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*Unverified author*
R Software Module: rwasp_multipleregression.wasp (opens new window with default values)
Title produced by software: Multiple Regression
Date of computation: Sat, 29 Nov 2008 02:51:58 -0700
 
Cite this page as follows:
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Nov/29/t1227952436w6ik90cxq7qlvf0.htm/, Retrieved Sat, 29 Nov 2008 09:54:07 +0000
 
BibTeX entries for LaTeX users:
@Manual{KEY,
    author = {{YOUR NAME}},
    publisher = {Office for Research Development and Education},
    title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2008/Nov/29/t1227952436w6ik90cxq7qlvf0.htm/},
    year = {2008},
}
@Manual{R,
    title = {R: A Language and Environment for Statistical Computing},
    author = {{R Development Core Team}},
    organization = {R Foundation for Statistical Computing},
    address = {Vienna, Austria},
    year = {2008},
    note = {{ISBN} 3-900051-07-0},
    url = {http://www.R-project.org},
}
 
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
 
Feedback Forum:
2008-11-27 13:41:43 [a2386b643d711541400692649981f2dc] [reply
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Original text written by user:
 
IsPrivate?
No (this computation is public)
 
User-defined keywords:
 
Dataseries X:
» Textbox « » Textfile « » CSV «
70.5 0 71.3 0 71.4 0 70.1 0 69.4 0 69.8 0 69.8 0 70.7 0 69.4 0 69.8 0 69.3 0 72.9 0 70.0 0 64.4 0 63.5 0 69.8 0 69.9 0 69.3 0 69.7 0 69.8 0 70.2 0 69.8 0 70.7 0 71.4 0 70.3 0 70.9 0 70.6 0 69.0 0 71.0 0 74.7 0 77.5 0 78.6 0 75.3 0 72.1 0 73.8 0 73.7 0 75.2 0 75.2 0 74.5 0 74.4 0 75.4 0 73.7 0 74.3 0 75.0 0 75.8 0 76.7 0 76.8 0 76.8 0 76.4 0 76.4 0 77.2 0 77.2 0 77.4 0 78.1 0 78.5 0 77.9 0 78.6 0 79.8 0 80.3 0 80.8 0 80.5 0 79.4 0 79.3 0 79.6 0 79.2 0 79.1 0 79.8 0 80.0 0 80.5 0 80.4 0 81.1 0 82.2 0 81.5 0 84.2 0 84.3 0 83.3 0 84.2 0 84.9 0 85.0 0 85.3 0 85.4 0 85.8 0 85.2 0 86.4 0 88.2 0 88.3 0 88.0 0 87.8 0 87.4 0 87.4 0 88.0 0 88.0 0 89.9 0 88.4 0 89.7 0 89.9 0 90.5 0 90.7 0 89.5 0 91.2 0 91.2 0 89.8 0 89.6 0 92.3 0 90.1 0 92.9 0 93.3 0 93.5 0 93.4 0 93.6 0 93.7 0 93.6 0 93.0 0 94.1 0 95.7 0 95.6 0 97.2 0 98.1 0 98.8 0 95.3 0 95.3 0 96.7 0 99.2 0 99.0 0 100.9 0 100.1 0 100.4 0 100.5 0 102.6 0 101.8 0 102.6 0 101.0 0 101.6 0 100.6 0 100.4 0 100.7 0 100.6 0 100.3 0 101.4 0 103.2 0 79.2 1 83.4 1 86.5 1 91.3 1 91.5 1 93.1 1 93.1 1 93.3 1 94.4 1 94.4 1 94.1 1 95.3 1 93.8 1 96.3 1 96.0 1 97.6 1 96.8 1 95.0 1 93.7 1 91.0 1 92.2 1 93.6 1 97.2 1 97.1 1 98.2 1 98.3 1 99.8 1 100.5 1 99.2 1 101.0 1 102.1 1 102.8 1 102.5 1 104.2 1 104.3 1 105.3 1 105.1 1 107.4 1 106.4 1 106.4 1 107.9 1 107.8 1 108.3 1 108.3 1 109.2 1 109.3 1 109.3 1 109.6 1 111.1 1 109.0 1 109.8 1 108.8 1 110.9 1 110.2 1 111.3 1 111.6 1 112.3 1 111.2 1 111.7 1 111.7 1 112.7 1 113.2 1 113.0 1 114.2 1 114.0 1 111.7 1 114.2 1 114.7 1 116.5 1 116.2 1 116.2 1 117.4 1 117.4 1 118.2 1 116.4 1 117.3 1 117.1 1 116.5 1 117.4 1 118.2 1 118.4 1 116.9 1 116.3 1 116.8 1 114.9 1
 
Output produced by software:

Enter (or paste) a matrix (table) containing all data (time) series. Every column represents a different variable and must be delimited by a space or Tab. Every row represents a period in time (or category) and must be delimited by hard returns. The easiest way to enter data is to copy and paste a block of spreadsheet cells. Please, do not use commas or spaces to seperate groups of digits!


Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time6 seconds
R Server'George Udny Yule' @ 72.249.76.132


Multiple Linear Regression - Estimated Regression Equation
Y[t] = + 63.9321609475528 -9.4077985103804D[t] + 0.0812139011440611M1[t] -0.39903741099861M2[t] -0.431920302088629M3[t] -0.506908456336537M4[t] -0.287159768479184M5[t] -0.462147922727095M6[t] -0.126609761185535M7[t] + 0.18787576877708M8[t] -0.791965095450813M9[t] -0.472830709048046M10[t] -0.303082021190697M11[t] + 0.280251312142648t + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)63.93216094755280.76002484.118600
D-9.40779851038040.698854-13.461800
M10.08121390114406110.9062930.08960.9286810.464341
M2-0.399037410998610.906227-0.44030.660150.330075
M3-0.4319203020886290.906191-0.47660.6341170.317058
M4-0.5069084563365370.906185-0.55940.5764910.288245
M5-0.2871597684791840.906209-0.31690.7516480.375824
M6-0.4621479227270950.906264-0.50990.610620.30531
M7-0.1266097611855350.906348-0.13970.8890360.444518
M80.187875768777080.9064620.20730.8360050.418002
M9-0.7919650954508130.906238-0.87390.3831640.191582
M10-0.4728307090480460.918374-0.51490.6071920.303596
M11-0.3030820211906970.918329-0.330.74170.37085
t0.2802513121426480.00521753.717700


Multiple Linear Regression - Regression Statistics
Multiple R0.983683269108614
R-squared0.96763277392421
Adjusted R-squared0.96563858463992
F-TEST (value)485.226142546715
F-TEST (DF numerator)13
F-TEST (DF denominator)211
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation2.75494274730870
Sum Squared Residuals1601.4287131402


