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*Unverified author*
R Software Module: rwasp_multipleregression.wasp (opens new window with default values)
Title produced by software: Multiple Regression
Date of computation: Sat, 13 Dec 2008 08:35:00 -0700
 
Cite this page as follows:
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Dec/13/t1229182575nz8cvh3tuwr4bb9.htm/, Retrieved Sat, 13 Dec 2008 16:36:25 +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/2008/Dec/13/t1229182575nz8cvh3tuwr4bb9.htm/},
    year = {2008},
}
@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 = {2008},
    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 «
46402 1 45329 1 42185 1 49341 0 50472 0 33020 0 29567 0 22870 0 25730 0 32609 0 23536 0 15135 0 36776 0 29982 0 38062 0 34226 0 24906 0 30233 0 27405 0 20784 0 22886 0 25425 0 20838 0 15655 0 37158 1 36364 1 43213 1 31635 0 30113 0 29985 0 20919 0 19429 0 21427 0 26064 0 20109 0 15369 0 35466 0 25954 0 33504 0 28115 0 28501 0 28618 0 21434 0 20177 0 21484 0 25642 0 23515 0 12941 0 36190 1 37785 1 38407 1 33326 0 30304 0 27576 0 27048 0 17291 0 21018 0 26792 0 19426 0 13927 0 35647 0 31746 0 31277 0 31583 0 25607 0 28151 0 24947 0 18077 0 23429 0 26313 0 18862 0 14753 0 36409 1 33163 1 34122 1 35225 0 28249 0 30374 0 26311 0 22069 0 23651 0 28628 0 23187 0 14727 0 43080 0 32519 0 39657 0 33614 0 28671 0 34243 0 27336 0 22916 0 24537 0 26128 0 22602 0 15744 0 41086 1 39690 1 43129 1 37863 0 35953 0 29133 0 24693 0 22205 0 21725 0 27192 0 21790 0 13253 0 37702 0 30364 0 32609 0 30212 0 29965 0 28352 0 25814 0 22414 0 20506 0 28806 0 22228 0 13971 0 36845 1 35338 1 35022 1 34777 0 26887 0 23970 0 22780 0 17351 0 21382 0 24561 0 17409 0 11514 0 31514 0 27071 0 29462 0 26105 0 22397 0 23843 0 21705 0 18089 0 20764 0 25316 0 17704 0 15548 0 28029 1 29383 1 36438 1 32034 0 22679 0 24319 0 18004 0 17537 0 20366 0 22782 0 19169 0 13807 0 29743 0 25591 0 29096 0 26482 0 22405 0 27044 0 17970 0 18730 0 19684 0 19785 0 18479 0 10698 0 31956 1 29506 1 34506 1 27165 0 26736 0 23691 0 18157 0 17328 0 18205 0 20995 0 17382 0 9367 0 31124 0 26551 0 30651 0 25859 0 25100 0 25778 0 20418 0 18688 0 20424 0 24776 0 19814 0 12738 0
 
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 time6 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135


Multiple Linear Regression - Estimated Regression Equation
X[t] = + 17757.3169862340 + 4210.07055063918Y[t] + 19705.8037016552M1[t] + 16071.1762946574M2[t] + 19548.7363876597M3[t] + 18332.4567559816M4[t] + 14708.7043489840M5[t] + 14085.0769419862M6[t] + 9511.01203498849M7[t] + 5891.25962799082M8[t] + 7885.00722099311M9[t] + 11962.0673139954M10[t] + 6641.62740699768M11[t] -39.8100930022944t + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0		2-tail p-value1-tail p-value
(Intercept)17757.3169862340923.25184319.233400
Y4210.07055063918942.1456534.46861.4e-057e-06
M119705.80370165521244.68942915.831900
M216071.17629465741244.62388212.912500
M319548.73638765971244.57289815.707200
M418332.45675598161152.69332815.90400
M514708.70434898401152.5753612.761600
M614085.07694198621152.47311112.221600
M79511.012034988491152.3865868.253300
M85891.259627990821152.3157875.11251e-060
M97885.007220993111152.2607196.843100
M1011962.06731399541152.22138310.381700
M116641.627406997681152.1977815.764300
t-39.81009300229444.257918-9.349700


