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paper, multiple regressie

*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: Mon, 27 Dec 2010 09:24:27 +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/27/t1293441829pl25ow105btanjd.htm/, Retrieved Mon, 27 Dec 2010 10:23:53 +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/27/t1293441829pl25ow105btanjd.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 «
30,00 1 1 2 0 0 5,00 1 1 1 1 2 5,00 0 1 2 1 2 30,00 0 1 1 1 2 25,00 0 1 2 1 2 50,00 1 1 1 0 0 65,00 1 1 2 1 0 40,00 0 1 1 0 0 55,00 1 1 2 2 0 75,00 0 1 1 0 0 50,00 0 1 1 1 0 20,00 1 1 2 1 0 25,00 1 1 2 0 0 30,00 1 1 2 0 0 80,00 1 1 1 0 0 0 1 1 0 0 25,00 0 1 1 0 1 50,00 1 1 2 0 1 35,00 1 1 2 0 0 40,00 0 1 1 0 0 40,00 1 1 1 1 1 50,00 1 1 2 1 1 30,00 1 1 1 0 0 45,00 1 1 2 0 0 30,00 1 1 2 0 0 25,00 0 1 1 0 0 25,00 1 1 1 1 0 20,00 1 1 2 1 0 35,00 1 1 2 0 0 30,00 1 1 1 0 0 45,00 0 1 1 0 0 40,00 1 1 1 0 0 30,00 1 1 2 0 0 60,00 1 1 2 0 0 45,00 0 1 1 0 0 45,00 1 1 2 0 0 25,00 1 1 2 0 1 1 1 1 0 0 45,00 0 1 1 0 0 50,00 0 1 1 0 0 0 1 1 0 0 45,00 1 1 2 0 0 60,00 1 1 2 2 0 60,00 1 1 2 0 0 45,00 1 1 2 0 0 45,00 0 1 1 0 0 0 1 1 0 0 45,00 1 1 1 0 0 55,00 1 1 2 0 0 40,00 1 1 1 0 1 60,00 1 1 2 0 1 35,00 0 1 1 0 0 30,00 0 1 1 0 0 20,00 0 1 1 0 0 15,00 1 1 1 1 2 15,00 1 1 2 1 2 40,00 1 1 1 1 2 40,00 1 1 2 1 2 50,00 0 1 1 0 0 1 1 2 0 0 40,00 0 1 1 1 0 80,00 1 1 2 1 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 time81 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk
R Framework
error message
The field 'Names of X columns' contains a hard return which cannot be interpreted.
Please, resubmit your request without hard returns in the 'Names of X columns'.


Multiple Linear Regression - Estimated Regression Equation
survived[t] = + 9.85104816533495 -0.225426356824898age[t] -0.226412239681569pclass[t] -0.209040088689753sex[t] -0.203180354100506sibsp[t] -0.196968235650721`parch `[t] + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)9.851048165334950.47190420.875100
age-0.2254263568248980.018741-12.028700
pclass-0.2264122396815690.025115-9.014900
sex-0.2090400886897530.022249-9.395400
sibsp-0.2031803541005060.025157-8.076600
`parch `-0.1969682356507210.025094-7.849200


Multiple Linear Regression - Regression Statistics
Multiple R0.390828684529463
R-squared0.152747060651031
Adjusted R-squared0.149495898182309
F-TEST (value)46.9822908330604
F-TEST (DF numerator)5
F-TEST (DF denominator)1303
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation9.42599893206683
Sum Squared Residuals115770.840995124


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
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Residuals
Prediction Error
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115718.5838643879081-7.58386438790809
115808.81911251055781-8.81911251055781
115902.0431315882459-2.0431315882459
116009.02074754516519-9.02074754516519
116118.75373126891074-7.75373126891074
116239.62463592565338-6.62463592565338
116314.0952602423476-3.0952602423476
116418.5838643879081-7.58386438790809
116500.673113553967788-0.673113553967788
116603.80871488431408-3.80871488431408
116704.65073497366233-4.65073497366233
116807.76409030128423-7.76409030128423
116936.49149173529723-3.49149173529723
117036.49149173529723-3.49149173529723
117137.31126582192109-4.31126582192109
11723-0.005137282220247123.00513728222025
11731-1.277735848207252.27773584820725
117417.68803719500664-6.68803719500664
117509.02074754516519-9.02074754516519
117608.96277135760049-8.96277135760049
117739.42766769000266-6.42766769000266
117825.11116201285013-3.11116201285013
117913.07935847184507-2.07935847184507
118018.5838643879081-7.58386438790809
118101.71831399741655-1.71831399741655
118208.81911251055781-8.81911251055781
118301.12011047852781-1.12011047852781
118402.97822455100302-2.97822455100302
118503.38423287534349-3.38423287534349
11860-5.672256711919255.67225671191925
