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*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, 09 Dec 2010 19:58:40 +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/09/t12919246007ftftu67h2p1ey7.htm/, Retrieved Thu, 09 Dec 2010 20:56:52 +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/09/t12919246007ftftu67h2p1ey7.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 «
235.1 280.7 264.6 240.7 201.4 240.8 241.1 223.8 206.1 174.7 203.3 220.5 299.5 347.4 338.3 327.7 351.6 396.6 438.8 395.6 363.5 378.8 357 369 464.8 479.1 431.3 366.5 326.3 355.1 331.6 261.3 249 205.5 235.6 240.9 264.9 253.8 232.3 193.8 177 213.2 207.2 180.6 188.6 175.4 199 179.6 225.8 234 200.2 183.6 178.2 203.2 208.5 191.8 172.8 148 159.4 154.5 213.2 196.4 182.8 176.4 153.6 173.2 171 151.2 161.9 157.2 201.7 236.4 356.1 398.3 403.7 384.6 365.8 368.1 367.9 347 343.3 292.9 311.5 300.9 366.9 356.9 329.7 316.2 269 289.3 266.2 253.6 233.8 228.4 253.6 260.1 306.6 309.2 309.5 271 279.9 317.9 298.4 246.7 227.3 209.1 259.9 266 320.6 308.5 282.2 262.7 263.5 313.1 284.3 252.6 250.3 246.5 312.7 333.2 446.4 511.6 515.5 506.4 483.2 522.3 509.8 460.7 405.8 375 378.5 406.8 467.8 469.8 429.8 355.8 332.7 378 360.5 334.7 319.5 323.1 363.6 352.1 411.9 388.6 416.4 360.7 338 417.2 388. 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 time23 seconds
R Server'George Udny Yule' @ 72.249.76.132


Multiple Linear Regression - Estimated Regression Equation
unemployment[t] = + 176.343118279570 + 72.2415821012546M1[t] + 81.1193268369179M2[t] + 57.8325554435488M3[t] + 17.8909453405018M4[t] -3.66679379480305M5[t] + 68.0399831989246M6[t] + 44.2499859991041M7[t] + 12.0857952508962M8[t] -6.03968581989235M9[t] -22.5006507616486M10[t] -1.44871247759849M11[t] + 1.01902945788530t + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)176.34311827957021.5824958.170700
M172.241582101254627.1256712.66320.0080880.004044
M281.119326836917927.1246422.99060.0029760.001488
M357.832555443548827.123712.13220.0336710.016835
M417.890945340501827.1228760.65960.5099170.254959
M5-3.6667937948030527.122141-0.13520.8925330.446267
M668.039983198924627.1215032.50870.0125570.006279
M744.249985999104127.1209641.63160.1036450.051823
M812.085795250896227.1205220.44560.6561310.328066
M9-6.0396858198923527.120179-0.22270.8238950.411948
M10-22.500650761648627.119934-0.82970.4072760.203638
M11-1.4487124775984927.119787-0.05340.9574280.478714
t1.019029457885300.05157719.757600


Multiple Linear Regression - Regression Statistics
Multiple R0.735625547908382
R-squared0.541144946735507
Adjusted R-squared0.525807173367334
F-TEST (value)35.2818452682604
F-TEST (DF numerator)12
F-TEST (DF denominator)359
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation106.770513988965
Sum Squared Residuals4092579.41403091


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
1235.1249.603729838712-14.5037298387122
2280.7259.50050403225921.1994959677414
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10174.7164.03276209677410.6672379032258
11203.3186.1037298387117.1962701612899
12220.5188.57147177419431.9285282258064
13299.5261.83208333333237.6679166666677
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32261.3221.03785618279640.2621438172043
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300411.6482.051955645161-70.4519556451612
301467.5555.312567204301-87.812567204301
302484.5565.209341397849-80.7093413978495
303451.2542.941599462366-91.7415994623656
304417.4504.019018817204-86.6190188172043
305379.9483.480309139785-103.580309139785
306484.7556.206115591398-71.5061155913979
307455533.435147849462-78.4351478494624
308420.8502.28998655914-81.4899865591398
309416.5485.183534946236-68.6835349462365
310376.3469.741599462366-93.4415994623656
311405.6491.812567204301-86.212567204301
312405.8494.280309139785-88.4803091397849
313500.8567.540920698925-66.7409206989247
314514577.437694892473-63.4376948924731
315475.5555.169952956989-79.6699529569892
316430.1516.247372311828-86.1473723118279
317414.4495.708662634409-81.3086626344086
318538568.434469086022-30.4344690860215
319526545.663501344086-19.663501344086
320488.5514.518340053763-26.0183400537635
321520.2497.4118884408622.7881115591399
322504.4481.96995295698922.4300470430108
323568.5504.04092069892564.4590793010754
324610.6506.508662634408104.091337365592
325818579.769274193548238.230725806452