Multiple Linear Regression - Regression Statistics
Multiple R0.914453602861614
R-squared0.836225391786587
Adjusted R-squared0.824264324894596
F-TEST (value)69.9122744933834
F-TEST (DF numerator)13
F-TEST (DF denominator)178
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation3258.88520315356
Sum Squared Residuals1890419232.58531


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast		Residuals
Prediction Error
14640241633.38114552614768.61885447389
24532937958.94364552597370.05635447406
34218541396.6936455262788.306354473834
44934135930.533370206313410.4666297937
55047232266.970870206418205.0291297936
63302031603.53337020641416.46662979356
72956726989.65837020662577.3416297934
82287023330.0958702065-460.095870206456
92573025284.0333702064445.966629793571
103260929321.28337020663287.71662979345
112353623961.0333702065-425.03337020652
121513517279.5958702065-2144.59587020650
133677636945.5894788594-169.589478859392
142998233271.1519788594-3289.15197885939
153806236708.90197885941353.09802114061
163422635452.812254179-1226.81225417897
172490631789.2497541790-6883.24975417896
183023331125.8122541790-892.812254178965
192740526511.9372541790893.062745821047
202078422852.3747541790-2068.37475417897
212288624806.3122541790-1920.31225417896
222542528843.5622541790-3418.56225417896
232083823483.3122541790-2645.31225417896
241565516801.8747541790-1146.87475417898
253715840677.938913471-3519.93891347099
263636437003.501413471-639.501413470994
274321340441.2514134712771.74858652902
283163534975.0911381514-3340.09113815144
293011331311.5286381514-1198.52863815143
302998530648.0911381514-663.091138151433
312091926034.2161381514-5115.21613815142
321942922374.6536381514-2945.65363815143
332142724328.5911381514-2901.59113815143
342606428365.8411381514-2301.84113815143
352010923005.5911381514-2896.59113815143
361536916324.1536381514-955.153638151447
373546635990.1472468043-524.147246804328
382595432315.7097468043-6361.70974680433
393350435753.4597468043-2249.45974680432
402811534497.3700221239-6382.3700221239
412850130833.8075221239-2332.8075221239
422861830170.3700221239-1552.37002212390
432143425556.4950221239-4122.49502212389
442017721896.9325221239-1719.9325221239
452148423850.8700221239-2366.8700221239
462564227888.1200221239-2246.12002212389
472351522527.8700221239987.129977876107
481294115846.4325221239-2905.43252212391
493619039722.4966814159-3532.49668141592
503778536048.05918141591736.94081858407
513840739485.8091814159-1078.80918141592
523332634019.6489060964-693.648906096374
533030430356.0864060964-52.0864060963661
542757629692.6489060964-2116.64890609637
552704825078.77390609641969.22609390364
561729121419.2114060964-4128.21140609637
572101823373.1489060964-2355.14890609637
582679227410.3989060964-618.39890609636
591942622050.1489060964-2624.14890609636
601392715368.7114060964-1441.71140609638
613564735034.7050147493612.294985250735
623174631360.2675147493385.732485250736
633127734798.0175147493-3521.01751474926
643158333541.9277900688-1958.92779006884
652560729878.3652900688-4271.36529006883
662815129214.9277900688-1063.92779006883
672494724601.0527900688345.947209931176
681807720941.4902900688-2864.49029006883
692342922895.4277900688533.572209931166
702631326932.6777900688-619.677790068828
711886221572.4277900688-2710.42779006883
721475314890.9902900689-137.990290068851
733640938767.0544493609-2358.05444936086
743316335092.6169493609-1929.61694936086
753412238530.3669493609-4408.36694936085
763522533064.20667404132160.79332595869
772824929400.6441740413-1151.6441740413
783037428737.20667404131636.79332595870
792631124123.33167404132187.66832595871
802206920463.76917404131605.2308259587
812365122417.70667404131233.29332595870
822862826454.95667404132173.04332595870
832318721094.70667404132092.29332595870
841472714413.2691740413313.730825958682
854308034079.26278269429000.73721730581
863251930404.82528269422114.1747173058
873965733842.57528269425814.4247173058
883361432586.48555801381027.51444198622
892867128922.9230580138-251.923058013768
903424328259.48555801385983.51444198623
912733623645.61055801383690.38944198624
922291619986.04805801382929.95194198623