118704.51629407375134-4.51629407375134
118803.18726463969277-3.18726463969277
118900.911070389838055-0.911070389838055
119002.25217167693565-2.25217167693565
119107.71550943332415-7.71550943332415
119212.05520344128493-1.05520344128493
119314.08182762823669-3.08182762823669
11940-1.353052006977631.35305200697763
119503.38423287534349-3.38423287534349
11960-7.936379108734947.93637910873494
119705.43931518346943-5.43931518346943
119803.38423287534349-3.38423287534349
119903.17519278665374-3.17519278665374
120001.12011047852781-1.12011047852781
120107.70343758028511-7.70343758028511
120218.82377930951447-7.82377930951447
120308.96277135760049-8.96277135760049
120435.68527121263896-2.68527121263896
120538.76057688635666-5.76057688635666
120618.5838643879081-7.58386438790809
120718.41310418621734-7.41310418621734
120800.894684121702911-0.894684121702911
120909.02074754516519-9.02074754516519
121008.96277135760049-8.96277135760049
121101.07284886872907-1.07284886872907
12120-1.18141469951991.1814146995199
121308.96277135760049-8.96277135760049
121413.32711243697805-2.32711243697805
121537.65495356914617-4.65495356914617
121637.01730676953101-4.01730676953101
121732.851529816835020.148470183164979
121830.8877071949170562.11229280508294
121935.68527121263896-2.68527121263896
12203-3.630137988149966.63013798814996
122139.17279732914691-6.17279732914691
122215.69161145498134-4.69161145498134
12231-0.4037991680338481.40379916803385
122416.72488537647569-5.72488537647569
122520.62947475346051.3705252465395
122612.64390614347375-1.64390614347375
122728.14841205953677-6.14841205953677
122801.71831399741655-1.71831399741655
122902.76351444086531-2.76351444086531
123002.76351444086531-2.76351444086531
12310-1.417287332929741.41728733292974
123204.85391532776284-4.85391532776284
123321.492887640591650.507112359408347
123434.85391532776284-1.85391532776284
123521.718313997416550.28168600258345
123613.38010817338867-2.38010817338867
123704.85391532776284-4.85391532776284
123805.8991157712116-5.8991157712116
123903.58328852748918-3.58328852748918
124003.80871488431408-3.80871488431408
124108.81911251055781-8.81911251055781
124209.02074754516519-9.02074754516519
124308.96277135760049-8.96277135760049
124401.07284886872907-1.07284886872907
12451-0.2633230040851661.26332300408517
12460-3.435678267768883.43567826776888
124704.25106386700203-4.25106386700203
124803.12393208287755-3.12393208287755
12491-2.720766926434653.72076692643465
125039.62463592565338-6.62463592565338
125118.5838643879081-7.58386438790809
125202.76351444086531-2.76351444086531
125303.80871488431408-3.80871488431408
125402.76351444086531-2.76351444086531
125509.0347171015579-9.0347171015579
125600.673113553967788-0.673113553967788
125702.76351444086531-2.76351444086531
125815.6959354171111-4.6959354171111
12591-1.642713689754632.64271368975463
126008.81911251055781-8.81911251055781
126109.02074754516519-9.02074754516519
1262158.620598955413966.37940104458604
126308.55055091481023-8.55055091481023
126402.19998065285356-2.19998065285356
126502.19998065285356-2.19998065285356
126633.71558885613175-0.715588856131747
126718.18795615089331-7.18795615089331
126817.79896759368411-6.79896759368411
126912.87377581955941-1.87377581955941
127014.08502923749459-3.08502923749459
12711-1.065588893455012.06558889345501
12721-3.40372574846844.4037257484684
127311.08502781442832-0.0850278144283159
12741-1.208617035136282.20861703513628
12751-6.017900522036687.01790052203668
12761-0.2237758568826781.22377585688268
127715.4762311239492-4.4762311239492
127814.03955134918913-3.03955134918913
127913.26375025962528-2.26375025962528
12801-6.584661522910787.58466152291078
128119.39920956882848-8.39920956882848
128214.54611295599739-3.54611295599739
12831-0.9394042208557381.93940422085574
128422.10830109065186-0.108301090651858
128521.49840764448980.501592355510201
128611.30143940883908-0.301439408839077
12871-1.165816460537312.16581646053731
