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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 14:00:21 +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/t1291211941g1tzua9jxmfp3nq.htm/, Retrieved Wed, 01 Dec 2010 14:59:01 +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/t1291211941g1tzua9jxmfp3nq.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 807 213118 6282154 29790 444 81767 4321023 87550 412 153198 4111912 84738 428 -26007 223193 54660 315 126942 1491348 42634 168 157214 1629616 40949 263 129352 1398893 45187 267 234817 1926517 37704 228 60448 983660 16275 129 47818 1443586 25830 104 245546 1073089 12679 122 48020 984885 18014 393 -1710 1405225 43556 190 32648 227132 24811 280 95350 929118 6575 63 151352 1071292 7123 102 288170 638830 21950 265 114337 856956 37597 234 37884 992426 17821 277 122844 444477 12988 73 82340 857217 22330 67 79801 711969 13326 103 165548 702380 16189 290 116384 358589 7146 83 134028 297978 15824 56 63838 585715 27664 236 74996 657954 11920 73 31080 209458 8568 34 32168 786690 14416 139 49857 439798 3369 26 87161 688779 11819 70 106113 574339 6984 40 80570 741409 4519 42 102129 597793 2220 12 301670 644190 18562 211 102313 377934 10327 74 88577 640273 5336 80 112477 697458 2365 83 191778 550608 4069 131 79804 207393 8636 203 128294 301607 13718 56 96448 345783 4525 89 93 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 time16 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24
R Framework
error message
Warning: there are blank lines in the 'Data X' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.


Multiple Linear Regression - Estimated Regression Equation
rijkdom[t] = + 164991.084543089 + 22.0155552515993kosten[t] + 1009.29401656902orders[t] + 1.56845176073623dividenden[t] + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0		2-tail p-value1-tail p-value
(Intercept)164991.08454308930632.055335.386200
kosten22.01555525159932.15471810.217400
orders1009.29401656902349.6844552.88630.0040960.002048
dividenden1.568451760736230.4114563.8120.0001587.9e-05


Multiple Linear Regression - Regression Statistics
Multiple R0.809710996062382
R-squared0.655631897144335
Adjusted R-squared0.653212449114904
F-TEST (value)270.984079496244
F-TEST (DF numerator)3
F-TEST (DF denominator)427
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation253522.115165969
Sum Squared Residuals27444768649002.9


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast		Residuals
Prediction Error
162821544892517.257737841389636.74226216
243210231397208.613964992923814.38603501
341119122748565.754488311363346.24551169
42231932421732.31960318-2198539.31960318
514913481885391.35322613-394043.353226125
616296161519746.23703575109869.762964247
713988931534832.75505323-135939.755053233
819265171797588.61922183128928.380778167
99836601319994.38756011-336334.387560109
101443586728493.400695156715092.599304844
1110730891223746.51045681-150657.510456814
12984885642577.23315009342307.766849910
131405225955549.792846165449675.207153835
142271321366873.28531438-1139741.28531438
159291181143373.22591604-214255.225916044
161071292610717.194257152460574.805742848
17638830876736.61818163-237906.618181629
188569561095027.50567378-238071.505673782
199924261288303.94171835-295877.941718349
204444771029579.62536734-585102.62536734
21857217653753.89733942203463.10266058
22711969849385.151379937-137416.151379937
23702380821981.709618871-119601.709618871
24358589996638.863037772-638049.863037772
25297978616302.098334201-318324.098334201
26585715670012.51927414-84297.5192741403
276579541129850.40118179-471896.401181795
28209458549842.447075373-340384.447075373
29786690438390.314741501348299.685258499
30439798700857.496788264-261059.496788264
31688779402110.958534052286668.041465948
32574339662276.634908576-87937.6349085756
33741409485489.641445537255919.358554463
34597793467054.137293195130738.862706805
35644190699131.988061765-54941.9880617652
36377934947077.863615544-569143.863615544
37640273605962.23246319534310.7675368049
38697458539624.357383473157833.642616527
