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*The author of this computation has been verified*
R Software Module: /rwasp_multipleregression.wasp (opens new window with default values)
Title produced by software: Multiple Regression
Date of computation: Fri, 03 Dec 2010 12:40:48 +0000
 
Cite this page as follows:
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/03/t1291379972ims64ezy89o64e5.htm/, Retrieved Fri, 03 Dec 2010 13:39:44 +0100
 
BibTeX entries for LaTeX users:
@Manual{KEY,
    author = {{YOUR NAME}},
    publisher = {Office for Research Development and Education},
    title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2010/Dec/03/t1291379972ims64ezy89o64e5.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 «
350 1595 17 10 60720 319369 143 7022 75 0 61 5565 47 43 94355 493408 38 6243 53 39 287 601 6 5 60720 319210 144 19868 198 0 268 188 11 9 77655 381180 67 16471 964 0 25 7146 105 83 134028 297978 367 933 14 305 418 1135 17 20 62285 290476 384 5322 80 -9 392 450 8 6 59325 292136 380 11517 205 -1 131 34 8 7 60630 314353 309 14294 3340 0 316 133 14 4 65990 339445 109 9960 1052 0 347 119 6 3 59118 303677 354 17280 872 0 68 2053 53 44 100423 397144 60 3720 96 33 70 4036 63 85 100269 424898 53 3570 56 32 147 0 0 0 60720 315380 203 0 169 4655 393 55 60720 341570 105 360 30 0 248 131 11 15 61808 308989 338 9908 834 0 152 1766 73 46 60438 305959 349 1451 60 0 351 312 14 3 58598 318690 147 8478 381 0 372 448 40 7 59781 323361 132 3084 275 0 137 115 13 10 60945 318903 145 9146 1037 0 352 60 10 7 61124 314049 314 11405 1916 0 338 0 0 0 60720 315380 180 0 258 364 35 26 47705 298466 365 2813 271 0 343 0 0 0 60720 315380 183 0 398 1442 118 239 121173 438493 49 2021 165 -3 115 1389 9 6 57530 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 time33 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135
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
CCScore [t] = + 61405.3709479282 + 0.00488340875864443Rank[t] -0.0483358374549209Costs[t] -0.0205374100407333Trades[t] -0.103834957118493Orders[t] -0.106421725421049Dividends[t] -0.0308988753153982Wealth[t] -0.142983169601531WRank[t] -0.228560046615442`Profit/Trades`[t] -0.0183775697123066`Profit/Cost`[t] + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)61405.37094792829120.6997026.732500
Rank0.004883408758644430.0407330.11990.9046290.452314
Costs-0.04833583745492090.047422-1.01930.3086580.154329
Trades-0.02053741004073330.015658-1.31160.1903620.095181
Orders-0.1038349571184930.042624-2.4360.0152630.007631
Dividends-0.1064217254210490.035805-2.97230.0031260.001563
Wealth-0.03089887531539820.020171-1.53180.1263160.063158
WRank-0.1429831696015310.042576-3.35830.0008560.000428
`Profit/Trades`-0.2285600466154420.084197-2.71460.0069090.003454
`Profit/Cost`-0.01837756971230660.021603-0.85070.3954130.197707


Multiple Linear Regression - Regression Statistics
Multiple R0.256870006830620
R-squared0.0659822004091629
Adjusted R-squared0.046015074052114
F-TEST (value)3.30454163655202
F-TEST (DF numerator)9
F-TEST (DF denominator)421
p-value0.00065451465540578
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation102897.274549976
Sum Squared Residuals4457484475231.33


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
1043371.753358227-43371.753358227
23934410.7678226152-34371.7678226152
3040486.6637503101-40486.6637503101
4037562.3113802455-37562.3113802455
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6-944473.4940174081-44482.4940174081
7-143354.1770454314-43355.1770454314
8041865.3725591553-41865.3725591553
9041577.1677500617-41577.1677500617
10041710.0025858401-41710.0025858401
113337481.7338440891-37448.7338440891
123236576.2725900705-36544.2725900705
13465545167.1429517689-40512.1429517689
1413124659.5488072140-24528.548807214
15176627587.3058691179-25821.3058691179