128822.89779062147282-0.89779062147282
128910.2855376383365460.714462361663454
129023.33324294984414-1.33324294984414
129124.54611295599739-2.54611295599739
129214.34914472034667-3.34914472034667
129315.13863425116764-4.13863425116764
129422.09092893966004-0.0909289396600418
129523.33324294984414-1.33324294984414
129610.4825058739872670.517494126012733
129711.30143940883908-0.301439408839077
129813.33324294984414-2.33324294984414
12992-2.762167673171054.76216767317105
130020.4825058739872671.51749412601273
130110.2855376383365460.714462361663454
130224.34914472034667-2.34914472034667
130329.01643313006907-7.01643313006907
130400.0218495818204677-0.0218495818204677
13050-1.023350861628291.02335086162829
130609.22547321875883-9.22547321875883
13070-1.143659534427341.14365953442734
13080-4.539843129650874.53984312965087
13090-4.990695843300664.99069584330066


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
90.0004794666895449530.0009589333790899060.999520533310455
103.00162468168263e-056.00324936336527e-050.999969983753183
113.8359396251215e-067.67187925024299e-060.999996164060375
122.25532211598253e-074.51064423196507e-070.999999774467788
131.26242775960278e-082.52485551920556e-080.999999987375722
146.72351947768399e-101.3447038955368e-090.999999999327648
158.77559861763938e-111.75511972352788e-100.999999999912244
161.41741573074394e-112.83483146148787e-110.999999999985826
179.0831246468806e-131.81662492937612e-120.999999999999092
184.88112104168407e-149.76224208336813e-140.999999999999951
192.73153551118045e-155.4630710223609e-150.999999999999997
201.37163123026868e-162.74326246053735e-161
217.99763852981981e-181.59952770596396e-171
223.81688437433016e-197.63376874866032e-191
231.76525209211253e-203.53050418422505e-201
247.99002538981379e-221.59800507796276e-211
253.6183328983351e-237.2366657966702e-231
261.91755750920927e-243.83511501841853e-241
278.39009917724552e-261.6780198354491e-251
284.10703333569621e-278.21406667139242e-271
291.67905843764031e-283.35811687528063e-281
306.75531913945136e-301.35106382789027e-291
312.64077865066329e-315.28155730132657e-311
321.08700081161152e-322.17400162322305e-321
335.8458420324387e-341.16916840648774e-331
342.26919443561649e-354.53838887123298e-351
358.3988787098055e-371.6797757419611e-361
363.20374823092808e-386.40749646185616e-381
372.03597837822689e-394.07195675645378e-391
381.06764073712924e-402.13528147425849e-401
393.81628534069578e-427.63257068139155e-421
402.0668400035359e-434.13368000707179e-431
417.25336444762485e-451.45067288952497e-441
422.79506235883978e-465.59012471767956e-461
431.14473292716976e-432.28946585433952e-431
441.59176506123667e-443.18353012247333e-441
451.50488267425857e-453.00976534851714e-451
461.56535015468523e-463.13070030937047e-461
471.41708166725893e-472.83416333451786e-471
486.4761325424639e-491.29522650849278e-481
493.01740951522098e-506.03481903044196e-501
501.25043123903817e-502.50086247807634e-501
511.25268369621147e-512.50536739242294e-511
521.01872938106807e-522.03745876213614e-521
538.6372060360783e-541.72744120721566e-531
547.2102118498259e-551.44204236996518e-541
554.42469795270493e-548.84939590540987e-541
561.65113311328285e-533.3022662265657e-531
571.84343981641119e-533.68687963282238e-531
588.93844917409684e-541.78768983481937e-531
599.18661642813573e-551.83732328562715e-541
609.51014185556378e-081.90202837111276e-070.999999904898581
610.9732597287075920.05348054258481680.0267402712924084
620.999035677265460.001928645469080140.000964322734540068
630.9999739901202735.2019759454309e-052.60098797271545e-05
640.9999817153154263.65693691488582e-051.82846845744291e-05
650.999992143435931.57131281405224e-057.85656407026122e-06
660.9999980107421043.97851579124022e-061.98925789562011e-06
670.999998248711223.50257756049282e-061.75128878024641e-06
680.9999997521608354.95678330628536e-072.47839165314268e-07
690.9999998788803952.42239209806985e-071.21119604903493e-07
