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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: Mon, 20 Dec 2010 20:30:54 +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/20/t1292876964ogsjyr30ylmkfwj.htm/, Retrieved Mon, 20 Dec 2010 21:29:27 +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/20/t1292876964ogsjyr30ylmkfwj.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 «
807 213118 6282154 444 81767 4321023 412 153198 4111912 428 -26007 223193 315 126942 1491348 168 157214 1629616 263 129352 1398893 267 234817 1926517 228 60448 983660 129 47818 1443586 104 245546 1073089 122 48020 984885 393 -1710 1405225 190 32648 227132 280 95350 929118 63 151352 1071292 102 288170 638830 265 114337 856956 234 37884 992426 277 122844 444477 73 82340 857217 67 79801 711969 103 165548 702380 290 116384 358589 83 134028 297978 56 63838 585715 236 74996 657954 73 31080 209458 34 32168 786690 139 49857 439798 26 87161 688779 70 106113 574339 40 80570 741409 42 102129 597793 12 301670 644190 211 102313 377934 74 88577 640273 80 112477 697458 83 191778 550608 131 79804 207393 203 128294 301607 56 96448 345783 89 93811 501749 88 117520 379983 39 69159 387475 25 101792 377305 49 210568 370837 149 136996 430866 58 121920 469107 41 76403 194493 90 108094 530670 136 134759 518365 97 188873 491303 63 146216 527021 114 156608 233773 77 61348 405972 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 time13 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk


Multiple Linear Regression - Estimated Regression Equation
rijkdom[t] = + 145478.134474853 + 4088.80913965477kosten[t] + 1.475846916875dividenden[t] + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0		2-tail p-value1-tail p-value
(Intercept)145478.13447485334065.6881024.27052.4e-051.2e-05
kosten4088.80913965477197.56474120.69600
dividenden1.4758469168750.4583583.21990.001380.00069


Multiple Linear Regression - Regression Statistics
Multiple R0.755936094718231
R-squared0.571439379297851
Adjusted R-squared0.569436759574943
F-TEST (value)285.345926019485
F-TEST (DF numerator)2
F-TEST (DF denominator)428
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation282489.672238382
Sum Squared Residuals34154577586337.3


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast		Residuals
Prediction Error
162821543759676.653406822522477.34659318
243210232081584.967333692239438.03266631
341119122056164.295984032055747.70401597
42231931857106.09547993-1633913.09547993
514913481620799.97278805-129451.972788052
616296161064421.86712644565194.13287356
713988931411738.68859567-12845.6885956722
819265171583744.12024251342772.879757487
99836601166938.6127474-183278.612747401
101443586743506.561361447700079.438638553
111073089933102.592049937139986.407950063
12984885715183.018461073269701.981538927
1314052251749856.42813132-344631.428131321
14227132970535.321151395-743403.321151395
159291181431066.69710222-501948.69710222
161071292626445.492835969444846.507164031
17638830987831.472755508-349001.472755508
188569561397756.4654181-540800.465418104
199924261158170.45775296-165744.457752962
204444771459377.20481582-1014900.20481582
21857217565482.436805139291734.563194861
22711969537202.406645264174766.593354735
23702380810948.981254117-108568.981254117
243585891502997.75254832-1144408.75254832
25297978682654.103641121-384676.103641121
26585715468666.561774986117048.438225014
276579541221119.70681134-563165.706811336
28209458489830.523846126-280372.523846126
29786690331972.68884515454717.31115485
30439798787403.904621503-347605.904621503
31688779380423.465227619308355.534772381
32574339588301.318141044-13962.3181410438
33741409427939.486153663313469.513846337
34597793467934.88811388129858.11188612
35644190639762.5835643914427.41643560888
