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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 17:22:11 +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/t1291224052dbtv4bd0qcywuwv.htm/, Retrieved Wed, 01 Dec 2010 18:20:52 +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/t1291224052dbtv4bd0qcywuwv.htm/},
    year = {2010},
}
@Manual{R,
    title = {R: A Language and Environment for Statistical Computing},
    author = {{R Development Core Team}},
    organization = {R Foundation for Statistical Computing},
    address = {Vienna, Austria},
    year = {2010},
    note = {{ISBN} 3-900051-07-0},
    url = {http://www.R-project.org},
}
 
Original text written by user:
 
IsPrivate?
No (this computation is public)
 
User-defined keywords:
 
Dataseries X:
» Textbox « » Textfile « » CSV «
1 162556 1081 213118 6282154 807 1 29790 309 81767 4321023 444 1 87550 458 153198 4111912 412 0 84738 588 -26007 223193 428 1 54660 302 126942 1491348 315 1 42634 156 157214 1629616 168 0 40949 481 129352 1398893 263 1 45187 353 234817 1926517 267 1 37704 452 60448 983660 228 1 16275 109 47818 1443586 129 0 25830 115 245546 1073089 104 0 12679 110 48020 984885 122 1 18014 239 -1710 1405225 393 0 43556 247 32648 227132 190 1 24811 505 95350 929118 280 0 6575 159 151352 1071292 63 0 7123 109 288170 638830 102 1 21950 519 114337 856956 265 1 37597 248 37884 992426 234 0 17821 373 122844 444477 277 1 12988 119 82340 857217 73 1 22330 84 79801 711969 67 0 13326 102 165548 702380 103 0 16189 295 116384 358589 290 0 7146 105 134028 297978 83 0 15824 64 63838 585715 56 1 27664 282 74996 657954 236 0 11920 182 31080 209458 73 0 8568 37 32168 786690 34 0 14416 361 49857 439798 139 1 3369 28 87161 688779 26 1 11819 85 106113 574339 70 1 6984 45 80570 741409 40 1 4519 49 102129 597793 42 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 time18 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24
R Framework
error message
The field 'Names of X columns' contains a hard return which cannot be interpreted.
Please, resubmit your request without hard returns in the 'Names of X columns'.


Multiple Linear Regression - Estimated Regression Equation
Wealth[t] = + 155435.183922991 + 37009.2326801244Group[t] + 21.7375380915535Costs[t] -1157.43373544825Trades[t] + 1.66865114930779Dividends[t] + 2499.58968458757`Orders `[t] + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0		2-tail p-value1-tail p-value
(Intercept)155435.18392299129863.4715875.204900
Group37009.232680124427057.1232251.36780.1720920.086046
Costs21.73753809155352.07851210.458200
Trades-1157.43373544825207.452419-5.579300
Dividends1.668651149307790.3986854.18543.5e-051.7e-05
`Orders `2499.58968458757437.988755.70700


Multiple Linear Regression - Regression Statistics
Multiple R0.825410329937655
R-squared0.681302212767788
Adjusted R-squared0.677552827035645
F-TEST (value)181.710355092822
F-TEST (DF numerator)5
F-TEST (DF denominator)425
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation244463.140753928
Sum Squared Residuals25398946554591.8


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast		Residuals
Prediction Error
162821544847614.261694471434539.73830553
243210231728617.070579322592405.92942068
341119122850926.194505061260985.80549494
42231932343287.42484491-2120094.42484491
514913482030265.92542257-538917.925422571
616296161620909.341666478706.65833353467
713988931362075.4549952036817.5450048018
819265171825342.5444448101174.455555201
99836601159649.57714376-175989.577143762
101443586822301.201848686621284.798151314
1110730891253498.85555631-180409.855556307
12984885688806.288195934296078.711804066
1314052251286883.11758983118341.882410173
142271321345749.42317721-1118617.42317721
159291181006261.4365623-77143.4365623004
