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mini-tutorial, Mini-tutorial 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 18:37:56 +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/t1291315077271yech5drtxx9s.htm/, Retrieved Thu, 02 Dec 2010 19:37:57 +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/t1291315077271yech5drtxx9s.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 time92 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24


Multiple Linear Regression - Estimated Regression Equation
survived[t] = + 0.145019265778679 -0.164514500634956pclass[t] + 0.507183007206067sex[t] -0.0273936121732979age[t] -0.0379358287916375sibsp[t] + 0.00381938386368818parch[t] + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)0.1450192657786790.055862.59610.0095350.004767
pclass-0.1645145006349560.014294-11.509200
sex0.5071830072060670.02339821.676800
age-0.02739361217329790.007168-3.82140.0001396.9e-05
sibsp-0.03793582879163750.011315-3.35270.0008230.000412
parch0.003819383863688180.0137330.27810.7809730.390487


Multiple Linear Regression - Regression Statistics
Multiple R0.594259390098298
R-squared0.353144222720001
Adjusted R-squared0.350662043989072
F-TEST (value)142.271875235948
F-TEST (DF numerator)5
F-TEST (DF denominator)1303
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.391670590273314
Sum Squared Residuals199.887824224415


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
110.9400835552092630.0599164447907371
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113210.07647793455998520.923522065440015
113300.158658771079879-0.158658771079879
113400.131265158906581-0.131265158906581
113500.103871546733283-0.103871546733283
113600.158658771079879-0.158658771079879
113700.665841778285946-0.665841778285946
113800.158658771079879-0.158658771079879
113900.158658771079879-0.158658771079879
114000.076477934559985-0.076477934559985
114100.103871546733283-0.103871546733283
11420-0.01665877239628080.0166587723962808
114300.0107348397770171-0.0107348397770171
114400.0107348397770171-0.0107348397770171
114500.0107348397770171-0.0107348397770171
114600.0107348397770171-0.0107348397770171
114700.602757861084493-0.602757861084493
114800.61105455393935-0.61105455393935
114900.076477934559985-0.076477934559985
115010.6658417782859460.334158221714054
115100.158658771079879-0.158658771079879
115200.665841778285946-0.665841778285946
11530-0.01624511857824830.0162451185782483
115400.518331500801116-0.518331500801116
115500.158658771079879-0.158658771079879
115600.158658771079879-0.158658771079879
115700.631725333357997-0.631725333357997
115800.0971487139786316-0.0971487139786316
115900.56390609732013-0.56390609732013
116010.6658417782859460.334158221714054
116100.0216907102133892-0.0216907102133892
116200.131265158906581-0.131265158906581
116310.1586587710798790.841341228920121
116400.158658771079879-0.158658771079879
116500.158658771079879-0.158658771079879
116600.103871546733283-0.103871546733283
116700.158658771079879-0.158658771079879
116800.158658771079879-0.158658771079879
116900.158658771079879-0.158658771079879
117000.076477934559985-0.076477934559985
11710-0.1371890915258450.137189091525845
11720-0.1645827036991420.164582703699142
117300.369993915680222-0.369993915680222
117400.369993915680222-0.369993915680222
117500.369993915680222-0.369993915680222
117600.369993915680222-0.369993915680222
11770-0.1371890915258450.137189091525845
11780-0.1371890915258450.137189091525845
11790-0.1371890915258450.137189091525845
118000.155097397061435-0.155097397061435
118100.662280404267502-0.662280404267502
118200.103871546733283-0.103871546733283
118310.611054553939350.38894544606065
118400.076477934559985-0.076477934559985
118500.0827871134966039-0.0827871134966039
118600.0827871134966039-0.0827871134966039
118700.0827871134966039-0.0827871134966039
118810.6317253333579960.368274666642004
118910.6186933216667260.381306678333274
119010.6317253333579960.368274666642004
119110.1038715467332830.896128453266717
119200.103871546733283-0.103871546733283
119300.103871546733283-0.103871546733283
119400.158658771079879-0.158658771079879
119500.158658771079879-0.158658771079879
119600.158658771079879-0.158658771079879
119710.1038715467332830.896128453266717
119800.158658771079879-0.158658771079879
119910.6658417782859460.334158221714054
120000.158658771079879-0.158658771079879
120100.158658771079879-0.158658771079879
120200.103871546733283-0.103871546733283
120300.158658771079879-0.158658771079879
120400.0490843223866871-0.0490843223866871
120500.103871546733283-0.103871546733283
120610.6384481661126480.361551833887352
120700.0524900524323428-0.0524900524323428
120800.0250964402590448-0.0250964402590448
120900.55967305963841-0.55967305963841
121000.55967305963841-0.55967305963841
121100.0264260290498024-0.0264260290498024
121200.533609036255869-0.533609036255869
121300.158658771079879-0.158658771079879