363779341159215.18854824-781281.188548241
37640273578776.10316534361496.8968346571
38697458638581.69931658458876.3006834161
39550608767884.263090652-217276.263090652
40207393798890.619123921-591497.619123921
413016071164848.69417833-863241.694178332
42345783516793.92973428-171010.92973428
43501749647832.823023088-146083.823023088
44379983678734.868435623-298751.868435623
45387475407009.787845547-19534.7878455473
46377305397927.772328762-20622.7723287623
47370837656595.915910471-285758.915910472
48430866956895.820507621-526029.820507621
49469107562564.32068023-93457.3206802296
50194493425878.441190699-231385.441190699
51530670673001.153676469-142331.153676469
52518365900439.83213906-382074.83213906
53491303820840.255752297-329537.255752297
54527021618865.543070898-91844.5430708984
55233773842731.810353457-608958.810353457
56405972550856.694884718-144884.694884718
57652925244319.881577438408605.118422562
58446211467113.455586902-20902.4555869023
59341340500837.934510223-159497.934510223
60387699622043.972971804-234344.972971804
61493408460550.46332174932857.5366782512
62146494365351.968051207-218857.968051207
63414462387416.79058677927045.2094132215
64364304581963.120351692-217659.120351692
65355178453373.885509423-98195.8855094226
663577601305818.92814104-948058.92814104
67261216326045.419830923-64829.4198309228
68397144473594.711553001-76450.7115530011
69374943637468.346022634-262525.346022634
70424898641008.605853648-216110.605853648
71202055386164.678556131-184109.678556131
72378525358468.46956961820056.5304303824
73310768446332.352072954-135564.352072954
74325738299289.9395361826448.0604638196
75394510459947.802548132-65437.802548132
76247060341813.982496537-94753.9824965366
77368078433433.598480751-65355.5984807513
78236761299689.844563559-62928.8445635587
79312378460615.915817623-148237.915817623
80339836372589.253535504-32753.2535355044
81347385354053.696209713-6668.69620971275
82426280548359.096156928-122079.096156928
83352850485508.757968496-132658.757968496
84301881265290.70565084736590.2943491534
85377516358416.64610565919099.353894341
86357312518324.086064511-161012.086064511
87458343687571.942851301-229228.942851301
88354228352061.698768692166.30123130994
89308636486816.061414278-178180.061414278
90386212355242.86205446730969.1379455333
91393343433693.912256748-40350.9122567479
92378509431382.637010732-52873.637010732
93452469517370.688956209-64901.6889562093
94364839451353.331745448-86514.3317454476
95358649376681.034729576-18032.0347295764
96376641357057.75786546419583.2421345356
97429112349040.73910403780071.2608959634
98330546339012.775561213-8466.77556121308
99403560415232.225890406-11672.2258904061
100317892290340.4038322527551.5961677496
101307528384563.830035175-77035.8300351747
102235133356779.832900655-121646.832900655
103299243530461.034851548-231218.034851548
104314073346082.428702708-32009.4287027081
105368186361349.5701868326836.42981316831
106269661369666.680743333-100005.680743333
107125390430042.37006183-304652.37006183
108510834355369.735402223155464.264597777
109321896487422.585010019-165526.585010019
110249898334923.253241647-85025.2532416473
111408881335699.49923282973181.5007671713
112158492351281.956725632-192789.956725632
113292154452472.390478686-160318.390478686
114289513307874.842077453-18361.8420774526
115378049254916.462440601123132.537559399
116343466371771.089985513-28305.0899855126
117332743303620.83705729829122.1629427025
118442882345733.1682149497148.8317850596
119214215304390.416993806-90175.4169938056
120315688321756.4602292-6068.46022919959
121375195684447.772876656-309252.772876656
122334280293425.58758133540854.4124186646
123355864740824.630230333-384960.630230333
124480382406465.54674288473916.4532571159
125353058307848.17785875945209.8221412408
