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MR 2 with seasonal dummies

*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, 29 Dec 2010 17:37:33 +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/29/t1293644160c1e35rs0c8j7k8p.htm/, Retrieved Wed, 29 Dec 2010 18:36:10 +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/29/t1293644160c1e35rs0c8j7k8p.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 «
34420 34070 33978 34484 34645 34410 34534 35019 35508 35488 35709 36534 36066 35724 35727 36281 36017 35780 36003 36285 36419 36413 36663 37451 37063 36613 36564 37064 36817 36621 36798 36967 36926 36975 37324 38159 37776 37465 37451 37944 37737 37603 37813 37960 37934 37975 38241 39176 39137 38797 38730 39031 38851 38727 39291 39407 39326 39326 39617 40458 40425 40092 39939 40174 40065 39922 40107 40163 40116 40118 40416 41215 40852 40497 40430 40766 40626 40442 40590 40673 40660 40736 41082 41873 41507 41104 40963 41227 41063 40873 41016 41433 41345 41375 41597 42225 41937 41642 41551 41866 41744 41615 41764 41828 41786 41852 42183 42937 42635 42292 42202 42577 42600 42433 42584 42660 42659 42712 43039 43664 43397 43110 43005 43159 43066 42977 43139 43226 43242 43348 43605 44225 43983 43754 43632 43868 43864 43808 43954 44032 44090 44210 44435 44919 44785 44616 44 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 time8 seconds
R Server'Herman Ole Andreas Wold' @ www.yougetit.org


Multiple Linear Regression - Estimated Regression Equation
Coins[t] = + 36761.6862745098 -405.517610748004M1[t] -764.330428467676M2[t] -908.254357298463M3[t] -671.400508351487M4[t] -827.87999273783M5[t] -1032.69281045751M6[t] -939.950072621637M7[t] -865.985112563539M8[t] -888.686819172112M9[t] -897.6107480029M10[t] -704.590232389247M11[t] + 51.9794843863471t + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0		2-tail p-value1-tail p-value
(Intercept)36761.6862745098225.33606163.141600
M1-405.517610748004282.21173-1.43690.1522860.076143
M2-764.330428467676282.198295-2.70850.0073390.003669
M3-908.254357298463282.187845-3.21860.0015010.00075
M4-671.400508351487282.18038-2.37930.0182750.009138
M5-827.87999273783282.175901-2.93390.0037340.001867
M6-1032.69281045751282.174408-3.65980.0003220.000161
M7-939.950072621637282.175901-3.33110.0010290.000514
M8-865.985112563539282.18038-3.06890.0024430.001222
M9-888.686819172112282.187845-3.14930.0018850.000942
M10-897.6107480029282.198295-3.18080.00170.00085
M11-704.590232389247282.21173-2.49670.0133360.006668
t51.97948438634710.91791356.627900


Multiple Linear Regression - Regression Statistics
Multiple R0.970124733214684
R-squared0.941141997994862
Adjusted R-squared0.93764548302426
F-TEST (value)269.165728134364
F-TEST (DF numerator)12
F-TEST (DF denominator)202
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation834.342398630352
Sum Squared Residuals140617702.106755


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast		Residuals
Prediction Error
13442036408.1481481482-1988.14814814824
23407036101.3148148148-2031.31481481482
33397836009.3703703704-2031.37037037038
43448436298.2037037037-1814.20370370372
53464536193.7037037037-1548.70370370369
63441036040.8703703704-1630.87037037037
73453436185.5925925926-1651.5925925926
83501936311.537037037-1292.53703703704
93550836340.8148148148-832.81481481482
103548836383.8703703704-895.87037037036
113570936628.8703703704-919.870370370367
123653437385.440087146-851.440087145965
133606637031.9019607843-965.901960784309
143572436725.068627451-1001.06862745098
153572736633.1241830065-906.124183006537
163628136921.9575163399-640.957516339868
173601736817.4575163399-800.457516339869
183578036664.6241830065-884.624183006537
193600336809.3464052288-806.346405228759
203628536935.2908496732-650.290849673203
213641936964.568627451-545.568627450979
223641337007.6241830065-594.624183006536