121400.158658771079879-0.158658771079879
121500.158658771079879-0.158658771079879
121600.158658771079879-0.158658771079879
121710.6658417782859460.334158221714054
121800.131265158906581-0.131265158906581
121900.076477934559985-0.076477934559985
122000.158658771079879-0.158658771079879
122100.076477934559985-0.076477934559985
122200.158658771079879-0.158658771079879
122300.076477934559985-0.076477934559985
122410.611054553939350.38894544606065
122500.103871546733283-0.103871546733283
12260-0.005702901959908710.00570290195990871
122700.131265158906581-0.131265158906581
122800.61105455393935-0.61105455393935
122910.07647793455998520.923522065440015
123000.103871546733283-0.103871546733283
123100.669661162149634-0.669661162149634
123200.5769381090114-0.5769381090114
123310.1312651589065810.868734841093419
123410.04908432238668730.950915677613313
123500.103871546733283-0.103871546733283
12360-0.03309651413320660.0330965141332066
123710.1312651589065810.868734841093419
123800.103871546733283-0.103871546733283
123910.1038715467332830.896128453266717
124000.076477934559985-0.076477934559985
124110.1624781549435670.837521845056433
124200.120722942288241-0.120722942288241
124300.158658771079879-0.158658771079879
124400.158658771079879-0.158658771079879
124510.6043317211846980.395668278815302
124600.158658771079879-0.158658771079879
124700.120722942288241-0.120722942288241
124810.6279059494943080.372094050505692
124900.076477934559985-0.076477934559985
125000.158658771079879-0.158658771079879
125100.158658771079879-0.158658771079879
125200.076477934559985-0.076477934559985
125300.0490843223866871-0.0490843223866871
125400.158658771079879-0.158658771079879
125510.1038715467332830.896128453266717
125600.158658771079879-0.158658771079879
125710.1245423261519300.87545767384807
125810.6317253333579960.368274666642004
125910.6186933216667260.381306678333274
126000.076477934559985-0.076477934559985
126110.6384481661126480.361551833887352
126210.5014801052461580.498519894753842
126300.124542326151930-0.124542326151930
126400.0971487139786316-0.0971487139786316
126500.0567230901140635-0.0567230901140635
126600.646086933840024-0.646086933840024
126700.0423614896320357-0.0423614896320357
126800.549544496838103-0.549544496838103
126900.158658771079879-0.158658771079879
127000.076477934559985-0.076477934559985
127100.103871546733283-0.103871546733283
127200.103871546733283-0.103871546733283
127300.0490843223866871-0.0490843223866871
127400.562576508529373-0.562576508529373
12750-0.03732955181492740.0373295518149274
127600.055393501323306-0.055393501323306
127700.545725112974414-0.545725112974414
127810.1038715467332830.896128453266717
127900.103871546733283-0.103871546733283
128000.638448166112648-0.638448166112648
128100.103871546733283-0.103871546733283
128200.103871546733283-0.103871546733283
128300.158658771079879-0.158658771079879
128400.158658771079879-0.158658771079879
128500.158658771079879-0.158658771079879
128600.076477934559985-0.076477934559985
128710.5836609417660520.416339058233948
128800.0216907102133892-0.0216907102133892
128900.0933293301149434-0.0933293301149434
129000.0659357179416455-0.0659357179416455
129110.5183315008011160.481668499198883
129200.158658771079879-0.158658771079879
129300.158658771079879-0.158658771079879
129400.158658771079879-0.158658771079879
129500.103871546733283-0.103871546733283
129600.103871546733283-0.103871546733283
129700.103871546733283-0.103871546733283
129800.158658771079879-0.158658771079879
129900.076477934559985-0.076477934559985
130000.0659357179416455-0.0659357179416455
130110.600512337321010.39948766267899
130200.0490843223866871-0.0490843223866871
130300.158658771079879-0.158658771079879
130400.158658771079879-0.158658771079879
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
90.9661667761823270.06766644763534630.0338332238176731
100.9401021093044440.1197957813911130.0598978906955563
110.978008390001310.04398321999737990.0219916099986900
120.959502995558050.08099400888389840.0404970044419492
130.9369115424751580.1261769150496850.0630884575248423
140.904445263335790.1911094733284200.0955547366642101
150.945931164378280.1081376712434410.0540688356217205
160.9535413021412470.09291739571750640.0464586978587532
170.9369293744549230.1261412510901540.0630706255450771
180.9194392590434150.1611214819131710.0805607409565854
190.8888069051962920.2223861896074170.111193094803708
200.8824900372540140.2350199254919730.117509962745986
210.9351026139182770.1297947721634450.0648973860817226
220.9158946043115380.1682107913769240.0841053956884622
230.9346668494851870.1306663010296250.0653331505148127
240.9125347738046950.1749304523906090.0874652261953047
250.8870352303361710.2259295393276580.112964769663829
260.8877133685705580.2245732628588850.112286631429442
270.8982205579722690.2035588840554620.101779442027731
280.8699207950859770.2601584098280460.130079204914023
290.8389139021019780.3221721957960430.161086097898021