700.9999998291725813.41654837487745e-071.70827418743872e-07
710.9999997567369884.86526023719318e-072.43263011859659e-07
720.9999996723168396.55366322780854e-073.27683161390427e-07
730.9999998233789143.53242172477345e-071.76621086238672e-07
740.9999997350912135.2981757447072e-072.6490878723536e-07
750.9999996193081227.61383756369605e-073.80691878184803e-07
760.9999994398332041.12033359090118e-065.60166795450592e-07
770.9999992607412661.4785174687915e-067.39258734395752e-07
780.9999989372164812.12556703787905e-061.06278351893953e-06
790.9999992509402831.49811943491375e-067.49059717456876e-07
800.999998961357392.07728521805945e-061.03864260902973e-06
810.9999985577006652.88459867002311e-061.44229933501156e-06
820.9999980032963263.99340734865278e-061.99670367432639e-06
830.9999972637976845.47240463203724e-062.73620231601862e-06
840.9999962833551657.4332896709177e-063.71664483545885e-06
850.9999947712119681.04575760634556e-055.2287880317278e-06
860.9999938370184741.23259630513752e-056.16298152568758e-06
870.9999922097979031.55804041946658e-057.79020209733291e-06
880.999990104140961.97917180776779e-059.89585903883893e-06
890.9999876485935852.47028128307138e-051.23514064153569e-05
900.999983459450533.30810989388577e-051.65405494694288e-05
910.9999818791011473.62417977053839e-051.8120898852692e-05
920.9999757187346174.85625307652291e-052.42812653826145e-05
930.9999794618975034.10762049942268e-052.05381024971134e-05
940.999972335127895.53297442213466e-052.76648721106733e-05
950.9999626782162477.46435675064893e-053.73217837532446e-05
960.9999536723394749.26553210519385e-054.63276605259693e-05
970.9999382956073540.000123408785292846.17043926464199e-05
980.9999180769875320.0001638460249353488.19230124676738e-05
990.9998918270187170.0002163459625667470.000108172981283374
1000.9998601015928370.0002797968143267240.000139898407163362
1010.9998429493738820.0003141012522363730.000157050626118187
1020.9997979580415830.0004040839168345780.000202041958417289
1030.9997395368317170.0005209263365662290.000260463168283115
1040.9996669339523540.0006661320952915340.000333066047645767
1050.9997473401640240.0005053196719519580.000252659835975979
1060.99980192779020.0003961444196009190.000198072209800459
1070.9998311244420790.0003377511158426660.000168875557921333
1080.9997846104296460.0004307791407076810.000215389570353841
1090.999745015480290.0005099690394220340.000254984519711017
1100.9996879091641380.0006241816717244850.000312090835862242
1110.9996094071561140.0007811856877727330.000390592843886366
1120.999523655373910.0009526892521790980.000476344626089549
1130.9994571573550640.001085685289870990.000542842644935495
1140.999360488986410.00127902202717810.000639511013589049
1150.9992391156573760.001521768685248640.000760884342624322
1160.9990861886155740.001827622768852980.00091381138442649
1170.999223052017050.001553895965899360.000776947982949682
1180.999030434188520.001939131622958370.000969565811479187
1190.9987930805465770.002413838906846330.00120691945342317
1200.9985459759851930.002908048029613520.00145402401480676
1210.998370411066950.003259177866099280.00162958893304964
1220.9980321490720270.0039357018559460.001967850927973
1230.9981066138517070.003786772296585580.00189338614829279
1240.9977241315175530.004551736964893390.00227586848244669
1250.997283892026090.005432215947820010.00271610797391
1260.9966981089830830.006603782033834690.00330189101691735
1270.9960929287080050.007814142583990140.00390707129199507
1280.9954717267740060.009056546451988770.00452827322599438
1290.9945505235353350.01089895292933030.00544947646466515
1300.9937121291252160.01257574174956730.00628787087478363
1310.9924889390537930.01502212189241420.00751106094620711
1320.9926910301029480.01461793979410450.00730896989705223
1330.9919443064113790.01611138717724270.00805569358862137
1340.9904542917212280.01909141655754340.00954570827877171
1350.9896431276150370.02071374476992650.0103568723849633
1360.9879122398074940.0241755203850130.0120877601925065
