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*The author of this computation has been verified*
R Software Module: /rwasp_multipleregression.wasp (opens new window with default values)
Title produced by software: Multiple Regression
Date of computation: Fri, 03 Dec 2010 16:10:40 +0000
 
Cite this page as follows:
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/03/t1291392685yzbsqeavx0ox51l.htm/, Retrieved Fri, 03 Dec 2010 17:11:37 +0100
 
BibTeX entries for LaTeX users:
@Manual{KEY,
    author = {{YOUR NAME}},
    publisher = {Office for Research Development and Education},
    title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2010/Dec/03/t1291392685yzbsqeavx0ox51l.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 807 213118 6282154 1 29790 309 444 81767 4321023 1 87550 458 412 153198 4111912 0 84738 588 428 -26007 223193 1 54660 302 315 126942 1491348 1 42634 156 168 157214 1629616 0 40949 481 263 129352 1398893 1 45187 353 267 234817 1926517 1 37704 452 228 60448 983660 1 16275 109 129 47818 1443586 0 25830 115 104 245546 1073089 0 12679 110 122 48020 984885 1 18014 239 393 -1710 1405225 0 43556 247 190 32648 227132 1 24811 505 280 95350 929118 0 6575 159 63 151352 1071292 0 7123 109 102 288170 638830 1 21950 519 265 114337 856956 1 37597 248 234 37884 992426 0 17821 373 277 122844 444477 1 12988 119 73 82340 857217 1 22330 84 67 79801 711969 0 13326 102 103 165548 702380 0 16189 295 290 116384 358589 0 7146 105 83 134028 297978 0 15824 64 56 63838 585715 1 27664 282 236 74996 657954 0 11920 182 73 31080 209458 0 8568 37 34 32168 786690 0 14416 361 139 49857 439798 1 3369 28 26 87161 688779 1 11819 85 70 106113 574339 1 6984 45 40 80570 741409 1 4519 49 42 102129 597793 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 time29 seconds
R Server'George Udny Yule' @ 72.249.76.132


Multiple Linear Regression - Estimated Regression Equation
Wealth[t] = + 155435.18392299 + 37009.2326801268Group[t] + 21.7375380915533Costs[t] -1157.43373544824Trades[t] + 2499.58968458757Orders[t] + 1.66865114930779Dividends[t] + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0		2-tail p-value1-tail p-value
(Intercept)155435.1839229929863.4715875.204900
Group37009.232680126827057.1232251.36780.1720920.086046
Costs21.73753809155332.07851210.458200
Trades-1157.43373544824207.452419-5.579300
Orders2499.58968458757437.988755.70700
Dividends1.668651149307790.3986854.18543.5e-051.7e-05


Multiple Linear Regression - Regression Statistics
Multiple R0.825410329937656
R-squared0.68130221276779
Adjusted R-squared0.677552827035646
F-TEST (value)181.710355092823
F-TEST (DF numerator)5
F-TEST (DF denominator)425
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation244463.140753927
Sum Squared Residuals25398946554591.7


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast		Residuals
Prediction Error
162821544847614.261694471434539.73830553
243210231728617.070579322592405.92942068
341119122850926.194505071260985.80549493
42231932343287.42484489-2120094.42484489
514913482030265.92542257-538917.925422567
616296161620909.341666468706.65833353801
713988931362075.4549951936817.5450048051
819265171825342.54444480101174.455555203
99836601159649.57714376-175989.577143762
101443586822301.201848687621284.798151313
1110730891253498.85555630-180409.855556304
12984885688806.288195933296078.711804067
1314052251286883.11758983118341.882410172
142271321345749.42317721-1118617.42317721
159291181006261.4365623-77143.4365622998
161071292524355.371817732546936.628182268
17638830919924.740109223-281094.740109223
18856956922055.101889183-65099.1018891833
199924261370786.23617395-378360.236173954
204444771008467.19134669-563990.191346689
21857217656903.729426768200313.270573232
22711969881251.747643131-169282.747643131
23702380860750.973493435-158370.973493435
243585891084986.54002135-726397.540021348
25297978620353.008963357-322375.008963357
26585715671834.602021459-86119.6020214587
276579541182440.68412760-524486.684127598
28209458438225.422818105-228767.422818105
29786690437520.581526746349169.418473254
30439798481606.861062717-41808.861062717
31688779443700.672465103245078.327534897
32574339703015.369121713-128676.369121713
33741409526601.675022587214807.324977413
34597793509362.53818221688430.4618177838
35644190711606.044733108-67416.0447331079
363779341077663.26547103-699729.265471031
37640273607366.01938038832906.9806196118
38697458602335.83737603695122.162623964
39550608679892.953021946-129284.953021946
40207393536668.619777855-329275.619777855
4130160775049.3555939606226557.644406039
42345783683942.361985919-338159.361985919
43501749371218.834471972130530.165528028
44379983599283.566162162-219300.566162162
45387475397161.861146801-9686.86114680102
46377305476043.431141680-98738.4311416796
47370837521444.024568868-150607.024568868