1631228296.0193877862-27984.0193877862
1744826771.7629683672-26323.7629683672
1811526450.1275570591-26335.1275570591
196026587.2445737402-26527.2445737402
20026874.5028654447-26874.5028654447
212627270.9859939837-27244.9859939837
22046834.2624971373-46834.2624971373
2343849344068.701620357394424.298379643
2437804960189.769509084317859.230490916
2531333259279.3777039013254052.622296099
2631986459066.8592672152260797.140732785
2743086658156.8444436189372709.155556381
2831538060208.216831766255171.783168234
295106-26846.394795271131952.3947952711
302999-14015.596442117117014.5964421171
310-19366.783392906019366.7833929060
32042834.7502955897-42834.7502955897
335829024.4210758815-28966.4210758815
343740557.5887948137-40520.5887948137
35942609.3811222432-42600.3811222432
36040545.7028880252-40545.7028880252
37-3146247.7468091016-46278.7468091016
3828651827.210428389031037.78957161097
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41042467.9516398402-42467.9516398402
423235349.8388526104-35317.8388526104
4337845168.4854180832-44790.4854180832
44106128905.4978650866-27844.4978650866
45027665.3906480283-27665.3906480283
46927308.5661747516-27299.5661747516
472544564.2309886803-44539.2309886803
481442777.1335125763-42763.1335125763
4923635115.5544102183-34879.5544102183
502829389.1868404497-29361.1868404497
511543169.5829997764-43154.5829997764
525644584.5758561858-44528.5758561858
536331260.3420797051-31197.3420797051
542341153.5405166134-919.5405166134
55413146.3500359778-13142.3500359778
562043559.2198101968-43539.2198101968
576848212.7547388296-48144.7547388296
58044173.6565694328-44173.6565694328
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602198-40818.101671598443016.1016715984
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7128328-85354.6562108399113682.656210840
72230045167.0989123152-42867.0989123152
7326723325.2195399325-23058.2195399325
7438225736.0344741875-25354.0344741875
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9127144945.622597121-44674.622597121
9213824366.1029170109-24228.1029170109
93024728.5237554541-24728.5237554541
942227292.0839440593-27270.0839440593
951245869.6395804235-45857.6395804235
961445591.7990150465-45577.7990150465
976847397.2161580222-47329.2161580222
98139457.846674437-39456.846674437
991241765.6741234983-41753.6741234983
100145410.9824794857-45409.9824794857
101039775.0283795284-39775.0283795284
102-717045304.6781237616-52474.6781237616
10332233160376.4348537828261954.565146217
104162961656932.8982890741572683.10171093
10529275459605.263588766233148.736411234
10631805660226.5133705954257829.486629405
10735517859998.7702454727295179.229754527
10820432559880.4217717286144444.578228271
10931538060190.7689865902255189.23101341
1107315-20858.90392686928173.903926869
1110-19368.260895882319368.2608958823
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20616041477.8069027424-41317.8069027424
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2089211878.2626303600-11786.2626303600
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210261314017.5677216860-11404.5677216860
21133714383.0323502475-14046.0323502475
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21315422416.8924145038-22262.8924145038
2143622300.0541745236-22264.0541745236
21519210468.8539993788-10276.8539993788
21610921396.9087398683-21287.9087398683
2177333744.3009866764-33671.3009866764
218151343.0041759564-51342.0041759564
2192240422.7039017468-40400.7039017468
2202431326.0189378403-31302.0189378403
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222043920.4483319968-43920.4483319968
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324051875.8077088234-51875.8077088234
3259026251429.921069830538832.0789301695
3266072063564.9563149377-2844.95631493775
32739739612.4444005222-39215.4444005222
32829841540.5947744381-41242.5947744381