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
170.564.2936261608396.20637383916097
271.364.09362616083957.20637383916053
371.464.3409945818927.05900541810795
470.164.54625773978685.55374226021322
569.465.04625773978684.35374226021322
669.865.15152089768154.64847910231847
769.865.76731037136574.03268962863428
870.766.3620472134714.33795278652901
969.465.66245766138573.73754233861426
1069.866.26184335993113.53815664006884
1169.366.71184335993112.58815664006886
1272.967.29517669326455.60482330673551
137067.65664190655122.34335809344877
1464.467.4566419065511-3.05664190655113
1563.567.7040103276038-4.20401032760382
1669.867.90927348549861.89072651450143
1769.968.40927348549861.49072651450144
1869.368.51453664339330.785463356606697
1969.769.13032611707750.569673882922489
2069.869.72506295918280.074937040817228
2170.269.02547340709751.17452659290247
2269.869.6248591056430.175140894357057
2370.770.0748591056430.625140894357065
2471.470.65819243897630.741807561023727
2570.371.019657652263-0.719657652262989
2670.970.8196576522630.080342347737036
2770.671.0670260733156-0.467026073315606
286971.2722892312103-2.27228923121034
297171.7722892312103-0.772289231210344
3074.771.87755238910512.82244761089493
3177.572.49334186278935.00665813721072
3278.673.08807870489455.51192129510545
3375.372.38848915280932.91151084719069
3472.172.9878748513547-0.887874851354722
3573.873.43787485135470.362125148645284
3673.774.021208184688-0.321208184688050
3775.274.38267339797480.81732660202524
3875.274.18267339797481.01732660202526
3974.574.43004181902740.0699581809726243
4074.474.6353049769221-0.235304976922106
4175.475.13530497692210.264695023077889
4273.775.2405681348169-1.54056813481685
4374.375.856357608501-1.55635760850106
447576.4510944506063-1.45109445060632
4575.875.7515048985210.0484951014789138
4676.776.35089059706650.349109402933511
4776.876.8008905970665-0.000890597066493526
4876.877.3842239303998-0.584223930399833
4976.477.7456891436865-1.34568914368654
5076.477.5456891436865-1.14568914368652
5177.277.7930575647392-0.593057564739149
5277.277.9983207226339-0.798320722633886
5377.478.4983207226339-1.09832072263389
5478.178.6035838805286-0.503583880528637
5578.579.2193733542128-0.71937335421284
5677.979.8141101963181-1.91411019631810
5778.679.1145206442329-0.514520644232866
5879.879.71390634277830.0860936572217265
5980.380.16390634277830.136093657221729
6080.880.74723967611160.0527603238883879
6180.581.1087048893983-0.608704889398321
6279.480.9087048893983-1.50870488939830
6379.381.156073310451-1.85607331045093
6479.681.3613364683457-1.76133646834567
6579.281.8613364683457-2.66133646834567
6679.181.9665996262404-2.86659962624041
6779.882.5823890999246-2.78238909992462
688083.1771259420299-3.17712594202988
6980.582.4775363899446-1.97753638994464
7080.483.07692208849-2.67692208849004
7181.183.52692208849-2.42692208849005
7282.284.1102554218234-1.91025542182338
7381.584.4717206351101-2.9717206351101
7484.284.2717206351101-0.071720635110078
7584.384.5190890561627-0.219089056162711
7683.384.7243522140574-1.42435221405745
7784.285.2243522140574-1.02435221405745
7884.985.3296153719522-0.429615371952181
798585.9454048456364-0.945404845636397
8085.386.5401416877417-1.24014168774166
8185.485.8405521356564-0.440552135656411
8285.886.4399378342018-0.639937834201828
8385.286.8899378342018-1.68993783420182
8486.487.4732711675352-1.07327116753516
8588.287.83473638082190.365263619178126
8688.387.63473638082190.665263619178139
878887.88210480187450.117895198125512
8887.888.0873679597692-0.287367959769226
8987.488.5873679597692-1.18736795976922
9087.488.692631117664-1.29263111766396
918889.3084205913482-1.30842059134817
928889.9031574334534-1.90315743345344
9389.989.20356788136820.696432118631808
9488.489.8029535799136-1.40295357991360
9589.790.2529535799136-0.552953579913602
9689.990.836286913247-0.936286913246937
9790.591.1977521265337-0.697752126533656
9890.790.9977521265336-0.297752126533634
9989.591.2451205475863-1.74512054758626
10091.291.450383705481-0.250383705481003
10191.291.950383705481-0.750383705481009
10289.892.0556468633757-2.25564686337575
10389.692.67143633706-3.07143633705996
10492.393.2661731791652-0.96617317916522
10590.192.56658362708-2.46658362707998
10692.993.1659693256254-0.265969325625379
10793.393.6159693256254-0.315969325625390
10893.594.1993026589587-0.699302658958721
10993.494.5607678722454-1.16076787224542
11093.694.3607678722454-0.76076787224542
11193.794.608136293298-0.908136293298043
11293.694.8133994511928-1.21339945119279
1139395.3133994511928-2.31339945119279
11494.195.4186626090875-1.31866260908753
