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workshop 4

*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 19:48:04 +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/t1291232880c2giog575vghka8.htm/, Retrieved Wed, 01 Dec 2010 20:48:12 +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/t1291232880c2giog575vghka8.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 «
0 807 6282154 0 444 4321023 0 412 4111912 1 428 223193 0 315 1491348 0 168 1629616 1 263 1398893 0 267 1926517 0 228 983660 0 129 1443586 1 104 1073089 1 122 984885 0 393 1405225 1 190 227132 0 280 929118 1 63 1071292 1 102 638830 0 265 856956 0 234 992426 1 277 444477 0 73 857217 0 67 711969 1 103 702380 1 290 358589 1 83 297978 1 56 585715 0 236 657954 1 73 209458 1 34 786690 1 139 439798 0 26 688779 0 70 574339 0 40 741409 0 42 597793 1 12 644190 1 211 377934 1 74 640273 0 80 697458 0 83 550608 1 131 207393 1 203 301607 1 56 345783 1 89 501749 1 88 379983 1 39 387475 0 25 377305 0 49 370837 0 149 430866 0 58 469107 1 41 194493 0 90 530670 0 136 518365 0 97 491303 0 63 527021 0 114 233773 1 77 405972 1 6 652925 1 47 446211 1 51 341340 0 85 387699 0 43 493408 1 32 146494 0 25 414462 0 77 364304 1 54 355178 1 251 357760 1 15 261216 0 44 397144 1 73 374943 0 85 424898 0 49 202055 1 38 378525 1 35 310768 1 9 325738 1 34 394510 0 20 24706 etc...
 
Output produced by software:

Enter (or paste) a matrix (table) containing all data (time) series. Every column represents a different variable and must be delimited by a space or Tab. Every row represents a period in time (or category) and must be delimited by hard returns. The easiest way to enter data is to copy and paste a block of spreadsheet cells. Please, do not use commas or spaces to seperate groups of digits!


Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time24 seconds
R Server'George Udny Yule' @ 72.249.76.132
R Framework
error message
The field 'Names of X columns' contains a hard return which cannot be interpreted.
Please, resubmit your request without hard returns in the 'Names of X columns'.


Multiple Linear Regression - Estimated Regression Equation
wealth [t] = + 282193.658198491 -50104.1337959421group[t] + 4263.11592275244orders[t] + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0		2-tail p-value1-tail p-value
(Intercept)282193.65819849128180.10510310.013900
group-50104.133795942131230.778551-1.60430.1093810.054691
orders4263.11592275244189.10542422.543600


Multiple Linear Regression - Regression Statistics
Multiple R0.750787700460838
R-squared0.563682171163273
Adjusted R-squared0.561643302804223
F-TEST (value)276.468153846815
F-TEST (DF numerator)2
F-TEST (DF denominator)428
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation285034.824210058
Sum Squared Residuals34772796233332.2


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast		Residuals
Prediction Error
162821543722528.207859742559625.79214026
243210232175017.127900582146005.87209942
341119122038597.418372522073314.58162748
42231932056703.1393406-1833510.1393406
514913481625075.17386551-133727.173865514
61629616998397.133220903631218.866779097
713988931353289.0120864545603.9879135551
819265171420445.60957340506071.390426604
99836601254184.08858605-270524.088586051
101443586832135.612233557611450.387766443
111073089675453.580368805397635.419631195
12984885752189.666978349232695.333021651
1314052251957598.21584021-552373.215840205
142271321042081.54972552-814949.549725516
159291181475866.11656918-546748.116569178
161071292500665.827535954570626.172464046
17638830666927.3485233-28097.3485232997
188569561411919.37772789-554963.377727891
199924261279762.78412257-287336.784122565
204444771412972.63500498-968495.63500498
21857217593401.12055942263815.87944058
22711969567822.425022905144146.574977095
23702380671190.46444605231189.5355539478
243585891468393.14200076-1109804.14200076
25297978585928.145991003-287950.145991003
26585715470824.016076687114890.983923313