233666337252.6241830065-589.624183006536
243745138009.1938997821-558.193899782129
253706337655.6557734205-592.655773420472
263661337348.8224400871-735.822440087147
273656437256.8779956427-692.877995642702
283706437545.711328976-481.711328976033
293681737441.211328976-624.211328976034
303662137288.3779956427-667.377995642702
313679837433.1002178649-635.100217864924
323696737559.0446623094-592.044662309366
333692637588.3224400871-662.322440087144
343697537631.3779956427-656.377995642701
353732437876.3779956427-552.377995642699
363815938632.9477124183-473.947712418294
373777638279.4095860566-503.409586056637
383746537972.5762527233-507.576252723309
393745137880.6318082789-429.631808278868
403794438169.4651416122-225.465141612199
413773738064.9651416122-327.965141612199
423760337912.1318082789-309.131808278867
433781338056.8540305011-243.854030501088
443796038182.7984749455-222.798474945532
453793438212.0762527233-278.076252723309
463797538255.1318082789-280.131808278866
473824138500.1318082789-259.131808278866
483917639256.7015250545-80.7015250544606
493913738903.1633986928233.836601307198
503879738596.3300653595200.669934640524
513873038504.385620915225.614379084966
523903138793.2189542484237.781045751637
533885138688.7189542484162.281045751634
543872738535.885620915191.114379084967
553929138680.6078431373610.392156862746
563940738806.5522875817600.447712418302
573932638835.8300653595490.169934640524
583932638878.885620915447.114379084968
593961739123.885620915493.114379084968
604045839880.4553376906577.544662309374
614042539526.917211329898.082788671033
624009239220.0838779956871.916122004357
633993939128.1394335512810.8605664488
644017439416.9727668845757.027233115471
654006539312.4727668845752.52723311547
663992239159.6394335512762.360566448801
674010739304.3616557734802.638344226581
684016339430.3061002179732.693899782137
694011639459.5838779956656.416122004359
704011839502.6394335512615.360566448803
714041639747.6394335512668.360566448802
724121540504.2091503268710.790849673208
734085240150.6710239651701.328976034867
744049739843.8376906318653.162309368191
754043039751.8932461874678.106753812635
764076640040.7265795207725.273420479305
774062639936.2265795207689.773420479304
784044239783.3932461874658.606753812636
794059039928.1154684096661.884531590414
804067340054.059912854618.940087145971
814066040083.3376906318576.662309368193
824073640126.3932461874609.606753812637
834108240371.3932461874710.606753812637
844187341127.962962963745.037037037042
854150740774.4248366013732.575163398701
864110440467.591503268636.408496732026
874096340375.6470588235587.352941176469
884122740664.4803921569562.519607843139
894106340559.9803921569503.019607843138
904087340407.1470588235465.85294117647
914101640551.8692810458464.130718954249
924143340677.8137254902755.186274509805
934134540707.091503268637.908496732027
944137540750.1470588235624.852941176471
954159740995.1470588235601.852941176471
964222541751.7167755991473.283224400876
974193741398.1786492375538.821350762535
984164241091.3453159041550.65468409586
994155140999.4008714597551.599128540303
1004186641288.234204793577.765795206973
1014174441183.734204793560.265795206972
1024161541030.9008714597584.099128540304
1034176441175.6230936819588.376906318083
1044182841301.5675381264526.43246187364
1054178641330.8453159041455.154684095861
1064185241373.9008714597478.099128540305
1074218341618.9008714597564.099128540305
1084293742375.4705882353561.52941176471
1094263542021.9324618736613.06753812637
1104229241715.0991285403576.900871459694
1114220241623.1546840959578.845315904137
1124257741911.9880174292665.011982570807
1134260041807.4880174292792.511982570806
1144243341654.6546840959778.345315904138
1154258441799.3769063181784.623093681917
1164266041925.3213507625734.678649237473
1174265941954.5991285403704.400871459696
