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workshop 7, multiple regression

*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: Thu, 02 Dec 2010 08:12:37 +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/02/t1291277885h50mxz8ftfobp76.htm/, Retrieved Thu, 02 Dec 2010 09:18:20 +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/02/t1291277885h50mxz8ftfobp76.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 «
1 1 2 2 0 0 1 1 1 0 1 2 0 1 2 0 1 2 0 1 1 3 1 2 0 1 2 2 1 2 1 1 1 4 0 0 1 1 2 6 1 0 0 1 1 3 0 0 1 1 2 5 2 0 0 1 1 7 0 0 0 1 1 4 1 0 1 1 2 1 1 0 1 1 2 2 0 0 1 1 2 2 0 0 1 1 1 8 0 0 0 1 1 0 0 0 0 1 1 2 0 1 1 1 2 5 0 1 1 1 2 3 0 0 0 1 1 3 0 0 1 1 1 3 1 1 1 1 2 4 1 1 1 1 1 2 0 0 1 1 2 4 0 0 1 1 2 2 0 0 0 1 1 2 0 0 1 1 1 2 1 0 1 1 2 1 1 0 1 1 2 3 0 0 1 1 1 2 0 0 0 1 1 4 0 0 1 1 1 4 0 0 1 1 2 3 0 0 1 1 2 5 0 0 0 1 1 4 0 0 1 1 2 4 0 0 1 1 2 2 0 1 1 1 1 0 0 0 0 1 1 4 0 0 0 1 1 4 0 0 0 1 1 0 0 0 1 1 2 4 0 0 1 1 2 5 2 0 1 1 2 6 0 0 1 1 2 4 0 0 0 1 1 4 0 0 0 1 1 0 0 0 1 1 1 4 0 0 1 1 2 5 0 0 1 1 1 3 0 1 1 1 2 5 0 1 0 1 1 3 0 0 0 1 1 2 0 0 0 1 1 1 0 0 1 1 1 1 1 2 1 1 2 1 1 2 1 1 1 3 1 2 1 1 2 3 1 2 0 1 1 4 0 0 1 1 2 0 0 0 0 1 1 3 1 0 1 1 2 7 1 0 0 1 1 4 1 0 1 1 2 4 1 0 1 1 1 2 1 0 1 1 2 3 1 0 1 1 2 3 0 0 1 1 2 3 0 0 1 1 1 4 0 0 1 1 2 0 0 1 0 1 1 0 0 0 0 1 1 2 1 0 1 1 2 2 1 0 1 1 2 2 0 0 0 1 1 0 0 0 0 1 1 4 0 0 1 1 2 3 1 1 0 1 1 3 1 1 1 1 2 6 0 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 time180 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135


Multiple Linear Regression - Estimated Regression Equation
survived[t] = + 0.145019265778636 -0.164514500634945pclass[t] + 0.507183007206079sex[t] -0.0273936121732978age[t] -0.0379358287916375sibsp[t] + 0.00381938386368801parch[t] + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)0.1450192657786360.055862.59610.0095350.004767
pclass-0.1645145006349450.014294-11.509200
sex0.5071830072060790.02339821.676800
age-0.02739361217329780.007168-3.82140.0001396.9e-05
sibsp-0.03793582879163750.011315-3.35270.0008230.000412
parch0.003819383863688010.0137330.27810.7809730.390487


Multiple Linear Regression - Regression Statistics
Multiple R0.594259390098299
R-squared0.353144222720002
Adjusted R-squared0.350662043989073
F-TEST (value)142.271875235949
F-TEST (DF numerator)5
F-TEST (DF denominator)1303
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.391670590273313
Sum Squared Residuals199.887824224415


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
110.9400835552093210.0599164447906786
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113210.07647793455998480.923522065440015
113300.158658771079878-0.158658771079878
113400.131265158906581-0.131265158906581
113500.103871546733283-0.103871546733283
113600.158658771079878-0.158658771079878
113700.665841778285946-0.665841778285946
113800.158658771079878-0.158658771079878
113900.158658771079878-0.158658771079878
114000.0764779345599848-0.0764779345599848
114100.103871546733283-0.103871546733283
11420-0.0166587723962820.016658772396282
114300.0107348397770158-0.0107348397770158
114400.0107348397770158-0.0107348397770158
114500.0107348397770158-0.0107348397770158
114600.0107348397770158-0.0107348397770158
114700.602757861084495-0.602757861084495
114800.61105455393935-0.61105455393935
114900.0764779345599848-0.0764779345599848
115010.6658417782859460.334158221714054
115100.158658771079878-0.158658771079878
115200.665841778285946-0.665841778285946
11530-0.01624511857824870.0162451185782487
115400.518331500801117-0.518331500801117
115500.158658771079878-0.158658771079878
115600.158658771079878-0.158658771079878
115700.631725333357997-0.631725333357997
115800.0971487139786312-0.0971487139786312
115900.563906097320132-0.563906097320132
116010.6658417782859460.334158221714054
116100.0216907102133891-0.0216907102133891
116200.131265158906581-0.131265158906581
116310.1586587710798780.841341228920122
116400.158658771079878-0.158658771079878
116500.158658771079878-0.158658771079878
116600.103871546733283-0.103871546733283
116700.158658771079878-0.158658771079878
116800.158658771079878-0.158658771079878
116900.158658771079878-0.158658771079878
117000.0764779345599848-0.0764779345599848
11710-0.1371890915258470.137189091525847