32942848656.0334973403-48228.0334973403
33021641684.570875293-41468.570875293
33117415298.5937585611-15124.5937585611
33217314356.2362984010-14183.2362984010
333421462.0407998458-21458.0407998458
334048789.3135234624-48789.3135234624
3357156151847.383990597419713.6160094026
3366072062623.7391962156-1903.73919621562
33725543231.1144070254-42976.1144070254
33824014363.6979742000-14123.6979742000
33915021443.0821698617-21293.0821698617
34015843907.0206664476-43749.0206664476
3411848926.9387486927-48908.9387486927
3421552592.5134950372-52577.5134950372
3431751734.4611927689-51717.4611927689
3441449650.8821445103-49636.8821445103
34511050656.0695982665-50546.0695982665
34615237779.9804591922-37627.9804591922
347651860.7546708618-51854.7546708618
348049788.5142834117-49788.5142834117
3496703851197.123181323315840.8768186767
35011376162346.825348498851414.1746515012
3515832062694.0628932862-4374.06289328621
3526284162599.2044376942241.795562305836
3537980462182.537611821817621.4623881782
3546255562373.6958328114181.304167188599
3559948961728.922423063337760.0775769367
3569013162333.762751241827797.2372487582
3579535059746.469957397235603.5300426028
3586424565789.5918947879-1544.59189478792
3596072061710.1866125066-990.186612506609
3606439503.944120269-39439.944120269
36138240982.849201383-40600.849201383
36240438994.3090179435-38590.3090179435
36312240809.3700375901-40687.3700375901
36416241692.3466179837-41530.3466179837
36535042222.8288007016-41872.8288007016
3667540414.2588002344-40339.2588002344
36728841720.7407588024-41432.7407588024
36824614378.9224101336-14132.9224101336
369021475.7677227807-21475.7677227807
3706072051965.24911635848754.75088364155
3719034118.1064740366-34028.1064740366
37216841903.1038739274-41735.1038739274
37320841554.6163745554-41346.6163745554
37422214365.8862060262-14143.8862060262
375021448.1433141691-21448.1433141691
3765966151931.2070634587729.79293654201
37710272562381.245327497440343.7546725026
37810847962460.23356435346018.766435647
3798741961459.319448084425959.6805519156
3805468363180.9066902595-8497.90669025951
38112284460131.026336956762712.9736630433
3826271063419.0603570558-709.060357055747
3836072062555.9757295732-1835.97572957317
3846072062395.7406033062-1675.74060330623
3858716162280.428748253224880.5712517468
38610148163537.734093070137943.2659069299
38712829461491.152858442466802.8471415576
3886262062761.0170511897-141.01705118968
3896072062538.1783243894-1818.17832438942
39022743225.9352438657-42998.9352438657
3914425766.1518137321-25722.1518137321
3921079686.23884949318-9579.23884949318
39364714070.9606591367-13423.9606591367
39440-14908.557489123614948.5574891236
3957021422.8311594-21352.8311594
39611774313317.1644385235104425.835561477
39733414354.8518189807-14020.8518189807
3989518214.8950001287-18119.8950001287
399818820.5435625023-18812.5435625023
400221-168562.573962026168783.573962026
40141920009.6875759639-19590.6875759639
40242424485.0827903124-24061.0827903124
40332761450.6847477964-61123.6847477964
4041221465.1774488087-21453.1774488087
405849412.01109654-49404.01109654
406048253.5544256394-48253.5544256394
4075672651907.02496323954818.9750367605
4086072062598.3992605336-1878.39926053363
4099435561996.948252006432358.0517479936
4106072063578.9142737128-2858.9142737128
4117765562490.80561987315164.194380127
41213402861777.167272959572250.8327270405
4136228562610.2516518782-325.251651878191
4145932562610.2804004085-3285.28040040848
4156063062545.047431094-1915.04743109397
4166599062253.12471467463736.8752853254
4175911862714.8006489234-3596.80064892342
41810042362117.240588705438305.7594112946
41910026962656.80367740437612.1963225960
4206072063390.6788219447-2670.67882194465
42110542247.3471381888-42142.3471381888
42233841558.1957003464-41220.1957003464
42334941764.3922002444-41415.3922002444