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137318903276311.71622034842591.2837796523
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139314913251446.79582612263466.2041738777
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172312412248603.6014843163808.39851569
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174309596273688.4230691535907.5769308502
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176315547268142.95302253947404.0469774606
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178316176235128.45544042581047.5445595749
179315380235091.55926750380288.4407324968
180315380235091.55926750380288.4407324968
181359335328898.13294705330436.8670529475
182330068296186.18398289733881.8160171025
183314289330038.814152512-15749.8141525124
184297413316972.626165886-19559.6261658863
185314806258243.78405824356562.2159417573
186333210279551.91338279953658.0866172006
187352108335263.36172534516844.6382746553
188313332261574.00788262451757.9921173764
189291787262951.73572307428835.2642769261
190315380235091.55926750380288.4407324968
191318745261912.69000649956832.3099935009
192315380235091.55926750380288.4407324968
193315366265056.24393944350309.7560605572
194315380235091.55926750380288.4407324968
195315688247608.88066233668079.1193376637
196315380235091.55926750380288.4407324968
197409642676921.765754694-267279.765754694
198315380235091.55926750380288.4407324968
199315380235091.55926750380288.4407324968
200269587341299.674589553-71712.6745895531
201315380235091.55926750380288.4407324968
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209343613323398.21620648620214.783793514
210306948247357.98668646859590.0133135325
211315380235091.55926750380288.4407324968
212315380235091.55926750380288.4407324968
213330059275522.85129973154536.1487002694
214288985277834.79023856311150.2097614373
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216315380243269.17754681372110.8224531873
217315688259788.23311320555899.7668867951
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222315380235091.55926750380288.4407324968
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228315380235091.55926750380288.4407324968
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230315380235091.55926750380288.4407324968
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233315380235091.55926750380288.4407324968
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271315380235091.55926750380288.4407324968
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307315380235091.55926750380288.4407324968
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327315380235091.55926750380288.4407324968
328315380235091.55926750380288.4407324968
329315380235091.55926750380288.4407324968
330315380235091.55926750380288.4407324968
331315380235091.55926750380288.4407324968
332315380235091.55926750380288.4407324968
333315380235091.55926750380288.4407324968
334313729250943.53202746862785.4679725321
335315388239190.69933557676197.3006644239
336315371251446.79582612263924.2041738777
337296139317170.290678558-21031.2906785579
338315380235091.55926750380288.4407324968
339313880239440.11746452874439.882535472
340317698274524.46560401243173.5343959879
341295580287476.4486594128103.55134058773
342315380235091.55926750380288.4407324968
343315380235091.55926750380288.4407324968
344315380235091.55926750380288.4407324968
345308256288246.07808301520009.9219169848
346315380235091.55926750380288.4407324968
347303677244993.67992563458683.3200743662
348315380235091.55926750380288.4407324968
349315380235091.55926750380288.4407324968
350319369275979.65066405143389.3493359491
351318690244226.23952885974463.7604711412
352314049264309.46539950449739.534600496
353325699274319.32288256651379.6771174335
354314210241165.38251035573044.6174896452