11595.796.0344520827717-0.334452082771732
11695.696.629188924877-1.02918892487700
11797.295.92959937279181.27040062720824
11898.196.52898507133721.57101492866282
11998.896.97898507133721.82101492866282
12095.397.5623184046705-2.26231840467051
12195.397.9237836179572-2.62378361795721
12296.797.7237836179572-1.02378361795719
12399.297.97115203900981.22884796099018
1249998.17641519690460.823584803095437
125100.998.67641519690462.22358480309544
126100.198.78167835479931.31832164520069
127100.499.39746782848351.00253217151650
128100.599.99220467058880.507795329411228
129102.699.29261511850353.30738488149646
130101.899.8920008170491.90799918295105
131102.6100.3420008170492.25799918295105
132101100.9253341503820.0746658496177176
133101.6101.2867993636690.313200636331007
134100.6101.086799363669-0.486799363668973
135100.4101.334167784722-0.934167784721591
136100.7101.539430942616-0.839430942616326
137100.6102.039430942616-1.43943094261634
138100.3102.144694100511-1.84469410051107
139101.4102.760483574195-1.36048357419528
140103.2103.355220416301-0.155220416300546
14179.293.2478323538349-14.0478323538349
14283.493.8472180523803-10.4472180523803
14386.594.2972180523803-7.79721805238031
14491.394.8805513857136-3.58055138571365
14591.595.2420165990004-3.74201659900036
14693.195.0420165990003-1.94201659900035
14793.195.289385020053-2.18938502005297
14893.395.4946481779477-2.19464817794770
14994.495.9946481779477-1.5946481779477
15094.496.0999113358424-1.69991133584244
15194.196.7157008095267-2.61570080952666
15295.397.310437651632-2.01043765163191
15393.896.6108480995467-2.81084809954667
15496.397.210233798092-0.910233798092086
1559697.6602337980921-1.66023379809208
15697.698.2435671314254-0.643567131425427
15796.898.605032344712-1.80503234471214
1589598.405032344712-3.40503234471212
15993.798.6524007657647-4.95240076576474
1609198.8576639236595-7.85766392365948
16192.299.3576639236595-7.15766392365948
16293.699.4629270815542-5.86292708155423
16397.2100.078716555238-2.87871655523843
16497.1100.673453397344-3.57345339734370
16598.299.9738638452584-1.77386384525845
16698.3100.573249543804-2.27324954380386
16799.8101.023249543804-1.22324954380386
168100.5101.606582877137-1.1065828771372
16999.2101.968048090424-2.76804809042391
170101101.768048090424-0.768048090423892
171102.1102.0154165114770.0845834885234738
172102.8102.2206796693710.579320330628738
173102.5102.720679669371-0.220679669371265
174104.2102.8259428272661.37405717273400
175104.3103.4417323009500.85826769904979
176105.3104.0364691430551.26353085694452
177105.1103.3368795909701.76312040902976
178107.4103.9362652895163.46373471048437
179106.4104.3862652895162.01373471048437
180106.4104.9695986228491.43040137715103
181107.9105.3310638361362.56893616386432
182107.8105.1310638361362.66893616386433
183108.3105.3784322571882.9215677428117
184108.3105.5836954150832.71630458491696
185109.2106.0836954150833.11630458491696
186109.3106.1889585729783.11104142702222
187109.3106.8047480466622.49525195333801
188109.6107.3994848887672.20051511123275
189111.1106.6998953366824.40010466331799
190109107.2992810352271.70071896477258
191109.8107.7492810352272.05071896477258
192108.8108.3326143685610.467385631439241
193110.9108.6940795818472.20592041815254
194110.2108.4940795818471.70592041815255
195111.3108.74144800292.55855199709992
196111.6108.9467111607952.65328883920518
197112.3109.4467111607952.85328883920518
198111.2109.5519743186901.64802568131045
199111.7110.1677637923741.53223620762624
200111.7110.7625006344790.937499365520977
201112.7110.0629110823942.63708891760622
202113.2110.6622967809392.53770321906081
203113111.1122967809391.88770321906081
204114.2111.6956301142732.50436988572747
205114112.0570953275591.94290467244075
206111.7111.857095327559-0.157095327559224
207114.2112.1044637486122.09553625138815
208114.7112.3097269065072.39027309349341
209116.5112.8097269065073.6902730934934
210116.2112.9149900644013.28500993559867
211116.2113.5307795380862.66922046191446
212117.4114.1255163801913.2744836198092
213117.4113.4259268281063.97407317189444
214118.2114.0253125266514.17468747334903
215116.4114.4753125266511.92468747334903
216117.3115.0586458599842.24135414001569
217117.1115.4201110732711.67988892672897
218116.5115.2201110732711.27988892672899
219117.4115.4674794943241.93252050567637
220118.2115.6727426522182.52725734778163
221118.4116.1727426522182.22725734778163
222116.9116.2780058101130.621994189886894
223116.3116.893795283797-0.593795283797326
224116.8117.488532125903-0.688532125902585
225114.9116.788942573817-1.88894257381734


