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MR ws10

*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: Tue, 21 Dec 2010 11:50:14 +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/21/t1292932147zsqyeaxepq9w3zg.htm/, Retrieved Tue, 21 Dec 2010 12:49:28 +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/21/t1292932147zsqyeaxepq9w3zg.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 «
4321023 29790 444 81767 1 1 4111912 87550 412 153198 1 1 223193 84738 428 -26007 0 1 1491348 54660 315 126942 1 1 1629616 42634 168 157214 1 0 1398893 40949 263 129352 0 1 1926517 45187 267 234817 1 0 983660 37704 228 60448 1 1 1443586 16275 129 47818 1 1 1073089 25830 104 245546 0 1 984885 12679 122 48020 0 1 1405225 18014 393 -1710 1 1 227132 43556 190 32648 0 1 929118 24811 280 95350 1 1 1071292 6575 63 151352 0 0 638830 7123 102 288170 0 0 856956 21950 265 114337 1 1 992426 37597 234 37884 1 1 444477 17821 277 122844 0 1 857217 12988 73 82340 1 1 711969 22330 67 79801 1 0 702380 13326 103 165548 0 0 358589 16189 290 116384 0 1 297978 7146 83 134028 0 1 585715 15824 56 63838 0 1 657954 27664 236 74996 1 1 209458 11920 73 31080 0 1 786690 8568 34 32168 0 1 439798 14416 139 49857 0 1 688779 3369 26 87161 1 1 574339 11819 70 106113 1 1 741409 6984 40 80570 1 0 597793 4519 42 102129 1 1 644190 2220 12 301670 0 1 377934 18562 211 102313 0 1 640273 10327 74 88577 0 1 697458 53 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 time32 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135
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] = + 197015.802758075 + 12.618255455013Costs[t] + 1501.73539589983Orders[t] + 1.35642034815964Dividends[t] + 66885.3606741214Group[t] -42165.6854887257`Gender `[t] + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0		2-tail p-value1-tail p-value
(Intercept)197015.80275807531235.5179676.307400
Costs12.6182554550132.3221615.433800
Orders1501.73539589983333.701784.50029e-064e-06
Dividends1.356420348159640.3839053.53320.0004560.000228
Group66885.360674121426738.7691552.50140.0127450.006373
`Gender `-42165.685488725724031.395653-1.75460.0800490.040024


Multiple Linear Regression - Regression Statistics
Multiple R0.689870844796982
R-squared0.475921782500902
Adjusted R-squared0.469741614841714
F-TEST (value)77.0079079963782
F-TEST (DF numerator)5
F-TEST (DF denominator)424
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation235614.370828409
Sum Squared Residuals23537991858127.7


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast		Residuals
Prediction Error
143210231375314.246335772945708.75366423
241119122152979.610637891958932.38936211
32231931831562.17346678-1608369.17346678
414913481556682.682659-65334.6826589983
516296161267407.68162795362208.318372045
613988931241967.15389347156925.846106530
719265171553556.18027692372960.819723085
89836601121882.74908999-138222.749089988
91443586685682.759753179757903.240246821
101073089970023.72765512103065.272344880
11984885563184.00160186421700.998398140
1214052251036903.26350335368321.736496655
132271321034064.98861557-806932.988615571
149291181084627.60508676-155509.605086764
151071292579887.09485113491404.90514887
16638830830952.298475075-192122.298475075
178569561051755.09844198-194799.098441982
189924261098936.73939583-106510.739395826
19444477962328.853646704-517851.853646704
20857217606935.715161329250281.284838671
21711969754526.779471409-42557.7794714088
22702380744398.096526389-42018.096526389
23358589952495.94544171-593906.94544171
24297978551462.515033696-253484.515033696
25585715525209.73594567860505.2640543223
266579541026942.55071388-368988.550713883
27209458457043.950614591-247585.950614591
28786690357655.663228092429034.336771908