11720-0.1645827036991440.164582703699144
117300.369993915680221-0.369993915680221
117400.369993915680221-0.369993915680221
117500.369993915680221-0.369993915680221
117600.369993915680221-0.369993915680221
11770-0.1371890915258470.137189091525847
11780-0.1371890915258470.137189091525847
11790-0.1371890915258470.137189091525847
118000.155097397061437-0.155097397061437
118100.662280404267504-0.662280404267504
118200.103871546733283-0.103871546733283
118310.611054553939350.38894544606065
118400.0764779345599848-0.0764779345599848
118500.0827871134966029-0.0827871134966029
118600.0827871134966029-0.0827871134966029
118700.0827871134966029-0.0827871134966029
118810.6317253333579970.368274666642003
118910.6186933216667270.381306678333273
119010.6317253333579970.368274666642003
119110.1038715467332830.896128453266717
119200.103871546733283-0.103871546733283
119300.103871546733283-0.103871546733283
119400.158658771079878-0.158658771079878
119500.158658771079878-0.158658771079878
119600.158658771079878-0.158658771079878
119710.1038715467332830.896128453266717
119800.158658771079878-0.158658771079878
119910.6658417782859460.334158221714054
120000.158658771079878-0.158658771079878
120100.158658771079878-0.158658771079878
120200.103871546733283-0.103871546733283
120300.158658771079878-0.158658771079878
120400.0490843223866869-0.0490843223866869
120500.103871546733283-0.103871546733283
120610.6384481661126480.361551833887352
120700.0524900524323421-0.0524900524323421
120800.0250964402590442-0.0250964402590442
120900.55967305963841-0.55967305963841
121000.55967305963841-0.55967305963841
121100.0264260290498031-0.0264260290498031
121200.533609036255871-0.533609036255871
121300.158658771079878-0.158658771079878
121400.158658771079878-0.158658771079878
121500.158658771079878-0.158658771079878
121600.158658771079878-0.158658771079878
121710.6658417782859460.334158221714054
121800.131265158906581-0.131265158906581
121900.0764779345599848-0.0764779345599848
122000.158658771079878-0.158658771079878
122100.0764779345599848-0.0764779345599848
122200.158658771079878-0.158658771079878
122300.0764779345599848-0.0764779345599848
122410.611054553939350.38894544606065
122500.103871546733283-0.103871546733283
12260-0.005702901959908780.00570290195990878
122700.131265158906581-0.131265158906581
122800.61105455393935-0.61105455393935
122910.07647793455998480.923522065440015
123000.103871546733283-0.103871546733283
123100.669661162149634-0.669661162149634
123200.576938109011401-0.576938109011401
123310.1312651589065810.868734841093419
123410.04908432238668680.950915677613313
123500.103871546733283-0.103871546733283
12360-0.03309651413320660.0330965141332066
123710.1312651589065810.868734841093419
123800.103871546733283-0.103871546733283
123910.1038715467332830.896128453266717
124000.0764779345599848-0.0764779345599848
124110.1624781549435670.837521845056433
124200.120722942288241-0.120722942288241
124300.158658771079878-0.158658771079878
124400.158658771079878-0.158658771079878
124510.6043317211846990.395668278815301
124600.158658771079878-0.158658771079878
124700.120722942288241-0.120722942288241
124810.6279059494943080.372094050505692
124900.0764779345599848-0.0764779345599848
125000.158658771079878-0.158658771079878
125100.158658771079878-0.158658771079878
125200.0764779345599848-0.0764779345599848
125300.0490843223866869-0.0490843223866869
125400.158658771079878-0.158658771079878
125510.1038715467332830.896128453266717
125600.158658771079878-0.158658771079878
125710.1245423261519290.875457673848071
125810.6317253333579970.368274666642003
125910.6186933216667270.381306678333273
126000.0764779345599848-0.0764779345599848
126110.6384481661126480.361551833887352
126210.5014801052461590.498519894753841
126300.124542326151929-0.124542326151929
126400.0971487139786312-0.0971487139786312
126500.0567230901140639-0.0567230901140639
126600.646086933840025-0.646086933840025
126700.0423614896320355-0.0423614896320355
126800.549544496838103-0.549544496838103
126900.158658771079878-0.158658771079878
127000.0764779345599848-0.0764779345599848
127100.103871546733283-0.103871546733283
127200.103871546733283-0.103871546733283
127300.0490843223866869-0.0490843223866869