276579541288289.01596807-630335.01596807
28209458543296.986763478-333838.986763478
29786690377035.465776133409654.534223867
30439798824662.63766514-384864.637665141
31688779393034.672190055295744.327809945
32574339580611.772791163-6272.7727911626
33741409452718.295108589288690.704891411
34597793461244.526954094136548.473045906
35644190283246.915475579360943.084524421
363779341131606.98410332-753672.984103317
37640273547560.10268623192712.897313769
38697458623242.93201868774215.0679813129
39550608636032.279786945-85424.2797869445
40207393790557.71028312-583164.710283121
413016071097502.05672130-795895.056721298
42345783470824.016076687-125041.016076687
43501749611506.841527518-109757.841527518
44379983607243.725604765-227260.725604765
45387475398351.045389895-10876.0453898951
46377305388771.556267302-11466.5562673022
47370837491086.338413361-120249.338413361
48430866917397.930688606-486531.930688606
49469107529454.381718133-60347.3817181331
50194493406877.2772354-212384.2772354
51530670665874.091246212-135204.091246212
52518365861977.423692825-343612.423692825
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54527021550769.961331895-23748.9613318954
55233773768188.87339227-534415.873392271
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60387699644558.511632449-256859.511632449
61493408465507.64287684627900.3571231537
62146494368509.233930628-222015.233930628
63414462388771.55626730225690.4437326978
64364304610453.58425043-246149.58425043
65355178462297.784231182-107119.784231182
663577601302131.62101342-944371.621013416
67261216296036.263243836-34820.2632438362
68397144469770.758799599-72626.7587995988
69374943543296.986763478-168353.986763479
70424898644558.511632449-219660.511632449
71202055491086.338413361-289031.338413361
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80339836337614.1651942732221.83480572727
81347385355719.886162371-8334.88616237055
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83352850372772.349853380-19922.3498533804
84301881296036.2632438365844.73675616382
85377516296036.26324383681479.7367561638
86357312572085.540945658-214773.540945658
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324315380282193.65819849133186.3418015092
325315380232089.52440254983290.4755974506
326312502236352.64032530276149.3596746982
327315380282193.65819849133186.3418015092
328315380282193.65819849133186.3418015092
329315380232089.52440254983290.4755974506
330315380232089.52440254983290.4755974506
331315380232089.52440254983290.4755974506
332315380232089.52440254983290.4755974506
333315380232089.52440254983290.4755974506
334313729249141.98809355964587.0119064408
335315388236352.64032530279035.3596746982
336315371249141.98809355966229.0119064408
337296139317351.842857598-21212.8428575984
338315380232089.52440254983290.4755974506
339313880236352.64032530277527.3596746982
340317698274720.68363007442977.3163699261
341295580283246.91547557912333.0845244212
342315380232089.52440254983290.4755974506
343315380232089.52440254983290.4755974506
344315380232089.52440254983290.4755974506
345308256287510.03139833120745.9686016687
346315380232089.52440254983290.4755974506
347303677244878.87217080758798.1278291933
348315380232089.52440254983290.4755974506
349315380232089.52440254983290.4755974506
350319369274720.68363007444648.3163699261
351318690244878.87217080773811.1278291933
352314049261931.33586181752117.6641381835
353325699274720.68363007450978.3163699261
354314210236352.64032530277857.3596746982
355315380232089.52440254983290.4755974506
356315380232089.52440254983290.4755974506
357322378296036.26324383626341.7367561638
358315380232089.52440254983290.4755974506
359315380232089.52440254983290.4755974506
360315380232089.52440254983290.4755974506
361315398249141.98809355966256.0119064408
362315380232089.52440254983290.4755974506
363315380232089.52440254983290.4755974506
364308336401560.904035560-93224.9040355595
365316386270457.56770732145928.4322926785
366315380232089.52440254983290.4755974506