932453721939.98555801382597.01444198623
942612825977.2355580138150.764441986238
952260220616.98555801381985.01444198624
961574413935.54805801381808.45194198622
974108637811.61221730583274.38778269421
983969034137.17471730585552.8252826942
994312937574.92471730585554.07528269421
1003786332108.76444198625754.23555801375
1013595328445.20194198627507.79805801376
1022913327781.76444198621351.23555801376
1032469323167.88944198621525.11055801377
1042220519508.32694198622696.67305801376
1052172521462.2644419862262.735558013763
1062719225499.51444198621692.48555801377
1072179020139.26444198621650.73555801377
1081325313457.8269419863-204.826941986252
1093770233123.82055063914578.17944936087
1103036429449.3830506391914.616949360865
1113260932887.1330506391-278.133050639127
1123021231631.0433259587-1419.04332595871
1132996527967.48082595871997.51917404130
1142835227304.04332595871047.95667404130
1152581422690.16832595873123.83167404131
1162241419030.60582595873383.39417404130
1172050620984.5433259587-478.543325958705
1182880625021.79332595873784.2066740413
1192222819661.54332595872566.4566740413
1201397112980.1058259587990.89417404128
1213684536856.1699852507-11.1699852507284
1223533833181.73248525072156.26751474927
1233502236619.4824852507-1597.48248525072
1243477731153.32220993123623.67779006882
1252688727489.7597099312-602.759709931171
1262397026826.3222099312-2856.32220993117
1272278022212.4472099312567.552790068838
1281735118552.8847099312-1201.88470993117
1292138220506.8222099312875.177790068828
1302456124544.072209931216.9277900688355
1311740919183.8222099312-1774.82220993117
1321151412502.3847099312-988.384709931187
1333151432168.3783185841-654.37831858407
1342707128493.9408185841-1422.94081858407
1352946231931.6908185841-2469.69081858406
1362610530675.6010939036-4570.60109390365
1372239727012.0385939036-4615.03859390364
1382384326348.6010939036-2505.60109390364
1392170521734.7260939036-29.7260939036296
1401808918075.163593903613.8364060963603
1412076420029.1010939036734.89890609636
1422531624066.35109390361249.64890609637
1431770418706.1010939036-1002.10109390363
1441554812024.66359390373523.33640609634
1452802935900.7277531957-7871.72775319566
1462938332226.2902531957-2843.29025319567
1473643835664.0402531957773.959746804343
1483203430197.87997787611836.12002212389
1492267926534.3174778761-3855.31747787611
1502431925870.8799778761-1551.87997787611
1511800421257.0049778761-3253.0049778761
1521753717597.4424778761-60.4424778761082
1532036619551.3799778761814.620022123891
1542278223588.6299778761-806.6299778761
1551916918228.3799778761940.620022123898
1561380711546.94247787612260.05752212388
1572974331212.936086529-1469.93608652901
1582559127538.498586529-1947.49858652901
1592909630976.248586529-1880.248586529
1602648229720.1588618486-3238.15886184858
1612240526056.5963618486-3651.59636184857
1622704425393.15886184861650.84113815142
1631797020779.2838618486-2809.28386184856
1641873017119.72136184861610.27863815142
1651968419073.6588618486610.341138151424
1661978523110.9088618486-3325.90886184857
1671847917750.6588618486728.34113815143
1681069811069.2213618486-371.22136184859
1693195634945.2855211406-2989.2855211406
1702950631270.8480211406-1764.84802114060
1713450634708.5980211406-202.598021140594
1722716529242.4377458210-2077.43774582105
1732673625578.87524582101157.12475417896
1742369124915.4377458210-1224.43774582104
1751815720301.5627458210-2144.56274582103
1761732816642.0002458210685.999754178956
1771820518595.9377458210-390.937745821042
1782099522633.1877458210-1638.18774582104
1791738217272.9377458210109.062254178963
180936710591.5002458211-1224.50024582106
1813112430257.4938544739866.506145526059
1822655126583.0563544739-32.0563544739416
1833065130020.8063544739630.193645526065
1842585928764.7166297935-2905.71662979352
1852510025101.1541297935-1.15412979350896
1862577824437.71662979351340.28337020649
1872041819823.8416297935594.158370206499
1881868816164.27912979352523.72087020649
1892042418118.21662979352305.78337020649
1902477622155.46662979352620.53337020650
1911981416795.21662979353018.78337020650
1921273810113.77912979352624.22087020647