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
170.860536202802460.2789275943950790.139463797197540
180.7967375194955580.4065249610088830.203262480504442
190.7313452559271740.5373094881456530.268654744072826
200.6347775942387910.7304448115224180.365222405761209
210.590795033602450.81840993279510.40920496639755
220.5088004654255720.9823990691488550.491199534574428
230.4779445575378760.9558891150757530.522055442462124
240.3864703983549170.7729407967098340.613529601645083
250.3339522729806140.6679045459612290.666047727019386
260.428610306461810.857220612923620.57138969353819
270.4702067310354440.9404134620708880.529793268964556
280.3928476903166120.7856953806332250.607152309683388
290.3399850487177970.6799700974355950.660014951282203
300.4961432786505030.9922865573010060.503856721349497
310.8001871203965420.3996257592069170.199812879603458
320.9474443539668130.1051112920663740.052555646033187
330.9603439155454530.07931216890909380.0396560844545469
340.9457085455651350.1085829088697310.0542914544348653
350.9356504689492140.1286990621015720.0643495310507862
360.9176742596171770.1646514807656460.0823257403828229
370.9124287679637560.1751424640724890.0875712320362443
380.921611978916680.1567760421666400.0783880210833198
390.9187773683807310.1624452632385370.0812226316192686
400.9034206964982420.1931586070035150.0965793035017576
410.8925153573156370.2149692853687250.107484642684363
420.8720776300714660.2558447398570670.127922369928534
430.8535909532109090.2928180935781830.146409046789091
440.8332156707735570.3335686584528860.166784329226443
450.8113181993151230.3773636013697540.188681800684877
460.8124305018774860.3751389962450270.187569498122514
470.7994451852262310.4011096295475380.200554814773769
480.7697910917791970.4604178164416060.230208908220803
490.7339269379116070.5321461241767860.266073062088393
500.7032219184574780.5935561630850440.296778081542522
510.6964085675767290.6071828648465420.303591432423271
520.6708761495071940.6582477009856120.329123850492806
530.636999214387030.7260015712259410.363000785612971
540.6125697661522430.7748604676955140.387430233847757
550.582106381058790.835787237882420.41789361894121
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610.5066578699007740.9866842601984510.493342130099226
620.4731375898396510.9462751796793030.526862410160349
630.4372870501724680.8745741003449370.562712949827532
640.3995987008062970.7991974016125930.600401299193703
650.3563537898009410.7127075796018810.64364621019906
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670.2839472645542970.5678945291085940.716052735445703
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690.2202247471699820.4404494943399650.779775252830018
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710.1590723638673210.3181447277346410.84092763613268
720.1348549612301480.2697099224602960.865145038769852
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750.1632119304434180.3264238608868360.836788069556582
760.1511384528047440.3022769056094880.848861547195256
770.1477507686837980.2955015373675960.852249231316202
780.1531484497513980.3062968995027960.846851550248602
790.1444879017146480.2889758034292960.855512098285352
800.1326316960946290.2652633921892580.867368303905371
810.1296505788054010.2593011576108020.870349421194599
820.1286733865886570.2573467731773130.871326613411343
830.1117002637836300.2234005275672590.88829973621637
840.09986036311682230.1997207262336450.900139636883178
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860.1541775496599790.3083550993199580.845822450340021
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880.1833154824530860.3666309649061720.816684517546914
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900.1525167945765000.3050335891530010.8474832054235
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930.134919891318480.269839782636960.86508010868152
940.1183570295490180.2367140590980360.881642970450982
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960.1000314395031390.2000628790062780.89996856049686
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980.09063011712800640.1812602342560130.909369882871994
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1000.07682374794048380.1536474958809680.923176252059516
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1080.02661521603128630.05323043206257260.973384783968714
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1190.01460052098463120.02920104196926240.985399479015369
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1350.02741400102747100.05482800205494210.972585998972529
1360.02186143114565350.04372286229130690.978138568854346
1370.01710009147635580.03420018295271160.982899908523644
1380.01350249749018600.02700499498037200.986497502509814
1390.01050029506408890.02100059012817780.98949970493591
1400.00835819935876350.0167163987175270.991641800641236
1410.0798489640117870.1596979280235740.920151035988213
1420.2639999787533410.5279999575066820.73600002124666
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1440.4965329568966890.9930659137933770.503467043103311
1450.5335962649260150.932807470147970.466403735073985
1460.581177891527110.837644216945780.41882210847289
1470.5969699466046460.8060601067907070.403030053395354
1480.5948369209317250.810326158136550.405163079068275
1490.598615824282980.802768351434040.40138417571702
1500.5902409853573970.8195180292852050.409759014642603
1510.5601411055231290.8797177889537420.439858894476871
1520.5354627664091590.9290744671816810.464537233590841
1530.5065430012582950.986913997483410.493456998741705
1540.4952244958190290.9904489916380590.504775504180971
1550.4657650250079320.9315300500158640.534234974992068
1560.4507043118934760.9014086237869520.549295688106524
1570.4160753117719480.8321506235438960.583924688228052
1580.3858230884451950.7716461768903910.614176911554805
1590.435597413684150.87119482736830.56440258631585
1600.7397444485662060.5205111028675890.260255551433794
1610.9357649471680110.1284701056639780.0642350528319889
1620.985903207293840.02819358541231890.0140967927061595
1630.9883980184235920.02320396315281580.0116019815764079
1640.9935290755711030.01294184885779380.0064709244288969
1650.9954770993978210.009045801204357520.00452290060217876
1660.9988230054268460.002353989146307260.00117699457315363
1670.9991819857384250.001636028523148980.00081801426157449
1680.9993510184261250.001297963147750100.000648981573875051
1690.9999202342798980.0001595314402048057.97657201024025e-05
1700.999936441718010.0001271165639820336.35582819910166e-05
1710.9999630094179557.39811640896351e-053.69905820448176e-05
1720.9999777052498744.45895002519878e-052.22947501259939e-05
1730.9999968235687586.35286248379475e-063.17643124189738e-06
1740.9999970360213865.92795722818127e-062.96397861409063e-06
1750.999996796474876.40705026063755e-063.20352513031878e-06
1760.9999958466309828.30673803532562e-064.15336901766281e-06
1770.9999958785896368.24282072861379e-064.12141036430689e-06
1780.99999498321131.00335774020907e-055.01678870104533e-06
1790.999992722210311.45555793795681e-057.27778968978406e-06
1800.9999900450809591.99098380825132e-059.95491904125662e-06
1810.9999846709810853.06580378296187e-051.53290189148093e-05
1820.999978318102964.33637940785498e-052.16818970392749e-05
1830.9999661185144836.77629710330991e-053.38814855165496e-05
1840.9999489893660840.0001020212678317145.1010633915857e-05
1850.9999257751189650.0001484497620701397.42248810350693e-05
1860.999879960803580.0002400783928405190.000120039196420260
1870.9997945500071860.0004108999856289090.000205449992814455
1880.9996355135921550.000728972815690550.000364486407845275
1890.9996906538434460.0006186923131078360.000309346156553918
1900.999687817412060.0006243651758805650.000312182587940282
1910.9994264788354270.001147042329144920.000573521164572462
1920.9995449127471070.0009101745057860540.000455087252893027
1930.9991452956602540.001709408679492310.000854704339746156
1940.9983516367969870.003296726406026060.00164836320301303
1950.996988409150840.006023181698321050.00301159084916052
1960.9948413932139610.01031721357207780.00515860678603892
1970.9919463402730160.01610731945396700.00805365972698352
1980.988179184884190.02364163023161960.0118208151158098
1990.9799757248561220.04004855028775590.0200242751438779
2000.9743447523149740.05131049537005260.0256552476850263
2010.9554322370981560.08913552580368770.0445677629018438
2020.9558092201328180.08838155973436440.0441907798671822
2030.9327488042446490.1345023915107020.067251195755351
2040.896462008037230.2070759839255390.103537991962769
2050.845952466285580.308095067428840.15404753371442
2060.8726577205848260.2546845588303470.127342279415173
2070.8417196814979010.3165606370041980.158280318502099
2080.8718422505124720.2563154989750550.128157749487528