326830.9589.666048387097241.233951612903
327835.9567.398306451613268.501693548387
328782528.475725806452253.524274193548
329762.3507.937016129032254.362983870968
330856.9580.662822580645276.237177419355
331820.9557.89185483871263.00814516129
332769.6526.746693548387242.853306451613
333752.2509.640241935484242.559758064516
334724.4494.198306451613230.201693548387
335723.1516.269274193548206.830725806452
336719.5518.737016129032200.762983870968
337817.4591.997627688172225.402372311828
338803.3601.89440188172201.405598118280
339752.5579.626659946237172.873340053763
340689540.704079301075148.295920698925
341630.4520.165369623656110.234630376344
342765.5592.891176075269172.608823924731
343757.7570.120208333333187.579791666667
344732.2538.975047043011193.224952956989
345702.6521.868595430107180.731404569893
346683.3506.426659946237176.873340053763
347709.5528.497627688172181.002372311828
348702.2530.965369623656171.234630376344
349784.8604.225981182796180.574018817204
350810.9614.122755376344196.777244623656
351755.6591.85501344086163.744986559140
352656.8552.932432795699103.867567204301
353615.1532.3937231182882.7062768817205
354745.3605.119529569893140.180470430107
355694.1582.348561827957111.751438172043
356675.7551.203400537634124.496599462366
357643.7534.096948924731109.603051075269
358622.1518.65501344086103.444986559140
359634.6540.72598118279693.8740188172043
360588543.19372311827944.8062768817206
361689.7616.4543346774273.2456653225807
362673.9626.35110887096847.5488911290322
363647.9604.08336693548443.8166330645161
364568.8565.1607862903223.6392137096775
365545.7544.6220766129031.07792338709684
366632.6617.34788306451615.2521169354839
367643.8594.57691532258149.2230846774193
368593.1563.43175403225829.6682459677420
369579.7546.32530241935533.3746975806452
370546530.88336693548415.1166330645162
371562.9552.9543346774199.94566532258072
372572.5555.42207661290317.0779233870969


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
160.0003991785126358250.000798357025271650.999600821487364
170.005459916818604510.01091983363720900.994540083181396
180.004117537829651930.008235075659303860.995882462170348
190.006375702376061250.01275140475212250.993624297623939
200.00338128175511520.00676256351023040.996618718244885
210.001357249370888160.002714498741776320.998642750629112
220.001146449409417550.002292898818835100.998853550590582
230.0004207207535566920.0008414415071133840.999579279246443
240.0001456653027827980.0002913306055655970.999854334697217
254.85615086243534e-059.71230172487067e-050.999951438491376
262.18707346218092e-054.37414692436184e-050.999978129265378
271.93823739557943e-053.87647479115885e-050.999980617626044
285.35346640481e-050.00010706932809620.999946465335952
290.0001894435905629150.000378887181125830.999810556409437
300.0004447663734047050.000889532746809410.999555233626595
310.001680610518826110.003361221037652210.998319389481174
320.00676285371772790.01352570743545580.993237146282272
330.01221291887378020.02442583774756050.98778708112622
340.02547333748168150.05094667496336290.974526662518319
350.03140855191180600.06281710382361190.968591448088194
360.03771295359303090.07542590718606180.962287046406969
370.05800570427692990.1160114085538600.94199429572307
380.1024909826622260.2049819653244520.897509017337774
390.1387262563952250.2774525127904510.861273743604775
400.1695034664536960.3390069329073910.830496533546304
410.1886705218242740.3773410436485470.811329478175726
420.2005141871951450.4010283743902890.799485812804855
430.2135317376368490.4270634752736970.786468262363151
440.2082083451441140.4164166902882270.791791654855886
450.1857449885472860.3714899770945730.814255011452714
460.1615205326405130.3230410652810270.838479467359487
470.1361636816428350.272327363285670.863836318357165
480.1206461398948270.2412922797896530.879353860105173
490.1033166531609910.2066333063219820.89668334683901
500.090432455207830.180864910415660.90956754479217
510.08017689970096010.160353799401920.91982310029904
520.0667730716451810.1335461432903620.933226928354819
530.0535761136714980.1071522273429960.946423886328502
540.04385962037653830.08771924075307660.956140379623462
550.03508237700583820.07016475401167650.964917622994162
560.02681128194134350.0536225638826870.973188718058656
570.02038222062392810.04076444124785630.979617779376072