161071292524355.371817733546936.628182267
17638830919924.740109226-281094.740109226
18856956922055.101889184-65099.1018891839
199924261370786.23617395-378360.236173953
204444771008467.19134669-563990.191346692
21857217656903.729426766200313.270573234
22711969881251.74764313-169282.747643130
23702380860750.973493437-158370.973493437
243585891084986.54002135-726397.54002135
25297978620353.008963359-322375.008963359
26585715671834.60202146-86119.6020214597
276579541182440.68412760-524486.684127598
28209458438225.422818106-228767.422818106
29786690437520.581526746349169.418473254
30439798481606.861062719-41808.8610627186
31688779443700.672465101245078.327534899
32574339703015.369121712-128676.369121712
33741409526601.675022585214807.324977415
34597793509362.53818221588430.461817785
35644190711606.044733111-67416.044733111
363779341077663.26547103-699729.265471033
37640273607366.0193803932906.9806196105
38697458602335.83737603595122.1626239652
39550608679892.953021946-129284.953021946
40207393536668.619777857-329275.619777857
4130160775049.3555939642226557.644406036
42345783683942.36198592-338159.36198592
43501749371218.834471973130530.165528027
44379983599283.566162164-219300.566162164
45387475397161.861146802-9686.86114680192
46377305476043.431141678-98738.431141678
47370837521444.024568868-150607.024568868
48430866583580.572410541-152714.572410541
49469107513164.574161727-44057.5741617268
50194493396861.538482961-202368.538482961
51530670541466.442490172-10796.4424901715
52518365673850.096699303-155485.096699303
53491303775320.849951739-284017.849951739
54527021431048.16623252695972.833767474
55233773657100.682066526-423327.682066526
56405972389823.21881575216148.7811842482
57652925325504.696546272327420.303453728
58446211459651.668466036-13440.6684660356
59341340353014.018785124-11674.0187851237
60387699636626.565114043-248927.565114043
61493408523942.366146745-30534.3661467451
62146494325317.579319795-178823.579319795
63414462441417.209939363-26955.2099393629
64364304586112.183824291-221808.183824291
65355178355602.461063912-424.461063911717
66357760126391.954852814231368.045147186
67261216261219.961292927-3.9612929270954
68397144453280.494815107-56136.4948151072
69374943478847.578100761-103904.578100761
70424898587037.900287272-162139.900287272
71202055359588.19389127-157533.193891270
72378525370122.2686088448402.73139115641
73310768413028.270981092-102260.270981092
74325738309541.32246993716196.6775300626
75394510441213.607469958-46703.6074699576
76247060387179.998480213-140119.998480213
77368078387030.042862372-18952.0428623718
78236761274273.640499354-37512.6404993542
79312378293731.00131795418646.9986820462
80339836238177.356427838101658.643572162
81347385329585.49460780817799.5053921923
82426280522673.468019733-96393.4680197326
83352850420569.255361588-67719.2553615883
84301881255909.87975158245971.1202484180
85377516358152.80705178219363.1929482176
86357312510003.834200302-152691.834200302
87458343535638.754901456-77295.7549014564
88354228356937.021577831-2709.02157783102
89308636417364.620793768-108728.620793768
90386212362469.60554041123742.394459589
91393343388171.9580135425171.04198645798
92378509447413.406896295-68904.4068962953
93452469365910.54852377086558.4514762304
94364839531904.841008307-167065.841008307
95358649314514.70340010344134.2965998966
96376641384601.86117851-7960.86117851034
97429112363133.8681776365978.1318223702
98330546166113.001169763164432.998830237
99403560450357.153987953-46797.1539879526
100317892354452.273658557-36560.2736585573
101307528386155.1326674-78627.1326674002
102235133348570.174805542-113437.174805542
103299243454500.078981377-155257.078981377
104314073356946.339498762-42873.3394987617
105368186330405.49424872037780.5057512796
106269661336928.857172635-67267.8571726347