355315380235091.55926750380288.4407324968
356315380235091.55926750380288.4407324968
357322378323077.491681087-699.491681087174
358315380235091.55926750380288.4407324968
359315380235091.55926750380288.4407324968
360315380235091.55926750380288.4407324968
361315398251449.74751995663948.252480044
362315380235091.55926750380288.4407324968
363315380235091.55926750380288.4407324968
364308336350876.960464687-42540.9604646867
365316386270289.54761958746096.4523804133
366315380235091.55926750380288.4407324968
367315380235091.55926750380288.4407324968
368315380235091.55926750380288.4407324968
369315380235091.55926750380288.4407324968
370315553263713.22324508751839.7767549134
371315380235091.55926750380288.4407324968
372323361262327.40299014161033.5970098591
373336639287214.60954940449424.390450596
374307424253408.95904565554015.040954345
375315380235091.55926750380288.4407324968
376315380235091.55926750380288.4407324968
377295370273365.16310725922004.8368927406
378322340263294.08272069459045.917279306
379319864275979.65066405143884.3493359491
380315380235091.55926750380288.4407324968
381315380235091.55926750380288.4407324968
382317291327452.565635521-10161.5656355209
383280398263935.16500124416462.8349987556
384315380235091.55926750380288.4407324968
385317330287079.44583877330250.5541612271
386238125364121.923876634-125996.923876634
387327071245795.06480149781275.9351985031
388309038256525.13557999452512.8644200057
389314210246882.76397923467327.2360207662
390307930264643.71998262943286.2800173712
391322327278916.58602863243410.4139713679
392292136257565.60765639134570.3923436089
393263276268141.477175623-4865.47717562256
394367655270457.13047529497197.8695247058
395283910305687.735920834-21777.7359208335
396283587264460.71496493619126.2850350637
397243650329728.123632963-86078.1236329628
3984384931301536.31731084-863043.317310837
399296261268362.14103324327898.8589667572
400230621344113.570301991-113492.570301991
401304252261666.32254557142585.6774544294
402333505272982.25506297360522.7449370274
403296919257366.36832261339552.631677387
404278990333694.585939801-54704.5859398015
405276898268952.4797999937945.5202000072
406327007294788.55695261732218.4430473832
407317046290820.0045931426225.99540686
408304555281515.50296215423039.4970378458
409298096268348.80892389629747.1910761039
410231861261024.32913673-29163.32913673
411309422481647.348588813-172225.348588813
412286963324697.823134531-37734.8231345314
413269753291405.81684495-21652.8168449497
414448243387347.99050031260895.009499688
415165404307666.797149268-142262.797149268
416204325262115.742675306-57790.7426753064
417407159291544.348506757115614.651493243
418290476319177.442485508-28701.4424855079
419275311345747.015555819-70436.0155558189
420246541246854.772374908-313.772374907953
421253468252536.783004877931.216995123315
422240897555318.992268532-314421.992268532
423-83265402050.962565431-485315.962565431
424-42143309650.85063708-351793.85063708
425272713308682.69505961-35969.6950596098
426215362579698.30954001-364336.309540011
42742754306983.232591281-264229.232591281
4283062751375265.81594288-1068990.81594288
429253537393664.615304537-140127.615304537
430372631611405.305727963-238774.305727963
431-7170467872.97239105-475042.97239105


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
617.07507186867353e-473.53753593433677e-47
711.64793266096988e-508.23966330484938e-51
813.94895572724858e-661.97447786362429e-66
919.85924833400397e-674.92962416700199e-67
1014.42232897570995e-872.21116448785498e-87
1112.72384447462075e-911.36192223731037e-91
1213.53940135817865e-971.76970067908933e-97
1311.4017175963531e-1077.0085879817655e-108
1412.97499038389788e-1081.48749519194894e-108
1511.36509956113287e-1136.82549780566434e-114
1612.56628885589915e-1211.28314442794958e-121