1370.9859229386960210.02815412260795720.0140770613039786
1380.984270928290970.03145814341805820.0157290717090291
1390.9816712704839720.03665745903205610.018328729516028
1400.9786875722088490.04262485558230250.0213124277911513
1410.9765202885462050.04695942290759040.0234797114537952
1420.9737443411716780.05251131765664460.0262556588283223
1430.9698160843461890.06036783130762250.0301839156538113
1440.965397894680150.06920421063970160.0346021053198508
1450.9656115116039780.06877697679204340.0343884883960217
1460.9606586498696160.07868270026076870.0393413501303843
1470.9553941022049020.0892117955901970.0446058977950985
1480.9494034541066940.1011930917866120.0505965458933058
1490.9436344231180130.1127311537639730.0563655768819867
1500.9454188097010840.1091623805978330.0545811902989164
1510.9525612325959820.09487753480803680.0474387674040184
1520.997200156779930.005599686440141360.00279984322007068
1530.9999298003637630.0001403992724741717.01996362370856e-05
1540.9999922671374021.54657251958744e-057.7328625979372e-06
1550.999993709669551.25806608980418e-056.29033044902088e-06
1560.9999918620077531.62759844946559e-058.13799224732795e-06
1570.99999054861251.89027749981394e-059.4513874990697e-06
1580.9999878117352252.43765295492102e-051.21882647746051e-05
1590.999984604010533.07919789412937e-051.53959894706468e-05
1600.9999803580568043.92838863927184e-051.96419431963592e-05
1610.9999753316626464.93366747087241e-052.46683373543621e-05
1620.9999692986640546.14026718920144e-053.07013359460072e-05
1630.9999612477492447.75045015114226e-053.87522507557113e-05
1640.9999513796522459.72406955109442e-054.86203477554721e-05
1650.9999386281998850.0001227436002291636.13718001145815e-05
1660.9999243090899540.0001513818200914887.56909100457438e-05
1670.9999064479001690.0001871041996621329.3552099831066e-05
1680.9998845172358780.0002309655282431990.0001154827641216
1690.9998573766029280.0002852467941450060.000142623397072503
1700.9998249074464150.0003501851071706430.000175092553585322
1710.999793585776280.00041282844744130.00020641422372065
1720.9997451821445770.0005096357108464020.000254817855423201
1730.999765091941020.0004698161179597240.000234908058979862
1740.9997112295864730.0005775408270542330.000288770413527117
1750.9996461685869610.000707662826077990.000353831413038995
1760.9996546298444080.0006907403111848330.000345370155592416
1770.999583047299740.0008339054005188390.000416952700259419
1780.9994923071019110.001015385796178210.000507692898089106
1790.999408912321940.001182175356119320.000591087678059659
1800.9992992205366460.001401558926708880.000700779463354438
1810.9993665561970140.001266887605972340.00063344380298617
1820.999233390646030.001533218707939170.000766609353969584
1830.9990948175736420.001810364852714950.000905182426357475
1840.9989895950605670.002020809878865130.00101040493943257
1850.998826578204360.002346843591280270.00117342179564013
1860.9986202968398730.0027594063202540.001379703160127
1870.9984224300816790.003155139836641920.00157756991832096
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122411.03872542249971e-435.19362711249853e-44
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122914.24998865154622e-402.12499432577311e-40
123012.17072005672377e-391.08536002836188e-39
123111.17264518205811e-385.86322591029055e-39
123215.50535512065135e-382.75267756032567e-38
123312.14342515112788e-371.07171257556394e-37
123415.87299710666595e-372.93649855333298e-37
123512.10014767542183e-361.05007383771091e-36
123611.0916026414029e-355.4580132070145e-36
123715.31593889251789e-352.65796944625895e-35
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124015.91119536515785e-332.95559768257893e-33
124112.19547391796193e-321.09773695898096e-32
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124816.91679874788172e-283.45839937394086e-28
124912.46642279220429e-271.23321139610215e-27
125011.01680634444125e-265.08403172220627e-27