107125390412201.985838897-286811.985838897
108510834417086.70325051893747.2967494817
109321896495596.270717206-173700.270717206
110249898364500.295358212-114602.295358212
111408881309415.97100698699465.0289930137
112158492375375.374541166-216883.374541166
113292154438463.861893823-146309.861893823
114289513384353.447083695-94840.447083695
115378049323215.99212045254833.0078795483
116343466324504.28033226418961.7196677364
117332743295895.77577051136847.224229489
118442882370118.25322073272763.746779268
119214215378802.492189499-164587.492189499
120315688248482.86564492567205.1343550749
121375195692942.186343346-317747.186343346
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123355864501347.570128355-145483.570128355
124480382436939.64077277743442.3592272228
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194315380256755.6817089658624.3182910398
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198315380293764.91438908521615.0856109153
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321315380256755.6817089658624.3182910398
322315380256755.6817089658624.3182910398
323315380256755.6817089658624.3182910398
324315380293764.91438908521615.0856109153
325315380256755.6817089658624.3182910398
326312502257421.96706296455080.0329370359
327315380293764.91438908521615.0856109153
328315380293764.91438908521615.0856109153
329315380256755.6817089658624.3182910398
330315380256755.6817089658624.3182910398
331315380256755.6817089658624.3182910398
332315380256755.6817089658624.3182910398
333315380256755.6817089658624.3182910398
334313729262484.66538494451244.3346150556
335315388256973.82201878858414.177981212
336315371267792.45873081747578.5412691829
337296139235156.19967062760982.8003293726
338315380256755.6817089658624.3182910398
339313880258956.69625075854923.3037492419
340317698267776.84222223549921.1577777646
341295580279750.25990691315829.7400930872
342315380256755.6817089658624.3182910398
343315380256755.6817089658624.3182910398
344315380256755.6817089658624.3182910398
345308256247192.53946193761063.4605380627
346315380256755.6817089658624.3182910398
347303677257223.43624173746453.5637582627
348315380256755.6817089658624.3182910398
349315380256755.6817089658624.3182910398
350319369296746.57830824322622.4216917565
351318690251291.61261218167398.387387819
352314049264656.85949640449392.1405035957
353325699278745.07604622846953.9239537724
354314210262119.3073608352090.69263917
355315380256755.6817089658624.3182910398
356315380256755.6817089658624.3182910398
357322378275371.90707002247006.092929978
358315380256755.6817089658624.3182910398
359315380256755.6817089658624.3182910398
360315380256755.6817089658624.3182910398
361315398262149.38034590853248.6196540923
362315380256755.6817089658624.3182910398
363315380256755.6817089658624.3182910398
364308336375766.708573578-67430.7085735783
365316386268622.48813979847763.5118602017
366315380256755.6817089658624.3182910398
367315380256755.6817089658624.3182910398
368315380256755.6817089658624.3182910398
369315380256755.6817089658624.3182910398
370315553254685.48436061960867.5156393813
371315380256755.6817089658624.3182910398
372323361236127.01371895987233.9862810408
373336639295341.92793039941297.0720696011
374307424273720.81836736733703.1816326330
375315380256755.6817089658624.3182910398
376315380256755.6817089658624.3182910398
377295370251523.98717758743846.0128224125
378322340274241.82710631248098.172893688
379319864313630.9405170776233.05948292332
380315380256755.6817089658624.3182910398
381315380256755.6817089658624.3182910398
382317291265036.72915431552254.2708456852
383280398179457.518641473100940.481358527
384315380256755.6817089658624.3182910398
385317330273231.2754036144098.7245963903
386238125348871.890195643-110746.890195643