39550608601623.817858822-51015.8178588223
40207393511958.619346182-304565.619346182
41301607761227.055251306-459620.055251306
42345783674794.97183188-329011.971831881
43501749501576.667657645172.332342355075
44379983589358.25794612-209375.25794612
45387475414714.096214439-27239.096214439
46377305431094.659909326-53789.6599093263
47370837652390.322445249-281553.322445249
48430866695122.00370492-264256.003704921
49469107522654.012461141-53547.0124611411
50194493376490.087292602-181997.087292602
51530670494936.92525437635733.0747456235
52518365604982.615915666-86617.6159156664
53491303719514.113563718-228211.113563718
54527021482874.98989005944146.0101099408
55233773628231.152139286-394458.152139286
56405972391413.18615636214558.8138436375
57652925332532.695878566320392.304121434
58446211468258.039029955-22047.0390299545
59341340400798.765110301-59458.7651103007
60387699593232.644254923-205533.644254923
61493408478898.55811497414509.4418850264
62146494325546.682415915-179052.682415915
63414462407441.3266417067020.67335829397
64364304538445.973454929-174141.973454929
65355178370949.889299214-15771.8892992142
66357760852556.94142727-494796.94142727
67261216326220.969614672-65004.9696146722
68397144412106.587372073-14962.5873720734
69374943475668.819491596-100725.819491596
70424898496902.946544171-72004.9465441714
71202055324349.643717012-122294.643717012
72378525377272.672793031252.32720696992
73310768399464.601134335-88696.601134335
74325738310626.04615156815111.9538484321
75394510429246.916496428-34736.9164964277
76247060345782.35091717-98722.3509171703
77368078396548.424614384-28470.4246143844
78236761310014.875550035-73253.8755500354
79312378354606.785686267-42228.7856862673
80339836377646.10714227-37810.1071422697
81347385320289.40254401427095.5974559858
82426280475937.367195291-49657.3671952912
83352850435552.723131542-82702.723131542
84301881260201.05778559941679.9422144009
85377516352565.69731257524950.3026874247
86357312459691.39081982-102379.390819820
87458343487672.731253889-29329.7312538892
88354228353056.5516404881171.44835951197
89308636423834.176425652-115198.176425652
90386212353695.66781599732516.3321840026
91393343395245.929388131-1902.92938813115
92378509400316.073963132-21807.0739631316
93452469382966.67647213569502.3235278654
94364839537140.446437323-172301.446437323
95358649308837.40035097649811.5996490236
96376641357021.93956287119619.0604371291
97429112357290.16842503571821.8315749649
98330546328405.766408882140.23359111981
99403560444733.866665213-41173.8666652135
100317892319365.849978039-1473.84997803922
101307528343421.951545673-35893.9515456726
102235133347631.048934703-112498.048934703
103299243464750.692984174-165507.692984174
104314073364175.037253676-50102.0372536763
105368186338115.90531675430070.0946832461
106269661322924.191691329-53263.1916913288
107125390377552.886998116-252162.886998116
108510834379697.342156183131136.657843817
109321896497128.652497725-175232.652497725
110249898342135.84737331-92237.8473733099
111408881314361.15679576394519.8432042371
112158492349285.440943689-190793.440943689
113292154457422.784836839-165268.784836839
114289513346979.992026265-57466.9920262652
115378049291859.48468213086189.5153178704
116343466321809.96970829521656.0302917048
117332743315218.40503175617524.5949682440
118442882370391.05251671572490.9474832846
119214215346360.545086258-132145.545086258
120315688300699.7704028514988.2295971502
121375195663763.03834916-288568.03834916
122334280301452.49155639432827.5084436062
123355864458947.959945387-103083.959945386
124480382395476.57618443984905.4238155612
125353058339111.24236126913946.757638731
126217193379662.919843094-162469.919843094
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129318056288363.66399860529692.3360013953
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131314353267899.90179106446453.0982089361
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134312846281621.95610623531224.0438937651
135312075278464.68465855033610.3153414497
136315009270884.34985221644124.6501477842
137318903273205.10612078245697.8938792175