127400.562576508529372-0.562576508529372
12750-0.03732955181492850.0373295518149285
127600.055393501323305-0.055393501323305
127700.545725112974415-0.545725112974415
127810.1038715467332830.896128453266717
127900.103871546733283-0.103871546733283
128000.638448166112648-0.638448166112648
128100.103871546733283-0.103871546733283
128200.103871546733283-0.103871546733283
128300.158658771079878-0.158658771079878
128400.158658771079878-0.158658771079878
128500.158658771079878-0.158658771079878
128600.0764779345599848-0.0764779345599848
128710.5836609417660520.416339058233948
128800.0216907102133891-0.0216907102133891
128900.0933293301149428-0.0933293301149428
129000.0659357179416449-0.0659357179416449
129110.5183315008011170.481668499198883
129200.158658771079878-0.158658771079878
129300.158658771079878-0.158658771079878
129400.158658771079878-0.158658771079878
129500.103871546733283-0.103871546733283
129600.103871546733283-0.103871546733283
129700.103871546733283-0.103871546733283
129800.158658771079878-0.158658771079878
129900.0764779345599848-0.0764779345599848
130000.0659357179416449-0.0659357179416449
130110.600512337321010.39948766267899
130200.0490843223866869-0.0490843223866869
130300.158658771079878-0.158658771079878
130400.158658771079878-0.158658771079878
130500.60051233732101-0.60051233732101
130600.627905949494308-0.627905949494308
130700.103871546733283-0.103871546733283
130800.103871546733283-0.103871546733283
130900.103871546733283-0.103871546733283


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
90.9661667761823270.0676664476353460.033833223817673
100.9401021093044440.1197957813911120.059897890695556
110.978008390001310.04398321999737990.0219916099986900
120.959502995558050.08099400888389830.0404970044419492
130.9369115424751580.1261769150496830.0630884575248417
140.904445263335790.191109473328420.09555473666421
150.945931164378280.1081376712434410.0540688356217207
160.9535413021412470.0929173957175070.0464586978587535
170.9369293744549230.1261412510901540.0630706255450772
180.9194392590434150.1611214819131700.0805607409565848
190.888806905196290.2223861896074190.111193094803709
200.8824900372540120.2350199254919760.117509962745988
210.9351026139182770.1297947721634450.0648973860817226
220.9158946043115390.1682107913769230.0841053956884613
230.9346668494851870.1306663010296250.0653331505148127
240.9125347738046960.1749304523906080.0874652261953038
250.887035230336170.2259295393276610.112964769663830
260.8877133685705560.2245732628588880.112286631429444
270.8982205579722680.2035588840554640.101779442027732
280.8699207950859760.2601584098280470.130079204914024
290.8389139021019770.3221721957960460.161086097898023
300.8562304724043730.2875390551912540.143769527595627
310.8708341762178670.2583316475642670.129165823782133
320.8808753259350380.2382493481299240.119124674064962
330.853396677143660.2932066457126810.146603322856341
340.8215627345917860.3568745308164280.178437265408214
350.838820104963560.322359790072880.16117989503644
360.8065793339136420.3868413321727160.193420666086358
370.787199037300220.4256019253995610.212800962699781
380.8041637724051930.3916724551896140.195836227594807
390.8197110912669460.3605778174661080.180288908733054
400.8288759793024330.3422480413951330.171124020697567
410.8376465287482850.3247069425034310.162353471251715
420.808028264102440.3839434717951190.191971735897560
430.7764136089463140.4471727821073720.223586391053686
440.7414845990565440.5170308018869120.258515400943456
450.7040968048014370.5918063903971260.295903195198563
460.7100717748393450.579856450321310.289928225160655
470.7102738944628720.5794522110742550.289726105537128
480.7476461630157660.5047076739684670.252353836984233
490.71216659087080.5756668182584010.287833409129200
500.781582529681070.436834940637860.21841747031893
510.7537185565947520.4925628868104960.246281443405248
520.75967431709760.48065136580480.2403256829024
530.7596505146843040.4806989706313920.240349485315696
540.7537058364059440.4925883271881130.246294163594056
550.8200234730103020.3599530539793960.179976526989698
560.7969006879204620.4061986241590760.203099312079538
570.8216933661208380.3566132677583250.178306633879162
580.7951759810134030.4096480379731940.204824018986597