29439798613123.157237084-173325.157237084
30688779421518.454830746267260.545169254
31574339619925.949283519-45586.9492835185
32741409521383.262817221220025.737182779
33597793480360.114709662117432.885290338
34644190610074.79555959434115.2044404059
35377934844715.778641416-466781.778641416
36640273516434.90582879123838.094171210
37697458561771.412223356135686.587776644
38550608636353.27148362-85745.2714836197
39207393511168.905043204-303775.905043204
40301607784859.93438202-483252.93438202
41345783542868.557510906-197085.557510906
42501749515015.008208295-13266.008208295
43379983575249.833633462-195266.833633462
44387475407789.444302339-20314.4443023394
45377305443900.347294374-66595.3472943743
46370837642655.119644308-271818.119644308
47430866725816.329051612-294950.329051612
48469107469167.60906418-60.609064179589
49194493348875.947820932-154382.947820932
50530670543386.251926262-12716.2519262623
51518365661127.101621793-142762.101621793
52491303715518.982753477-224215.982753477
53527021571149.952686378-44128.9526863784
54233773664135.424870084-430362.424870084
55405972425945.024766008-19973.0247660083
56652925279449.515619974373475.484380026
57446211454355.209354803-8144.20935480349
58341340382601.984737985-41261.9847379853
59387699585650.365639627-197951.365639627
60493408526681.419013637-33273.4190136374
61146494346179.443685207-199685.443685207
62414462427085.370731789-12623.3707317891
63364304586744.365608892-222440.365608892
64355178391915.207166161-36737.2071661612
65357760822217.744988479-464457.744988479
66261216298066.769356423-36850.769356423
67397144449932.914435439-52788.9144354391
68374943460293.607307273-85350.607307273
69424898536317.177501005-111419.177501005
70202055370814.068318278-168759.068318278
71378525371627.8914482836897.10855171745
72310768412614.254083734-101846.254083734
73325738282900.03665836242837.9633416385
74394510392082.7826631592427.21733684078
75247060379330.82342476-132270.823424760
76368078409009.454277228-40931.4542772276
77236761324151.131100569-87390.1311005686
78312378343315.464323465-30937.464323465
79339836409541.706240435-69705.7062404351
80347385298530.86194983348854.1380501675
81426280544286.802724655-118006.802724655
82352850403964.069316727-51114.0693167274
83301881283561.24993277818319.7500672221
84377516323200.21177642254315.7882235782
85357312482811.681660018-125499.681660018
86458343473412.556692073-15069.5566920725
87354228364365.680245155-10137.6802451552
88308636435688.943511285-127052.943511285
89386212365373.91002422220838.0899757778
90393343405934.72686295-12591.7268629503
91378509431467.445239775-52958.4452397746
92452469371655.89293119680813.1070688038
93364839519864.173697104-155025.173697104
94358649294163.01025294764485.9897470529
95376641429222.252439828-52581.2524398284
96429112325066.618556509104045.381443491
97330546367814.875581891-37268.8755818906
98403560434426.52637632-30866.5263763196
99317892352020.598113449-34128.5981134486
100307528387443.473724959-79915.4737249586
101235133318488.048660368-83355.0486603679
102299243427061.734853422-127818.734853422
103314073328439.850805624-14366.8508056237
104368186311353.7392888756832.2607111299
105269661304880.458854535-35219.4588545351
106125390415252.234209802-289862.234209802
107510834404347.564564716106486.435435284
108321896477197.552321438-155301.552321438
109249898375104.94548019-125206.94548019
110408881291852.825118655117028.174881345
111158492379799.707966366-221307.707966366
112292154444639.141517712-152485.141517712
113289513371906.23058661-82393.2305866104
114378049326307.50977550651741.4902244937
115343466344995.056067122-1529.05606712220
116332743329384.3900082763358.60999172405