1184271241997.6546840959714.34531590414
1194303942242.6546840959796.34531590414
1204366442999.2244008715664.775599128546
1214339742645.6862745098751.313725490204
1224311042338.8529411765771.147058823528
1234300542246.908496732758.091503267972
1244315942535.7418300654623.258169934642
1254306642431.2418300654634.758169934641
1264297742278.408496732698.591503267973
1274313942423.1307189542715.869281045752
1284322642549.0751633987676.924836601308
1294324242578.3529411765663.647058823531
1304334842621.408496732726.591503267975
1314360542866.408496732738.591503267975
1324422543622.9782135076602.021786492379
1334398343269.440087146713.559912854038
1344375442962.6067538126791.393246187363
1354363242870.6623093682761.337690631806
1364386843159.4956427015708.504357298476
1374386443054.9956427015809.004357298475
1384380842902.1623093682905.837690631807
1394395443046.8845315904907.115468409586
1404403243172.8289760349859.171023965142
1414409043202.1067538126887.893246187365
1424421043245.1623093682964.837690631809
1434443543490.1623093682944.837690631809
1444491944246.7320261438672.267973856213
1454478543893.1938997821891.806100217872
1464461643586.36056644881029.6394335512
1474449643494.41612200441001.58387799564
1484460043783.2494553377816.750544662311
1494446343678.7494553377784.250544662309
1504423243525.9161220044706.083877995642
1514424843670.6383442266577.361655773421
1524428243796.582788671485.417211328977
1534431143825.8605664488485.139433551198
1544436243868.9161220044493.083877995643
1554461744113.9161220044503.083877995642
1564502244870.48583878151.514161220047
1574488244516.9477124183365.052287581706
1584459444210.114379085383.885620915031
1594450244118.1699346405383.830065359475
1604475244407.0032679739344.996732026145
1614469044302.5032679739387.496732026143
1624453344149.6699346405383.330065359475
1634460444294.3921568627309.607843137255
1644464644420.3366013072225.66339869281
1654465244449.614379085202.385620915033
1664471844492.6699346405225.330065359477
1674492844737.6699346405190.330065359477
1684528545494.2396514161-209.23965141612
1694518345140.701525054542.2984749455409
1704496444833.8681917211130.131808278865
1714487544741.9237472767133.076252723309
1724507145030.7570806140.2429193899788
1734498544926.2570806158.7429193899771
1744485444773.423747276780.576252723309
1754492544918.14596949896.8540305010892
1764497045044.0904139434-74.0904139433559
1774501145073.3681917211-62.3681917211333
1784510745116.4237472767-9.42374727668926
1794530645361.4237472767-55.423747276689
1804577346117.9934640523-344.993464052286
1814562545764.4553376906-139.455337690625
1824539145457.6220043573-66.6220043573017
1834532545365.6775599129-40.6775599128576
1844543045654.5108932462-224.510893246188
1854532145550.0108932462-229.010893246189
1864523845397.1775599129-159.177559912858
1874524645541.8997821351-295.899782135078
1884528145667.8442265795-386.844226579523
1894529745697.1220043573-400.1220043573
1904534945740.1775599129-391.177559912855
1914553645985.1775599129-449.177559912855
1924590346741.7472766885-838.74727668845
1934571646388.2091503268-672.209150326791
1944541946081.3758169935-662.375816993467
1954523745989.431372549-752.431372549023
1964534946278.2647058823-929.264705882353
1974526046173.7647058824-913.764705882355
1984513946020.931372549-881.931372549024
1994515446165.6535947712-1011.65359477124
2004518646291.5980392157-1105.59803921569
2014526246320.8758169935-1058.87581699347
2024522746363.931372549-1136.93137254902
2034531346608.931372549-1295.93137254902
2044556447365.5010893246-1801.50108932462
2054539247011.962962963-1619.96296296296
2064511446705.1296296296-1591.12962962963
2074499646613.1851851852-1617.18518518519
2084515946902.0185185185-1743.01851851852
2094510746797.5185185185-1690.51851851852
2104496346644.6851851852-1681.68518518519