42414742089.1361385598-41942.1361385598
42513241733.6786926182-41601.6786926182
42614541588.5894656741-41443.5894656741
42731441613.7035817202-41299.7035817202
42818041659.2745783939-41479.2745783939
42927117094.2574304229-16823.2574304229
43039814376.7535290687-13978.7535290687
4311151826.48554393017-1711.48554393017


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
131.92809480841727e-073.85618961683454e-070.99999980719052
149.36548527741344e-101.87309705548269e-090.999999999063451
151.66453872691962e-103.32907745383925e-100.999999999833546
161.29994801201395e-122.5998960240279e-120.9999999999987
179.3869458957096e-141.87738917914192e-130.999999999999906
181.37685500211195e-152.7537100042239e-150.999999999999999
191.81519557353191e-173.63039114706382e-171
201.72522210429290e-193.45044420858580e-191
212.24918675267987e-214.49837350535974e-211
227.2125133576278e-231.44250267152556e-221
233.70923495228369e-197.41846990456738e-191
241.59168742315858e-153.18337484631716e-150.999999999999998
256.22898884362548e-091.24579776872510e-080.999999993771011
261.97478365354211e-093.94956730708423e-090.999999998025216
273.70958925432135e-067.4191785086427e-060.999996290410746
281.44751254716885e-062.8950250943377e-060.999998552487453
291.43594852464973e-062.87189704929946e-060.999998564051475
305.58723330705432e-071.11744666141086e-060.99999944127667
312.38695150113343e-074.77390300226685e-070.99999976130485
328.39102775724785e-081.67820555144957e-070.999999916089722
339.59923212713746e-081.91984642542749e-070.999999904007679
343.20307321986679e-086.40614643973359e-080.999999967969268
351.43037926160361e-082.86075852320722e-080.999999985696207
361.02520255079135e-082.0504051015827e-080.999999989747975
374.94496044216553e-099.88992088433105e-090.99999999505504
383.62116442412283e-087.24232884824566e-080.999999963788356
391.38514035381482e-082.77028070762964e-080.999999986148596
406.14234373777647e-091.22846874755529e-080.999999993857656
412.41847672763026e-094.83695345526052e-090.999999997581523
429.14904232265782e-101.82980846453156e-090.999999999085096
433.45660891389665e-106.9132178277933e-100.99999999965434
441.19853208315727e-102.39706416631454e-100.999999999880147
454.04537493094907e-118.09074986189813e-110.999999999959546
461.34480896660858e-112.68961793321716e-110.999999999986552
475.66290115561035e-121.13258023112207e-110.999999999994337
483.87323488290331e-127.74646976580662e-120.999999999996127
491.58179483987785e-123.1635896797557e-120.999999999998418
505.31294098585123e-131.06258819717025e-120.999999999999469
511.79976604162919e-133.59953208325838e-130.99999999999982
525.99188580127787e-141.19837716025557e-130.99999999999994
531.88609943494064e-143.77219886988127e-140.999999999999981
541.50939401300601e-143.01878802601201e-140.999999999999985
555.64949981257173e-151.12989996251435e-140.999999999999994
561.90454094377090e-153.80908188754181e-150.999999999999998
576.27854492695207e-161.25570898539041e-151
582.08525959975713e-164.17051919951426e-161
591.19636813173167e-152.39273626346334e-150.999999999999999
604.08872763998426e-168.17745527996853e-161
611.29094758961183e-162.58189517922366e-161
623.58615608912419e-157.17231217824837e-150.999999999999996
631.44716752937502e-152.89433505875004e-150.999999999999999
645.37154312266954e-161.07430862453391e-151
651.99480678689834e-163.98961357379669e-161
667.11046606114095e-171.42209321222819e-161
672.60664609693521e-175.21329219387043e-171
681.11560443976599e-172.23120887953199e-171
693.65141618490942e-187.30283236981883e-181
701.20566592968560e-182.41133185937121e-181
715.41811417012486e-191.08362283402497e-181
721.78181787924593e-193.56363575849186e-191
735.72590547227011e-201.14518109445402e-191
741.81357582110919e-203.62715164221838e-201
755.70676119077403e-211.14135223815481e-201
761.87638781436422e-213.75277562872845e-211