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
170.9551235791490210.08975284170195850.0448764208509792
180.9997058117305050.0005883765389905240.000294188269495262
190.9999636181975637.27636048737244e-053.63818024368622e-05
200.999983552058693.28958826183361e-051.64479413091681e-05
210.9999830386404983.3922719003592e-051.6961359501796e-05
220.9999622861942717.54276114576708e-053.77138057288354e-05
230.999955118693258.97626135010951e-054.48813067505475e-05
240.9999723302031025.53395937969543e-052.76697968984772e-05
250.999956986875718.60262485804266e-054.30131242902133e-05
260.99995009155369.98168927988767e-054.99084463994384e-05
270.9999799156968564.01686062887458e-052.00843031443729e-05
280.9999697966490536.04067018932402e-053.02033509466201e-05
290.9999398264285740.0001203471428522556.01735714261276e-05
300.9999417127808630.0001165744382736085.82872191368038e-05
310.9999162180444820.0001675639110355168.37819555177582e-05
320.999906389340110.0001872213197796149.36106598898069e-05
330.9998800411753650.0002399176492699380.000119958824634969
340.9998341890911840.000331621817631210.000165810908815605
350.9998058681616550.0003882636766894090.000194131838344704
360.9998233981648790.0003532036702423820.000176601835121191
370.999874630426810.0002507391463804370.000125369573190218
380.9998875888023840.0002248223952325590.000112411197616279
390.999844423697890.000311152604220530.000155576302110265
400.999889467379280.0002210652414405690.000110532620720285
410.9998198252657380.0003603494685244240.000180174734262212
420.999800780535880.0003984389282383960.000199219464119198
430.9997771364127650.0004457271744703050.000222863587235153
440.9998153938455230.0003692123089531260.000184606154476563
450.9998118659334150.0003762681331692360.000188134066584618
460.9997816015231570.0004367969536867860.000218398476843393
470.9998814667943080.00023706641138320.0001185332056916
480.9998661827875620.0002676344248753410.000133817212437670
490.9998231174027420.000353765194516030.000176882597258015
500.9998729458989160.0002541082021684430.000127054101084222
510.9998025500528920.0003948998942163110.000197449947108155
520.999739063689190.0005218726216188720.000260936310809436
530.9996226845381750.0007546309236504280.000377315461825214
540.9995357634855720.000928473028855420.00046423651442771
550.999729117743620.0005417645127591820.000270882256379591
560.9997615736102880.0004768527794237510.000238426389711876
570.9997487658218910.0005024683562176470.000251234178108824
580.9997167948529110.0005664102941778260.000283205147088913
590.9996917552306380.0006164895387244370.000308244769362218
600.9996731470075130.0006537059849744210.000326852992487210
610.9997476276655240.0005047446689512560.000252372334475628
620.999747264491510.0005054710169807670.000252735508490383
630.9997754999766770.0004490000466459360.000224500023322968
640.9997116502605180.0005766994789633040.000288349739481652
650.9997704832745660.0004590334508685080.000229516725434254
660.999734037706510.0005319245869775680.000265962293488784
670.999699570813140.0006008583737180180.000300429186859009
680.9997797518474460.000440496305108610.000220248152554305
690.999792194474830.0004156110503381650.000207805525169082
700.9997630985910.0004738028180011580.000236901409000579
710.999812224003030.0003755519939404990.000187775996970249
720.9998103785905660.0003792428188685110.000189621409434255
730.999784096742420.0004318065151603290.000215903257580164
740.9997375690362310.0005248619275382440.000262430963769122
750.9998608289528240.0002783420943525910.000139171047176296
760.9998556887391670.0002886225216665880.000144311260833294
770.9998200659670.0003598680659989130.000179934032999457
780.9998145300728460.000370939854307660.00018546992715383