2114500546789.4074074074-1784.40740740741
2124502446915.3518518519-1891.35185185185
2134502546944.6296296296-1919.62962962963
2144505346987.6851851852-1934.68518518519
2154514347232.6851851852-2089.68518518519


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
160.0005067597210189810.001013519442037960.999493240278981
170.001305264389125710.002610528778251430.998694735610874
180.0005675492585007850.001135098517001570.9994324507415
190.0001199130059580780.0002398260119161550.999880086994042
207.1501829306663e-050.0001430036586133260.999928498170693
210.0003185657837144770.0006371315674289530.999681434216286
220.0003805890493776060.0007611780987552110.999619410950622
230.0002883824462577780.0005767648925155570.999711617553742
240.000211187109588420.000422374219176840.999788812890412
258.66579685797975e-050.0001733159371595950.99991334203142
264.26069686411638e-058.52139372823276e-050.99995739303136
271.969528789389e-053.939057578778e-050.999980304712106
288.84516200169203e-061.76903240033841e-050.999991154837998
297.1307411770486e-061.42614823540972e-050.999992869258823
304.50202495924418e-069.00404991848836e-060.99999549797504
312.64901721525091e-065.29803443050182e-060.999997350982785
323.15349067425634e-066.30698134851269e-060.999996846509326
331.77127211675368e-053.54254423350736e-050.999982287278832
343.8975968377828e-057.7951936755656e-050.999961024031622
354.46921310076419e-058.93842620152838e-050.999955307868992
364.23959972327209e-058.47919944654418e-050.999957604002767
372.82929143716116e-055.65858287432232e-050.999971707085628
381.84517452830431e-053.69034905660861e-050.999981548254717
391.17645234707554e-052.35290469415108e-050.99998823547653
406.88910385415002e-061.37782077083e-050.999993110896146
414.66172988299468e-069.32345976598937e-060.999995338270117
423.03250938419284e-066.06501876838568e-060.999996967490616
431.94513372816559e-063.89026745633118e-060.999998054866272
441.41457011619541e-062.82914023239082e-060.999998585429884
451.78124214681708e-063.56248429363416e-060.999998218757853
462.01821279469547e-064.03642558939093e-060.999997981787205
472.31170394001935e-064.6234078800387e-060.99999768829606
481.77757128737024e-063.55514257474047e-060.999998222428713
491.86890616042193e-063.73781232084385e-060.99999813109384
502.06815972231576e-064.13631944463151e-060.999997931840278
511.99992871941447e-063.99985743882893e-060.99999800007128
521.35154326478321e-062.70308652956643e-060.999998648456735
539.88297530718791e-071.97659506143758e-060.999999011702469
547.67846124757121e-071.53569224951424e-060.999999232153875
551.12848029194043e-062.25696058388085e-060.999998871519708
569.20869688421521e-071.84173937684304e-060.999999079130311
575.68196493347813e-071.13639298669563e-060.999999431803507
583.64715635824013e-077.29431271648026e-070.999999635284364
592.30422377921533e-074.60844755843066e-070.999999769577622
601.30808245962947e-072.61616491925894e-070.999999869191754
611.62700864283914e-073.25401728567828e-070.999999837299136
622.03383075672193e-074.06766151344385e-070.999999796616924
631.68555412600257e-073.37110825200514e-070.999999831444587
649.48862478417095e-081.89772495683419e-070.999999905113752
655.52487270334156e-081.10497454066831e-070.999999944751273
663.35415250550212e-086.70830501100425e-080.999999966458475
671.82862245703494e-083.65724491406988e-080.999999981713775
681.11229633171998e-082.22459266343996e-080.999999988877037
699.37465991778542e-091.87493198355708e-080.99999999062534
708.33076027487928e-091.66615205497586e-080.99999999166924
716.56843367788812e-091.31368673557762e-080.999999993431566
725.19644764913972e-091.03928952982794e-080.999999994803552
734.57935793165698e-099.15871586331395e-090.999999995420642
744.21459518240431e-098.42919036480862e-090.999999995785405
753.74326069105418e-097.48652138210836e-090.99999999625674