48430866583580.572410542-152714.572410542
49469107513164.574161725-44057.5741617253
50194493396861.53848296-202368.538482960
51530670541466.442490173-10796.4424901725
52518365673850.096699304-155485.096699304
53491303775320.849951739-284017.849951739
54527021431048.16623252795972.8337674734
55233773657100.682066526-423327.682066526
56405972389823.21881575116148.7811842492
57652925325504.696546271327420.303453729
58446211459651.668466035-13440.6684660345
59341340353014.018785122-11674.0187851224
60387699636626.565114044-248927.565114044
61493408523942.366146747-30534.3661467466
62146494325317.579319795-178823.579319795
63414462441417.209939364-26955.2099393645
64364304586112.183824293-221808.183824293
65355178355602.461063911-424.461063910901
66357760126391.954852811231368.045147189
67261216261219.961292926-3.96129292619298
68397144453280.494815109-56136.4948151085
69374943478847.578100759-103904.578100759
70424898587037.900287273-162139.900287273
71202055359588.193891272-157533.193891272
72378525370122.2686088438402.73139115698
73310768413028.270981091-102260.270981091
74325738309541.32246993716196.6775300633
75394510441213.607469956-46703.6074699563
76247060387179.998480214-140119.998480214
77368078387030.042862371-18952.0428623706
78236761274273.640499353-37512.6404993535
79312378293731.00131795318646.9986820472
80339836238177.356427839101658.643572161
81347385329585.49460780717799.5053921929
82426280522673.468019734-96393.468019734
83352850420569.255361587-67719.2553615868
84301881255909.87975158245971.1202484184
85377516358152.80705178119363.1929482186
86357312510003.834200303-152691.834200303
87458343535638.754901455-77295.7549014551
88354228356937.02157783-2709.02157783000
89308636417364.620793766-108728.620793766
90386212362469.6055404123742.3944595900
91393343388171.9580135415171.04198645905
92378509447413.406896297-68904.4068962968
93452469365910.54852376986558.4514762313
94364839531904.841008308-167065.841008308
95358649314514.70340010344134.2965998971
96376641384601.861178512-7960.86117851216
97429112363133.86817762965978.1318223713
98330546166113.001169765164432.998830235
99403560450357.153987951-46797.1539879513
100317892354452.273658559-36560.273658559
101307528386155.132667402-78627.1326674019
102235133348570.174805541-113437.174805541
103299243454500.078981375-155257.078981375
104314073356946.339498761-42873.3394987607
105368186330405.4942487237780.5057512804
106269661336928.857172634-67267.857172634
107125390412201.985838899-286811.985838899
108510834417086.7032505293747.2967494802
109321896495596.270717204-173700.270717204
110249898364500.295358214-114602.295358214
111408881309415.97100698699465.0289930144
112158492375375.374541168-216883.374541168
113292154438463.861893822-146309.861893822
114289513384353.447083697-94840.4470836967
115378049323215.99212045454833.0078795462
116343466324504.28033226318961.7196677371
117332743295895.7757705136847.2242294898
118442882370118.25322073172763.7467792688
119214215378802.492189501-164587.492189501
120315688248482.86564492467205.1343550756
121375195692942.186343344-317747.186343344
122334280300046.16067549734233.8393245028
123355864501347.570128354-145483.570128354
124480382436939.64077277943442.3592272215
125353058354643.186672309-1585.18667230906
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137318903269580.20338313149322.796616869
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154297765267981.00669927429783.9933007264
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181359335304249.03358861355085.9664113874
182330068339452.035493273-9384.03549327268
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184297413300399.050766016-2986.05076601557
185314806304037.63236986910768.3676301311
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193315366271891.67250516243474.3274948377
194315380256755.6817089658624.3182910403
195315688262831.90505377252856.0949462283
196315380293764.91438908721615.0856109133
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198315380293764.91438908721615.0856109133
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201315380293764.91438908721615.0856109133
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322315380256755.6817089658624.3182910403
323315380256755.6817089658624.3182910403
324315380293764.91438908721615.0856109133
325315380256755.6817089658624.3182910403
326312502257421.96706296455080.0329370364
327315380293764.91438908721615.0856109133
328315380293764.91438908721615.0856109133
329315380256755.6817089658624.3182910403
330315380256755.6817089658624.3182910403
331315380256755.6817089658624.3182910403
332315380256755.6817089658624.3182910403
333315380256755.6817089658624.3182910403
334313729262484.66538494451244.3346150561
335315388256973.82201878758414.1779812125
336315371267792.45873081747578.5412691835