138314887261346.84724782053540.1527521803
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140315380260227.47545499355152.5245450073
141325506274152.45703434351353.5429656567
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150315877260999.95494969354877.045050307
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152305959345092.167394964-39133.1673949644
153315380265273.94553783850106.0544621622
154297765274089.75143746623675.2485625341
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169341570418221.056062484-76651.0560624835
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172312412265371.69077981947040.3092201813
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174309596275690.65356476533905.3464352348
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178316176261829.79117187554346.2088281254
179315380260227.47545499355152.5245450073
180315380260227.47545499355152.5245450073
181359335317933.81160512041401.1883948803
182330068300149.03115485129918.9688451485
183314289331910.777066496-17621.7770664959
184297413302191.002092693-4778.0020926927
185314806268658.41228957646147.5877104245
186333210284826.67577151548383.3242284854
187352108340590.79507709611517.2049229039
188313332271635.48206282841696.5179371724
189291787278130.93112239913656.0688776012
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191318745271433.30011706747311.6998829326
192315380260227.47545499355152.5245450073
193315366271824.01796372143541.9820362787
194315380260227.47545499355152.5245450073
195315688264138.42985107051549.5701489303
196315380260227.47545499355152.5245450073
197409642542507.929501234-132865.929501234
198315380260227.47545499355152.5245450073
199315380260227.47545499355152.5245450073
200269587320105.734124787-50518.7341247865
201315380260227.47545499355152.5245450073
202315380260227.47545499355152.5245450073
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204300962261255.39371043539706.6062895648
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208315380260227.47545499355152.5245450073
209343613292346.81607414451266.1839258565
210306948269089.47964637437858.5203536265
211315380260227.47545499355152.5245450073
212315380260227.47545499355152.5245450073
213330059272377.03146636157681.9685336387
214288985282727.3326731866257.66732681364
215304485280010.31038759124474.6896124094
216315380262246.06348813153133.9365118693
217315688266787.57102862348900.4289713775
218317736275916.64357556641819.3564244337
219315380262246.06348813153133.9365118693
220322331322518.5433539-187.543353900227
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222315380260227.47545499355152.5245450073
223315354261268.31019858054085.6898014197
224312161290716.63564412221444.3643558784
225315576261810.39897625653765.6010237438
226314922289625.08918379925296.9108162007
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229312339273618.91631835238720.083681648
230315380260227.47545499355152.5245450073
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232321376285558.60137979435817.3986202059
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234303230282965.14640385020264.8535961503
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254304376331545.890235276-27169.8902352763
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260315380260227.47545499355152.5245450073
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270331420303775.47217792527644.5278220746
271315380260227.47545499355152.5245450073
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275315380260227.47545499355152.5245450073
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327315380260227.47545499355152.5245450073
328315380260227.47545499355152.5245450073
329315380260227.47545499355152.5245450073
330315380260227.47545499355152.5245450073
331315380260227.47545499355152.5245450073
332315380260227.47545499355152.5245450073
333315380260227.47545499355152.5245450073
334313729265843.30277501147885.6972249887
335315388261269.76418913854118.2358108616
336315371271177.53587027144193.4641297291