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level310.161458333333333NOK
5% type I error level630.328125NOK
10% type I error level790.411458333333333NOK
 
Charts produced by software:
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/29/t1227952436w6ik90cxq7qlvf0/108etj1227952310.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/29/t1227952436w6ik90cxq7qlvf0/108etj1227952310.ps (open in new window)


http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/29/t1227952436w6ik90cxq7qlvf0/1eq0h1227952310.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/29/t1227952436w6ik90cxq7qlvf0/1eq0h1227952310.ps (open in new window)


http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/29/t1227952436w6ik90cxq7qlvf0/2uh3d1227952310.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/29/t1227952436w6ik90cxq7qlvf0/2uh3d1227952310.ps (open in new window)


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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/29/t1227952436w6ik90cxq7qlvf0/3etft1227952310.ps (open in new window)


http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/29/t1227952436w6ik90cxq7qlvf0/4ci4d1227952310.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/29/t1227952436w6ik90cxq7qlvf0/4ci4d1227952310.ps (open in new window)


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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/29/t1227952436w6ik90cxq7qlvf0/52zf31227952310.ps (open in new window)


http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/29/t1227952436w6ik90cxq7qlvf0/66h3u1227952310.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/29/t1227952436w6ik90cxq7qlvf0/66h3u1227952310.ps (open in new window)


http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/29/t1227952436w6ik90cxq7qlvf0/7m2xk1227952310.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/29/t1227952436w6ik90cxq7qlvf0/7m2xk1227952310.ps (open in new window)


http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/29/t1227952436w6ik90cxq7qlvf0/8lg2a1227952310.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/29/t1227952436w6ik90cxq7qlvf0/8lg2a1227952310.ps (open in new window)


http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/29/t1227952436w6ik90cxq7qlvf0/9x8d71227952310.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/29/t1227952436w6ik90cxq7qlvf0/9x8d71227952310.ps (open in new window)


 
Parameters (Session):
par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;
 
Parameters (R input):
par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;
 