337296139235156.19967062760982.8003293733
338315380256755.6817089658624.3182910403
339313880258956.69625075854923.3037492424
340317698267776.84222223549921.1577777651
341295580279750.25990691215829.7400930878
342315380256755.6817089658624.3182910403
343315380256755.6817089658624.3182910403
344315380256755.6817089658624.3182910403
345308256247192.53946193761063.4605380633
346315380256755.6817089658624.3182910403
347303677257223.43624173746453.5637582633
348315380256755.6817089658624.3182910403
349315380256755.6817089658624.3182910403
350319369296746.57830824322622.4216917571
351318690251291.61261218067398.3873878195
352314049264656.85949640449392.1405035963
353325699278745.07604622746953.923953773
354314210262119.30736082952090.6926391705
355315380256755.6817089658624.3182910403
356315380256755.6817089658624.3182910403
357322378275371.90707002147006.0929299788
358315380256755.6817089658624.3182910403
359315380256755.6817089658624.3182910403
360315380256755.6817089658624.3182910403
361315398262149.38034590753248.6196540929
362315380256755.6817089658624.3182910403
363315380256755.6817089658624.3182910403
364308336375766.70857358-67430.7085735801
365316386268622.48813979847763.5118602022
366315380256755.6817089658624.3182910403
367315380256755.6817089658624.3182910403
368315380256755.6817089658624.3182910403
369315380256755.6817089658624.3182910403
370315553254685.48436061860867.5156393819
371315380256755.6817089658624.3182910403
372323361236127.01371895987233.9862810415
373336639295341.92793039841297.0720696018
374307424273720.81836736633703.1816326336
375315380256755.6817089658624.3182910403
376315380256755.6817089658624.3182910403
377295370251523.98717758743846.0128224130
378322340274241.82710631148098.1728936885
379319864313630.9405170766233.05948292391
380315380256755.6817089658624.3182910403
381315380256755.6817089658624.3182910403
382317291265036.72915431452254.270845686
383280398179457.518641473100940.481358527
384315380256755.6817089658624.3182910403
385317330273231.27540360944098.7245963910
386238125348871.890195642-110746.890195642
387327071258390.36427290968680.6357270905
388309038279053.33017785729984.6698221434
389314210261809.94662889252400.0533711076
390307930267096.41774733840833.5822526618
391322327282127.65960982240199.3403901779
392292136269947.87372081422188.1262791862
393263276282554.901494810-19278.9014948096
394367655289827.50080435677827.4991956437
395283910415035.196007715-131125.196007715
396283587270144.43083025313442.5691697468
397243650366818.909475703-123168.909475703
398438493886810.166079746-448317.166079746
399296261280591.31465279015669.6853472103
400230621216459.08694860514161.9130513949
401304252297708.3828931586543.61710684166
402333505289060.79065974244444.2093402582
403296919273222.34944839723696.6505516026
404278990364894.065576605-85904.0655766054
405276898284943.107483177-8045.1074831772
406327007311541.42626600815465.5737339923
407317046291387.36324981325658.6367501872
408304555292530.52644936512024.4735506348
409298096272036.49670607926059.5032939212
410231861292015.311853436-60154.3118534356
411309422372209.325459523-62787.325459523
412286963478191.545202157-191228.545202157
413269753331211.466586202-61458.4665862017
414448243431719.85028559416523.1497144056
415165404339829.511835537-174425.511835537
416204325300567.959306800-96242.9593067996
417407159266132.497168118141026.502831882
418290476351363.879360798-60887.8793607977
419275311328419.404046706-53108.4040467056
420246541278828.46884212-32287.4688421198
421253468294061.82291063-40593.8229106299
422240897445960.890124954-205063.890124954
423-83265507715.961826441-590980.961826441
424-42143410353.667744419-452496.667744419
425272713318928.512715169-46215.5127151691
426215362508059.81625786-292697.81625786
42742754345653.678768327-302899.678768327
4283062751544047.51639173-1237772.51639173
429253537513655.389832792-260118.389832791
430372631726644.335972482-354013.335972482
431-7170557958.803665207-565128.803665207


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
919.97446048003492e-444.98723024001746e-44
1011.33146519642334e-566.65732598211669e-57
1113.38623967640832e-581.69311983820416e-58
1212.14360279939616e-691.07180139969808e-69
1313.13254119316939e-951.56627059658469e-95
1416.8219497753819e-973.41097488769095e-97
1514.69535020864689e-1002.34767510432345e-100
1615.38101488742996e-1122.69050744371498e-112
1712.50537596295677e-1191.25268798147839e-119
1817.0212026471293e-1223.51060132356465e-122
1919.83850097747875e-1274.91925048873937e-127
2011.19774310434740e-1285.98871552173701e-129
2112.7190066621477e-1341.35950333107385e-134
2219.14664678430161e-1364.57332339215080e-136
2313.13662358447510e-1361.56831179223755e-136
2419.1397982462108e-1404.5698991231054e-140
2512.18036002113652e-1391.09018001056826e-139