337296139299316.017029674-3177.01702967384
338315380260227.47545499355152.5245450073
339313880262085.22141799351794.7785820072
340317698271525.86659104746172.1334089531
341295580282559.18046020313020.8195397971
342315380260227.47545499355152.5245450073
343315380260227.47545499355152.5245450073
344315380260227.47545499355152.5245450073
345308256287019.95748163321236.0425183669
346315380260227.47545499355152.5245450073
347303677263362.54885894140314.4511410594
348315380260227.47545499355152.5245450073
349315380260227.47545499355152.5245450073
350319369305435.22624698413933.7737530163
351318690266795.95610691651894.0438930836
352314049269247.12139740944801.8786025908
353325699281479.03832254344219.9616774566
354314210266318.43704871847891.5629512822
355315380260227.47545499355152.5245450073
356315380260227.47545499355152.5245450073
357322378315009.1199017467368.88009825368
358315380260227.47545499355152.5245450073
359315380260227.47545499355152.5245450073
360315380260227.47545499355152.5245450073
361315398264289.80398004251108.1960199582
362315380260227.47545499355152.5245450073
363315380260227.47545499355152.5245450073
364308336328681.369376943-20345.3693769427
365316386271572.15138900344813.8486109971
366315380260227.47545499355152.5245450073
367315380260227.47545499355152.5245450073
368315380260227.47545499355152.5245450073
369315380260227.47545499355152.5245450073
370315553272091.92461582443461.0753841755
371315380260227.47545499355152.5245450073
372323361275682.72612036147678.273879639
373336639297266.09045105339372.9095489475
374307424273516.71633749733907.2836625035
375315380260227.47545499355152.5245450073
376315380260227.47545499355152.5245450073
377295370266869.68392543128500.3160745685
378322340280210.53530864742129.4646913525
379319864319018.823837220845.176162779548
380315380260227.47545499355152.5245450073
381315380260227.47545499355152.5245450073
382317291310002.7392708227288.26072917764
383280398256746.75650377523651.2434962251
384315380260227.47545499355152.5245450073
385317330277161.75144970340168.2485502966
386238125355404.631229780-117279.631229780
387327071264478.40482804062592.5951719604
388309038283309.84835408725728.1516459132
389314210264335.43601585849874.5639841422
390307930277538.23842348430391.7615765159
391322327282181.81005943340145.1899405671
392292136274002.24921139918133.7507886006
393263276282356.246859009-19080.2468590089
394367655293074.47082282174580.5291771794
395283910380631.943661701-96721.943661701
396283587277123.5948526376463.4051473632
397243650382314.720082238-138664.720082238
398438493628012.790379583-189519.790379583
399296261283879.38534539112381.6146546091
400230621286116.265114540-55495.2651145405
401304252301820.0014469842431.99855301571
402333505290891.1641429742613.83585703
403296919277335.01261920719583.9873807925
404278990328555.694263797-49565.694263797
405276898285893.746030536-8995.74603053621
406327007312995.83380622514011.1661937746
407317046296427.54052545820618.4594745415
408304555291304.85914593513250.1408540652
409298096275189.65057854722906.3494214526
410231861293762.513921778-61901.5139217783
411309422360783.857340672-51361.8573406722
412286963448732.079428023-161769.079428023
413269753295660.256029886-25907.2560298864
414448243388154.60691627860088.3930837224
415165404342929.62364609-177525.62364609
416204325303520.203290526-99195.2032905256
417407159315175.41938933691983.5806106643
418290476307855.638002491-17379.6380024905
419275311325720.168663788-50409.1686637879
420246541283945.000648697-37404.0006486972
421253468297733.015376095-44265.0153760946
422240897416290.860230336-175393.860230336
423-83265464605.26775031-547870.26775031
424-42143416417.14024831-458560.14024831
425272713321557.939410951-48844.9394109507
426215362465376.534818405-250014.534818405
42742754354612.753983437-311858.753983437
4283062751442223.92089398-1135948.92089398
429253537525684.009757232-272147.009757232
430372631708680.274132805-336049.274132805
431-7170675313.139588432-682483.139588432


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