367315380232089.52440254983290.4755974506
368315380232089.52440254983290.4755974506
369315380232089.52440254983290.4755974506
370315553261931.33586181753621.6641381835
371315380232089.52440254983290.4755974506
372323361261931.33586181761429.6641381835
373336639261931.33586181774707.6641381835
374307424244878.87217080762545.1278291933
375315380232089.52440254983290.4755974506
376315380232089.52440254983290.4755974506
377295370278983.79955282616386.2004471736
378322340261931.33586181760408.6641381835
379319864274720.68363007445143.3163699261
380315380232089.52440254983290.4755974506
381315380232089.52440254983290.4755974506
382317291308825.6110120948465.38898790645
383280398291773.147321084-11375.1473210837
384315380232089.52440254983290.4755974506
385317330283246.91547557934083.0845244212
386238125355719.886162371-117594.886162371
387327071244878.87217080782192.1278291933
388309038257668.21993906451369.7800609359
389314210244878.87217080769331.1278291933
390307930266194.45178456941735.5482154310
391322327274720.68363007447606.3163699261
392292136257668.21993906434467.7800609359
393263276266194.451784569-2918.45178456897
394367655257668.219939064109986.780060936
395283910320561.701503263-36651.7015032629
396283587266194.45178456917392.5482154310
397243650393034.672190055-149384.672190055
3984384931301078.36373633-862585.363736328
399296261261931.33586181734329.6641381835
400230621456981.411031341-226360.411031341
401304252244878.87217080759373.1278291933
402333505266194.45178456967310.548215431
403296919257668.21993906439250.7800609359
404278990371719.092576292-92729.0925762923
405276898261931.33586181714966.6641381835
406327007278983.79955282648023.2004471736
407317046278983.79955282638062.2004471736
408304555283246.91547557921308.0845244212
409298096270457.56770732127638.4322926785
410231861244878.872170807-13017.8721708067
411309422475087.131999439-165665.131999439
412286963371719.092576292-84756.0925762923
413269753346140.397039778-76387.3970397776
414448243418613.36772656929629.6322734307
415165404278983.799552826-113579.799552826
416204325240615.756248054-36290.7562480543
417407159330141.19062585677017.8093741442
418290476367455.97665354-76979.97665354
419275311334404.306548608-59093.3065486083
420246541236352.64032530210188.3596746982
421253468236352.64032530217115.3596746982
422240897547560.102686231-306663.102686231
423-83265572085.540945658-655350.540945658
424-42143317351.842857598-359494.842857598
425272713317351.842857598-44638.8428575984
426215362631769.163864192-416407.163864192
42742754321614.958780351-278860.958780351
4283062751272289.80955415-966014.809554149
429253537368509.233930628-114972.233930628
430372631598717.49375926-226086.493759260
431-7170526244.523072469-533414.523072469


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
616.72632816298346e-233.36316408149173e-23
713.08217907736578e-461.54108953868289e-46
811.37780779321088e-546.8890389660544e-55
911.00930124041409e-605.04650620207044e-61
1013.85715078899539e-681.92857539449770e-68
1115.44967835109998e-902.72483917554999e-90
1211.34487966956190e-976.72439834780948e-98
1313.64257618679736e-1171.82128809339868e-117
1414.09034907195245e-1182.04517453597622e-118
1514.18864724671598e-1262.09432362335799e-126
1612.37601099455402e-1411.18800549727701e-141
1714.16484146912216e-1422.08242073456108e-142
1812.34805766474467e-1481.17402883237233e-148
1916.20904017646492e-1553.10452008823246e-155
2012.59445805557035e-1571.29722902778517e-157
2112.7576742840105e-1621.37883714200525e-162
2212.02716227744476e-1641.01358113872238e-164
2311.74131344193586e-1678.70656720967928e-168
2411.28963313399705e-1706.44816566998526e-171
2517.91498496255132e-1703.95749248127566e-170
2614.87830544554198e-1722.43915272277099e-172
2714.309772011593e-1762.1548860057965e-176
2811.18770619409305e-1755.93853097046527e-176
2912.6712887273414e-1841.3356443636707e-184
3012.09749774695465e-1831.04874887347732e-183
3119.44454755577942e-1874.72227377788971e-187