763.92404232916484e-097.84808465832967e-090.999999996075958
774.12705657321209e-098.25411314642417e-090.999999995872943
784.48881650287311e-098.97763300574622e-090.999999995511184
796.3125286800438e-091.26250573600876e-080.999999993687471
801.39596808841858e-082.79193617683716e-080.999999986040319
814.07399270160022e-088.14798540320044e-080.999999959260073
827.77327037677783e-081.55465407535557e-070.999999922267296
839.90270249784586e-081.98054049956917e-070.999999900972975
841.23108993420847e-072.46217986841693e-070.999999876891007
851.61063647526837e-073.22127295053674e-070.999999838936352
862.64594489539659e-075.29188979079319e-070.99999973540551
875.48594169358174e-071.09718833871635e-060.99999945140583
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930.0001195570379352510.0002391140758705020.999880442962065
940.0002022506033995460.0004045012067990910.9997977493966
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960.000987122228544590.001974244457089180.999012877771455
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980.003630811911968560.007261623823937110.996369188088031
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1000.01068653489904670.02137306979809330.989313465100953
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1180.8788442900689960.2423114198620070.121155709931004
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1300.9998224281473090.0003551437053826740.000177571852691337
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1320.9999571458609438.57082781133479e-054.28541390566739e-05
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1360.9999991658404831.66831903349684e-068.34159516748422e-07
1370.9999995935281158.12943769304167e-074.06471884652083e-07
1380.9999997168381775.66323646665205e-072.83161823332602e-07
1390.9999997275778755.44844250492847e-072.72422125246424e-07
1400.9999997287621055.4247578957677e-072.71237894788385e-07
1410.9999997061005985.87798804768536e-072.93899402384268e-07
1420.999999598602058.0279590054003e-074.01397950270015e-07
1430.999999418525771.16294845868659e-065.81474229343294e-07
1440.9999992881451451.42370971013424e-067.11854855067119e-07
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1460.999998067959573.86408086144308e-061.93204043072154e-06
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1490.9999936307995291.27384009418271e-056.36920047091355e-06
1500.9999936364971431.27270057133081e-056.36350285665404e-06
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1550.9999989488280442.10234391274224e-061.05117195637112e-06
1560.9999994731100561.05377988738857e-065.26889943694283e-07
1570.9999996443682767.11263448103999e-073.55631724051999e-07
1580.999999793936644.12126719258884e-072.06063359629442e-07
1590.999999879081842.41836319156216e-071.20918159578108e-07
1600.9999999007988061.98402388302058e-079.92011941510292e-08
1610.9999999098258751.80348250772467e-079.01741253862336e-08
1620.9999999336022471.32795506787534e-076.63977533937672e-08
1630.9999999506889939.86220132479978e-084.93110066239989e-08
1640.9999999679435346.41129324326912e-083.20564662163456e-08
1650.9999999845724583.08550836476352e-081.54275418238176e-08
1660.999999992412461.51750809353959e-087.58754046769793e-09
1670.9999999954193199.16136267027436e-094.58068133513718e-09
1680.999999998977342.04532143088021e-091.02266071544011e-09
1690.9999999996122687.75463698925058e-103.87731849462529e-10
1700.9999999998100833.7983292491087e-101.89916462455435e-10
1710.9999999999033391.93322728380951e-109.66613641904753e-11
1720.9999999999338071.32386019818712e-106.6193009909356e-11
1730.9999999999638617.22776252683777e-113.61388126341889e-11
1740.9999999999884932.30139090604696e-111.15069545302348e-11
1750.999999999996337.34154717625624e-123.67077358812812e-12
1760.9999999999993331.33339990296003e-126.66699951480015e-13