2618.67193705556201e-1444.33596852778101e-144
2717.62489196429552e-1493.81244598214776e-149
2812.91840724695893e-1511.45920362347946e-151
2913.73941996637801e-1671.86970998318901e-167
3012.37239742098899e-1701.18619871049450e-170
3112.40610630238591e-1741.20305315119295e-174
3216.5043378635595e-1763.25216893177975e-176
3318.75765374520404e-1844.37882687260202e-184
3411.02754211291584e-1855.13771056457918e-186
3516.846050432554e-1853.423025216277e-185
3615.17824088545297e-1862.58912044272648e-186
3712.88438054325363e-1921.44219027162682e-192
3811.09718240493560e-1975.48591202467801e-198
3913.13050371652225e-1981.56525185826112e-198
4011.16569782584916e-1985.82848912924578e-199
4119.04546501522968e-2014.52273250761484e-201
4214.95565348564722e-2002.47782674282361e-200
4311.75211237206756e-2018.7605618603378e-202
4412.08892276572983e-2001.04446138286491e-200
4511.11903420735722e-2005.59517103678609e-201
4618.64265401307845e-2004.32132700653923e-200
4718.80847493918425e-2014.40423746959212e-201
4812.11776698134574e-2001.05888349067287e-200
4914.56058622221421e-2002.28029311110710e-200
5011.97133526623060e-2009.85667633115298e-201
5116.60875837462633e-2013.30437918731316e-201
5213.74616480119857e-2011.87308240059929e-201
5312.29577364993712e-2011.14788682496856e-201
5417.23501996158364e-2013.61750998079182e-201
5515.08459186116779e-2052.54229593058390e-205
5615.16466888182038e-2052.58233444091019e-205
5713.87272852216482e-2191.93636426108241e-219
5819.25581840048844e-2204.62790920024422e-220
5915.04818689382955e-2192.52409344691477e-219
6017.27906171076482e-2193.63953085538241e-219
6112.31711372581344e-2201.15855686290672e-220
6216.22961777178189e-2223.11480888589095e-222
6312.34262539531487e-2211.17131269765744e-221
6417.84102103691406e-2213.92051051845703e-221
6512.54466483612207e-2201.27233241806104e-220
6613.60207700298946e-2201.80103850149473e-220
6715.5128934572036e-2202.7564467286018e-220
6815.42048703872451e-2192.71024351936226e-219
6912.97469932897869e-2181.48734966448934e-218
7011.07259392686618e-2175.36296963433089e-218
7117.79723314491516e-2173.89861657245758e-217
7213.99019369049124e-2181.99509684524562e-218
7311.19594268974247e-2175.97971344871237e-218
7416.82110916686584e-2173.41055458343292e-217
7516.91776576126405e-2163.45888288063202e-216
7611.5737127059523e-2157.8685635297615e-216
7711.12557347390940e-2145.62786736954702e-215
7811.09840310237363e-2145.49201551186815e-215
7917.5610851824513e-2143.78054259122565e-214
8012.29450269160943e-2131.14725134580471e-213
8111.04578903168346e-2125.2289451584173e-213
8211.57485601847689e-2127.87428009238446e-213
8311.31431177432589e-2126.57155887162947e-213
8415.0455406667299e-2122.52277033336495e-212
8513.9807734952559e-2111.99038674762795e-211
8618.48294127348929e-2114.24147063674465e-211
8716.36825332637792e-2113.18412666318896e-211
8813.93356029156313e-2101.96678014578156e-210
8917.40997827655744e-2103.70498913827872e-210
9016.02361878104796e-2093.01180939052398e-209
9114.66110440660965e-2082.33055220330483e-208
9212.95748144371012e-2071.47874072185506e-207
9318.97894696850039e-2094.48947348425019e-209
9417.4033926721595e-2083.70169633607975e-208
9512.09184937876252e-2081.04592468938126e-208
9612.03351947507029e-2081.01675973753515e-208
9711.52449121710299e-2077.62245608551496e-208
9819.48461769783539e-2074.74230884891770e-207
9917.29493291973918e-2063.64746645986959e-206
10017.83081659694017e-2053.91540829847009e-205
10116.98308364766236e-2043.49154182383118e-204
10214.85418114916066e-2052.42709057458033e-205
10313.64595184982707e-2051.82297592491353e-205
10414.10904706698644e-2062.05452353349322e-206
10511.53065565446495e-2057.65327827232476e-206
10615.00730757955962e-2052.50365378977981e-205
10712.45892964470833e-2071.22946482235416e-207
10811.35707920052272e-2086.7853960026136e-209
10919.41101295685763e-2084.70550647842882e-208
11011.78273231332577e-2078.91366156662887e-208
11111.03070433840256e-2075.15352169201279e-208
11215.7767869255618e-2082.8883934627809e-208
11314.02607623299209e-2072.01303811649605e-207
11413.19026352092814e-2061.59513176046407e-206
11512.35538926410584e-2061.17769463205292e-206
11617.8207369333742e-2063.9103684666871e-206
11714.12743563599935e-2052.06371781799968e-205
11813.03164942736073e-2051.51582471368036e-205
11912.67852043059871e-2061.33926021529936e-206
12011.98736883751682e-2059.93684418758412e-206
12118.44920711067016e-2054.22460355533508e-205
12216.54971166262272e-2043.27485583131136e-204
12315.08597138222244e-2032.54298569111122e-203
12419.43096798436996e-2034.71548399218498e-203
12512.92823817657738e-2021.46411908828869e-202
12617.89213867737586e-2033.94606933868793e-203
12715.90808985437214e-2022.95404492718607e-202
12814.93793985369638e-2012.46896992684819e-201
12914.0081112241048e-2002.0040556120524e-200