590.7977553095539360.4044893808921280.202244690446064
600.7747832634500650.4504334730998710.225216736549935
610.7791130984155620.4417738031688760.220886901584438
620.7503805224671980.4992389550656050.249619477532802
630.7522786074820560.4954427850358870.247721392517944
640.7224679198338030.5550641603323940.277532080166197
650.7612132781568250.477573443686350.238786721843175
660.7321682568899540.5356634862200930.267831743110046
670.7027230979916940.5945538040166120.297276902008306
680.6719151035088810.6561697929822370.328084896491119
690.7090455300026930.5819089399946140.290954469997307
700.6804762804393250.639047439121350.319523719560675
710.6735365663897530.6529268672204940.326463433610247
720.6726751707824110.6546496584351770.327324829217589
730.6417081736848050.716583652630390.358291826315195
740.6103451420719450.779309715856110.389654857928055
750.5990466095058550.801906780988290.400953390494145
760.599505391340160.800989217319680.40049460865984
770.5660695755446560.8678608489106880.433930424455344
780.568144192959360.863711614081280.43185580704064
790.5349973889007650.930005222198470.465002611099235
800.5017468669277180.9965062661445640.498253133072282
810.4879302534541470.9758605069082940.512069746545853
820.5006367185931250.998726562813750.499363281406875
830.4676158584709920.9352317169419840.532384141529008
840.4352506012999130.8705012025998260.564749398700087
850.4284856534444050.856971306888810.571514346555595
860.3973513759386730.7947027518773460.602648624061327
870.4446909804672950.8893819609345910.555309019532705
880.5019217560072260.9961564879855480.498078243992774
890.4703158387205560.9406316774411120.529684161279444
900.4641545222353790.9283090444707580.535845477764621
910.4332631878935710.8665263757871420.566736812106429
920.4874869129807850.974973825961570.512513087019215
930.4579680389320910.9159360778641830.542031961067909
940.4937605736705940.9875211473411870.506239426329407
950.5374722540193080.9250554919613830.462527745980692
960.5071241302802960.9857517394394080.492875869719704
970.5092703535759130.9814592928481750.490729646424087
980.4791897898696380.9583795797392760.520810210130362
990.4498023039669090.8996046079338170.550197696033091
1000.4207492079740840.8414984159481680.579250792025916
1010.4634563947658910.9269127895317810.536543605234109
1020.4636182519189150.927236503837830.536381748081085
1030.4342126834770960.8684253669541930.565787316522904
1040.4057424754326950.811484950865390.594257524567305
1050.3777459437796960.7554918875593920.622254056220304
1060.5119529562662510.9760940874674970.488047043733749
1070.5037644764159770.9924710471680460.496235523584023
1080.4786944746283920.9573889492567840.521305525371608
1090.4533462340257510.9066924680515020.546653765974249
1100.4965743531262050.993148706252410.503425646873795
1110.495754420743140.991508841486280.50424557925686
1120.467555743438750.93511148687750.53244425656125
1130.4395991472342510.8791982944685020.560400852765749
1140.4120248141617030.8240496283234060.587975185838297
1150.4154550729409940.8309101458819890.584544927059006
1160.434270803233720.868541606467440.56572919676628
1170.4073832789454820.8147665578909640.592616721054518
1180.3808536758097630.7617073516195260.619146324190237
1190.3753893187929820.7507786375859650.624610681207018
1200.4093065833763770.8186131667527540.590693416623623
1210.4431602296810170.8863204593620350.556839770318983
1220.4176249485513890.8352498971027780.582375051448611
1230.3924527266309130.7849054532618250.607547273369087
1240.4179849507331940.8359699014663880.582015049266806
1250.3919439924511790.7838879849023580.608056007548821
1260.3854362496070890.7708724992141780.614563750392911
1270.3883060911592880.7766121823185760.611693908840712
1280.3631207746285810.7262415492571620.636879225371419
1290.3651246861412680.7302493722825370.634875313858732
1300.340872963894720.681745927789440.65912703610528
1310.3177362250886710.6354724501773410.682263774911329
1320.2946253211057660.5892506422115320.705374678894234
1330.2913357060557120.5826714121114250.708664293944288
1340.3211260060989580.6422520121979160.678873993901042
1350.2995010219123460.5990020438246910.700498978087654
1360.3084543396505850.616908679301170.691545660349415