1770.9999999999999627.60539793619024e-143.80269896809512e-14
1780.9999999999999984.10923012473137e-152.05461506236569e-15
17911.95141524682304e-169.7570762341152e-17
18011.46176017922115e-167.30880089610575e-17
18111.72081655807197e-168.60408279035984e-17
18215.11109979886463e-162.55554989943231e-16
1830.9999999999999983.84039779504364e-151.92019889752182e-15
1840.999999999999992.07594994076036e-141.03797497038018e-14
1850.999999999999975.90377915437316e-142.95188957718658e-14
1860.9999999999998363.27988120221715e-131.63994060110858e-13
1870.9999999999994231.15394542929182e-125.76972714645908e-13
1880.9999999999981143.77232610348573e-121.88616305174287e-12
1890.999999999997964.07945557770393e-122.03972778885196e-12
1900.9999999999950569.88769043815905e-124.94384521907953e-12
1910.999999999947111.05781542581324e-105.28907712906621e-11
1920.99999999990571.88600175495962e-109.4300087747981e-11
1930.9999999998787852.42429668757587e-101.21214834378794e-10
1940.9999999999456061.08788147849811e-105.43940739249053e-11
1950.9999999997867384.26523813079213e-102.13261906539607e-10
1960.9999999943365181.13269637876166e-085.66348189380831e-09
1970.999999872443882.55112240001071e-071.27556120000535e-07
1980.9999962160966467.56780670780476e-063.78390335390238e-06
1990.9999300287805830.0001399424388341586.99712194170792e-05


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level1570.853260869565217NOK
5% type I error level1620.880434782608696NOK
10% type I error level1650.896739130434783NOK
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Dec/29/t1293644160c1e35rs0c8j7k8p/10ni971293644245.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/29/t1293644160c1e35rs0c8j7k8p/10ni971293644245.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/29/t1293644160c1e35rs0c8j7k8p/19qbg1293644245.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/29/t1293644160c1e35rs0c8j7k8p/19qbg1293644245.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/29/t1293644160c1e35rs0c8j7k8p/29qbg1293644245.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/29/t1293644160c1e35rs0c8j7k8p/29qbg1293644245.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/29/t1293644160c1e35rs0c8j7k8p/39qbg1293644245.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/29/t1293644160c1e35rs0c8j7k8p/39qbg1293644245.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/29/t1293644160c1e35rs0c8j7k8p/49qbg1293644245.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/29/t1293644160c1e35rs0c8j7k8p/49qbg1293644245.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/29/t1293644160c1e35rs0c8j7k8p/510b11293644245.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/29/t1293644160c1e35rs0c8j7k8p/510b11293644245.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/29/t1293644160c1e35rs0c8j7k8p/610b11293644245.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/29/t1293644160c1e35rs0c8j7k8p/610b11293644245.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/29/t1293644160c1e35rs0c8j7k8p/7c9a41293644245.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/29/t1293644160c1e35rs0c8j7k8p/7c9a41293644245.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/29/t1293644160c1e35rs0c8j7k8p/8c9a41293644245.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/29/t1293644160c1e35rs0c8j7k8p/8c9a41293644245.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/29/t1293644160c1e35rs0c8j7k8p/9ni971293644245.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/29/t1293644160c1e35rs0c8j7k8p/9ni971293644245.ps (open in new window)


 
Parameters (Session):
par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;
 
Parameters (R input):
par1 = 1 ; par2 = Include Monthly Dummies ; par3 = 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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