387327071258390.3642729168680.63572709
388309038279053.33017785729984.6698221429
389314210261809.94662889352400.0533711071
390307930267096.41774733940833.5822526613
391322327282127.65960982340199.3403901773
392292136269947.87372081422188.1262791856
393263276282554.90149481-19278.9014948101
394367655289827.50080435777827.499195643
395283910415035.196007713-131125.196007713
396283587270144.43083025413442.5691697463
397243650366818.909475704-123168.909475704
398438493886810.166079745-448317.166079745
399296261280591.31465279015669.6853472097
400230621216459.08694860314161.9130513969
401304252297708.3828931596543.61710684101
402333505289060.79065974244444.2093402576
403296919273222.34944839823696.6505516021
404278990364894.065576604-85904.0655766036
405276898284943.107483178-8045.10748317778
406327007311541.42626600815465.5737339916
407317046291387.36324981325658.6367501865
408304555292530.52644936612024.4735506342
409298096272036.49670607926059.5032939207
410231861292015.311853436-60154.3118534362
411309422372209.325459524-62787.3254595239
412286963478191.545202155-191228.545202155
413269753331211.4665862-61458.4665861997
414448243431719.85028559316523.1497144072
415165404339829.511835538-174425.511835538
416204325300567.9593068-96242.9593068002
417407159266132.497168118141026.502831882
418290476351363.879360796-60887.8793607958
419275311328419.404046706-53108.4040467063
420246541278828.468842120-32287.4688421204
421253468294061.822910630-40593.8229106305
422240897445960.890124955-205063.890124955
423-83265507715.961826439-590980.961826439
424-42143410353.66774442-452496.66774442
425272713318928.51271517-46215.5127151697
426215362508059.816257859-292697.816257859
42742754345653.678768328-302899.678768328
4283062751544047.51639173-1237772.51639173
429253537513655.389832793-260118.389832793
430372631726644.335972484-354013.335972484
431-7170557958.803665208-565128.803665208


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
919.97446048002032e-444.98723024001016e-44
1011.33146519642250e-566.65732598211252e-57
1113.38623967640554e-581.69311983820277e-58
1212.14360279940022e-691.07180139970011e-69
1313.13254119317072e-951.56627059658536e-95
1416.82194977537843e-973.41097488768921e-97
1514.69535020864980e-1002.34767510432490e-100
1615.38101488743057e-1122.69050744371528e-112
1712.50537596295918e-1191.25268798147959e-119
1817.02120264712256e-1223.51060132356128e-122
1919.83850097747707e-1274.91925048873853e-127
2011.19774310434984e-1285.98871552174919e-129
2112.71900666214970e-1341.35950333107485e-134
2219.1466467843011e-1364.57332339215055e-136
2313.13662358447510e-1361.56831179223755e-136
2419.13979824620666e-1404.56989912310333e-140
2512.18036002113689e-1391.09018001056844e-139
2618.6719370555625e-1444.33596852778125e-144
2717.6248919642994e-1493.8124459821497e-149
2812.91840724696222e-1511.45920362348111e-151
2913.73941996637569e-1671.86970998318784e-167
3012.37239742099113e-1701.18619871049557e-170
3112.40610630238604e-1741.20305315119302e-174
3216.504337863572e-1763.252168931786e-176
3318.75765374519463e-1844.37882687259732e-184
3411.02754211291607e-1855.13771056458034e-186
3516.84605043255282e-1853.42302521627641e-185
3615.17824088544683e-1862.58912044272341e-186
3712.88438054326194e-1921.44219027163097e-192
3811.09718240493554e-1975.4859120246777e-198
3913.13050371652366e-1981.56525185826183e-198
4011.16569782584863e-1985.82848912924314e-199
4119.04546501522661e-2014.52273250761331e-201
4214.95565348564833e-2002.47782674282417e-200
4311.75211237206756e-2018.7605618603378e-202
4412.08892276573030e-2001.04446138286515e-200
4511.11903420735709e-2005.59517103678546e-201
4618.64265401308626e-2004.32132700654313e-200
4718.80847493918327e-2014.40423746959164e-201
4812.11776698134669e-2001.05888349067335e-200