1370.3402007348207960.6804014696415910.659799265179204
1380.3182794836930530.6365589673861060.681720516306947
1390.3168659654417600.6337319308835210.68313403455824
1400.2944918326105400.5889836652210810.70550816738946
1410.3353540935969620.6707081871939240.664645906403038
1420.3125754658681150.6251509317362290.687424534131885
1430.3140501900001290.6281003800002570.685949809999871
1440.3482424678720600.6964849357441190.65175753212794
1450.3253208376440360.6506416752880710.674679162355964
1460.3519978167330950.7039956334661890.648002183266905
1470.3292493534650430.6584987069300860.670750646534957
1480.3243115344624250.6486230689248510.675688465537575
1490.3309205577515510.6618411155031020.669079442248449
1500.308781830385390.617563660770780.69121816961461
1510.3097526905301450.619505381060290.690247309469855
1520.3487787237407040.6975574474814070.651221276259296
1530.3922258460566440.7844516921132890.607774153943356
1540.3694654564704170.7389309129408340.630534543529583
1550.375841683221120.751683366442240.62415831677888
1560.3534689361298680.7069378722597360.646531063870132
1570.3543958441822090.7087916883644180.645604155817791
1580.3510568491299720.7021136982599450.648943150870028
1590.3521070096081930.7042140192163860.647892990391807
1600.3308634487072780.6617268974145570.669136551292722
1610.3096880969533080.6193761939066160.690311903046692
1620.2893683638241930.5787367276483860.710631636175807
1630.2922522688455480.5845045376910950.707747731154452
1640.2721773885836750.544354777167350.727822611416325
1650.3059963887584880.6119927775169770.694003611241512
1660.3351728761854720.6703457523709440.664827123814528
1670.3323276305494610.6646552610989220.667672369450539
1680.3113165657039720.6226331314079430.688683434296028
1690.2911142809607300.5822285619214590.70888571903927
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13000.2335616676961790.4671233353923580.766438332303821


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level1760.136222910216718NOK
5% type I error level3900.301857585139319NOK
10% type I error level5670.438854489164087NOK
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Dec/02/t1291277885h50mxz8ftfobp76/10kycc1291277375.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/02/t1291277885h50mxz8ftfobp76/10kycc1291277375.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/02/t1291277885h50mxz8ftfobp76/166f41291277375.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/02/t1291277885h50mxz8ftfobp76/166f41291277375.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/02/t1291277885h50mxz8ftfobp76/266f41291277375.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/02/t1291277885h50mxz8ftfobp76/266f41291277375.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/02/t1291277885h50mxz8ftfobp76/366f41291277375.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/02/t1291277885h50mxz8ftfobp76/366f41291277375.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/02/t1291277885h50mxz8ftfobp76/4yywp1291277375.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/02/t1291277885h50mxz8ftfobp76/4yywp1291277375.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/02/t1291277885h50mxz8ftfobp76/5yywp1291277375.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/02/t1291277885h50mxz8ftfobp76/5yywp1291277375.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/02/t1291277885h50mxz8ftfobp76/6yywp1291277375.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/02/t1291277885h50mxz8ftfobp76/6yywp1291277375.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/02/t1291277885h50mxz8ftfobp76/7r7ds1291277375.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/02/t1291277885h50mxz8ftfobp76/7r7ds1291277375.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/02/t1291277885h50mxz8ftfobp76/8kycc1291277375.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/02/t1291277885h50mxz8ftfobp76/8kycc1291277375.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/02/t1291277885h50mxz8ftfobp76/9kycc1291277375.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/02/t1291277885h50mxz8ftfobp76/9kycc1291277375.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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