125114.69297308773322e-262.34648654386661e-26
125212.16146940526198e-251.08073470263099e-25
125319.44833340506175e-254.72416670253088e-25
125414.19650780748016e-242.09825390374008e-24
125511.30939044000633e-236.54695220003167e-24
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126512.11642678570815e-401.05821339285407e-40
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126913.36614347048555e-381.68307173524278e-38
127016.75000566518035e-373.37500283259017e-37
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128012.47411982262276e-241.23705991131138e-24
128113.40246144763067e-231.70123072381534e-23
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128718.2557041518216e-174.1278520759108e-17
128817.72927797135962e-163.86463898567981e-16
12890.9999999999999968.54654435196141e-154.27327217598071e-15
12900.9999999999999578.5292720023097e-144.26463600115485e-14
12910.9999999999995538.94555314678478e-134.47277657339239e-13
12920.999999999993941.2122702038069e-116.0613510190345e-12
12930.9999999999171181.6576455437699e-108.2882277188495e-11
12940.9999999991314151.73717079923226e-098.6858539961613e-10
12950.9999999920748651.5850270065789e-087.9251350328945e-09
12960.9999999329925511.34014897341987e-076.70074486709936e-08
12970.99999918617051.62765899964162e-068.1382949982081e-07
12980.9999901079328791.97841342415374e-059.89206712076869e-06
12990.9998808850645120.0002382298709760270.000119114935488013
13000.9985660132657070.002867973468586180.00143398673429309


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level9920.767801857585139NOK
5% type I error level10980.84984520123839NOK
10% type I error level11540.893188854489164NOK
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Dec/27/t1293441829pl25ow105btanjd/10nz5b1293441779.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/27/t1293441829pl25ow105btanjd/10nz5b1293441779.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/27/t1293441829pl25ow105btanjd/1gy8z1293441779.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/27/t1293441829pl25ow105btanjd/1gy8z1293441779.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/27/t1293441829pl25ow105btanjd/2gy8z1293441779.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/27/t1293441829pl25ow105btanjd/2gy8z1293441779.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/27/t1293441829pl25ow105btanjd/3rp7k1293441779.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/27/t1293441829pl25ow105btanjd/3rp7k1293441779.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/27/t1293441829pl25ow105btanjd/4rp7k1293441779.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/27/t1293441829pl25ow105btanjd/4rp7k1293441779.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/27/t1293441829pl25ow105btanjd/5rp7k1293441779.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/27/t1293441829pl25ow105btanjd/5rp7k1293441779.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/27/t1293441829pl25ow105btanjd/6jypn1293441779.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/27/t1293441829pl25ow105btanjd/6jypn1293441779.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/27/t1293441829pl25ow105btanjd/7jypn1293441779.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/27/t1293441829pl25ow105btanjd/7jypn1293441779.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/27/t1293441829pl25ow105btanjd/8uq6q1293441779.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/27/t1293441829pl25ow105btanjd/8uq6q1293441779.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/27/t1293441829pl25ow105btanjd/9uq6q1293441779.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/27/t1293441829pl25ow105btanjd/9uq6q1293441779.ps (open in new window)


 
Parameters (Session):
par1 = 2 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;
 
Parameters (R input):
par1 = 2 ; 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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