117442882370962.85709560871919.1429043923
118214215371159.400862791-156944.400862791
119315688280045.06376804735642.9362319533
120375195576123.670335855-200928.670335855
121334280316957.76435870417322.2356412956
122355864469325.794499638-113461.794499638
123480382426132.18043480254249.8195651984
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173309596254941.20521412754654.7947858733
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177316176305027.12812973411148.8718702663
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180359335292824.70067657166510.2993234291
181330068384295.856596210-54227.8565962104
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185333210328192.1106970645017.88930293596
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198315380304097.32148372411282.6785162763
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200315380304097.32148372411282.6785162763
201315380304097.32148372411282.6785162763
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208343613383096.850055888-39483.8500558877
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214304485254035.98486358250449.0151364184
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318315372286897.58511293428474.4148870662
319315380279377.64629832836002.3537016722
320315380237211.96080960278168.0391903976
321315380237211.96080960278168.0391903976
322315380237211.96080960278168.0391903976
323315380346263.006972449-30883.0069724492
324315380237211.96080960278168.0391903976
325312502238994.01066620973507.9893337912
326315380346263.006972449-30883.0069724492
327315380304097.32148372411282.6785162763
328315380237211.96080960278168.0391903976
329315380237211.96080960278168.0391903976
330315380237211.96080960278168.0391903976
331315380279377.64629832836002.3537016722
332315380237211.96080960278168.0391903976
333313729243967.71557816069761.2844218396
334315388280901.4948921234486.5051078802
335315371289346.72009480126024.2799051989
336296139278174.54250300217964.4574969978
337315380279377.64629832836002.3537016722
338313880281446.18631733432433.8136826659
339317698252469.16623719265228.8337628083
340295580304285.010070460-8705.01007046053
341315380279377.64629832836002.3537016722
342315380279377.64629832836002.3537016722
343315380237211.96080960278168.0391903976
344308256306736.1430825881519.85691741158
345315380279377.64629832836002.3537016722
346303677283211.43948742220465.5605125779
347315380279377.64629832836002.3537016722
348315380237211.96080960278168.0391903976
349319369314521.1177080724847.88229192846
350318690242775.73872047175914.261279529
351314049291194.88321758422854.1167824162
352325699258110.25782901367588.7421709866
353314210284407.23154892929802.7684510709
354315380279377.64629832836002.3537016722
355315380279377.64629832836002.3537016722
356322378332886.412028465-10508.4120284647
357315380279377.64629832836002.3537016722
358315380279377.64629832836002.3537016722
359315380237211.96080960278168.0391903976
360315398285399.91897807829998.0810219216
361315380237211.96080960278168.0391903976
362315380279377.64629832836002.3537016722
363308336369585.546842487-61249.5468424867
364316386251527.1492768564858.8507231502
365315380237211.96080960278168.0391903976
366315380237211.96080960278168.0391903976
367315380279377.64629832836002.3537016722
368315380237211.96080960278168.0391903976
369315553292640.57375881922912.4262411807
370315380237211.96080960278168.0391903976
371323361252103.40831782571257.5916821751
372336639314353.77568200922285.2243179915
373307424249474.06687392957949.9331260714
374315380237211.96080960278168.0391903976
375315380237211.96080960278168.0391903976
376295370249096.99785321646273.0021467843
377322340297163.85175194225176.1482480580