712.43059187002269e-321.21529593501135e-32
818.73968155061824e-534.36984077530912e-53
912.60618008799798e-531.30309004399899e-53
1013.34487615575644e-751.67243807787822e-75
1113.78985864503987e-781.89492932251994e-78
1218.07485195155996e-844.03742597577998e-84
1313.2285601411492e-1051.6142800705746e-105
1412.61548246771382e-1071.30774123385691e-107
1518.42807890605133e-1164.21403945302567e-116
1612.05813802484545e-1231.02906901242272e-123
1711.76946324886654e-1338.84731624433268e-134
1811.34902563231465e-1396.74512816157323e-140
1911.67438956271478e-1448.3719478135739e-145
2019.979505635638e-1534.989752817819e-153
2114.71414664334412e-1612.35707332167206e-161
2212.5226609493253e-1641.26133047466265e-164
2317.25440310876795e-1653.62720155438398e-165
2414.52395190007508e-1712.26197595003754e-171
2511.14822093254683e-1705.74110466273414e-171
2617.16166077435967e-1733.58083038717983e-173
2716.18820574488839e-1763.09410287244419e-176
2813.08914681987606e-1751.54457340993803e-175
2914.70616549517285e-1892.35308274758642e-189
3014.32837635725264e-1892.16418817862632e-189
3116.44204650125655e-1953.22102325062827e-195
3212.90465294295645e-1961.45232647147822e-196
3311.15296707453426e-2055.76483537267128e-206
3414.25153453103015e-2082.12576726551507e-208
3512.16612380567733e-2071.08306190283867e-207
3611.98391168418227e-2089.91955842091136e-209
3714.71658419539691e-2142.35829209769846e-214
3816.24474774560244e-2203.12237387280122e-220
3914.57850347918046e-2192.28925173959023e-219
4011.14392730640348e-2195.71963653201741e-220
4113.04489879161380e-2211.52244939580690e-221
4211.87541980413821e-2209.37709902069106e-221
4318.0536263429629e-2214.02681317148145e-221
4419.40740008042252e-2204.70370004021126e-220
4512.08886078731957e-2191.04443039365978e-219
4611.80848413971682e-2189.04242069858411e-219
4714.58538582192862e-2192.29269291096431e-219
4812.17406597658238e-2181.08703298829119e-218
4918.20890625768011e-2184.10445312884006e-218
5014.34340244785222e-2182.17170122392611e-218
5111.57470332317005e-2187.87351661585026e-219
5214.48425635971645e-2182.24212817985822e-218
5312.73082634264659e-2171.36541317132330e-217
5418.42376625000354e-2174.21188312500177e-217
5515.05176672423383e-2202.52588336211691e-220
5611.09834567332593e-2195.49172836662965e-220
5713.51808330017777e-2331.75904165008888e-233
5811.41642759526982e-2337.08213797634908e-234
5911.30164042180755e-2326.50820210903773e-233
6013.36675783528787e-2321.68337891764393e-232
6116.71749963214634e-2343.35874981607317e-234
6211.97248622004423e-2359.86243110022114e-236
6315.45236203476753e-2352.72618101738377e-235
6413.00439527081683e-2341.50219763540841e-234
6511.67149630092614e-2338.3574815046307e-234
6618.48017566696292e-2344.24008783348146e-234
6712.27392219042630e-2331.13696109521315e-233
6812.14269248751838e-2321.07134624375919e-232
6911.21471548434443e-2316.07357742172214e-232
7016.70720629019067e-2313.35360314509533e-231
7114.72345307813035e-2302.36172653906518e-230
7213.81753026813851e-2311.90876513406925e-231
7311.31070514664715e-2306.55352573323573e-231
7411.12415794737838e-2295.62078973689192e-230
7511.34986865870349e-2286.74934329351743e-229
7613.16441721191054e-2281.58220860595527e-228
7712.85478304758093e-2271.42739152379047e-227
7813.83742733689769e-2271.91871366844885e-227
7914.03620723247289e-2262.01810361623644e-226
8011.52557749866762e-2257.62788749333811e-226
8119.07595630623219e-2254.53797815311609e-225
8211.49752257767914e-2247.48761288839572e-225
8311.45955034119606e-2247.29775170598028e-225
8418.1798042299183e-2244.08990211495915e-224
8517.94582008027438e-2233.97291004013719e-223
8612.12371418679139e-2221.06185709339569e-222
8711.69400833514697e-2228.47004167573486e-223
8811.26703187725090e-2216.33515938625449e-222
8912.73834960876463e-2211.36917480438231e-221
9012.66401976639564e-2201.33200988319782e-220
9112.42177793864934e-2191.21088896932467e-219
9211.57776673788929e-2187.88883368944646e-219
9315.30898354052642e-2202.65449177026321e-220
9415.40222954244682e-2192.70111477122341e-219
9511.92382934087199e-2199.61914670435995e-220