790.9998088465130650.0003823069738704790.000191153486935240
800.9998464356469160.0003071287061674110.000153564353083705
810.9998379827141750.0003240345716501530.000162017285825077
820.9998250926958330.0003498146083331510.000174907304166575
830.9998266434823490.0003467130353026210.000173356517651311
840.9998104079347640.0003791841304728470.000189592065236424
850.9999913466420351.73067159300995e-058.65335796504973e-06
860.9999882936553372.34126893252522e-051.17063446626261e-05
870.999994802170531.03956589402772e-055.1978294701386e-06
880.9999915721416891.68557166225366e-058.42785831126831e-06
890.999987366865432.52662691394815e-051.26331345697407e-05
900.9999948907494271.02185011461487e-055.10925057307437e-06
910.9999945137487931.09725024147702e-055.48625120738509e-06
920.9999933881484541.32237030919163e-056.61185154595813e-06
930.9999908560334731.82879330539629e-059.14396652698146e-06
940.999986586542782.68269144390939e-051.34134572195470e-05
950.9999805623573583.8875285284489e-051.94376426422445e-05
960.999971728176715.65436465784559e-052.82718232892279e-05
970.9999686358342136.27283315738117e-053.13641657869059e-05
980.9999854065498452.91869003089631e-051.45934501544815e-05
990.9999944770160331.10459679337041e-055.52298396685207e-06
1000.999998363439523.2731209601612e-061.6365604800806e-06
1010.999999930729811.38540381932066e-076.92701909660328e-08
1020.9999998828520942.34295812492653e-071.17147906246327e-07
1030.9999998095259113.80948176887884e-071.90474088443942e-07
1040.9999997087433095.82513382652046e-072.91256691326023e-07
1050.9999994903509321.01929813673103e-065.09649068365517e-07
1060.9999991339451531.73210969403766e-068.66054847018829e-07
1070.9999985095560712.98088785787822e-061.49044392893911e-06
1080.9999977077609374.58447812614913e-062.29223906307456e-06
1090.999999273869261.45226148185139e-067.26130740925695e-07
1100.9999988071512982.38569740382782e-061.19284870191391e-06
1110.9999979652980894.06940382296936e-062.03470191148468e-06
1120.9999969828225156.03435496974274e-063.01717748487137e-06
1130.9999974201323185.15973536460913e-062.57986768230457e-06
1140.9999962052757027.5894485967123e-063.79472429835615e-06
1150.9999976214470934.7571058131239e-062.37855290656195e-06
1160.9999976555097464.68898050821661e-062.34449025410831e-06
1170.99999613724717.7255057999117e-063.86275289995585e-06
1180.999997913937574.17212485781876e-062.08606242890938e-06
1190.999997653430654.69313870090384e-062.34656935045192e-06
1200.9999958685829698.26283406296144e-064.13141703148072e-06
1210.9999965258109166.94837816714726e-063.47418908357363e-06
1220.9999987770246982.445950603349e-061.2229753016745e-06
1230.9999981101299033.77974019364282e-061.88987009682141e-06
1240.9999998781630562.43673887503104e-071.21836943751552e-07
1250.9999998840005922.31998815504558e-071.15999407752279e-07
1260.9999998377405493.2451890235803e-071.62259451179015e-07
1270.9999998768584272.46283145284043e-071.23141572642021e-07
1280.999999775533084.48933841617578e-072.24466920808789e-07
1290.9999996157590447.68481912555138e-073.84240956277569e-07
1300.999999425882271.14823546162359e-065.74117730811794e-07
1310.9999990466504021.90669919675177e-069.53349598375886e-07
1320.9999983122873393.37542532220355e-061.68771266110177e-06
1330.999998240514113.5189717805139e-061.75948589025695e-06
1340.9999970033894435.99322111450816e-062.99661055725408e-06
1350.9999958219024588.35619508322163e-064.17809754161082e-06
1360.9999956673126828.66537463700114e-064.33268731850057e-06
1370.99999558120398.8375921991502e-064.4187960995751e-06
1380.9999935901847091.28196305819988e-056.40981529099941e-06
1390.9999933838885061.32322229885244e-056.61611149426219e-06
1400.99998711374842.57725031985331e-051.28862515992666e-05
1410.9999769485502284.61028995445418e-052.30514497722709e-05