580.0154841434686790.0309682869373580.98451585653132
590.01173796776175440.02347593552350890.988262032238246
600.00897149261060930.01794298522121860.99102850738939
610.006598153554830220.01319630710966040.99340184644517
620.005225848261931360.01045169652386270.994774151738069
630.003953849484281460.007907698968562930.996046150515719
640.002817605323173240.005635210646346490.997182394676827
650.002002056408367140.004004112816734290.997997943591633
660.001505016563831180.003010033127662360.998494983436169
670.001114071150717340.002228142301434680.998885928849283
680.0007896166761080560.001579233352216110.999210383323892
690.0005406139080128350.001081227816025670.999459386091987
700.000371214342230060.000742428684460120.99962878565777
710.000272738233522260.000545476467044520.999727261766478
720.0002331912550853270.0004663825101706540.999766808744915
730.0004118396391897250.000823679278379450.99958816036081
740.0008765142195833210.001753028439166640.999123485780417
750.002194295044982930.004388590089965870.997805704955017
760.004899727909204290.009799455818408570.995100272090796
770.009050973519486090.01810194703897220.990949026480514
780.01137393500831140.02274787001662280.988626064991689
790.01358488102658220.02716976205316430.986415118973418
800.01672881605304840.03345763210609690.983271183946952
810.02073804194011110.04147608388022210.979261958059889
820.02082970026079970.04165940052159950.9791702997392
830.02050927560989080.04101855121978150.97949072439011
840.01866329175601130.03732658351202260.981336708243989
850.01718754560287870.03437509120575740.982812454397121
860.01440515419985190.02881030839970380.985594845800148
870.01177998166123430.02355996332246870.988220018338766
880.009928386294227590.01985677258845520.990071613705772
890.007809531498357740.01561906299671550.992190468501642
900.006022653077125710.01204530615425140.993977346922874
910.004580369259972080.009160738519944150.995419630740028
920.003458106553908010.006916213107816020.996541893446092
930.002585248024110950.00517049604822190.997414751975889
940.001931429821845650.00386285964369130.998068570178154
950.001440475517741780.002880951035483550.998559524482258
960.001069195292290140.002138390584580280.99893080470771
970.0007791116190797180.001558223238159440.99922088838092
980.0005631927536277620.001126385507255520.999436807246372
990.000406710969255290.000813421938510580.999593289030745
1000.0002895535781725210.0005791071563450420.999710446421827
1010.0002126651401810340.0004253302803620690.99978733485982
1020.0001571402113547420.0003142804227094840.999842859788645
1030.0001112533536989230.0002225067073978460.999888746646301
1047.72868560652615e-050.0001545737121305230.999922713143935
1055.3496906692715e-050.000106993813385430.999946503093307
1063.67874561006927e-057.35749122013853e-050.9999632125439
1072.53937331283655e-055.07874662567309e-050.999974606266872
1081.74397854759989e-053.48795709519979e-050.999982560214524
1091.18413435256532e-052.36826870513064e-050.999988158656474
1107.96619132592526e-061.59323826518505e-050.999992033808674
1115.36755535482594e-061.07351107096519e-050.999994632444645
1123.5412713241476e-067.0825426482952e-060.999996458728676
1132.32189338924435e-064.64378677848871e-060.99999767810661
1141.57196323725913e-063.14392647451826e-060.999998428036763
1151.02104880155917e-062.04209760311834e-060.999998978951198
1166.59109172687584e-071.31821834537517e-060.999999340890827
1174.22704330627277e-078.45408661254553e-070.99999957729567
1182.75955080694566e-075.51910161389133e-070.99999972404492
1192.15330693461612e-074.30661386923224e-070.999999784669307
1201.8604866596728e-073.7209733193456e-070.999999813951334
1212.70602516879263e-075.41205033758526e-070.999999729397483
1228.0811693741337e-071.61623387482674e-060.999999191883063
1233.0624279935591e-066.1248559871182e-060.999996937572006
1241.34320135237388e-052.68640270474776e-050.999986567986476
1254.46655500078963e-058.93311000157926e-050.999955334449992
1260.0001197760134387950.000239552026877590.99988022398656
1270.0002800730405976970.0005601460811953940.999719926959402
1280.0004963991562669220.0009927983125338440.999503600843733
1290.0005936114241772910.001187222848354580.999406388575823
1300.0006388656134687970.001277731226937590.999361134386531
1310.0006048980657467280.001209796131493460.999395101934253
1320.0006531668316947750.001306333663389550.999346833168305