3211.80351998640351e-1879.01759993201754e-188
3311.04953145700079e-1925.24765728500395e-193
3412.31796183577377e-1941.15898091788688e-194
3514.40276503159674e-2002.20138251579837e-200
3613.34736934270954e-2001.67368467135477e-200
3716.96668437873255e-2043.48334218936627e-204
3818.85442330152794e-2094.42721165076397e-209
3914.37038733725881e-2102.18519366862941e-210
4011.65652368420553e-2108.28261842102766e-211
4115.49558725527387e-2112.74779362763693e-211
4214.31701214936296e-2102.15850607468148e-210
4311.72902717383266e-2108.6451358691633e-211
4411.69390586385134e-2098.46952931925672e-210
4515.1098317312055e-2092.55491586560275e-209
4613.85330215677995e-2081.92665107838997e-208
4712.33257172325320e-2071.16628586162660e-207
4814.02557702813222e-2082.01278851406611e-208
4914.22476018961201e-2082.11238009480600e-208
5015.1321858496754e-2082.5660929248377e-208
5113.95247147765565e-2091.97623573882783e-209
5211.77673108267825e-2108.88365541339126e-211
5314.06638395916724e-2112.03319197958362e-211
5411.63091712741190e-2128.15458563705948e-213
5512.67370576591824e-2131.33685288295912e-213
5611.1159296200831e-2125.5796481004155e-213
5716.89946038684177e-2213.44973019342089e-221
5813.47248900729843e-2211.73624450364921e-221
5913.20843182182870e-2201.60421591091435e-220
6011.14029581234047e-2195.70147906170236e-220
6111.04670325265164e-2205.23351626325822e-221
6211.03210040118422e-2215.16050200592112e-222
6312.36131698366868e-2211.18065849183434e-221
6411.22923156910168e-2206.14615784550841e-221
6519.96793690544439e-2204.98396845272219e-220
6618.19226153967017e-2214.09613076983509e-221
6713.52671959406937e-2201.76335979703469e-220
6811.32149721222519e-2196.60748606112596e-220
6919.15258822747667e-2194.57629411373834e-219
7019.8607471389724e-2194.9303735694862e-219
7118.07174396995348e-2194.03587198497674e-219
7212.95626018858852e-2181.47813009429426e-218
7312.54152933383412e-2171.27076466691706e-217
7411.26281719504260e-2166.31408597521298e-217
7512.96238184811749e-2161.48119092405874e-216
7611.56287397979764e-2157.8143698989882e-216
7716.71701621283352e-2153.35850810641676e-215
7812.00213944686405e-2141.00106972343202e-214
7912.15100177193074e-2131.07550088596537e-213
8012.10840214788553e-2121.05420107394277e-212
8111.37094667804732e-2116.85473339023662e-212
8211.54311728873951e-2117.71558644369753e-212
8319.84280761893646e-2114.92140380946823e-211
8417.13766165057111e-2103.56883082528556e-210
8512.03703002734297e-2091.01851501367149e-209
8611.14240846222056e-2085.7120423111028e-209
8713.22113315964214e-2091.61056657982107e-209
8811.48605264728890e-2087.43026323644449e-209
8911.53636036095686e-2077.6818018047843e-208
9013.43406283931832e-2071.71703141965916e-207
9118.6823897718128e-2074.3411948859064e-207
9213.83868204292651e-2061.91934102146326e-206
9319.26202741810979e-2074.63101370905490e-207
9415.49488043668527e-2062.74744021834264e-206
9513.33979166995521e-2051.66989583497761e-205
9611.45965543029123e-2047.29827715145614e-205
9715.4298113257741e-2052.71490566288705e-205
9815.17981366500454e-2042.58990683250227e-204
9916.67632866601809e-2043.33816433300904e-204
10016.88572505709865e-2033.44286252854933e-203
10116.85735819531245e-2023.42867909765623e-202
10212.39864340255892e-2011.19932170127946e-201
10312.46699862631793e-2001.23349931315897e-200
10411.80834218609009e-1999.04171093045045e-200
10517.83009923582717e-1993.91504961791359e-199
10615.81022235250441e-1982.90511117625220e-198
10716.73091155648036e-2003.36545577824018e-200
10811.88729057187220e-2029.43645285936098e-203
10911.88519013257832e-2019.4259506628916e-202
11019.8566009314787e-2014.92830046573935e-201
11119.71875446789672e-2014.85937723394836e-201
11217.82769659374572e-2023.91384829687286e-202
11317.79608434530293e-2013.89804217265146e-201
11417.49151903969164e-2003.74575951984582e-200
11512.80429490545534e-1991.40214745272767e-199
11612.08127252894506e-1981.04063626447253e-198
11711.39742594383157e-1976.98712971915785e-198