771.21546720934171e-212.43093441868342e-211
784.02100648122136e-228.04201296244271e-221
791.22651619259412e-222.45303238518824e-221
803.73137124551795e-237.4627424910359e-231
811.80133792044292e-213.60267584088585e-211
822.32729040981172e-214.65458081962344e-211
839.7911923847532e-221.95823847695064e-211
843.47349765197944e-226.94699530395887e-221
852.73319693292368e-195.46639386584736e-191
861.01669089324235e-192.03338178648471e-191
873.66640247949237e-207.33280495898474e-201
881.35476394815011e-202.70952789630022e-201
895.32272444855717e-211.06454488971143e-201
905.55599690315116e-211.11119938063023e-201
912.06971706010087e-214.13943412020174e-211
927.54562434711967e-221.50912486942393e-211
932.68803825603211e-225.37607651206422e-221
949.5750492122564e-231.91500984245128e-221
953.43265639588008e-236.86531279176016e-231
961.21811432674201e-232.43622865348402e-231
974.39951006763448e-248.79902013526896e-241
981.51580552826483e-243.03161105652967e-241
995.24355895761883e-251.04871179152377e-241
1001.78849033763206e-253.57698067526412e-251
1016.00407125136195e-261.20081425027239e-251
1023.20723931699149e-246.41447863398297e-241
1031.69094839432151e-233.38189678864302e-231
1040.999999999999984.11859465786710e-142.05929732893355e-14
10511.14101928234482e-155.7050964117241e-16
10615.13315376477639e-182.56657688238820e-18
10715.32817484599173e-222.66408742299587e-22
10815.26980604659584e-252.63490302329792e-25
10911.21934638374079e-296.09673191870396e-30
11011.24470017208458e-296.22350086042288e-30
11118.576256175843e-304.2881280879215e-30
11211.95508046883191e-299.77540234415957e-30
11314.43895408682595e-292.21947704341297e-29
11419.9469440237387e-294.97347201186935e-29
11512.20116779688658e-281.10058389844329e-28
11614.90148170057712e-282.45074085028856e-28
11711.06780319555444e-275.33901597777221e-28
11812.33782350252324e-271.16891175126162e-27
11914.50321509624199e-272.25160754812099e-27
12018.93292629423714e-274.46646314711857e-27
12111.91479274951517e-269.57396374757584e-27
12214.12793066319955e-262.06396533159978e-26
12314.23761137430262e-262.11880568715131e-26
12412.14414283341017e-411.07207141670508e-41
12514.83738118147203e-502.41869059073602e-50
12612.22622070188497e-641.11311035094249e-64
12714.22327992803526e-852.11163996401763e-85
12812.06797488707263e-881.03398744353632e-88
12918.76266906336442e-884.38133453168221e-88
13013.01741494393487e-871.50870747196744e-87
13118.5154478109161e-874.25772390545805e-87
13216.09097929081655e-873.04548964540828e-87
13316.38108224092904e-873.19054112046452e-87
13414.73314722441791e-1152.36657361220896e-115
13511.71259648178382e-1148.5629824089191e-115
13615.61163577215439e-1142.80581788607719e-114
13712.74459322337785e-1131.37229661168893e-113
13817.59471348104597e-1143.79735674052298e-114
13912.73241023335594e-1131.36620511667797e-113
14013.69491099924379e-1131.84745549962190e-113
14112.07877277973195e-1161.03938638986597e-116
14216.45411079405396e-1183.22705539702698e-118
14318.15236697520972e-1184.07618348760486e-118
14411.76369135928624e-1248.81845679643119e-125
14518.40435196418176e-1244.20217598209088e-124
14614.72675455377143e-1232.36337727688572e-123
14715.43375497228713e-1232.71687748614357e-123
14812.01110957660664e-1221.00555478830332e-122
14916.70510449964804e-1223.35255224982402e-122
15012.02395230137721e-1211.01197615068861e-121
15118.42914573091719e-1214.21457286545859e-121
15213.47058720108558e-1201.73529360054279e-120
15311.56174042326126e-1197.80870211630632e-120
15415.86489140311834e-1192.93244570155917e-119
15511.21779951669635e-1186.08899758348177e-119
15611.16875658421437e-1185.84378292107187e-119
15711.79857211796678e-1188.99286058983392e-119
15817.17930189039286e-1263.58965094519643e-126
15912.03463394787818e-1271.01731697393909e-127
16011.20397470405925e-1266.01987352029626e-127