4914.56058622221112e-2002.28029311110556e-200
5011.97133526622904e-2009.85667633114518e-201
5116.60875837462035e-2013.30437918731017e-201
5213.74616480119899e-2011.87308240059950e-201
5312.29577364993815e-2011.14788682496908e-201
5417.23501996158037e-2013.61750998079018e-201
5515.08459186116493e-2052.54229593058246e-205
5615.1646688818338e-2052.5823344409169e-205
5713.87272852216176e-2191.93636426108088e-219
5819.25581840048845e-2204.62790920024422e-220
5915.04818689382384e-2192.52409344691192e-219
6017.27906171075084e-2193.63953085537542e-219
6112.31711372581239e-2201.15855686290619e-220
6216.22961777177764e-2223.11480888588882e-222
6312.34262539531646e-2211.17131269765823e-221
6417.84102103691407e-2213.92051051845703e-221
6512.54466483612264e-2201.27233241806132e-220
6613.60207700298824e-2201.80103850149412e-220
6715.51289345720296e-2202.75644672860148e-220
6815.42048703872389e-2192.71024351936195e-219
6912.97469932897834e-2181.48734966448917e-218
7011.07259392686618e-2175.36296963433089e-218
7117.79723314491339e-2173.89861657245669e-217
7213.99019369048718e-2181.99509684524359e-218
7311.1959426897422e-2175.97971344871101e-218
7416.82110916686661e-2173.41055458343331e-217
7516.91776576126014e-2163.45888288063007e-216
7611.57371270595284e-2157.86856352976418e-216
7711.12557347390915e-2145.62786736954574e-215
7811.09840310237351e-2145.49201551186753e-215
7917.56108518245554e-2143.78054259122777e-214
8012.29450269160865e-2131.14725134580432e-213
8111.04578903168382e-2125.22894515841909e-213
8211.57485601847707e-2127.87428009238535e-213
8311.31431177432560e-2126.57155887162798e-213
8415.04554066672991e-2122.52277033336495e-212
8513.98077349525320e-2111.99038674762660e-211
8618.48294127349508e-2114.24147063674754e-211
8716.36825332637647e-2113.18412666318823e-211
8813.93356029156268e-2101.96678014578134e-210
8917.40997827655997e-2103.70498913827998e-210
9016.02361878105207e-2093.01180939052603e-209
9114.66110440661204e-2082.33055220330602e-208
9212.95748144371214e-2071.47874072185607e-207
9318.97894696850039e-2094.48947348425019e-209
9417.40339267216329e-2083.70169633608165e-208
9512.09184937876109e-2081.04592468938055e-208
9612.03351947506948e-2081.01675973753474e-208
9711.52449121710308e-2077.62245608551539e-208
9819.48461769783917e-2074.74230884891958e-207
9917.29493291973876e-2063.64746645986938e-206
10017.83081659694195e-2053.91540829847098e-205
10116.98308364766355e-2043.49154182383177e-204
10214.85418114916397e-2052.42709057458199e-205
10313.64595184982831e-2051.82297592491416e-205
10414.10904706698644e-2062.05452353349322e-206
10511.53065565446504e-2057.65327827232519e-206
10615.0073075795673e-2052.50365378978365e-205
10712.45892964471210e-2071.22946482235605e-207
10811.35707920052280e-2086.78539600261398e-209
10919.4110129568512e-2084.7055064784256e-208
11011.78273231332456e-2078.91366156662279e-208
11111.03070433840238e-2075.15352169201191e-208
11215.77678692556016e-2082.88839346278008e-208
11314.02607623299163e-2072.01303811649582e-207
11413.19026352092778e-2061.59513176046389e-206
11512.35538926410717e-2061.17769463205359e-206
11617.82073693337242e-2063.91036846668621e-206
11714.12743563599700e-2052.06371781799850e-205
11813.03164942736193e-2051.51582471368097e-205
11912.67852043059856e-2061.33926021529928e-206
12011.9873688375166e-2059.93684418758299e-206
12118.44920711067257e-2054.22460355533629e-205
12216.54971166262272e-2043.27485583131136e-204
12315.08597138222475e-2032.54298569111238e-203
12419.43096798436781e-2034.71548399218391e-203
12512.92823817657488e-2021.46411908828744e-202
12617.89213867737496e-2033.94606933868748e-203
12715.90808985437113e-2022.95404492718557e-202
12814.93793985369666e-2012.46896992684833e-201
12914.00811122410366e-2002.00405561205183e-200
