0589740981763095
4210.8946609220915780.2106781558168430.105339077908422
4220.9067877063687220.1864245872625560.093212293631278
4230.9487446641019660.1025106717960670.0512553358980336
4240.9109696138441580.1780607723116830.0890303861558416
4250.8035448835837760.3929102328324470.196455116416224


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level4100.976190476190476NOK
5% type I error level4130.983333333333333NOK
10% type I error level4140.985714285714286NOK
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Dec/02/t12912976049ct3t1e2mx2udl0/10kqb51291297533.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/02/t12912976049ct3t1e2mx2udl0/10kqb51291297533.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/02/t12912976049ct3t1e2mx2udl0/1v7wc1291297533.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/02/t12912976049ct3t1e2mx2udl0/1v7wc1291297533.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/02/t12912976049ct3t1e2mx2udl0/2v7wc1291297533.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/02/t12912976049ct3t1e2mx2udl0/2v7wc1291297533.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/02/t12912976049ct3t1e2mx2udl0/36zef1291297533.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/02/t12912976049ct3t1e2mx2udl0/36zef1291297533.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/02/t12912976049ct3t1e2mx2udl0/46zef1291297533.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/02/t12912976049ct3t1e2mx2udl0/46zef1291297533.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/02/t12912976049ct3t1e2mx2udl0/56zef1291297533.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/02/t12912976049ct3t1e2mx2udl0/56zef1291297533.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/02/t12912976049ct3t1e2mx2udl0/6hqv01291297533.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/02/t12912976049ct3t1e2mx2udl0/6hqv01291297533.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/02/t12912976049ct3t1e2mx2udl0/79hc21291297533.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/02/t12912976049ct3t1e2mx2udl0/79hc21291297533.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/02/t12912976049ct3t1e2mx2udl0/89hc21291297533.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/02/t12912976049ct3t1e2mx2udl0/89hc21291297533.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/02/t12912976049ct3t1e2mx2udl0/99hc21291297533.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/02/t12912976049ct3t1e2mx2udl0/99hc21291297533.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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