1330.0006652421699488910.001330484339897780.999334757830051
1340.0006376682453645040.001275336490729010.999362331754636
1350.0005591769772429970.001118353954485990.999440823022757
1360.0004445371814606550.000889074362921310.99955546281854
1370.0003529305840741370.0007058611681482730.999647069415926
1380.0002651718419933760.0005303436839867520.999734828158007
1390.0002003351414960260.0004006702829920510.999799664858504
1400.0001514781842739420.0003029563685478840.999848521815726
1410.0001145221406488330.0002290442812976660.99988547785935
1428.97027561842686e-050.0001794055123685370.999910297243816
1437.43557326688881e-050.0001487114653377760.999925644267331
1445.87440787828728e-050.0001174881575657460.999941255921217
1454.4763985718145e-058.952797143629e-050.999955236014282
1463.31680421771903e-056.63360843543806e-050.999966831957823
1472.63672292067048e-055.27344584134096e-050.999973632770793
1482.03512226304026e-054.07024452608053e-050.99997964877737
1491.57496546633976e-053.14993093267951e-050.999984250345337
1501.21265046191535e-052.42530092383069e-050.99998787349538
1519.12600146918587e-061.82520029383717e-050.99999087399853
1527.14785279332256e-061.42957055866451e-050.999992852147207
1535.2776279607864e-061.05552559215728e-050.99999472237204
1544.40640381640768e-068.81280763281536e-060.999995593596184
1554.12499719819859e-068.24999439639718e-060.999995875002802
1565.64132172378465e-061.12826434475693e-050.999994358678276
1578.98498626418482e-061.79699725283696e-050.999991015013736
1581.81013353041292e-053.62026706082584e-050.999981898664696
1593.49835891964552e-056.99671783929103e-050.999965016410804
1605.71391145673299e-050.0001142782291346600.999942860885433
1619.31857227369458e-050.0001863714454738920.999906814277263
1620.0001478826855773530.0002957653711547060.999852117314423
1630.0002063179502475590.0004126359004951190.999793682049752
1640.0002480517960005720.0004961035920011440.999751948204
1650.0002612048880260860.0005224097760521720.999738795111974
1660.0002764528026438810.0005529056052877610.999723547197356
1670.0002789449012465260.0005578898024930520.999721055098753
1680.0003004059553491460.0006008119106982920.99969959404465
1690.0002990310154055470.0005980620308110940.999700968984594
1700.0002819456338474210.0005638912676948430.999718054366153
1710.0002794313672544620.0005588627345089240.999720568632745
1720.0002834838243198280.0005669676486396550.99971651617568
1730.0003253319939609030.0006506639879218060.999674668006039
1740.0002889902089234370.0005779804178468740.999711009791077
1750.0002632399061994810.0005264798123989620.9997367600938
1760.0002561811544578300.0005123623089156590.999743818845542
1770.0002373335280985680.0004746670561971370.999762666471901
1780.0002198350973174820.0004396701946349650.999780164902683
1790.0002234737786843040.0004469475573686080.999776526221316
1800.0002391893736143140.0004783787472286290.999760810626386
1810.0002615803435903710.0005231606871807420.99973841965641
1820.0003157299521959460.0006314599043918920.999684270047804
1830.0003633020190540110.0007266040381080220.999636697980946
1840.0004309605611010240.0008619211222020480.999569039438899
1850.0005763478028281280.001152695605656260.999423652197172
1860.000624092508535560.001248185017071120.999375907491464
1870.0006654463377210240.001330892675442050.999334553662279
1880.0007061806382955750.001412361276591150.999293819361704
1890.0007257548020378060.001451509604075610.999274245197962
1900.0007739410321183850.001547882064236770.999226058967882
1910.0009562546078482080.001912509215696420.999043745392152
1920.001208456553822940.002416913107645880.998791543446177
1930.001461129317665210.002922258635330420.998538870682335
1940.001722647397296500.003445294794593010.998277352602704
1950.002124319693669680.004248639387339360.99787568030633
1960.002769511472286500.005539022944572990.997230488527713
1970.00370716915840390.00741433831680780.996292830841596
1980.004329541447405400.008659082894810810.995670458552595
1990.004633960238598030.009267920477196070.995366039761402
2000.005170571264184520.01034114252836900.994829428735815
2010.00557903310867520.01115806621735040.994420966891325
2020.00623220451744140.01246440903488280.993767795482559
2030.007210616748456590.01442123349691320.992789383251543
2040.008943801213759280.01788760242751860.99105619878624