9611.70764933322935e-2198.53824666614673e-220
9711.53317127697414e-2187.66585638487071e-219
9811.50611714648021e-2177.53058573240104e-218
9911.31793540011688e-2166.58967700058442e-217
10011.29577711081643e-2156.47888555408213e-216
10111.17021790578663e-2145.85108952893315e-215
10219.19177359799409e-2164.59588679899704e-216
10318.4327061979712e-2164.2163530989856e-216
10411.40365824322734e-2167.01829121613671e-217
10516.19157328897933e-2163.09578664448966e-216
10612.18758581473996e-2151.09379290736998e-215
10711.34618952995067e-2176.73094764975335e-218
10815.64966428867134e-2192.82483214433567e-219
10914.29918558985093e-2182.14959279492547e-218
11018.6208519893218e-2184.3104259946609e-218
11116.13486834521099e-2183.06743417260550e-218
11213.81116313007255e-2181.90558156503628e-218
11312.94683910492711e-2171.47341955246356e-217
11412.38776149859528e-2161.19388074929764e-216
11511.58463804066966e-2167.9231902033483e-217
11616.3657810661596e-2163.1828905330798e-216
11714.58581539574445e-2152.29290769787223e-215
11813.68647580516409e-2151.84323790258204e-215
11913.97861251686958e-2161.98930625843479e-216
12014.08825267337115e-2152.04412633668558e-215
12111.97557323755367e-2149.87786618776834e-215
12211.83293186157737e-2139.16465930788685e-214
12311.58962862716054e-2127.9481431358027e-213
12412.19867780744085e-2121.09933890372043e-212
12516.31830643510483e-2123.15915321755241e-212
12612.06302286208456e-2121.03151143104228e-212
12711.92641423094510e-2119.63207115472548e-212
12811.90240333105232e-2109.51201665526162e-211
12911.81886465480420e-2099.09432327402102e-210
13011.71006984731684e-2088.5503492365842e-209
13111.66894621569374e-2078.34473107846868e-208
13211.43541124824849e-2077.17705624124244e-208
13311.36757478214420e-2066.83787391072098e-207
13411.41736951442348e-2057.08684757211742e-206
13511.40197259062069e-2047.00986295310346e-205
13611.35831304770281e-2036.79156523851405e-204
13711.32200439596673e-2026.61002197983365e-203
13811.26975055663691e-2016.34875278318456e-202
13911.21427449662231e-2006.07137248311156e-201
14011.15877097543800e-1995.79385487718999e-200
14119.5898733027284e-1994.7949366513642e-199
14219.15111515516484e-1984.57555757758242e-198
14319.3690984850762e-1974.6845492425381e-197
14419.0367562622402e-1964.5183781311201e-196
14518.27108868443046e-1954.13554434221523e-195
14617.58434963929277e-1943.79217481964638e-194
14717.19171612089171e-1933.59585806044586e-193
14816.97585447073103e-1923.48792723536552e-192
14916.00605863375904e-1913.00302931687952e-191
15015.67764291141169e-1902.83882145570585e-190
15115.52793004063645e-1892.76396502031823e-189
15215.70621573599308e-1882.85310786799654e-188
15315.41989370051817e-1872.70994685025909e-187
15415.31781415955697e-1862.65890707977849e-186
15514.99980316288243e-1852.49990158144121e-185
15614.65230092692628e-1842.32615046346314e-184
15714.32032598617015e-1832.16016299308507e-183
15814.05716516167045e-1822.02858258083522e-182
15912.83767469122773e-1811.41883734561386e-181
16012.61948811364236e-1801.30974405682118e-180
16112.41239753924643e-1791.20619876962321e-179
16212.21628300922628e-1781.10814150461314e-178
16312.03101163976433e-1771.01550581988217e-177
16411.93972756306305e-1769.69863781531523e-177
16511.80940414039180e-1759.04702070195901e-176
16611.64978967943884e-1748.2489483971942e-175
16711.4934761195055e-1737.4673805975275e-174
16811.85079521188084e-1749.2539760594042e-175
16913.30398625609064e-1741.65199312804532e-174
17013.02732080930475e-1731.51366040465238e-173
17112.76575163496066e-1721.38287581748033e-172
17212.57425457799331e-1711.28712728899665e-171
17312.33744285288676e-1701.16872142644338e-170
17412.19403988766041e-1691.09701994383020e-169
17511.97918957107904e-1689.89594785539519e-169
17611.80531875655758e-1679.0265937827879e-168
17711.69598912136057e-1668.47994560680286e-167
17811.50532580303751e-1657.52662901518754e-166
17911.33838266711689e-1646.69191333558447e-165
18011.18609250638843e-1635.93046253194215e-164
18117.91125038742731e-1633.95562519371366e-163
18217.25004550723182e-1623.62502275361591e-162