1420.9999802651046383.94697907247834e-051.97348953623917e-05
1430.99996475210977.04957806007741e-053.52478903003871e-05
1440.999984195406213.16091875820714e-051.58045937910357e-05
1450.9999980681510633.8636978741145e-061.93184893705725e-06
1460.999996207791197.58441761830855e-063.79220880915428e-06
1470.9999963468919177.30621616615157e-063.65310808307579e-06
1480.9999999041102011.91779597367904e-079.5889798683952e-08
1490.9999998469165923.06166815616426e-071.53083407808213e-07
1500.9999996401219767.19756047443493e-073.59878023721747e-07
1510.999999194084461.61183108018061e-068.05915540090305e-07
1520.9999980214764393.9570471227748e-061.9785235613874e-06
1530.9999963852876977.22942460642383e-063.61471230321191e-06
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1570.9999940396374171.19207251657147e-055.96036258285736e-06
1580.9999852577738452.94844523091994e-051.47422261545997e-05
1590.9999661235934966.77528130085878e-053.38764065042939e-05
1600.9999315195200830.0001369609598345856.84804799172926e-05
1610.9999292525136220.0001414949727563527.0747486378176e-05
1620.9999660988228616.78023542777305e-053.39011771388653e-05
1630.9999108584069550.0001782831860898848.91415930449419e-05
1640.9998803056133820.0002393887732361950.000119694386618098
1650.9998331433594370.0003337132811256480.000166856640562824
1660.9996802036253170.0006395927493661760.000319796374683088
1670.9994255890437450.001148821912509990.000574410956254996
1680.9990759465478230.001848106904353720.000924053452176862
1690.9985708489736670.002858302052666020.00142915102633301
1700.9961936769172940.007612646165411140.00380632308270557
1710.9897941503635380.02041169927292360.0102058496364618
1720.991261098363610.01747780327278200.00873890163639102
1730.9993517176995470.001296564600905780.000648282300452892
1740.9966813612086670.006637277582666020.00331863879133301
1750.983382274839080.03323545032184160.0166177251609208


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level1550.974842767295597NOK
5% type I error level1580.9937106918239NOK
10% type I error level1591NOK
 
Charts produced by software:
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/13/t1229182575nz8cvh3tuwr4bb9/10ymfp1229182493.png (open in new window)
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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/13/t1229182575nz8cvh3tuwr4bb9/18dku1229182492.ps (open in new window)


http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/13/t1229182575nz8cvh3tuwr4bb9/2p9xh1229182492.png (open in new window)
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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/13/t1229182575nz8cvh3tuwr4bb9/353yv1229182492.ps (open in new window)


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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/13/t1229182575nz8cvh3tuwr4bb9/5n0e31229182492.ps (open in new window)


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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/13/t1229182575nz8cvh3tuwr4bb9/6ohiw1229182492.ps (open in new window)


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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/13/t1229182575nz8cvh3tuwr4bb9/7d9j81229182493.ps (open in new window)


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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/13/t1229182575nz8cvh3tuwr4bb9/803dh1229182493.ps (open in new window)


http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/13/t1229182575nz8cvh3tuwr4bb9/9d74c1229182493.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/13/t1229182575nz8cvh3tuwr4bb9/9d74c1229182493.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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