378319864322306.581323814-2442.58132381449
379315380237211.96080960278168.0391903976
380315380237211.96080960278168.0391903976
381317291330340.730701835-13049.7307018347
382280398281505.368946102-1107.36894610163
383315380237211.96080960278168.0391903976
384317330301068.40726397316261.5927360273
385238125321778.006864587-83653.0068645869
386327071284099.39480193342971.6051980671
387309038255020.54023884354017.4597611571
388314210284354.59952668129855.4004733192
389307930253540.74655200754389.2534479934
390322327259938.03867707862388.9613229217
391292136292174.0672428-38.0672427998215
392263276257386.3755498965889.62445010443
393367655307101.25331499760553.7466850026
394283910434058.176441822-150148.176441822
395283587253246.36787428530340.6321257153
396243650327573.114641701-83923.1146417013
397438493763207.284777202-324714.284777202
398296261258671.88981330637589.1101866942
399230621338619.224004421-107998.224004421
400304252310421.316799204-6169.31679920369
401333505305944.33112065727560.6688793433
402296919294022.4896240552896.51037594466
403278990408762.172135661-129772.172135661
404276898302175.093534961-25277.0935349608
405327007324340.4501535952666.54984640473
406317046271448.50903840645597.4909615938
407304555265284.24778220239270.7522177979
408298096295164.6519151392931.34808486135
409231861263438.472881599-31577.4728815994
410309422351654.216476997-42232.2164769969
411286963432687.127600945-145724.127600945
412269753336699.172588113-66946.1725881132
413448243413600.93896040734642.0610395932
414165404303323.16114871-137919.161148710
415204325311879.221450214-107554.221450214
416407159278288.888409194128870.111590806
417290476392742.232676755-102266.232676755
418275311342955.063302272-67644.0633022723
419246541296273.434360421-49732.4343604213
420253468305937.278621000-52469.2786210005
421240897400453.555245279-159556.555245279
422-83265449587.599786064-532852.599786064
423-42143342960.508324512-385103.508324512
424272713288291.691826854-15578.6918268544
425215362500276.154826842-284914.154826842
42642754306366.219831720-263612.219831720
4273062751184121.36571613-877846.365716134
428253537427498.731290095-173961.731290095
429372631581292.293190792-208661.293190792
430-7170523528.163204072-530698.163204072


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
913.11906389362840e-531.55953194681420e-53
1019.39120217352388e-544.69560108676194e-54
1112.80423300220605e-651.40211650110303e-65
1212.17879389164546e-891.08939694582273e-89
1314.18187728724627e-912.09093864362313e-91
1412.08725127355830e-1061.04362563677915e-106
1512.65518998398729e-1171.32759499199364e-117
1615.03847256303284e-1222.51923628151642e-122
1712.11285195669624e-1321.05642597834812e-132
1812.89649162375314e-1371.44824581187657e-137
1911.73237260350711e-1408.66186301753554e-141
2012.89508664543805e-1451.44754332271902e-145
2111.46376383129085e-1467.31881915645426e-147
2213.20386096736647e-1471.60193048368324e-147
2311.6263358310701e-1498.1316791553505e-150
2415.98300781287862e-1492.99150390643931e-149
2511.14965446505843e-1525.74827232529213e-153
2612.92868519125484e-1581.46434259562742e-158
2716.00823887551752e-1583.00411943775876e-158
2811.73959461096126e-1728.69797305480632e-173
2911.16159522221851e-1725.80797611109253e-173
3011.2615765614197e-1766.3078828070985e-177
3111.08667365540908e-1785.43336827704541e-179
3213.22501732342204e-1861.61250866171102e-186
3312.19313578339356e-1881.09656789169678e-188
3412.00257173460145e-1871.00128586730072e-187
3513.010327162888e-1871.505163581444e-187
3611.67678458244160e-1938.38392291220802e-194
3712.67512086599644e-1991.33756043299822e-199
3814.07513659067123e-2002.03756829533561e-200