18314.2259104805611e-1612.11295524028055e-161
18412.56850339039695e-1601.28425169519847e-160
18512.29305018281665e-1591.14652509140833e-159
18611.53085636401833e-1587.65428182009165e-159
18715.72608191360165e-1582.86304095680083e-158
18815.09283546903045e-1572.54641773451523e-157
18913.60017615462453e-1561.80008807731227e-156
19013.10158999609644e-1551.55079499804822e-155
19112.53966350331334e-1541.26983175165667e-154
19212.172515763813e-1531.0862578819065e-153
19311.88344296449892e-1529.4172148224946e-153
19411.59939043891837e-1517.99695219459184e-152
19511.35895016154546e-1506.7947508077273e-151
19611.14560285438912e-1495.72801427194559e-150
19718.78755010084874e-1494.39377505042437e-149
19817.3510603280731e-1483.67553016403655e-148
19916.12684685565346e-1473.06342342782673e-147
20016.34481635825209e-1473.17240817912604e-147
20115.30108294740103e-1462.65054147370052e-146
20214.41261116752926e-1452.20630558376463e-145
20313.65933774741463e-1441.82966887370731e-144
20412.80877786649111e-1431.40438893324556e-143
20511.23529179669549e-1426.17645898347744e-143
20611.02778686729320e-1415.13893433646598e-142
20718.5504705533681e-1414.27523527668405e-141
20816.98126721250013e-1403.49063360625007e-140
20911.00513832592981e-1395.02569162964907e-140
21018.40389328666368e-1394.20194664333184e-139
21116.8313750282176e-1383.4156875141088e-138
21215.53153008639975e-1372.76576504319988e-137
21313.3526557456017e-1361.67632787280085e-136
21412.52067488242744e-1351.26033744121372e-135
21512.07021906314035e-1341.03510953157018e-134
21611.65528533759708e-1338.27642668798541e-134
21711.32212205625823e-1326.61061028129113e-133
21811.02130187486900e-1315.10650937434498e-132
21918.06698492432235e-1314.03349246216118e-131
22013.86663554911917e-1301.93331777455958e-130
22113.04611849643705e-1291.52305924821852e-129
22212.37735725322091e-1281.18867862661046e-128
22311.84904185310026e-1279.2452092655013e-128
22411.45126572107877e-1267.25632860539383e-127
22511.11910710573625e-1255.59553552868127e-126
22618.7231328113294e-1254.3615664056647e-125
22716.72339086774401e-1243.36169543387201e-124
22815.11706153074331e-1232.55853076537166e-123
22913.91790829726264e-1221.95895414863132e-122
23012.95773960496738e-1211.47886980248369e-121
23112.14715181466980e-1201.07357590733490e-120
23211.48167607280574e-1197.40838036402868e-120
23311.10526301594791e-1185.52631507973954e-119
23418.4195696816369e-1184.20978484081845e-118
23516.22757408783121e-1173.11378704391561e-117
23614.58570672967866e-1162.29285336483933e-116
23713.36327758012234e-1151.68163879006117e-115
23812.44582329081543e-1141.22291164540772e-114
23911.77853989328763e-1138.89269946643817e-114
24011.28778492093654e-1126.43892460468268e-113
24119.2844821007195e-1124.64224105035975e-112
24216.75956053426842e-1113.37978026713421e-111
24314.83133070702751e-1102.41566535351375e-110
24413.40537754535048e-1091.70268877267524e-109
24512.47183081656359e-1081.23591540828179e-108
24611.74317393936337e-1078.71586969681683e-108
24711.2239423925668e-1066.119711962834e-107
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3810.9999999999999983.48190289943276e-151.74095144971638e-15
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3830.9999999999999852.96251350600436e-141.48125675300218e-14
3840.9999999999999578.65849626611282e-144.32924813305641e-14
3850.9999999999998732.54911441098212e-131.27455720549106e-13
3860.999999999999666.81279472891074e-133.40639736445537e-13
3870.999999999999111.78147893361308e-128.90739466806542e-13
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3890.9999999999933171.33666255979946e-116.68331279899728e-12
3900.9999999999819763.60483239118915e-111.80241619559457e-11
3910.9999999999524579.508510818804e-114.754255409402e-11
3920.9999999998666072.66785650083545e-101.33392825041772e-10
3930.9999999996198447.60312302602354e-103.80156151301177e-10
3940.9999999992366621.52667664446335e-097.63338322231677e-10
3950.9999999979289234.14215310536781e-092.07107655268390e-09
3960.9999999944050521.11898964415732e-085.5949482207866e-09