13013.09825260858656e-1991.54912630429328e-199
13112.55125202885239e-1981.27562601442619e-198
13211.88303389263135e-1989.41516946315674e-199
13311.51128607445885e-1977.55643037229423e-198
13411.45909245804930e-1967.29546229024652e-197
13511.24412948919731e-1956.22064744598653e-196
13611.02597276922464e-1945.12986384612322e-195
13718.68406514204751e-1944.34203257102376e-194
13817.19999060526755e-1933.59999530263378e-193
13916.0263713494907e-1923.01318567474535e-192
14015.00905453105674e-1912.50452726552837e-191
14113.5841031577394e-1901.7920515788697e-190
14213.00300693643515e-1891.50150346821758e-189
14312.75968791937393e-1881.37984395968697e-188
14412.37672221505751e-1871.18836110752875e-187
14511.96508813367744e-1869.82544066838718e-187
14611.60098446530548e-1858.00492232652738e-186
14711.35184182115863e-1846.75920910579315e-185
14811.18867212941681e-1835.94336064708403e-184
14919.09250588903802e-1834.54625294451901e-183
15017.69317308048979e-1823.84658654024490e-182
15116.89225114827889e-1813.44612557413945e-181
15216.65737427615027e-1803.32868713807514e-180
15315.80740672964128e-1792.90370336482064e-179
15415.21536769928397e-1782.60768384964198e-178
15514.44220155438605e-1772.22110077719303e-177
15613.74532860306626e-1761.87266430153313e-176
15713.1568188170331e-1751.57840940851655e-175
15812.70835800661850e-1741.35417900330925e-174
15911.69732365012156e-1738.4866182506078e-174
16011.42833507800395e-1727.14167539001977e-173
16111.20077734044841e-1716.00388670224205e-172
16211.00831426054286e-1705.04157130271432e-171
16318.45605975679863e-1704.22802987839931e-170
16417.22561408842189e-1693.61280704421094e-169
16516.06533378454584e-1683.03266689227292e-168
16615.07115154144377e-1672.53557577072189e-167
16714.22234063432261e-1662.11117031716130e-166
16814.00760636384321e-1672.00380318192160e-167
16914.98921120910966e-1672.49460560455483e-167
17014.25743609591062e-1662.12871804795531e-166
17113.62477675398598e-1651.81238837699299e-165
17213.15610255743378e-1641.57805127871689e-164
17312.67380309429939e-1631.33690154714969e-163
17412.36831067594108e-1621.18415533797054e-162
17511.99513850833322e-1619.9756925416661e-162
17611.70502886553855e-1608.52514432769276e-161
17711.50287806070507e-1597.51439030352535e-160
17811.33734307799134e-1586.68671538995672e-159
17911.11031022166374e-1575.55155110831871e-158
18019.19271719255789e-1574.59635859627894e-157
18115.50387070233153e-1562.75193535116577e-156
18214.88903286948421e-1552.44451643474210e-155
18312.48575852975827e-1541.24287926487913e-154
18411.43455046268186e-1537.17275231340929e-154
18511.25769844078711e-1526.28849220393553e-153
18618.76537224567385e-1524.38268612283693e-152
18713.44547316907676e-1511.72273658453838e-151
18812.88172971763368e-1501.44086485881684e-150
18911.94327857591162e-1499.7163928795581e-150
19011.56330307589187e-1487.81651537945936e-149
19111.20593474745050e-1476.02967373725251e-148
19219.63891009509482e-1474.81945504754741e-147
19317.86387878043338e-1463.93193939021669e-146
19416.24371222612021e-1453.12185611306011e-145
19514.97979404638672e-1442.48989702319336e-144
19614.15060145727451e-1432.07530072863726e-143
19712.51318247806643e-1421.25659123903321e-142
19812.0751301311953e-1411.03756506559765e-141
19911.70596797753368e-1408.52983988766841e-141
20011.45953714209964e-1407.29768571049818e-141
20111.20416566911821e-1396.02082834559104e-140
20219.89196479693154e-1394.94598239846577e-139
20318.09076656922944e-1384.04538328461472e-138
20416.16199591259982e-1373.08099795629991e-137
20512.32964849172038e-1361.16482424586019e-136
20611.89944617815956e-1359.49723089079781e-136
20711.51264131454307e-1347.56320657271535e-135
20811.21583200112048e-1336.07916000560238e-134
20912.01021465460940e-1331.00510732730470e-133
21011.59793088722216e-1327.98965443611081e-133
21111.20830112131086e-1316.04150560655429e-132
21219.10559676808411e-1314.55279838404205e-131
21314.9113306156848e-1302.4556653078424e-130
21413.5076285884192e-1291.7538142942096e-129
21512.71033204609189e-1281.35516602304595e-128
21612.02847832125172e-1271.01423916062586e-127
21711.51272674274855e-1267.56363371374274e-127
21811.06181423560061e-1255.30907117800304e-126
21917.8597024835832e-1253.9298512417916e-125
22013.49115692286991e-1241.74557846143496e-124
22112.59717264677245e-1231.29858632338623e-123
22211.89331513127971e-1229.46657565639853e-123
22311.37489249841764e-1216.87446249208821e-122
22411.01491099620136e-1205.07455498100678e-121
22517.30988233377554e-1203.65494116688777e-120
22615.35077071972739e-1192.67538535986370e-119
22713.85264784743711e-1181.92632392371855e-118
22812.74220763185465e-1171.37110381592733e-117
22911.97985015963412e-1169.89925079817061e-117
23011.39847978299712e-1156.99239891498559e-116
23119.66506186792963e-1154.83253093396481e-115
23216.22627123563282e-1143.11313561781641e-114