11812.09305495775873e-1981.04652747887937e-198
11913.01537634895539e-1981.50768817447770e-198
12012.72566356416949e-1971.36283178208474e-197
12118.26605913049877e-1974.13302956524938e-197
12215.78020654847349e-1962.89010327423674e-196
12312.01886192088751e-1951.00943096044376e-195
12412.95954968483640e-1971.47977484241820e-197
12511.92355350352356e-1969.6177675176178e-197
12613.01846561487451e-1961.50923280743725e-196
12712.21258897548003e-1951.10629448774001e-195
12811.83551114353282e-1949.17755571766408e-195
12911.65961207998672e-1938.29806039993358e-194
13011.23591816227450e-1926.17959081137249e-193
13111.00436733628449e-1915.02183668142243e-192
13213.62371250781139e-1911.81185625390569e-191
13312.74410972493316e-1901.37205486246658e-190
13412.50458943404456e-1891.25229471702228e-189
13512.01588431888248e-1881.00794215944124e-188
13611.60767994929551e-1878.03839974647753e-188
13711.32443722082198e-1866.62218610410988e-187
13811.03098838866259e-1855.15494194331296e-186
13918.27835359684915e-1854.13917679842457e-185
14016.40271184922933e-1843.20135592461467e-184
14114.95408841906172e-1832.47704420953086e-183
14213.84854615952247e-1821.92427307976124e-182
14313.32847012450891e-1811.66423506225446e-181
14412.67496478380011e-1801.33748239190006e-180
14512.07034678124122e-1791.03517339062061e-179
14611.74596460346611e-1788.72982301733053e-179
14711.35960681980776e-1776.79803409903878e-178
14811.11982491020508e-1765.59912455102542e-177
14918.307592680069e-1764.1537963400345e-176
15016.46478458470781e-1753.23239229235391e-175
15115.23989069809912e-1742.61994534904956e-174
15214.79795603450101e-1732.39897801725051e-173
15313.85819641591786e-1721.92909820795893e-172
15413.17978667796611e-1711.58989333898305e-171
15512.49923261460603e-1701.24961630730301e-170
15611.93367858809803e-1699.66839294049017e-170
15711.49558906860924e-1687.47794534304619e-169
15811.17304466864081e-1675.86522334320404e-168
15917.80262148031571e-1673.90131074015785e-167
16016.02257627925573e-1663.01128813962786e-166
16114.64431256303676e-1652.32215628151838e-165
16213.57767650311951e-1641.78883825155975e-164
16312.75275171165048e-1631.37637585582524e-163
16412.2507043373641e-1621.12535216868205e-162
16511.94366640694814e-1619.7183320347407e-162
16611.49666126002605e-1607.48330630013027e-161
16711.14115891450401e-1595.70579457252007e-160
16812.81796601613941e-1591.40898300806971e-159
16911.69262941350003e-1588.46314706750016e-159
17011.28483569448887e-1576.42417847244437e-158
17119.73529449468275e-1574.86764724734137e-157
17217.56615122351911e-1563.78307561175956e-156
17315.70894836679833e-1552.85447418339917e-155
17414.56890837076942e-1542.28445418538471e-154
17513.43016188954782e-1531.71508094477391e-153
17612.6651021882493e-1521.33255109412465e-152
17711.12186890713838e-1515.6093445356919e-152
17819.16972300928612e-1514.58486150464306e-151
17916.79160991651932e-1503.39580495825966e-150
18015.01893269029241e-1492.50946634514620e-149
18112.22390232719767e-1481.11195116359883e-148
18211.66452421769375e-1478.32262108846875e-148
18311.31410367038340e-1466.57051835191702e-147
18411.02791044337892e-1455.1395522168946e-146
18518.21092398426683e-1454.10546199213341e-145
18615.86612839023337e-1442.93306419511668e-144
18713.14364294657392e-1431.57182147328696e-143
18812.33873684727976e-1421.16936842363988e-142
18911.70545658458006e-1418.5272829229003e-142
19011.21937203346624e-1406.09686016733121e-141
19118.80351111989585e-1404.40175555994793e-140
19216.25917215125805e-1393.12958607562903e-139
19314.5631359104776e-1382.2815679552388e-138
19413.22544046189741e-1371.61272023094871e-137
19512.2992818506109e-1361.14964092530545e-136
19611.74065248673895e-1358.70326243369474e-136
19718.21902942297572e-1364.10951471148786e-136
19816.21330351102456e-1353.10665175551228e-135
19914.67489932059618e-1342.33744966029809e-134
20012.79458759741982e-1331.39729379870991e-133
20112.08754301090682e-1321.04377150545341e-132
20211.55203850211360e-1317.76019251056799e-132