1713.12259813865641e-1281.56129906932821e-128
1812.98077098183844e-1331.49038549091922e-133
1917.54143699803904e-1423.77071849901952e-142
2011.06963566862719e-1495.34817834313596e-150
2113.7023305297797e-1591.85116526488985e-159
2213.558736019129e-1641.7793680095645e-164
2315.79616850223545e-1652.89808425111773e-165
2412.45644302032664e-1731.22822151016332e-173
2516.20596464443956e-1733.10298232221978e-173
2614.42898563430304e-1762.21449281715152e-176
2712.7374619880219e-1791.36873099401095e-179
2818.12535599392599e-1794.06267799696299e-179
2915.0704777383439e-1932.53523886917195e-193
3017.13067071434271e-1933.56533535717136e-193
3111.17941317195835e-1985.89706585979175e-199
3211.76015054511098e-1998.8007527255549e-200
3315.1609759132127e-2082.58048795660635e-208
3414.12312505547063e-2102.06156252773531e-210
3511.46016935139302e-2097.30084675696508e-210
3612.90977268173838e-2111.45488634086919e-211
3712.19389792568605e-2151.09694896284303e-215
3811.1022152273638e-2205.511076136819e-221
3913.34265312427182e-2201.67132656213591e-220
4011.18319653793346e-2205.9159826896673e-221
4112.442955697275e-2231.2214778486375e-223
4213.16429518395827e-2221.58214759197913e-222
4311.23674923711924e-2226.1837461855962e-223
4411.32584956558731e-2216.62924782793655e-222
4513.70825361822742e-2211.85412680911371e-221
4612.99082206381104e-2201.49541103190552e-220
4713.83217627636231e-2211.91608813818115e-221
4814.5899695549644e-2212.2949847774822e-221
4912.48025828980253e-2201.24012914490126e-220
5011.88555704931136e-2209.42778524655678e-221
5113.70808484712129e-2211.85404242356065e-221
5211.51214731817931e-2217.56073659089656e-222
5316.82555149689926e-2213.41277574844963e-221
5411.34163984574498e-2206.70819922872488e-221
5512.34883759078939e-2231.1744187953947e-223
5613.26810339034905e-2231.63405169517453e-223
5711.35458167736014e-2346.77290838680068e-235
5811.5022648066759e-2347.51132403337948e-235
5911.83565722398985e-2339.17828611994923e-234
6011.35207946757904e-2326.76039733789522e-233
6112.03659774074726e-2331.01829887037363e-233
6211.92226054727089e-2349.61130273635444e-235
6317.18507210293993e-2343.59253605146996e-234
6416.97665152092826e-2333.48832576046413e-233
6513.42890625990005e-2321.71445312995003e-232
6611.5007475609188e-2347.503737804594e-235
6714.24630847683865e-2342.12315423841932e-234
6813.68653849303724e-2331.84326924651862e-233
6913.68146279269909e-2321.84073139634955e-232
7011.26417025057734e-2316.32085125288671e-232
7119.98473182089358e-2314.99236591044679e-231
7213.65234261800324e-2311.82617130900162e-231
7312.01233584016817e-2301.00616792008408e-230
7411.35947944753098e-2296.79739723765489e-230
7511.59360981250223e-2287.96804906251114e-229
7613.78152847169004e-2281.89076423584502e-228
7713.91989862539048e-2271.95994931269524e-227
7816.12012274315005e-2273.06006137157503e-227
7917.27505426859332e-2263.63752713429666e-226
8013.2307707726911e-2251.61538538634555e-225
8111.65068444982706e-2248.2534222491353e-225
8213.51840711195109e-2241.75920355597554e-224
8319.54207954303694e-2244.77103977151847e-224
8414.29050609984115e-2232.14525304992057e-223
8513.86760471441506e-2221.93380235720753e-222
8611.64668273227999e-2218.23341366139996e-222
8712.6427386085705e-2221.32136930428525e-222
8812.02960370838093e-2211.01480185419046e-221
8918.87073780902053e-2214.43536890451026e-221
9017.81743732322054e-2203.90871866161027e-220
9116.43741718124017e-2193.21870859062008e-219
9214.29639552554649e-2182.14819776277324e-218
9315.98864861550635e-2202.99432430775318e-220
9413.01219906932551e-2191.50609953466275e-219
9518.8383437284806e-2204.4191718642403e-220
9611.33763138743044e-2196.68815693715222e-220
9711.06148503565865e-2185.30742517829325e-219
9819.44167767522698e-2184.72083883761349e-218