2050.01006952452299740.02013904904599480.989930475477003
2060.01177566714147540.02355133428295080.988224332858525
2070.01378539686648470.02757079373296940.986214603133515
2080.01728738206994300.03457476413988600.982712617930057
2090.02225002000304610.04450004000609210.977749979996954
2100.02400415834338470.04800831668676940.975995841656615
2110.02538655778828570.05077311557657150.974613442211714
2120.02718011756330470.05436023512660940.972819882436695
2130.02840619979740660.05681239959481310.971593800202593
2140.02992220647887050.0598444129577410.97007779352113
2150.03261960218919310.06523920437838620.967380397810807
2160.03688956731291980.07377913462583960.96311043268708
2170.04047083210955270.08094166421910540.959529167890447
2180.04674817957947560.09349635915895110.953251820420524
2190.0524285515882720.1048571031765440.947571448411728
2200.05852309354683780.1170461870936760.941476906453162
2210.06533498331041670.1306699666208330.934665016689583
2220.06350398527868950.1270079705573790.93649601472131
2230.06317008702064190.1263401740412840.936829912979358
2240.0625053001250560.1250106002501120.937494699874944
2250.06163107778198350.1232621555639670.938368922218016
2260.06008986757077490.1201797351415500.939910132429225
2270.06019416513613560.1203883302722710.939805834863864
2280.06105813309146210.1221162661829240.938941866908538
2290.06122305811078860.1224461162215770.938776941889211
2300.06207116097991640.1241423219598330.937928839020084
2310.06313279943419060.1262655988683810.93686720056581
2320.0639118430390160.1278236860780320.936088156960984
2330.06554641232997790.1310928246599560.934453587670022
2340.05957510189290330.1191502037858070.940424898107097
2350.05429651900975880.1085930380195180.945703480990241
2360.04958568219825090.09917136439650180.95041431780175
2370.04440197368240110.08880394736480220.9555980263176
2380.04041149052935150.0808229810587030.959588509470649
2390.03683752905634340.07367505811268690.963162470943657
2400.03439920954799810.06879841909599610.965600790452002
2410.03376874119106210.06753748238212420.966231258808938
2420.03191626929490450.06383253858980910.968083730705095
2430.03129900551333080.06259801102666150.96870099448667
2440.03118695630645930.06237391261291870.96881304369354
2450.03092924817879480.06185849635758950.969070751821205
2460.02649852873858060.05299705747716130.97350147126142
2470.02307739986603250.0461547997320650.976922600133967
2480.02057541372238070.04115082744476140.97942458627762
2490.01825318271901860.03650636543803730.981746817280981
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2900.0006542974070650740.001308594814130150.999345702592935
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2950.0001788453143202420.0003576906286404850.99982115468568
2960.0001376028523083790.0002752057046167580.999862397147692
2970.0001044485643043500.0002088971286086990.999895551435696
2987.78610969688502e-050.0001557221939377000.999922138903031
2995.57735806067862e-050.0001115471612135720.999944226419393
3004.04688735184171e-058.09377470368343e-050.999959531126482
3014.35977872951015e-058.7195574590203e-050.999956402212705
3024.50237122153241e-059.00474244306482e-050.999954976287785
3034.81828882952675e-059.6365776590535e-050.999951817111705
3044.33447121867859e-058.66894243735718e-050.999956655287813
3054.15129184511982e-058.30258369023965e-050.999958487081549
3064.39375684244566e-058.78751368489133e-050.999956062431576
3075.26607579116613e-050.0001053215158233230.999947339242088
3086.59061952608613e-050.0001318123905217230.99993409380474
3098.35980276708226e-050.0001671960553416450.99991640197233
3100.0001323851955843620.0002647703911687230.999867614804416
3110.0002213325278783520.0004426650557567040.999778667472122
3120.0004115826762511280.0008231653525022560.999588417323749
3130.001448472699296450.00289694539859290.998551527300704
3140.004973330644883820.009946661289767640.995026669355116
3150.01999962003805300.03999924007610590.980000379961947
3160.06113288350845420.1222657670169080.938867116491546
3170.1558520757824720.3117041515649440.844147924217528
3180.3496114726947310.6992229453894620.650388527305269
3190.647662328162310.7046753436753790.352337671837690
3200.9266566610483780.1466866779032450.0733433389516223
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3220.9999402921668530.0001194156662930565.97078331465281e-05