13013.09825260858639e-1991.54912630429319e-199
13112.55125202885442e-1981.27562601442721e-198
13211.88303389263178e-1989.41516946315888e-199
13311.51128607445824e-1977.55643037229122e-198
13411.45909245804881e-1967.29546229024403e-197
13511.24412948919731e-1956.22064744598653e-196
13611.02597276922470e-1945.12986384612351e-195
13718.684065142048e-1944.342032571024e-194
13817.19999060526919e-1933.59999530263459e-193
13916.02637134948933e-1923.01318567474467e-192
14015.00905453105588e-1912.50452726552794e-191
14113.58410315773879e-1901.79205157886939e-190
14213.00300693643464e-1891.50150346821732e-189
14312.75968791937425e-1881.37984395968712e-188
14412.37672221505805e-1871.18836110752902e-187
14511.96508813367744e-1869.82544066838718e-187
14611.60098446530548e-1858.00492232652738e-186
14711.35184182115848e-1846.75920910579239e-185
14811.18867212941613e-1835.94336064708065e-184
14919.09250588904009e-1834.54625294452004e-183
15017.6931730804876e-1823.8465865402438e-182
15116.8922511482781e-1813.44612557413905e-181
15216.65737427615027e-1803.32868713807514e-180
15315.80740672964128e-1792.90370336482064e-179
15415.21536769928516e-1782.60768384964258e-178
15514.44220155438909e-1772.22110077719454e-177
15613.74532860306626e-1761.87266430153313e-176
15713.15681881703292e-1751.57840940851646e-175
15812.70835800661866e-1741.35417900330933e-174
15911.69732365012214e-1738.48661825061069e-174
16011.42833507800420e-1727.14167539002099e-173
16111.20077734044827e-1716.00388670224137e-172
16211.00831426054264e-1705.04157130271318e-171
16318.45605975679718e-1704.22802987839859e-170
16417.22561408842107e-1693.61280704421053e-169
16516.06533378454687e-1683.03266689227344e-168
16615.07115154144291e-1672.53557577072145e-167
16714.22234063432429e-1662.11117031716214e-166
16814.00760636384161e-1672.00380318192081e-167
16914.98921120910994e-1672.49460560455497e-167
17014.2574360959111e-1662.12871804795555e-166
17113.62477675398742e-1651.81238837699371e-165
17213.15610255743378e-1641.57805127871689e-164
17312.67380309429924e-1631.33690154714962e-163
17412.36831067594242e-1621.18415533797121e-162
17511.99513850833356e-1619.9756925416678e-162
17611.70502886553855e-1608.52514432769276e-161
17711.50287806070507e-1597.51439030352535e-160
17811.33734307799127e-1586.68671538995633e-159
17911.11031022166406e-1575.55155110832029e-158
18019.19271719255527e-1574.59635859627764e-157
18115.50387070232872e-1562.75193535116436e-156
18214.88903286948504e-1552.44451643474252e-155
18312.48575852975714e-1541.24287926487857e-154
18411.43455046268153e-1537.17275231340766e-154
18511.25769844078639e-1526.28849220393195e-153
18618.76537224567833e-1524.38268612283917e-152
18713.44547316907715e-1511.72273658453858e-151
18812.88172971763335e-1501.44086485881668e-150
18911.94327857591096e-1499.71639287955479e-150
19011.56330307589161e-1487.81651537945803e-149
19111.20593474745037e-1476.02967373725183e-148
19219.63891009509208e-1474.81945504754604e-147
19317.86387878043472e-1463.93193939021736e-146
19416.24371222611915e-1453.12185611305957e-145
19514.97979404638729e-1442.48989702319365e-144
19614.15060145727546e-1432.07530072863773e-143
19712.51318247806757e-1421.25659123903379e-142
19812.07513013119577e-1411.03756506559789e-141
19911.70596797753378e-1408.52983988766889e-141
20011.45953714209922e-1407.2976857104961e-141
20111.20416566911718e-1396.02082834558591e-140
20219.89196479693435e-1394.94598239846718e-139
20318.09076656923082e-1384.04538328461541e-138
20416.16199591260157e-1373.08099795630079e-137
20512.32964849171958e-1361.16482424585979e-136
20611.89944617815924e-1359.4972308907962e-136
20711.51264131454393e-1347.56320657271965e-135
20811.21583200112075e-1336.07916000560376e-134
20912.01021465460872e-1331.00510732730436e-133
21011.59793088722189e-1327.98965443610945e-133