20311.14843155132915e-1305.74215775664577e-131
20418.5343735428391e-1304.26718677141955e-130
20515.91092886797183e-1292.95546443398592e-129
20614.30430135027678e-1282.15215067513839e-128
20713.08778631082243e-1271.54389315541122e-127
20812.22843298413872e-1261.11421649206936e-126
20911.1775170273376e-1255.887585136688e-126
21018.56885622617451e-1254.28442811308725e-125
21115.74394482388608e-1242.87197241194304e-124
21213.83917592843911e-1231.91958796421956e-123
21312.39600550979700e-1221.19800275489850e-122
21411.61730173261442e-1218.0865086630721e-122
21511.11170132588721e-1205.55850662943606e-121
21617.38686684814965e-1203.69343342407482e-120
21714.94452236894541e-1192.47226118447271e-119
21813.2766349771579e-1181.63831748857895e-118
21912.15452088122912e-1171.07726044061456e-117
22011.39566476201660e-1166.97832381008302e-117
22119.23102452435151e-1164.61551226217576e-116
22215.96479604610384e-1152.98239802305192e-115
22313.85445037571429e-1141.92722518785714e-114
22412.59390995562382e-1131.29695497781191e-113
22511.66206619897380e-1128.31033099486901e-113
22611.09741641294214e-1115.4870820647107e-112
22717.14021707314863e-1113.57010853657431e-111
22814.51168383660639e-1102.25584191830319e-110
22912.88466896091857e-1091.44233448045929e-109
23011.80997601615868e-1089.04988008079338e-109
23111.1728148113923e-1075.86407405696149e-108
23217.24783048988939e-1073.62391524494469e-107
23314.49740410259904e-1062.24870205129952e-106
23412.92344111222934e-1051.46172055611467e-105
23511.80014665242903e-1049.00073326214515e-105
23611.10403180780186e-1035.52015903900928e-104
23716.7487674092112e-1033.3743837046056e-103
23814.16030559088671e-1022.08015279544335e-102
23912.52373409197307e-1011.26186704598654e-101
24011.52522483494541e-1007.62612417472706e-101
24119.18298216469299e-1004.59149108234649e-100
24215.59029338666642e-992.79514669333321e-99
24313.33976108836332e-981.66988054418166e-98
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35611.50646645947042e-247.53233229735209e-25
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36115.06338464528560e-222.53169232264280e-22
36211.58448637148639e-217.92243185743196e-22
36314.91415384296109e-212.45707692148054e-21
36411.4368328686693e-207.1841643433465e-21
36514.39545775466181e-202.19772887733090e-20
36611.32936954584067e-196.64684772920336e-20
36713.98269826785477e-191.99134913392738e-19
36811.18176125177914e-185.90880625889571e-19
36913.4724029422821e-181.73620147114105e-18
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37218.1098394199403e-174.05491970997015e-17
37312.08382176142329e-161.04191088071165e-16
37415.98617476171178e-162.99308738085589e-16
37511.65258721689016e-158.26293608445078e-16
3760.9999999999999984.51133581721027e-152.25566790860513e-15
3770.9999999999999941.29695640429270e-146.48478202146351e-15
3780.9999999999999833.3865156368192e-141.6932578184096e-14
3790.9999999999999568.8474811877516e-144.4237405938758e-14
3800.9999999999998852.30621238327452e-131.15310619163726e-13
3810.9999999999997035.93622840891021e-132.96811420445511e-13
3820.9999999999992411.51726678951484e-127.58633394757422e-13
3830.999999999997914.17904911036163e-122.08952455518081e-12
3840.9999999999948141.03720109598493e-115.18600547992466e-12
3850.9999999999872732.54534103816366e-111.27267051908183e-11
3860.9999999999671326.57367976848659e-113.28683988424330e-11
3870.9999999999247351.50530449371916e-107.5265224685958e-11
3880.9999999998169833.66033444220167e-101.83016722110084e-10
3890.999999999570718.58582187771494e-104.29291093885747e-10
3900.9999999989812732.03745424815756e-091.01872712407878e-09
3910.9999999977442354.51153059106399e-092.25576529553199e-09
3920.999999994570531.08589385582030e-085.42946927910152e-09
3930.9999999865244122.69511760731553e-081.34755880365777e-08
3940.9999999781913284.36173431979061e-082.18086715989530e-08
3950.9999999481449431.03710114833135e-075.18550574165674e-08
3960.9999998794252042.41149592364279e-071.20574796182139e-07