9916.56165017693471e-2173.28082508846736e-217
10015.18306530588717e-2162.59153265294358e-216
10115.23466562872569e-2152.61733281436284e-215
10211.08451077533721e-2155.42255387668604e-216
10311.90151320582686e-2159.50756602913429e-216
10415.54072340979789e-2162.77036170489895e-216
10512.37345243432523e-2151.18672621716261e-215
10611.44642109294283e-2147.23210546471414e-215
10714.69983892024941e-2162.34991946012471e-216
10817.73622052006478e-2173.86811026003239e-217
10913.82337460743124e-2161.91168730371562e-216
11018.23689767600511e-2164.11844883800256e-216
11116.33999972416272e-2163.16999986208136e-216
11214.45238501690611e-2162.22619250845306e-216
11312.43307038493266e-2151.21653519246633e-215
11411.35416187131728e-2146.77080935658642e-215
11511.63439423289004e-2148.1719711644502e-215
11615.43198434159779e-2142.71599217079889e-214
11713.75931842368454e-2131.87965921184227e-213
11816.8097807983037e-2133.40489039915185e-213
11916.26333609548557e-2143.13166804774279e-214
12015.80880615154211e-2132.90440307577106e-213
12114.70764221125885e-2122.35382110562942e-212
12213.9639732495143e-2111.98198662475715e-211
12311.74164817498089e-2108.70824087490446e-211
12413.76314887038737e-2101.88157443519369e-210
12511.77494653883671e-2098.87473269418355e-210
12614.31937225732173e-2102.15968612866086e-210
12713.38109143070429e-2091.69054571535214e-209
12812.97753116273432e-2081.48876558136716e-208
12912.3926941713787e-2071.19634708568935e-207
13011.90943043566776e-2069.5471521783388e-207
13111.65617760103899e-2058.28088800519493e-206
13211.78091923442774e-2058.90459617213869e-206
13311.45645346173056e-2047.2822673086528e-205
13411.39107041568808e-2036.95535207844038e-204
13511.21161829491372e-2026.05809147456861e-203
13611.04073988104556e-2015.20369940522778e-202
13719.1107586838375e-2014.55537934191875e-201
13817.68924115286051e-2003.84462057643026e-200
13916.68688164348268e-1993.34344082174134e-199
14015.61788221814847e-1982.80894110907424e-198
14114.28136049119612e-1972.14068024559806e-197
14213.62056705017521e-1961.8102835250876e-196
14313.43620986218126e-1951.71810493109063e-195
14413.00811395372137e-1941.50405697686069e-194
14512.51590276015356e-1931.25795138007678e-193
14612.10715593171621e-1921.0535779658581e-192
14711.79380298551352e-1918.96901492756758e-192
14811.60701643511035e-1908.03508217555177e-191
14911.28936638990472e-1896.44683194952358e-190
15011.10270757048149e-1885.51353785240744e-189
15111.0079381448701e-1875.03969072435048e-188
15218.6884715165335e-1874.34423575826675e-187
15317.63152648487109e-1863.81576324243555e-186
15417.02170715507524e-1853.51085357753762e-185
15516.07264362123297e-1843.03632181061648e-184
15615.16768524163795e-1832.58384262081898e-183
15714.39883503012728e-1822.19941751506364e-182
15813.82246892793463e-1811.91123446396731e-181
15912.64596836916658e-1801.32298418458329e-180
16012.2522230760935e-1791.12611153804675e-179
16111.91642001029078e-1789.58210005145389e-179
16211.6298999466815e-1778.14949973340751e-178
16311.38536225905266e-1766.9268112952633e-177
16411.25533608757678e-1756.27668043788388e-176
16511.21910451630909e-1746.09552258154546e-175
16611.0375073384447e-1735.18753669222352e-174
16718.75317392518065e-1734.37658696259033e-173
16811.51129877535425e-1737.55649387677127e-174
16914.02753381388585e-1732.01376690694292e-173
17013.43920228567747e-1721.71960114283873e-172
17112.93291130261826e-1711.46645565130913e-171
17212.57682842625791e-1701.28841421312895e-170
17312.19016553141868e-1691.09508276570934e-169
17411.9836621102592e-1689.91831055129598e-169
17511.67882592889239e-1678.39412964446194e-168
17611.45328785651156e-1667.2664392825578e-167
17711.10720921695569e-1665.53604608477843e-167
17819.34186421536038e-1664.67093210768019e-166
17917.89168467247753e-1653.94584233623877e-165