21111.20830112131113e-1316.04150560655566e-132
21219.10559676808204e-1314.55279838404102e-131
21314.91133061568564e-1302.45566530784282e-130
21413.50762858842040e-1291.75381429421020e-129
21512.71033204609159e-1281.35516602304579e-128
21612.02847832125195e-1271.01423916062597e-127
21711.51272674274812e-1267.56363371374059e-127
21811.06181423560006e-1255.30907117800032e-126
21917.85970248358587e-1253.92985124179294e-125
22013.49115692287070e-1241.74557846143535e-124
22112.59717264677319e-1231.29858632338659e-123
22211.89331513127852e-1229.46657565639261e-123
22311.37489249841749e-1216.87446249208743e-122
22411.01491099620170e-1205.07455498100851e-121
22517.30988233378094e-1203.65494116689047e-120
22615.35077071972922e-1192.67538535986461e-119
22713.85264784743754e-1181.92632392371877e-118
22812.74220763185465e-1171.37110381592733e-117
22911.97985015963311e-1169.89925079816555e-117
23011.39847978299775e-1156.99239891498877e-116
23119.66506186792908e-1154.83253093396454e-115
23216.22627123563034e-1143.11313561781517e-114
23314.34751341993155e-1132.17375670996578e-113
23413.13398421393557e-1121.56699210696778e-112
23512.17049675747651e-1111.08524837873826e-111
23611.4951370017654e-1107.475685008827e-111
23711.02708699570920e-1095.13543497854599e-110
23817.00393235548756e-1093.50196617774378e-109
23914.77128563188162e-1082.38564281594081e-108
24013.23682965841894e-1071.61841482920947e-107
24112.18667626766097e-1061.09333813383049e-106
24211.49721079007699e-1057.48605395038493e-106
24311.00290848362128e-1045.0145424181064e-105
24416.6207634814206e-1043.3103817407103e-104
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35412.86961438459564e-271.43480719229782e-27
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35613.73635109053421e-261.86817554526710e-26
35711.18771450820499e-255.93857254102497e-26
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35911.47770992321047e-247.38854961605237e-25
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36111.77982576732907e-238.89912883664535e-24
36216.07345526917792e-233.03672763458896e-23
36312.05213789722799e-221.02606894861399e-22
36416.86230615528981e-223.43115307764491e-22
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37418.43011944007484e-174.21505972003742e-17
37512.51939892213427e-161.25969946106714e-16
37617.43534509722516e-163.71767254861258e-16
3770.9999999999999992.30756853423001e-151.15378426711501e-15
3780.9999999999999976.29579854493668e-153.14789927246834e-15
3790.9999999999999921.54582599839726e-147.72912999198628e-15
3800.9999999999999784.33365774604438e-142.16682887302219e-14
3810.999999999999941.19735886427167e-135.98679432135834e-14
3820.999999999999833.41508344740082e-131.70754172370041e-13
3830.9999999999995029.9509433992724e-134.9754716996362e-13
3840.9999999999986682.66326475550112e-121.33163237775056e-12
3850.999999999996317.38138737730882e-123.69069368865441e-12
3860.9999999999909191.81626658147104e-119.08133290735522e-12
3870.9999999999782234.35546249653741e-112.17773124826871e-11
3880.9999999999464241.07153020174991e-105.35765100874957e-11
3890.9999999998653382.69324106431717e-101.34662053215859e-10
3900.9999999996613836.77234889093231e-103.38617444546616e-10
3910.9999999991838541.63229251431631e-098.16146257158155e-10
3920.9999999978922414.21551778801941e-092.10775889400971e-09
3930.9999999942983131.14033735074646e-085.7016867537323e-09
3940.999999989532752.09345018717603e-081.04672509358802e-08
3950.999999976188154.7623701697437e-082.38118508487185e-08
3960.9999999404110441.19177911798101e-075.95889558990505e-08
3970.9999998592770852.814458304076e-071.407229152038e-07
3980.999999709058155.8188370191866e-072.9094185095933e-07
3990.9999992951685251.40966294958383e-067.04831474791915e-07