3912.00782508463585e-2001.00391254231793e-200
4012.31541996150448e-2011.15770998075224e-201
4111.14502195610858e-2005.72510978054291e-201
4213.23541728325686e-2011.61770864162843e-201
4313.95257537478553e-2001.97628768739277e-200
4415.80151163819898e-2002.90075581909949e-200
4512.54924570016325e-1991.27462285008163e-199
4611.92182473964454e-2019.6091236982227e-202
4713.6381429152173e-2021.81907145760865e-202
4816.83535752268695e-2023.41767876134348e-202
4913.43430420322835e-2021.71715210161417e-202
5018.50966574680438e-2034.25483287340219e-203
5114.62459400781632e-2032.31229700390816e-203
5215.66080938339062e-2032.83040469169531e-203
5319.42550468649837e-2034.71275234324919e-203
5415.85201148527434e-2072.92600574263717e-207
5511.49412863112902e-2067.47064315564512e-207
5611.14918814388467e-2205.74594071942333e-221
5715.27096015136402e-2212.63548007568201e-221
5813.86306311042434e-2201.93153155521217e-220
5914.91212303973923e-2202.45606151986962e-220
6011.56251388041147e-2217.81256940205734e-222
6114.19859951052139e-2232.09929975526070e-223
6211.54366956914169e-2227.71834784570847e-223
6312.85155834046462e-2221.42577917023231e-222
6411.71224589250359e-2218.56122946251795e-222
6513.1677593330848e-2211.5838796665424e-221
6616.53047915768111e-2213.26523957884055e-221
6716.0283453994067e-2203.01417269970335e-220
6813.16463494505843e-2191.58231747252921e-219
6911.18013950020759e-2185.90069750103797e-219
7017.19656082856224e-2183.59828041428112e-218
7116.92482506358439e-2193.46241253179219e-219
7212.19722642562005e-2181.09861321281002e-218
7311.18926977386058e-2175.94634886930289e-218
7411.00880149269695e-2165.04400746348473e-217
7512.12050479599569e-2161.06025239799785e-216
7611.79576334402079e-2158.97881672010393e-216
7712.35740312077679e-2151.17870156038839e-215
7811.98535847264947e-2149.92679236324735e-215
7917.3464516775558e-2143.6732258387779e-214
8013.00309969521490e-2131.50154984760745e-213
8113.50325106258945e-2131.75162553129473e-213
8213.07836955216566e-2131.53918477608283e-213
8311.97628557302796e-2129.8814278651398e-213
8411.35431142697957e-2116.77155713489786e-212
8512.78073966852942e-2111.39036983426471e-211
8611.95603604701371e-2119.78018023506853e-212
8711.40367692777871e-2107.01838463889355e-211
8812.73550344866315e-2101.36775172433157e-210
8912.59266598986159e-2091.29633299493079e-209
9012.33528534490532e-2081.16764267245266e-208
9111.44945217280838e-2077.24726086404192e-208
9213.66583836732194e-2091.83291918366097e-209
9312.86134882178419e-2081.43067441089210e-208
9417.67101208511166e-2093.83550604255583e-209
9518.18386499690255e-2094.09193249845127e-209
9615.04135582459131e-2082.52067791229566e-208
9715.29933112445976e-2072.64966556222988e-207
9814.17514535062426e-2062.08757267531213e-206
9914.53803888683432e-2052.26901944341716e-205
10013.97692175350548e-2041.98846087675274e-204
10113.14893481860159e-2051.57446740930080e-205
10213.00084139970270e-2051.50042069985135e-205
10314.30684881283167e-2062.15342440641584e-206
10411.52464645538489e-2057.62323227692445e-206
10514.73971094978473e-2052.36985547489236e-205
10612.01168257319305e-2071.00584128659652e-207
10711.00579502024713e-2085.02897510123563e-209
10817.11521508561652e-2083.55760754280826e-208
10911.38954955961322e-2076.9477477980661e-208
11017.61887969754557e-2083.80943984877278e-208
11113.66867992432087e-2081.83433996216044e-208
11212.63109980314740e-2071.31554990157370e-207
11312.07671547060566e-2061.03835773530283e-206
11411.73760915706772e-2068.68804578533858e-207
11517.19663521612704e-2063.59831760806352e-206
11614.94305045680738e-2052.47152522840369e-205
11714.02891190127593e-2052.01445595063796e-205
11813.82597869406253e-2061.91298934703127e-206