18016.65393316614177e-1643.32696658307089e-164
18114.40135871200607e-1632.20067935600303e-163
18213.95559638353217e-1621.97779819176609e-162
18312.57938604112814e-1611.28969302056407e-161
18411.88977432644424e-1609.44887163222118e-161
18511.62947145884288e-1598.14735729421438e-160
18611.07611682650063e-1585.38058413250316e-159
18715.20788606985282e-1582.60394303492641e-158
18814.4757396076161e-1572.23786980380805e-157
18913.23625714309468e-1561.61812857154734e-156
19012.66548423243189e-1551.33274211621595e-155
19112.100319203004e-1541.050159601502e-154
19211.72107587252898e-1538.6053793626449e-154
19311.44094052529023e-1527.20470262645116e-153
19411.17421517707889e-1515.87107588539447e-152
19519.61577707045139e-1514.80788853522569e-151
19617.79334754279952e-1503.89667377139976e-150
19714.21716345858641e-1492.1085817292932e-149
19813.39897405213007e-1481.69948702606504e-148
19912.73209325765467e-1471.36604662882733e-147
20015.64452695049813e-1472.82226347524906e-147
20114.53704785290933e-1462.26852392645466e-146
20213.63663586463072e-1451.81831793231536e-145
20312.90662215262462e-1441.45331107631231e-144
20412.03014434590555e-1431.01507217295277e-143
20519.98628230676272e-1434.99314115338136e-143
20618.04801036787987e-1424.02400518393993e-142
20716.48162600292891e-1413.24081300146445e-141
20815.11308895503413e-1402.55654447751706e-140
20916.25115727909897e-1403.12557863954949e-140
21015.07318304763575e-1392.53659152381788e-139
21113.99447858666353e-1381.99723929333177e-138
21213.13531726213384e-1371.56765863106692e-137
21311.78483267321927e-1368.92416336609634e-137
21411.38988803546453e-1356.94944017732264e-136
21511.1108010833402e-1345.55400541670102e-135
21618.63605001229898e-1344.31802500614949e-134
21716.68899892433215e-1333.34449946216607e-133
21815.06664098590897e-1322.53332049295449e-132
21913.89685353672909e-1311.94842676836455e-131
22011.8026031154857e-1309.01301557742851e-131
22111.39060497992124e-1296.95302489960622e-130
22211.05753713783299e-1285.28768568916493e-129
22318.02418682585675e-1284.01209341292837e-128
22415.868847479557e-1272.9344237397785e-127
22514.42058580841605e-1262.21029290420803e-126
22613.13216678037945e-1251.56608339018973e-125
22712.33496711893306e-1241.16748355946653e-124
22811.73681505816343e-1238.68407529081715e-124
22911.29853486596145e-1226.49267432980725e-123
23019.59123699150832e-1224.79561849575416e-122
23117.06254823630227e-1213.53127411815113e-121
23214.8967592106902e-1202.4483796053451e-120
23313.57768990149565e-1191.78884495074783e-119
23412.7271255084485e-1181.36356275422425e-118
23511.97692559823023e-1179.88462799115113e-118
23611.4275918879114e-1167.13795943955698e-117
23711.02725603264474e-1155.1362801632237e-116
23817.28462347904101e-1153.6423117395205e-115
23915.20185934954899e-1142.6009296747745e-114
24013.70058003590767e-1131.85029001795384e-113
24112.6225909216887e-1121.31129546084435e-112
24211.87995429949916e-1119.39977149749581e-112
24311.32196956362467e-1106.60984781812333e-111
24419.04763556342096e-1104.52381778171048e-110
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3920.9999999999721025.57965808448419e-112.78982904224209e-11
3930.9999999999177621.64475083559554e-108.22375417797768e-11
3940.9999999998301163.39768918356795e-101.69884459178397e-10
3950.9999999995401499.19702934558426e-104.59851467279213e-10
3960.9999999987428172.51436665277459e-091.2571833263873e-09
3970.9999999965232566.95348818655256e-093.47674409327628e-09
3980.999999997408815.18238006680056e-092.59119003340028e-09
3990.9999999927749461.44501086420874e-087.22505432104369e-09
4000.9999999886368792.2726242236136e-081.1363121118068e-08
4010.9999999680077876.39844260660378e-083.19922130330189e-08
4020.9999999250180131.4996397381947e-077.4981986909735e-08