16117.2338408872487e-1263.61692044362435e-126
16214.32726465804178e-1252.16363232902089e-125
16312.71069491949229e-1241.35534745974615e-124
16411.62725471029576e-1238.1362735514788e-124
16518.24950176802069e-1234.12475088401034e-123
16614.47712559319134e-1222.23856279659567e-122
16712.59454317885614e-1211.29727158942807e-121
16811.59329716295768e-1207.96648581478838e-121
16919.14305100791279e-1204.57152550395639e-120
17014.04892757663962e-1192.02446378831981e-119
17111.93846827173993e-1189.69234135869964e-119
17219.42166274614333e-1184.71083137307167e-118
17314.54063338183324e-1172.27031669091662e-117
17412.07954225569282e-1161.03977112784641e-116
17513.67994480061964e-1161.83997240030982e-116
17614.10068547592176e-1162.05034273796088e-116
17711.86792617644228e-1169.33963088221139e-117
17811.06131982890892e-1155.30659914454462e-116
17916.08620776246339e-1153.04310388123170e-115
18012.15021348491049e-1141.07510674245524e-114
18111.20655523947804e-1136.03277619739018e-114
18215.23462106467141e-1132.61731053233570e-113
18312.68737241123847e-1121.34368620561923e-112
18411.3454325058729e-1116.7271625293645e-112
18515.19551870615907e-1112.59775935307953e-111
18612.03860960790462e-1101.01930480395231e-110
18712.23477008381053e-1121.11738504190526e-112
18818.4842011366732e-1124.2421005683366e-112
18914.09792474091547e-1112.04896237045773e-111
19015.01835302670204e-1112.50917651335102e-111
19111.83553661265714e-1109.17768306328571e-111
19211.01500207298719e-1095.07501036493597e-110
19315.15597292131749e-1092.57798646065874e-109
19411.92552884662588e-1089.6276442331294e-109
19511.92020069401573e-1099.60100347007864e-110
19613.38282620122713e-1091.69141310061357e-109
19711.30570352626515e-1086.52851763132577e-109
19812.76312361361751e-1081.38156180680876e-108
19911.97852082986580e-1089.89260414932899e-109
20012.25154523853943e-1091.12577261926972e-109
20116.8089407319426e-1093.4044703659713e-109
20211.89699766547573e-1089.48498832737865e-109
20316.10557707484885e-1083.05278853742443e-108
20411.58528999566675e-1087.92644997833374e-109
20515.79880734198605e-1082.89940367099302e-108
20612.17153810246819e-1071.08576905123410e-107
20719.53500942090474e-1074.76750471045237e-107
20815.52399457567311e-1062.76199728783655e-106
20913.32195538859027e-1051.66097769429513e-105
21011.90011455498931e-1049.50057277494657e-105
21111.05401283327491e-1035.27006416637453e-104
21215.53675921475011e-1032.76837960737506e-103
21312.91738945630816e-1021.45869472815408e-102
21411.50308074628944e-1017.51540373144722e-102
21517.45249251217756e-1013.72624625608878e-101
21613.83010548465968e-1001.91505274232984e-100
21711.90939878790523e-999.54699393952614e-100
21817.44418660434801e-993.72209330217401e-99
21913.12391619998747e-981.56195809999374e-98
22011.50557174453504e-977.5278587226752e-98
22115.25281530073651e-972.62640765036826e-97
22212.33956915297042e-961.16978457648521e-96
22313.84964358601491e-961.92482179300745e-96
22412.05637254243692e-951.02818627121846e-95
22511.10565601731880e-945.52828008659401e-95
22616.06192423852609e-943.03096211926304e-94
22711.44316425698260e-937.21582128491299e-94
22817.94186222236049e-933.97093111118024e-93
22914.44694434836449e-922.22347217418224e-92
23012.41125802594099e-911.20562901297050e-91
23111.24441984873509e-906.22209924367543e-91
23216.11782604406241e-903.05891302203120e-90
23312.80669758868683e-891.40334879434342e-89
23411.16271524252333e-885.81357621261664e-89
23515.56168923205135e-882.78084461602567e-88
23611.94397552352097e-879.71987761760486e-88
23713.17637806853624e-871.58818903426812e-87
23811.70779469992854e-868.53897349964269e-87
23916.14706863223025e-863.07353431611512e-86
24012.4568407929147e-851.22842039645735e-85
24111.23148373966272e-846.15741869831362e-85
24215.79280593301289e-842.89640296650645e-84
24318.93207295972395e-844.46603647986197e-84