11913.22998711969845e-2051.61499355984922e-205
12011.98458565320043e-2049.92292826600214e-205
12111.83295699607143e-2039.16478498035716e-204
12211.57595780429032e-2027.87978902145158e-203
12312.46487003664083e-2021.23243501832042e-202
12417.42170166932188e-2023.71085083466094e-202
12511.41520002107459e-2027.07600010537293e-203
12611.32249310618322e-2016.61246553091608e-202
12711.30834744510534e-2006.54173722552669e-201
12811.2589091096155e-1996.2945455480775e-200
12919.26889960655278e-1994.63444980327639e-199
13019.0835541312234e-1984.5417770656117e-198
13115.93107036947404e-1982.96553518473702e-198
13214.58248907817881e-1972.29124453908940e-197
13314.73027205858725e-1962.36513602929362e-196
13414.64834084542904e-1952.32417042271452e-195
13514.50995352903409e-1942.25497676451705e-194
13613.62991602144288e-1931.81495801072144e-193
13713.50188270315337e-1921.75094135157669e-192
13813.32546645490062e-1911.66273322745031e-191
13913.18898728882979e-1901.59449364441490e-190
14012.673567619423e-1891.3367838097115e-189
14112.08591640609976e-1881.04295820304988e-188
14212.09403860013827e-1871.04701930006913e-187
14312.01958473132078e-1861.00979236566039e-186
14411.54043212425804e-1857.7021606212902e-186
14511.41527038460152e-1847.07635192300759e-185
14611.11450296493962e-1835.5725148246981e-184
14711.07531508416740e-1825.37657542083701e-183
14817.61752584561516e-1823.80876292280758e-182
14916.07597295025396e-1813.03798647512698e-181
15015.7319416563966e-1802.8659708281983e-180
15115.55390100803083e-1792.77695050401541e-179
15215.22839357564438e-1782.61419678782219e-178
15314.50013246576532e-1772.25006623288266e-177
15414.18649260307085e-1762.09324630153543e-176
15513.85710511497638e-1751.92855255748819e-175
15613.54348373199675e-1741.77174186599838e-174
15713.27661614616719e-1731.63830807308360e-173
15812.29347458573179e-1721.14673729286590e-172
15912.08816596089390e-1711.04408298044695e-171
16011.89489719473522e-1709.4744859736761e-171
16111.47645990058678e-1697.3822995029339e-170
16211.33081503066532e-1686.6540751533266e-169
16311.22960327615994e-1676.14801638079972e-168
16411.04538279219846e-1665.22691396099231e-167
16519.34099782056242e-1664.67049891028121e-166
16617.23005896088013e-1653.61502948044006e-165
16716.86481545086103e-1663.43240772543052e-166
16811.05024703135472e-1655.2512351567736e-166
16919.44373287093209e-1654.72186643546604e-165
17018.45935535979562e-1644.22967767989781e-164
17116.88202032005776e-1633.44101016002888e-163
17215.40305600880657e-1622.70152800440328e-162
17314.53357081771229e-1612.26678540885614e-161
17413.56297111500474e-1601.78148555750237e-160
17513.16175435323936e-1591.58087717661968e-159
17612.49019283880051e-1581.24509641940026e-158
17712.21646133666461e-1571.10823066833230e-157
17811.91893427246420e-1569.59467136232098e-157
17911.65477624262153e-1558.27388121310766e-156
18019.2877931427713e-1554.64389657138565e-155
18117.68549816322077e-1543.84274908161039e-154
18214.33166896760339e-1532.16583448380169e-153
18311.95174714357425e-1529.75873571787123e-153
18411.70701394439634e-1518.53506972198169e-152
18511.16392650331237e-1505.81963251656184e-151
18614.75278262244342e-1502.37639131122171e-150
18714.05537135237464e-1492.02768567618732e-149
18812.71479434502279e-1481.35739717251140e-148
18912.2556320639522e-1471.1278160319761e-147
19011.78516001088607e-1468.92580005443036e-147
19111.47105024175012e-1457.35525120875058e-146
19211.22329437433582e-1446.11647187167909e-145
19319.13386992876522e-1444.56693496438261e-144
19417.46162112032518e-1433.73081056016259e-143
19516.19026634598814e-1423.09513317299407e-142
19614.03431872483709e-1412.01715936241855e-141
19713.31492790094289e-1401.65746395047144e-140
19812.71029489589726e-1391.35514744794863e-139