23314.3475134199318e-1132.1737567099659e-113
23413.13398421393637e-1121.56699210696818e-112
23512.17049675747639e-1111.08524837873819e-111
23611.49513700176544e-1107.47568500882721e-111
23711.02708699570870e-1095.13543497854351e-110
23817.00393235549095e-1093.50196617774547e-109
23914.77128563188081e-1082.38564281594041e-108
24013.23682965841912e-1071.61841482920956e-107
24112.18667626766203e-1061.09333813383102e-106
24211.49721079007767e-1057.48605395038833e-106
24311.00290848362074e-1045.01454241810369e-105
24416.62076348142192e-1043.31038174071096e-104
24514.5367779790228e-1032.2683889895114e-103
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35011.71157067796389e-298.55785338981945e-30
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35711.18771450820468e-255.93857254102340e-26
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36111.77982576732932e-238.89912883664662e-24
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37617.43534509722533e-163.71767254861266e-16
3770.9999999999999992.30756853422914e-151.15378426711457e-15
3780.9999999999999976.29579854493735e-153.14789927246867e-15
3790.9999999999999921.54582599839664e-147.72912999198319e-15
3800.9999999999999784.3336577460443e-142.16682887302215e-14
3810.999999999999941.19735886427184e-135.9867943213592e-14
3820.999999999999833.41508344740091e-131.70754172370045e-13
3830.9999999999995029.95094339927354e-134.97547169963677e-13
3840.9999999999986682.66326475550213e-121.33163237775107e-12
3850.999999999996317.38138737730901e-123.69069368865451e-12
3860.9999999999909191.81626658147136e-119.08133290735679e-12
3870.9999999999782234.35546249653698e-112.17773124826849e-11
3880.9999999999464241.07153020174997e-105.35765100874987e-11
3890.9999999998653382.69324106431728e-101.34662053215864e-10
3900.9999999996613836.77234889093207e-103.38617444546604e-10
3910.9999999991838541.63229251431623e-098.16146257158117e-10
3920.999999997892244.2155177880189e-092.10775889400945e-09
3930.9999999942983131.14033735074604e-085.70168675373018e-09
3940.999999989532752.09345018717560e-081.04672509358780e-08
3950.999999976188154.76237016974407e-082.38118508487204e-08
3960.9999999404110441.19177911798094e-075.95889558990472e-08
3970.9999998592770852.81445830407608e-071.40722915203804e-07
3980.9999997090581495.81883701918792e-072.90941850959396e-07
3990.9999992951685251.40966294958395e-067.04831474791976e-07
4000.9999982492614293.50147714252621e-061.75073857126311e-06
4010.9999958580549758.28389005039666e-064.14194502519833e-06
4020.9999920314326481.59371347034052e-057.96856735170262e-06
4030.9999834089149743.31821700529389e-051.65910850264694e-05
4040.9999641727126637.1654574673695e-053.58272873368475e-05
4050.9999197041168910.0001605917662173438.02958831086714e-05
4060.999837952379850.0003240952402997380.000162047620149869
4070.9996707191603040.000658561679391780.00032928083969589
4080.9994271950372220.001145609925556340.000572804962778168
4090.9989885050934750.002022989813050180.00101149490652509
4100.9979016084327270.00419678313454510.00209839156727255
4110.9958307786627440.008338442674510950.00416922133725548
4120.9922711760519330.01545764789613300.00772882394806651
4130.9852129432038780.02957411359224440.0147870567961222
4140.9839799182374940.0320401635250130.0160200817625065
4150.9756372933949980.04872541321000430.0243627066050022
4160.9573504409353330.0852991181293350.0426495590646675
4170.9837380931674440.03252381366511120.0162619068325556
4180.9667559144390220.06648817112195520.0332440855609776
4190.9333786713580180.1332426572839650.0666213286419824
4200.8719773083476370.2560453833047260.128022691652363
4210.7708062014861640.4583875970276710.229193798513836
4220.6147456252924550.7705087494150910.385254374707545


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/03/t1291392685yzbsqeavx0ox51l/10x7d11291392609.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/03/t1291392685yzbsqeavx0ox51l/10x7d11291392609.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/03/t1291392685yzbsqeavx0ox51l/186hp1291392609.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/03/t1291392685yzbsqeavx0ox51l/186hp1291392609.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/03/t1291392685yzbsqeavx0ox51l/2jfgs1291392609.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/03/t1291392685yzbsqeavx0ox51l/2jfgs1291392609.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/03/t1291392685yzbsqeavx0ox51l/3jfgs1291392609.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/03/t1291392685yzbsqeavx0ox51l/3jfgs1291392609.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/03/t1291392685yzbsqeavx0ox51l/4jfgs1291392609.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/03/t1291392685yzbsqeavx0ox51l/4jfgs1291392609.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/03/t1291392685yzbsqeavx0ox51l/5coxd1291392609.