300.8562304724043740.2875390551912520.143769527595626
310.8708341762178650.2583316475642710.129165823782135
320.8808753259350380.2382493481299240.119124674064962
330.853396677143660.2932066457126810.146603322856340
340.8215627345917880.3568745308164230.178437265408212
350.8388201049635610.3223597900728780.161179895036439
360.8065793339136440.3868413321727120.193420666086356
370.787199037300220.4256019253995590.212800962699780
380.8041637724051950.391672455189610.195836227594805
390.8197110912669460.3605778174661090.180288908733054
400.8288759793024280.3422480413951430.171124020697572
410.8376465287482840.3247069425034320.162353471251716
420.808028264102440.383943471795120.19197173589756
430.7764136089463150.447172782107370.223586391053685
440.7414845990565420.5170308018869160.258515400943458
450.7040968048014360.5918063903971280.295903195198564
460.7100717748393520.5798564503212960.289928225160648
470.710273894462870.5794522110742610.289726105537130
480.7476461630157650.5047076739684690.252353836984235
490.7121665908708030.5756668182583940.287833409129197
500.781582529681070.4368349406378610.218417470318930
510.7537185565947510.4925628868104980.246281443405249
520.7596743170975980.4806513658048050.240325682902402
530.7596505146843070.4806989706313860.240349485315693
540.7537058364059540.4925883271880920.246294163594046
550.8200234730103010.3599530539793980.179976526989699
560.7969006879204590.4061986241590820.203099312079541
570.8216933661208390.3566132677583230.178306633879161
580.7951759810134080.4096480379731850.204824018986592
590.7977553095539330.4044893808921330.202244690446067
600.7747832634500650.4504334730998710.225216736549935
610.779113098415560.441773803168880.22088690158444
620.7503805224671950.4992389550656090.249619477532805
630.7522786074820560.4954427850358890.247721392517944
640.7224679198338020.5550641603323960.277532080166198
650.7612132781568260.4775734436863490.238786721843174
660.732168256889950.53566348622010.26783174311005
670.7027230979916910.5945538040166180.297276902008309
680.6719151035088840.6561697929822320.328084896491116
690.7090455300026940.5819089399946120.290954469997306
700.6804762804393260.6390474391213470.319523719560674
710.673536566389760.652926867220480.32646343361024
720.6726751707824150.654649658435170.327324829217585
730.6417081736848050.716583652630390.358291826315195
740.6103451420719450.7793097158561090.389654857928054
750.5990466095058460.8019067809883070.400953390494154
760.5995053913401610.8009892173196790.400494608659839
770.5660695755446510.8678608489106980.433930424455349
780.5681441929593660.8637116140812690.431855807040634
790.534997388900760.930005222198480.46500261109924
800.5017468669277180.9965062661445630.498253133072282
810.4879302534541510.9758605069083030.512069746545849
820.5006367185931260.9987265628137470.499363281406874
830.4676158584709890.9352317169419790.532384141529011
840.4352506012999120.8705012025998240.564749398700088
850.4284856534444090.8569713068888170.571514346555591
860.3973513759386690.7947027518773380.602648624061331
870.4446909804672950.889381960934590.555309019532705
880.5019217560072240.9961564879855510.498078243992776
890.4703158387205610.9406316774411220.529684161279439
900.4641545222353770.9283090444707550.535845477764623
910.433263187893570.866526375787140.56673681210643
920.4874869129807870.9749738259615740.512513087019213
930.45796803893210.91593607786420.5420319610679
940.4937605736705950.987521147341190.506239426329405
950.5374722540193080.9250554919613850.462527745980692
960.5071241302802980.9857517394394030.492875869719702
970.509270353575910.981459292848180.49072964642409
980.4791897898696450.958379579739290.520810210130355
990.4498023039669070.8996046079338140.550197696033093
1000.4207492079740830.8414984159481650.579250792025917
1010.4634563947658860.9269127895317720.536543605234114
1020.4636182519189170.9272365038378340.536381748081083
1030.4342126834770940.8684253669541870.565787316522906
1040.4057424754326910.8114849508653810.59425752456731
1050.3777459437796990.7554918875593970.622254056220301
1060.5119529562662540.9760940874674920.488047043733746
1070.5037644764159790.9924710471680410.496235523584021
1080.478694474628390.957388949256780.52130552537161
1090.4533462340257560.9066924680515120.546653765974244
1100.4965743531261940.9931487062523870.503425646873806
1110.4957544207431440.9915088414862870.504245579256856
1120.4675557434387480.9351114868774970.532444256561252
1130.4395991472342470.8791982944684940.560400852765753
1140.412024814161710.824049628323420.58797518583829
1150.4154550729409910.8309101458819820.584544927059009
1160.4342708032337300.8685416064674590.56572919676627
1170.4073832789454770.8147665578909550.592616721054523
1180.3808536758097630.7617073516195260.619146324190237
1190.3753893187929850.750778637585970.624610681207015
1200.4093065833763900.8186131667527790.59069341662361