19912.28242943210533e-1391.14121471605267e-139
20011.87487338764116e-1389.37436693820578e-139
20111.53266175536276e-1377.6633087768138e-138
20211.24685601573825e-1366.23428007869125e-137
20319.34234471580442e-1364.67117235790221e-136
20413.47934765105946e-1351.73967382552973e-135
20512.81273589682066e-1341.40636794841033e-134
20612.23036690935647e-1331.11518345467823e-133
20711.78190213799268e-1328.90951068996339e-133
20813.02436888350155e-1321.51218444175077e-132
20912.35049524306653e-1311.17524762153326e-131
21011.81140751112467e-1309.05703755562337e-131
21111.29497347517878e-1296.47486737589389e-130
21216.81418569626692e-1293.40709284813346e-129
21314.7762801099466e-1282.3881400549733e-128
21413.56267037312675e-1271.78133518656338e-127
21512.54058407650060e-1261.27029203825030e-126
21611.92300995518117e-1259.61504977590585e-126
21711.40319407399315e-1247.01597036996574e-125
21811.04972665574580e-1235.24863327872898e-124
21914.65885559495289e-1232.32942779747645e-123
22013.35414913849208e-1221.67707456924604e-122
22112.34111446337803e-1211.17055723168901e-121
22211.63277912766384e-1208.1638956383192e-121
22311.20255685082615e-1196.01278425413075e-120
22418.76059025679882e-1194.38029512839941e-119
22516.40927480886758e-1183.20463740443379e-118
22614.6582123257114e-1172.3291061628557e-117
22713.18235182601742e-1161.59117591300871e-116
22812.22273903521149e-1151.11136951760575e-115
22911.58341201629912e-1147.91706008149561e-115
23011.06631867942575e-1135.33159339712874e-114
23116.6148485584575e-1133.30742427922875e-113
23214.45328902570790e-1122.22664451285395e-112
23313.19751521115270e-1111.59875760557635e-111
23412.23060490282935e-1101.11530245141467e-110
23511.54852071873312e-1097.74260359366558e-110
23611.07035345451953e-1085.35176727259763e-109
23717.32048771857732e-1083.66024385928866e-108
23814.81067301913695e-1072.40533650956847e-107
23913.15129823000369e-1061.57564911500185e-106
24012.13956005504816e-1051.06978002752408e-105
24111.41880691638174e-1047.09403458190868e-105
24219.54583215116695e-1044.77291607558348e-104
24316.11136648844065e-1033.05568324422032e-103
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3750.9999999999999992.17792997403805e-151.08896498701903e-15
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3770.999999999999991.80476160659217e-149.02380803296083e-15
3780.9999999999999774.65906267549475e-142.32953133774737e-14
3790.9999999999999351.29131531935958e-136.45657659679792e-14
3800.9999999999998243.51543883369206e-131.75771941684603e-13
3810.999999999999481.04151290183567e-125.20756450917837e-13
3820.9999999999987062.58835954855760e-121.29417977427880e-12
3830.9999999999965926.81687349232088e-123.40843674616044e-12
3840.9999999999907051.85908586402502e-119.2954293201251e-12
3850.9999999999762784.74435561738075e-112.37217780869037e-11
3860.999999999942881.14240233516087e-105.71201167580436e-11
3870.999999999859132.81740550928232e-101.40870275464116e-10
3880.9999999996443887.11224859494796e-103.55612429747398e-10
3890.9999999991336471.73270674351811e-098.66353371759056e-10
3900.9999999979544784.09104380904782e-092.04552190452391e-09
3910.9999999947440831.05118343167678e-085.2559171583839e-09
3920.999999986211552.75769011171562e-081.37884505585781e-08
3930.9999999746757885.06484239839254e-082.53242119919627e-08
3940.9999999431294371.13741126089374e-075.68705630446869e-08
3950.9999998612369952.77526009976645e-071.38763004988323e-07
3960.9999996779685436.44062914153702e-073.22031457076851e-07
3970.9999993968133511.20637329709839e-066.03186648549194e-07
3980.9999985883598072.82328038585952e-061.41164019292976e-06
3990.9999970617459245.87650815141509e-062.93825407570754e-06