4030.9999998099750633.80049873143506e-071.90024936571753e-07
4040.9999994896662531.02066749352294e-065.10333746761471e-07
4050.9999986577159852.68456803066332e-061.34228401533166e-06
4060.999996780824326.43835136173201e-063.219175680866e-06
4070.9999924261156491.51477687027816e-057.57388435139078e-06
4080.9999836264951123.27470097770154e-051.63735048885077e-05
4090.9999645653333187.08693333639826e-053.54346666819913e-05
4100.9999181307635780.0001637384728436178.18692364218083e-05
4110.9998376666505430.0003246666989147950.000162333349457398
4120.9996490661765960.000701867646809010.000350933823404505
4130.99925541017790.001489179644198810.000744589822099407
4140.999368387568520.001263224862961790.000631612431480896
4150.9989102828900730.002179434219854170.00108971710992708
4160.9977835901544260.004432819691147230.00221640984557362
4170.99950914904120.0009817019175997290.000490850958799865
4180.9989669028971250.002066194205750620.00103309710287531
4190.997501084212380.00499783157523990.00249891578761995
4200.9936654273117110.01266914537657750.00633457268828873
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4220.9669321682413850.06613566351723080.0330678317586154
4230.9276852638387420.1446294723225160.0723147361612578
4240.9473775083719830.1052449832560350.0526224916280174
4250.8850881935968250.2298236128063490.114911806403175


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level4140.985714285714286NOK
5% type I error level4160.99047619047619NOK
10% type I error level4170.992857142857143NOK
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Dec/20/t1292876964ogsjyr30ylmkfwj/107maf1292877036.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/20/t1292876964ogsjyr30ylmkfwj/107maf1292877036.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/20/t1292876964ogsjyr30ylmkfwj/1jlv31292877036.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/20/t1292876964ogsjyr30ylmkfwj/1jlv31292877036.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/20/t1292876964ogsjyr30ylmkfwj/2buc61292877036.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/20/t1292876964ogsjyr30ylmkfwj/2buc61292877036.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/20/t1292876964ogsjyr30ylmkfwj/3buc61292877036.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/20/t1292876964ogsjyr30ylmkfwj/3buc61292877036.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/20/t1292876964ogsjyr30ylmkfwj/4buc61292877036.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/20/t1292876964ogsjyr30ylmkfwj/4buc61292877036.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/20/t1292876964ogsjyr30ylmkfwj/5mmcr1292877036.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/20/t1292876964ogsjyr30ylmkfwj/5mmcr1292877036.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/20/t1292876964ogsjyr30ylmkfwj/6mmcr1292877036.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/20/t1292876964ogsjyr30ylmkfwj/6mmcr1292877036.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/20/t1292876964ogsjyr30ylmkfwj/7fvtu1292877036.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/20/t1292876964ogsjyr30ylmkfwj/7fvtu1292877036.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/20/t1292876964ogsjyr30ylmkfwj/8fvtu1292877036.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/20/t1292876964ogsjyr30ylmkfwj/8fvtu1292877036.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/20/t1292876964ogsjyr30ylmkfwj/97maf1292877036.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/20/t1292876964ogsjyr30ylmkfwj/97maf1292877036.ps (open in new window)


 
Parameters (Session):
par1 = 3 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;
 
Parameters (R input):
par1 = 3 ; 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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