24411.95929832897219e-839.79649164486094e-84
24519.06052244299566e-834.53026122149783e-83
24614.82777858828853e-822.41388929414426e-82
24712.33816112269375e-811.16908056134688e-81
24811.20078987210223e-806.00394936051115e-81
24915.7506727297153e-802.87533636485765e-80
25013.01786741940853e-791.50893370970427e-79
25111.38601204448831e-786.93006022244154e-79
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3990.9999999999988142.37257787268950e-121.18628893634475e-12
4000.999999999996087.83931150301573e-123.91965575150787e-12
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4050.999999999136571.72686058870294e-098.63430294351471e-10
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4070.999999994476071.10478585195763e-085.52392925978813e-09
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4090.9999999025379791.94924041843276e-079.7462020921638e-08
4100.9999996710213276.57957345049675e-073.28978672524838e-07
4110.9999991233631641.75327367246147e-068.76636836230734e-07
4120.999999618479157.63041701480187e-073.81520850740094e-07
4130.9999972366450735.52670985482685e-062.76335492741342e-06
4140.999984191384713.16172305804812e-051.58086152902406e-05
4150.9999633960882417.32078235170297e-053.66039117585149e-05
4160.9997874842343150.0004250315313704290.000212515765685215
4170.9992908665818370.001418266836326910.000709133418163453
4180.9997987602774240.0004024794451526610.000201239722576331


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level4061NOK
5% type I error level4061NOK
10% type I error level4061NOK
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Dec/03/t1291379972ims64ezy89o64e5/10xm0t1291380013.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/03/t1291379972ims64ezy89o64e5/10xm0t1291380013.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/03/t1291379972ims64ezy89o64e5/18klz1291380013.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/03/t1291379972ims64ezy89o64e5/18klz1291380013.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/03/t1291379972ims64ezy89o64e5/28klz1291380013.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/03/t1291379972ims64ezy89o64e5/28klz1291380013.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/03/t1291379972ims64ezy89o64e5/3ic221291380013.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/03/t1291379972ims64ezy89o64e5/3ic221291380013.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/03/t1291379972ims64ezy89o64e5/4ic221291380013.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/03/t1291379972ims64ezy89o64e5/4ic221291380013.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/03/t1291379972ims64ezy89o64e5/5ic221291380013.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/03/t1291379972ims64ezy89o64e5/5ic221291380013.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/03/t1291379972ims64ezy89o64e5/6t3251291380013.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/03/t1291379972ims64ezy89o64e5/6t3251291380013.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/03/t1291379972ims64ezy89o64e5/7mcj81291380013.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/03/t1291379972ims64ezy89o64e5/7mcj81291380013.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/03/t1291379972ims64ezy89o64e5/8mcj81291380013.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/03/t1291379972ims64ezy89o64e5/8mcj81291380013.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/03/t1291379972ims64ezy89o64e5/9mcj81291380013.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/03/t1291379972ims64ezy89o64e5/9mcj81291380013.ps (open in new window)


 
Parameters (Session):
par1 = 10 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;
 
Parameters (R input):
par1 = 10 ; 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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