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/03/t1291392685yzbsqeavx0ox51l/5coxd1291392609.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/03/t1291392685yzbsqeavx0ox51l/6coxd1291392609.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/03/t1291392685yzbsqeavx0ox51l/6coxd1291392609.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/03/t1291392685yzbsqeavx0ox51l/7mgwg1291392609.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/03/t1291392685yzbsqeavx0ox51l/7mgwg1291392609.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/03/t1291392685yzbsqeavx0ox51l/8x7d11291392609.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/03/t1291392685yzbsqeavx0ox51l/8x7d11291392609.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/03/t1291392685yzbsqeavx0ox51l/9x7d11291392609.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/03/t1291392685yzbsqeavx0ox51l/9x7d11291392609.ps (open in new window)


 
Parameters (Session):
par1 = 6 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;
 
Parameters (R input):
par1 = 6 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;
 
R code (references can be found in the software module):
library(lattice)
library(lmtest)
n25 <- 25 #minimum number of obs. for Goldfeld-Quandt test
par1 <- as.numeric(par1)
x <- t(y)
k <- length(x[1,])
n <- length(x[,1])
x1 <- cbind(x[,par1], x[,1:k!=par1])
mycolnames <- c(colnames(x)[par1], colnames(x)[1:k!=par1])
colnames(x1) <- mycolnames #colnames(x)[par1]
x <- x1
if (par3 == 'First Differences'){
x2 <- array(0, dim=c(n-1,k), dimnames=list(1:(n-1), paste('(1-B)',colnames(x),sep='')))
for (i in 1:n-1) {
for (j in 1:k) {
x2[i,j] <- x[i+1,j] - x[i,j]
}
}
x <- x2
}
if (par2 == 'Include Monthly Dummies'){
x2 <- array(0, dim=c(n,11), dimnames=list(1:n, paste('M', seq(1:11), sep ='')))
for (i in 1:11){
x2[seq(i,n,12),i] <- 1
}
x <- cbind(x, x2)
}
if (par2 == 'Include Quarterly Dummies'){
x2 <- array(0, dim=c(n,3), dimnames=list(1:n, paste('Q', seq(1:3), sep ='')))
for (i in 1:3){
x2[seq(i,n,4),i] <- 1
}
x <- cbind(x, x2)
}
k <- length(x[1,])
if (par3 == 'Linear Trend'){
x <- cbind(x, c(1:n))
colnames(x)[k+1] <- 't'
}
x
k <- length(x[1,])
df <- as.data.frame(x)
(mylm <- lm(df))
(mysum <- summary(mylm))
if (n > n25) {
kp3 <- k + 3
nmkm3 <- n - k - 3
gqarr <- array(NA, dim=c(nmkm3-kp3+1,3))
numgqtests <- 0
numsignificant1 <- 0
numsignificant5 <- 0
numsignificant10 <- 0
for (mypoint in kp3:nmkm3) {
j <- 0
numgqtests <- numgqtests + 1
for (myalt in c('greater', 'two.sided', 'less')) {
j <- j + 1
gqarr[mypoint-kp3+1,j] <- gqtest(mylm, point=mypoint, alternative=myalt)$p.value
}
if (gqarr[mypoint-kp3+1,2] < 0.01) numsignificant1 <- numsignificant1 + 1
if (gqarr[mypoint-kp3+1,2] < 0.05) numsignificant5 <- numsignificant5 + 1
if (gqarr[mypoint-kp3+1,2] < 0.10) numsignificant10 <- numsignificant10 + 1
}
gqarr
}
bitmap(file='test0.png')
plot(x[,1], type='l', main='Actuals and Interpolation', ylab='value of Actuals and Interpolation (dots)', xlab='time or index')
points(x[,1]-mysum$resid)
grid()
dev.off()
bitmap(file='test1.png')
plot(mysum$resid, type='b', pch=19, main='Residuals', ylab='value of Residuals', xlab='time or index')
grid()
dev.off()
bitmap(file='test2.png')
hist(mysum$resid, main='Residual Histogram', xlab='values of Residuals')
grid()
dev.off()
bitmap(file='test3.png')
densityplot(~mysum$resid,col='black',main='Residual Density Plot', xlab='values of Residuals')
dev.off()
bitmap(file='test4.png')
qqnorm(mysum$resid, main='Residual Normal Q-Q Plot')
qqline(mysum$resid)
grid()
dev.off()
(myerror <- as.ts(mysum$resid))
bitmap(file='test5.png')
dum <- cbind(lag(myerror,k=1),myerror)
dum
dum1 <- dum[2:length(myerror),]
dum1
z <- as.data.frame(dum1)
z
plot(z,main=paste('Residual Lag plot, lowess, and regression line'), ylab='values of Residuals', xlab='lagged values of Residuals')
lines(lowess(z))
abline(lm(z))
grid()
dev.off()
bitmap(file='test6.png')
acf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Autocorrelation Function')
grid()
dev.off()
bitmap(file='test7.png')
pacf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Partial Autocorrelation Function')
grid()
dev.off()
bitmap(file='test8.png')
opar <- par(mfrow = c(2,2), oma = c(0, 0, 1.1, 0))
plot(mylm, las = 1, sub='Residual Diagnostics')
par(opar)
dev.off()
if (n > n25) {
bitmap(file='test9.png')
plot(kp3:nmkm3,gqarr[,2], main='Goldfeld-Quandt test',ylab='2-sided p-value',xlab='breakpoint')
grid()
dev.off()
}
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Estimated Regression Equation', 1, TRUE)
a<-table.row.end(a)
myeq <- colnames(x)[1]
myeq <- paste(myeq, '[t] = ', sep='')
for (i in 1:k){
if (mysum$coefficients[i,1] > 0) myeq <- paste(myeq, '+', '')
myeq <- paste(myeq, mysum$coefficients[i,1], sep=' ')
if (rownames(mysum$coefficients)[i] != '(Intercept)') {