R code (references can be found in the software module):
library(lattice)
library(lmtest)
n25 <- 25 #minimum number of obs. for Goldfeld-Quandt test
par1 <- as.numeric(par1)
x <- t(y)
k <- length(x[1,])
n <- length(x[,1])
x1 <- cbind(x[,par1], x[,1:k!=par1])
mycolnames <- c(colnames(x)[par1], colnames(x)[1:k!=par1])
colnames(x1) <- mycolnames #colnames(x)[par1]
x <- x1
if (par3 == 'First Differences'){
x2 <- array(0, dim=c(n-1,k), dimnames=list(1:(n-1), paste('(1-B)',colnames(x),sep='')))
for (i in 1:n-1) {
for (j in 1:k) {
x2[i,j] <- x[i+1,j] - x[i,j]
}
}
x <- x2
}
if (par2 == 'Include Monthly Dummies'){
x2 <- array(0, dim=c(n,11), dimnames=list(1:n, paste('M', seq(1:11), sep ='')))
for (i in 1:11){
x2[seq(i,n,12),i] <- 1
}
x <- cbind(x, x2)
}
if (par2 == 'Include Quarterly Dummies'){
x2 <- array(0, dim=c(n,3), dimnames=list(1:n, paste('Q', seq(1:3), sep ='')))
for (i in 1:3){
x2[seq(i,n,4),i] <- 1
}
x <- cbind(x, x2)
}
k <- length(x[1,])
if (par3 == 'Linear Trend'){
x <- cbind(x, c(1:n))
colnames(x)[k+1] <- 't'
}
x
k <- length(x[1,])
df <- as.data.frame(x)
(mylm <- lm(df))
(mysum <- summary(mylm))
if (n > n25) {
kp3 <- k + 3
nmkm3 <- n - k - 3
gqarr <- array(NA, dim=c(nmkm3-kp3+1,3))
numgqtests <- 0
numsignificant1 <- 0
numsignificant5 <- 0
numsignificant10 <- 0
for (mypoint in kp3:nmkm3) {
j <- 0
numgqtests <- numgqtests + 1
for (myalt in c('greater', 'two.sided', 'less')) {
j <- j + 1
gqarr[mypoint-kp3+1,j] <- gqtest(mylm, point=mypoint, alternative=myalt)$p.value
}
if (gqarr[mypoint-kp3+1,2] < 0.01) numsignificant1 <- numsignificant1 + 1
if (gqarr[mypoint-kp3+1,2] < 0.05) numsignificant5 <- numsignificant5 + 1
if (gqarr[mypoint-kp3+1,2] < 0.10) numsignificant10 <- numsignificant10 + 1
}
gqarr
}
bitmap(file='test0.png')
plot(x[,1], type='l', main='Actuals and Interpolation', ylab='value of Actuals and Interpolation (dots)', xlab='time or index')
points(x[,1]-mysum$resid)
grid()
dev.off()
bitmap(file='test1.png')
plot(mysum$resid, type='b', pch=19, main='Residuals', ylab='value of Residuals', xlab='time or index')
grid()
dev.off()
bitmap(file='test2.png')
hist(mysum$resid, main='Residual Histogram', xlab='values of Residuals')
grid()
dev.off()
bitmap(file='test3.png')
densityplot(~mysum$resid,col='black',main='Residual Density Plot', xlab='values of Residuals')
dev.off()
bitmap(file='test4.png')
qqnorm(mysum$resid, main='Residual Normal Q-Q Plot')
qqline(mysum$resid)
grid()
dev.off()
(myerror <- as.ts(mysum$resid))
bitmap(file='test5.png')
dum <- cbind(lag(myerror,k=1),myerror)
dum
dum1 <- dum[2:length(myerror),]
dum1
z <- as.data.frame(dum1)
z
plot(z,main=paste('Residual Lag plot, lowess, and regression line'), ylab='values of Residuals', xlab='lagged values of Residuals')
lines(lowess(z))
abline(lm(z))
grid()
dev.off()
bitmap(file='test6.png')
acf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Autocorrelation Function')
grid()
dev.off()
bitmap(file='test7.png')
pacf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Partial Autocorrelation Function')
grid()
dev.off()
bitmap(file='test8.png')
opar <- par(mfrow = c(2,2), oma = c(0, 0, 1.1, 0))
plot(mylm, las = 1, sub='Residual Diagnostics')
par(opar)
dev.off()
if (n > n25) {
bitmap(file='test9.png')
plot(kp3:nmkm3,gqarr[,2], main='Goldfeld-Quandt test',ylab='2-sided p-value',xlab='breakpoint')
grid()
dev.off()
}
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Estimated Regression Equation', 1, TRUE)
a<-table.row.end(a)
myeq <- colnames(x)[1]
myeq <- paste(myeq, '[t] = ', sep='')
for (i in 1:k){
if (mysum$coefficients[i,1] > 0) myeq <- paste(myeq, '+', '')
myeq <- paste(myeq, mysum$coefficients[i,1], sep=' ')
if (rownames(mysum$coefficients)[i] != '(Intercept)') {
myeq <- paste(myeq, rownames(mysum$coefficients)[i], sep='')
if (rownames(mysum$coefficients)[i] != 't') myeq <- paste(myeq, '[t]', sep='')
}
}
myeq <- paste(myeq, ' + e[t]')
a<-table.row.start(a)
a<-table.element(a, myeq)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,hyperlink('http://www.xycoon.com/ols1.htm','Multiple Linear Regression - Ordinary Least Squares',''), 6, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Variable',header=TRUE)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'S.D.',header=TRUE)