3230.9999999651079446.978411129635e-083.4892055648175e-08
3240.9999999999993261.34862878006138e-126.74314390030692e-13
3250.9999999999999041.91466545653566e-139.57332728267828e-14
3260.9999999999999735.48582628733222e-142.74291314366611e-14
3270.999999999999959.92858004591825e-144.96429002295912e-14
3280.9999999999999251.50080651178752e-137.50403255893762e-14
3290.9999999999999627.53232717590489e-143.76616358795244e-14
3300.9999999999999461.07453032733339e-135.37265163666694e-14
3310.9999999999998632.73200258438187e-131.36600129219094e-13
3320.9999999999996497.02822907031687e-133.51411453515843e-13
3330.9999999999989652.07006233604904e-121.03503116802452e-12
3340.9999999999968976.2054389326539e-123.10271946632695e-12
3350.9999999999946361.07286996605331e-115.36434983026654e-12
3360.999999999986842.63181667673297e-111.31590833836649e-11
3370.9999999999580638.3873421355345e-114.19367106776725e-11
3380.9999999999208141.58371383511822e-107.9185691755911e-11
3390.9999999999201031.59794716703227e-107.98973583516137e-11
3400.9999999997628474.7430645441025e-102.37153227205125e-10
3410.9999999998622142.75571849905803e-101.37785924952901e-10
3420.9999999996991956.01610027867943e-103.00805013933971e-10
3430.999999999004851.99030041685643e-099.95150208428216e-10
3440.999999995911858.17630029480756e-094.08815014740378e-09
3450.9999999871359372.57281253578105e-081.28640626789052e-08
3460.9999999508828929.82342156129844e-084.91171078064922e-08
3470.999999772528414.54943180670553e-072.27471590335276e-07
3480.9999988906824272.21863514665183e-061.10931757332591e-06
3490.999995275230369.4495392823276e-064.7247696411638e-06
3500.9999964822264517.03554709786324e-063.51777354893162e-06
3510.9999911992731051.76014537902644e-058.80072689513222e-06
3520.9999588100844548.23798310922406e-054.11899155461203e-05
3530.9997651957373450.0004696085253104640.000234804262655232
3540.999701294916970.000597410166061490.000298705083030745
3550.9981846924050110.003630615189977380.00181530759498869
3560.9918338459448530.01633230811029410.00816615405514705


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level2130.624633431085044NOK
5% type I error level2770.812316715542522NOK
10% type I error level3020.885630498533724NOK
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Dec/09/t12919246007ftftu67h2p1ey7/10m4mn1291924695.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/09/t12919246007ftftu67h2p1ey7/10m4mn1291924695.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/09/t12919246007ftftu67h2p1ey7/1flpb1291924695.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/09/t12919246007ftftu67h2p1ey7/1flpb1291924695.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/09/t12919246007ftftu67h2p1ey7/2flpb1291924695.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/09/t12919246007ftftu67h2p1ey7/2flpb1291924695.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/09/t12919246007ftftu67h2p1ey7/3qcow1291924695.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/09/t12919246007ftftu67h2p1ey7/3qcow1291924695.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/09/t12919246007ftftu67h2p1ey7/4qcow1291924695.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/09/t12919246007ftftu67h2p1ey7/4qcow1291924695.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/09/t12919246007ftftu67h2p1ey7/5qcow1291924695.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/09/t12919246007ftftu67h2p1ey7/5qcow1291924695.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/09/t12919246007ftftu67h2p1ey7/60l5z1291924695.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/09/t12919246007ftftu67h2p1ey7/60l5z1291924695.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/09/t12919246007ftftu67h2p1ey7/7bdnk1291924695.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/09/t12919246007ftftu67h2p1ey7/7bdnk1291924695.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/09/t12919246007ftftu67h2p1ey7/8bdnk1291924695.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/09/t12919246007ftftu67h2p1ey7/8bdnk1291924695.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/09/t12919246007ftftu67h2p1ey7/9bdnk1291924695.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/09/t12919246007ftftu67h2p1ey7/9bdnk1291924695.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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