4000.9999931319335071.3736132986125e-056.8680664930625e-06
4010.9999865262457822.69475084365904e-051.34737542182952e-05
4020.9999719339631445.6132073711086e-052.8066036855543e-05
4030.999939272315610.0001214553687800856.07276843900423e-05
4040.9998667627408810.0002664745182372610.000133237259118631
4050.999739264680640.0005214706387178350.000260735319358917
4060.9994817812127570.001036437574486240.000518218787243121
4070.9990712125108460.001857574978307930.000928787489153964
4080.9983555810718220.003288837856355420.00164441892817771
4090.9967620737102820.006475852579435770.00323792628971788
4100.9938543318252970.01229133634940690.00614566817470346
4110.9887839223252380.02243215534952410.0112160776747620
4120.9793192243662040.04136155126759150.0206807756337958
4130.981096934259330.0378061314813380.018903065740669
4140.9692121636792130.06157567264157340.0307878363207867
4150.9489259821816310.1021480356367380.0510740178183689
4160.9843746607934730.03125067841305430.0156253392065271
4170.9668673695617630.06626526087647370.0331326304382369
4180.9315350022583510.1369299954832980.0684649977416488
4190.8669904456045460.2660191087909080.133009554395454
4200.7595128670986640.4809742658026720.240487132901336
4210.6009843285107460.7980313429785080.399015671489254


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level4010.97094430992736NOK
5% type I error level4060.983050847457627NOK
10% type I error level4080.987893462469734NOK
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Dec/21/t1292932147zsqyeaxepq9w3zg/10zbds1292932180.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/21/t1292932147zsqyeaxepq9w3zg/10zbds1292932180.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/21/t1292932147zsqyeaxepq9w3zg/13jx21292932180.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/21/t1292932147zsqyeaxepq9w3zg/13jx21292932180.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/21/t1292932147zsqyeaxepq9w3zg/23jx21292932180.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/21/t1292932147zsqyeaxepq9w3zg/23jx21292932180.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/21/t1292932147zsqyeaxepq9w3zg/33jx21292932180.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/21/t1292932147zsqyeaxepq9w3zg/33jx21292932180.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/21/t1292932147zsqyeaxepq9w3zg/4esxn1292932180.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/21/t1292932147zsqyeaxepq9w3zg/4esxn1292932180.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/21/t1292932147zsqyeaxepq9w3zg/5esxn1292932180.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/21/t1292932147zsqyeaxepq9w3zg/5esxn1292932180.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/21/t1292932147zsqyeaxepq9w3zg/6esxn1292932180.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/21/t1292932147zsqyeaxepq9w3zg/6esxn1292932180.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/21/t1292932147zsqyeaxepq9w3zg/7p2wq1292932180.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/21/t1292932147zsqyeaxepq9w3zg/7p2wq1292932180.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/21/t1292932147zsqyeaxepq9w3zg/8zbds1292932180.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/21/t1292932147zsqyeaxepq9w3zg/8zbds1292932180.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/21/t1292932147zsqyeaxepq9w3zg/9zbds1292932180.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/21/t1292932147zsqyeaxepq9w3zg/9zbds1292932180.ps (open in new window)


 
Parameters (Session):
par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;
 
Parameters (R input):
par1 = 1 ; 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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