a<-table.element(a,'T-STAT<br />H0: parameter = 0',header=TRUE)
a<-table.element(a,'2-tail p-value',header=TRUE)
a<-table.element(a,'1-tail p-value',header=TRUE)
a<-table.row.end(a)
for (i in 1:k){
a<-table.row.start(a)
a<-table.element(a,rownames(mysum$coefficients)[i],header=TRUE)
a<-table.element(a,mysum$coefficients[i,1])
a<-table.element(a, round(mysum$coefficients[i,2],6))
a<-table.element(a, round(mysum$coefficients[i,3],4))
a<-table.element(a, round(mysum$coefficients[i,4],6))
a<-table.element(a, round(mysum$coefficients[i,4]/2,6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Regression Statistics', 2, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Multiple R',1,TRUE)
a<-table.element(a, sqrt(mysum$r.squared))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'R-squared',1,TRUE)
a<-table.element(a, mysum$r.squared)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Adjusted R-squared',1,TRUE)
a<-table.element(a, mysum$adj.r.squared)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (value)',1,TRUE)
a<-table.element(a, mysum$fstatistic[1])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (DF numerator)',1,TRUE)
a<-table.element(a, mysum$fstatistic[2])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (DF denominator)',1,TRUE)
a<-table.element(a, mysum$fstatistic[3])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'p-value',1,TRUE)
a<-table.element(a, 1-pf(mysum$fstatistic[1],mysum$fstatistic[2],mysum$fstatistic[3]))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Residual Statistics', 2, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Residual Standard Deviation',1,TRUE)
a<-table.element(a, mysum$sigma)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Sum Squared Residuals',1,TRUE)
a<-table.element(a, sum(myerror*myerror))
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable3.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Actuals, Interpolation, and Residuals', 4, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Time or Index', 1, TRUE)
a<-table.element(a, 'Actuals', 1, TRUE)
a<-table.element(a, 'Interpolation<br />Forecast', 1, TRUE)
a<-table.element(a, 'Residuals<br />Prediction Error', 1, TRUE)
a<-table.row.end(a)
for (i in 1:n) {
a<-table.row.start(a)
a<-table.element(a,i, 1, TRUE)
a<-table.element(a,x[i])
a<-table.element(a,x[i]-mysum$resid[i])
a<-table.element(a,mysum$resid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable4.tab')
if (n > n25) {
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Goldfeld-Quandt test for Heteroskedasticity',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'p-values',header=TRUE)
a<-table.element(a,'Alternative Hypothesis',3,header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'breakpoint index',header=TRUE)
a<-table.element(a,'greater',header=TRUE)
a<-table.element(a,'2-sided',header=TRUE)
a<-table.element(a,'less',header=TRUE)
a<-table.row.end(a)
for (mypoint in kp3:nmkm3) {
a<-table.row.start(a)
a<-table.element(a,mypoint,header=TRUE)
a<-table.element(a,gqarr[mypoint-kp3+1,1])
a<-table.element(a,gqarr[mypoint-kp3+1,2])
a<-table.element(a,gqarr[mypoint-kp3+1,3])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable5.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Description',header=TRUE)
a<-table.element(a,'# significant tests',header=TRUE)
a<-table.element(a,'% significant tests',header=TRUE)
a<-table.element(a,'OK/NOK',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'1% type I error level',header=TRUE)
a<-table.element(a,numsignificant1)
a<-table.element(a,numsignificant1/numgqtests)
if (numsignificant1/numgqtests < 0.01) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'5% type I error level',header=TRUE)
a<-table.element(a,numsignificant5)
a<-table.element(a,numsignificant5/numgqtests)
if (numsignificant5/numgqtests < 0.05) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'10% type I error level',header=TRUE)
a<-table.element(a,numsignificant10)
a<-table.element(a,numsignificant10/numgqtests)
if (numsignificant10/numgqtests < 0.1) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable6.tab')
}
 





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Software written by Ed van Stee & Patrick Wessa


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