4000.9999982492614293.50147714252597e-061.75073857126298e-06
4010.9999958580549758.2838900503979e-064.14194502519895e-06
4020.9999920314326481.59371347034064e-057.96856735170322e-06
4030.9999834089149743.31821700529362e-051.65910850264681e-05
4040.9999641727126637.16545746736988e-053.58272873368494e-05
4050.9999197041168910.0001605917662173348.02958831086672e-05
4060.999837952379850.0003240952402997330.000162047620149867
4070.9996707191603040.000658561679391740.00032928083969587
4080.9994271950372220.00114560992555630.00057280496277815
4090.9989885050934750.002022989813050140.00101149490652507
4100.9979016084327270.004196783134545370.00209839156727269
4110.9958307786627450.008338442674510560.00416922133725528
4120.9922711760519330.01545764789613360.00772882394806679
4130.9852129432038780.02957411359224490.0147870567961225
4140.9839799182374930.03204016352501450.0160200817625072
4150.9756372933949980.04872541321000480.0243627066050024
4160.9573504409353310.08529911812933770.0426495590646688
4170.9837380931674440.03252381366511290.0162619068325565
4180.9667559144390230.06648817112195440.0332440855609772
4190.9333786713580170.1332426572839650.0666213286419826
4200.8719773083476370.2560453833047270.128022691652364
4210.7708062014861650.4583875970276690.229193798513835
4220.6147456252924590.7705087494150820.385254374707541


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level4030.973429951690821NOK
5% type I error level4080.985507246376812NOK
10% type I error level4100.990338164251208NOK
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Dec/01/t1291224052dbtv4bd0qcywuwv/10wx411291224108.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/01/t1291224052dbtv4bd0qcywuwv/10wx411291224108.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/01/t1291224052dbtv4bd0qcywuwv/1qe781291224108.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/01/t1291224052dbtv4bd0qcywuwv/1qe781291224108.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/01/t1291224052dbtv4bd0qcywuwv/2in6a1291224108.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/01/t1291224052dbtv4bd0qcywuwv/2in6a1291224108.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/01/t1291224052dbtv4bd0qcywuwv/3in6a1291224108.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/01/t1291224052dbtv4bd0qcywuwv/3in6a1291224108.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/01/t1291224052dbtv4bd0qcywuwv/4in6a1291224108.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/01/t1291224052dbtv4bd0qcywuwv/4in6a1291224108.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/01/t1291224052dbtv4bd0qcywuwv/5bwov1291224108.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/01/t1291224052dbtv4bd0qcywuwv/5bwov1291224108.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/01/t1291224052dbtv4bd0qcywuwv/6bwov1291224108.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/01/t1291224052dbtv4bd0qcywuwv/6bwov1291224108.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/01/t1291224052dbtv4bd0qcywuwv/74ong1291224108.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/01/t1291224052dbtv4bd0qcywuwv/74ong1291224108.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/01/t1291224052dbtv4bd0qcywuwv/8wx411291224108.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/01/t1291224052dbtv4bd0qcywuwv/8wx411291224108.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/01/t1291224052dbtv4bd0qcywuwv/9wx411291224108.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/01/t1291224052dbtv4bd0qcywuwv/9wx411291224108.ps (open in new window)


 
Parameters (Session):
par1 = 5 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;
 
Parameters (R input):
par1 = 5 ; 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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