1210.4431602296810140.8863204593620290.556839770318986
1220.4176249485513860.8352498971027710.582375051448614
1230.3924527266309170.7849054532618350.607547273369083
1240.4179849507331960.8359699014663920.582015049266804
1250.3919439924511820.7838879849023630.608056007548818
1260.3854362496070870.7708724992141740.614563750392913
1270.3883060911592870.7766121823185740.611693908840713
1280.3631207746285820.7262415492571650.636879225371418
1290.3651246861412710.7302493722825420.634875313858729
1300.3408729638947110.6817459277894220.659127036105289
1310.3177362250886690.6354724501773390.68226377491133
1320.2946253211057760.5892506422115530.705374678894224
1330.2913357060557070.5826714121114130.708664293944293
1340.3211260060989580.6422520121979170.678873993901042
1350.2995010219123510.5990020438247010.70049897808765
1360.3084543396505990.6169086793011980.691545660349401
1370.3402007348207970.6804014696415930.659799265179203
1380.3182794836930630.6365589673861270.681720516306937
1390.3168659654417570.6337319308835150.683134034558243
1400.2944918326105330.5889836652210660.705508167389467
1410.3353540935969670.6707081871939340.664645906403033
1420.3125754658681120.6251509317362230.687424534131888
1430.3140501900001320.6281003800002640.685949809999868
1440.3482424678720620.6964849357441240.651757532127938
1450.3253208376440290.6506416752880590.67467916235597
1460.3519978167330880.7039956334661750.648002183266912
1470.3292493534650420.6584987069300840.670750646534958
1480.3243115344624260.6486230689248520.675688465537574
1490.3309205577515530.6618411155031070.669079442248447
1500.3087818303853870.6175636607707750.691218169614613
1510.3097526905301380.6195053810602770.690247309469862
1520.3487787237407080.6975574474814150.651221276259292
1530.3922258460566460.7844516921132920.607774153943354
1540.3694654564704220.7389309129408430.630534543529578
1550.3758416832211220.7516833664422440.624158316778878
1560.3534689361298720.7069378722597430.646531063870128
1570.3543958441822050.708791688364410.645604155817795
1580.3510568491299790.7021136982599580.648943150870021
1590.3521070096081940.7042140192163880.647892990391806
1600.3308634487072800.6617268974145590.66913655129272
1610.3096880969533020.6193761939066040.690311903046698
1620.2893683638242010.5787367276484020.710631636175799
1630.2922522688455510.5845045376911020.707747731154449
1640.2721773885836720.5443547771673440.727822611416328
1650.3059963887584970.6119927775169940.694003611241503
1660.3351728761854790.6703457523709580.664827123814521
1670.3323276305494650.664655261098930.667672369450535
1680.3113165657039720.6226331314079430.688683434296029
1690.2911142809607350.582228561921470.708885719039265
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13000.2335616676961800.4671233353923590.76643833230382


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/t1291315077271yech5drtxx9s/106wo31291314978.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/02/t1291315077271yech5drtxx9s/106wo31291314978.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/02/t1291315077271yech5drtxx9s/1cs1l1291314978.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/02/t1291315077271yech5drtxx9s/1cs1l1291314978.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/02/t1291315077271yech5drtxx9s/2cs1l1291314978.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/02/t1291315077271yech5drtxx9s/2cs1l1291314978.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/02/t1291315077271yech5drtxx9s/3511o1291314978.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/02/t1291315077271yech5drtxx9s/3511o1291314978.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/02/t1291315077271yech5drtxx9s/4511o1291314978.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/02/t1291315077271yech5drtxx9s/4511o1291314978.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/02/t1291315077271yech5drtxx9s/5511o1291314978.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/02/t1291315077271yech5drtxx9s/5511o1291314978.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/02/t1291315077271yech5drtxx9s/6xsir1291314978.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/02/t1291315077271yech5drtxx9s/6xsir1291314978.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/02/t1291315077271yech5drtxx9s/78jzc1291314978.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/02/t1291315077271yech5drtxx9s/78jzc1291314978.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/02/t1291315077271yech5drtxx9s/88jzc1291314978.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/02/t1291315077271yech5drtxx9s/88jzc1291314978.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/02/t1291315077271yech5drtxx9s/98jzc1291314978.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/02/t1291315077271yech5drtxx9s/98jzc1291314978.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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