3970.999999985552092.88958211895994e-081.44479105947997e-08
3980.9999999707385165.85229677295349e-082.92614838647674e-08
3990.999999923745321.52509358200523e-077.62546791002616e-08
4000.999999839159583.21680840110819e-071.60840420055410e-07
4010.9999995906651428.18669717017249e-074.09334858508624e-07
4020.9999991203215661.75935686828644e-068.79678434143222e-07
4030.9999979515198684.09696026423441e-062.04848013211720e-06
4040.9999949422463391.01155073223510e-055.05775366117548e-06
4050.9999878008352232.43983295540651e-051.21991647770325e-05
4060.9999732218921365.35562157284404e-052.67781078642202e-05
4070.9999411884490320.0001176231019367745.88115509683872e-05
4080.9998804596144310.0002390807711374820.000119540385568741
4090.999756251042820.0004874979143599250.000243748957179962
4100.9994845521035560.001030895792887680.000515447896443842
4110.9989024028541890.002195194291622540.00109759714581127
4120.9982032391275020.003593521744995220.00179676087249761
4130.9964342037258970.007131592548206310.00356579627410316
4140.9968652844695480.00626943106090370.00313471553045185
4150.9949696325603540.01006073487929250.00503036743964623
4160.9905244144080820.01895117118383550.00947558559191774
4170.9977197834509330.004560433098134450.00228021654906723
4180.9952420661216820.009515867756636120.00475793387831806
4190.9890590900878020.02188181982439560.0109409099121978
4200.9754772354501960.04904552909960840.0245227645498042
4210.9482407820462810.1035184359074370.0517592179537187
4220.8942305230259060.2115389539481880.105769476974094
4230.8019683793187950.396063241362410.198031620681205
4240.8245668399751340.3508663200497310.175433160024866


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level4100.980861244019139NOK
5% type I error level4140.99043062200957NOK
10% type I error level4140.99043062200957NOK
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Dec/01/t1291211941g1tzua9jxmfp3nq/10gnli1291212001.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/01/t1291211941g1tzua9jxmfp3nq/10gnli1291212001.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/01/t1291211941g1tzua9jxmfp3nq/1kv5r1291212001.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/01/t1291211941g1tzua9jxmfp3nq/1kv5r1291212001.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/01/t1291211941g1tzua9jxmfp3nq/2kv5r1291212001.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/01/t1291211941g1tzua9jxmfp3nq/2kv5r1291212001.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/01/t1291211941g1tzua9jxmfp3nq/3kv5r1291212001.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/01/t1291211941g1tzua9jxmfp3nq/3kv5r1291212001.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/01/t1291211941g1tzua9jxmfp3nq/4d5nc1291212001.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/01/t1291211941g1tzua9jxmfp3nq/4d5nc1291212001.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/01/t1291211941g1tzua9jxmfp3nq/5d5nc1291212001.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/01/t1291211941g1tzua9jxmfp3nq/5d5nc1291212001.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/01/t1291211941g1tzua9jxmfp3nq/6d5nc1291212001.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/01/t1291211941g1tzua9jxmfp3nq/6d5nc1291212001.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/01/t1291211941g1tzua9jxmfp3nq/76vmx1291212001.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/01/t1291211941g1tzua9jxmfp3nq/76vmx1291212001.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/01/t1291211941g1tzua9jxmfp3nq/8gnli1291212001.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/01/t1291211941g1tzua9jxmfp3nq/8gnli1291212001.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/01/t1291211941g1tzua9jxmfp3nq/9gnli1291212001.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/01/t1291211941g1tzua9jxmfp3nq/9gnli1291212001.ps (open in new window)


 
Parameters (Session):
par1 = 4 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;
 
Parameters (R input):
par1 = 4 ; 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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