3970.9999997168478245.66304351175521e-072.83152175587761e-07
3980.999999779721024.40557958880616e-072.20278979440308e-07
3990.9999994949242931.01015141345887e-065.05075706729433e-07
4000.9999988294233652.34115326892583e-061.17057663446292e-06
4010.9999974552717845.08945643284441e-062.54472821642220e-06
4020.9999951279713879.74405722647071e-064.87202861323536e-06
4030.9999896486489642.07027020721299e-051.03513510360650e-05
4040.999977641848214.47163035793439e-052.23581517896720e-05
4050.9999523140050629.53719898756155e-054.76859949378077e-05
4060.9999133998519430.0001732002961130138.66001480565064e-05
4070.9998413797553190.0003172404893619820.000158620244680991
4080.9997054064413090.0005891871173821070.000294593558691053
4090.9994584432244060.001083113551187880.000541556775593938
4100.9989082069693150.002183586061369360.00109179303068468
4110.9981264340088760.003747131982248880.00187356599112444
4120.9965396776339460.006920644732108090.00346032236605404
4130.993691551340190.01261689731961830.00630844865980915
4140.996200247271890.007599505456218190.00379975272810909
4150.992665972580080.01466805483984080.0073340274199204
4160.9858898101723330.02822037965533420.0141101898276671
4170.9858735906845220.02825281863095620.0141264093154781
4180.986107659331410.02778468133717910.0138923406685896
4190.9761109600401570.04777807991968690.0238890399598434
4200.9594300735965260.08113985280694860.0405699264034743
4210.9381104480738890.1237791038522230.0618895519261114
4220.8907580860141620.2184838279716760.109241913985838
4230.8826825908972440.2346348182055120.117317409102756
4240.8624195096028380.2751609807943240.137580490397162
4250.7740979215199650.451804156960070.225902078480035


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level4080.971428571428571NOK
5% type I error level4140.985714285714286NOK
10% type I error level4150.988095238095238NOK
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Dec/01/t1291232880c2giog575vghka8/106yfh1291232858.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/01/t1291232880c2giog575vghka8/106yfh1291232858.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/01/t1291232880c2giog575vghka8/1hxin1291232858.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/01/t1291232880c2giog575vghka8/1hxin1291232858.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/01/t1291232880c2giog575vghka8/2hxin1291232858.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/01/t1291232880c2giog575vghka8/2hxin1291232858.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/01/t1291232880c2giog575vghka8/3r6hq1291232858.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/01/t1291232880c2giog575vghka8/3r6hq1291232858.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/01/t1291232880c2giog575vghka8/4r6hq1291232858.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/01/t1291232880c2giog575vghka8/4r6hq1291232858.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/01/t1291232880c2giog575vghka8/5r6hq1291232858.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/01/t1291232880c2giog575vghka8/5r6hq1291232858.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/01/t1291232880c2giog575vghka8/62fzt1291232858.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/01/t1291232880c2giog575vghka8/62fzt1291232858.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/01/t1291232880c2giog575vghka8/7d6gw1291232858.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/01/t1291232880c2giog575vghka8/7d6gw1291232858.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/01/t1291232880c2giog575vghka8/8d6gw1291232858.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/01/t1291232880c2giog575vghka8/8d6gw1291232858.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/01/t1291232880c2giog575vghka8/9d6gw1291232858.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/01/t1291232880c2giog575vghka8/9d6gw1291232858.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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