myeq <- paste(myeq, rownames(mysum$coefficients)[i], sep='')
if (rownames(mysum$coefficients)[i] != 't') myeq <- paste(myeq, '[t]', sep='')
}
}
myeq <- paste(myeq, ' + e[t]')
a<-table.row.start(a)
a<-table.element(a, myeq)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,hyperlink('http://www.xycoon.com/ols1.htm','Multiple Linear Regression - Ordinary Least Squares',''), 6, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Variable',header=TRUE)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'S.D.',header=TRUE)
a<-table.element(a,'T-STAT<br />H0: parameter = 0',header=TRUE)
a<-table.element(a,'2-tail p-value',header=TRUE)
a<-table.element(a,'1-tail p-value',header=TRUE)
a<-table.row.end(a)
for (i in 1:k){
a<-table.row.start(a)
a<-table.element(a,rownames(mysum$coefficients)[i],header=TRUE)
a<-table.element(a,mysum$coefficients[i,1])
a<-table.element(a, round(mysum$coefficients[i,2],6))
a<-table.element(a, round(mysum$coefficients[i,3],4))
a<-table.element(a, round(mysum$coefficients[i,4],6))
a<-table.element(a, round(mysum$coefficients[i,4]/2,6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Regression Statistics', 2, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Multiple R',1,TRUE)
a<-table.element(a, sqrt(mysum$r.squared))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'R-squared',1,TRUE)
a<-table.element(a, mysum$r.squared)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Adjusted R-squared',1,TRUE)
a<-table.element(a, mysum$adj.r.squared)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (value)',1,TRUE)
a<-table.element(a, mysum$fstatistic[1])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (DF numerator)',1,TRUE)
a<-table.element(a, mysum$fstatistic[2])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (DF denominator)',1,TRUE)
a<-table.element(a, mysum$fstatistic[3])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'p-value',1,TRUE)
a<-table.element(a, 1-pf(mysum$fstatistic[1],mysum$fstatistic[2],mysum$fstatistic[3]))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Residual Statistics', 2, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Residual Standard Deviation',1,TRUE)
a<-table.element(a, mysum$sigma)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Sum Squared Residuals',1,TRUE)
a<-table.element(a, sum(myerror*myerror))
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable3.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Actuals, Interpolation, and Residuals', 4, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Time or Index', 1, TRUE)
a<-table.element(a, 'Actuals', 1, TRUE)
a<-table.element(a, 'Interpolation<br />Forecast', 1, TRUE)
a<-table.element(a, 'Residuals<br />Prediction Error', 1, TRUE)
a<-table.row.end(a)
for (i in 1:n) {
a<-table.row.start(a)
a<-table.element(a,i, 1, TRUE)
a<-table.element(a,x[i])
a<-table.element(a,x[i]-mysum$resid[i])
a<-table.element(a,mysum$resid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable4.tab')
if (n > n25) {
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Goldfeld-Quandt test for Heteroskedasticity',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'p-values',header=TRUE)
a<-table.element(a,'Alternative Hypothesis',3,header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'breakpoint index',header=TRUE)
a<-table.element(a,'greater',header=TRUE)
a<-table.element(a,'2-sided',header=TRUE)
a<-table.element(a,'less',header=TRUE)
a<-table.row.end(a)
for (mypoint in kp3:nmkm3) {
a<-table.row.start(a)
a<-table.element(a,mypoint,header=TRUE)
a<-table.element(a,gqarr[mypoint-kp3+1,1])
a<-table.element(a,gqarr[mypoint-kp3+1,2])
a<-table.element(a,gqarr[mypoint-kp3+1,3])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable5.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Description',header=TRUE)
a<-table.element(a,'# significant tests',header=TRUE)
a<-table.element(a,'% significant tests',header=TRUE)
a<-table.element(a,'OK/NOK',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'1% type I error level',header=TRUE)
a<-table.element(a,numsignificant1)
a<-table.element(a,numsignificant1/numgqtests)
if (numsignificant1/numgqtests < 0.01) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'5% type I error level',header=TRUE)
a<-table.element(a,numsignificant5)
a<-table.element(a,numsignificant5/numgqtests)
if (numsignificant5/numgqtests < 0.05) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'10% type I error level',header=TRUE)
a<-table.element(a,numsignificant10)
a<-table.element(a,numsignificant10/numgqtests)
if (numsignificant10/numgqtests < 0.1) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable6.tab')
}
 




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Software written by Ed van Stee & Patrick Wessa


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