Verbetering Workshop 7 (linear trend)

*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: Fri, 27 Nov 2009 06:37:40 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Nov/27/t1259329132deia2e6by501j6a.htm/, Retrieved Fri, 27 Nov 2009 14:39:06 +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/2009/Nov/27/t1259329132deia2e6by501j6a.htm/}, year = {2009}, } @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 = {2009}, 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 «

384 257.9 367.6 275.8 457.1 319.4 429.4 299.8 442.2 331.1 507.5 339.3 348.5 209.6 393.2 280.9 426.8 285.5 403 247.6 454.8 275.1 413 262.3 388.9 267.8 406.5 448.2 447.4 563.4 474.4 346.6 428.5 455.1 472.8 424.4 411 381.2 463.9 382.9 497.3 466.6 474 400.2 518.1 493.6 566 367.5 509.4 307.1 445.1 316.7 466.6 314.2 600.5 403.7 538.7 370.6 548 343.7 591.9 383 547.3 365.4 610.2 417.2 621.6 411 582.4 420.8 635.8 493 663.9 471.8 624.2 452.4 654.1 464.8 723.5 541.5 641.2 484 565.5 449.4 698.6 436.8 651 490 721.6 475.4 643.5 393.6 604 486.8 618.2 536.7 783.5 467 672.9 475.5 726.7 532.8 738.6 554.1 692.2 507.3 669.5 455.2 546.2 465.3 715 563.2 789.8 680.1 684 518.2 639 426.6 768.5 612.4 643.8 518.1 623 540 692.8 541.7 936.5 627.6 795.9 637 695.7 564.2 648.3 665 675.2 703.2 826.5 824.4 742.4 700.3 793.9 1219.6 685.3 764.7 756.1 479.9 704 543.4 860.6 593.3 795.9 584.3 816.7 645.9 777.9 548.9 746.4 421.8 694.7 460.3 909.2 553.4 783.6 424.4 730 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 Input view raw input (R code) Raw Output view raw output of R engine Computing time 4 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation yt[t] = + 219.151207387327 + 0.532138256307442xt[t] + 3.48234302529478t + e[t] Multiple Linear Regression - Ordinary Least Squares Variable Parameter S.D. T-STAT H0: parameter = 0 2-tail p-value 1-tail p-value (Intercept) 219.151207387327 21.419773 10.2313 0 0 xt 0.532138256307442 0.053892 9.8742 0 0 t 3.48234302529478 0.304854 11.423 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.933737552987903 R-squared 0.871865817859836 Adjusted R-squared 0.869675489960005 F-TEST (value) 398.052646787162 F-TEST (DF numerator) 2 F-TEST (DF denominator) 117 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 80.8886789273304 Sum Squared Residuals 765528.470297224 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 384 359.87200671431 24.1279932856903 2 367.6 372.879624527508 -5.27962452750764 3 457.1 399.563195527808 57.5368044721924 4 429.4 392.615628729477 36.7843712705234 5 442.2 412.753899177194 29.4461008228056 6 507.5 420.59977590421 86.9002240957899 7 348.5 355.063787086430 -6.56378708642963 8 393.2 396.487587786445 -3.28758778644505 9 426.8 402.417766790754 24.3822332092459 10 403 385.732069901997 17.2679300980032 11 454.8 403.848214975746 50.9517850242538 12 413 400.519188320306 12.4808116796943 13 388.9 406.928291755291 -18.0282917552915 14 406.5 506.408376218449 -99.9083762184489 15 447.4 571.193046370361 -123.793046370361 16 474.4 459.307815428202 15.0921845717977 17 428.5 520.527159262855 -92.0271592628546 18 472.8 507.672857819511 -34.8728578195108 19 411 488.166828172324 -77.1668281723241 20 463.9 492.553806233342 -28.6538062333415 21 497.3 540.576121311569 -43.2761213115693 22 474 508.72448411805 -34.7244841180499 23 518.1 561.90854028246 -43.8085402824597 24 566 498.288249187386 67.711750812614 25 509.4 469.629441531711 39.7705584682887 26 445.1 478.220311817558 -33.1203118175575 27 466.6 480.372309202084 -13.7723092020837 28 600.5 531.481026166895 69.0189738331054 29 538.7 517.349592908413 21.3504070915870 30 548 506.517416839038 41.4825831609624 31 591.9 530.912793337215 60.9872066627851 32 547.3 525.029503051499 22.2704969485013 33 610.2 556.076607753519 54.1233922464811 34 621.6 556.259693589708 65.3403064102925 35 582.4 564.956991526815 17.4430084731847 36 635.8 606.859716657507 28.9402833424925 37 663.9 599.060728649084 64.8392713509156 38 624.2 592.219589502015 31.9804104979853 39 654.1 602.300446905522 51.7995530944781 40 723.5 646.597794189597 76.9022058104025 41 641.2 619.482187477214 21.7178125227857 42 565.5 604.552546834272 -39.0525468342716 43 698.6 601.329947830093 97.2700521699074 44 651 633.122046090943 17.8779539090567 45 721.6 628.835170574149 92.7648294258506 46 643.5 588.788604233495 54.7113957665046 47 604 641.866232746644 -37.8662327466438 48 618.2 671.90227476168 -53.70227476168 49 783.5 638.294581322346 145.205418677654 50 672.9 646.300099526254 26.5999004737459 51 726.7 680.273964637965 46.4260353620348 52 738.6 695.090852522609 43.5091474773914 53 692.2 673.669125152715 18.5308748472850 54 669.5 649.427065024392 20.0729349756079 55 546.2 658.284004438392 -112.084004438392 56 715 713.862682756185 1.13731724381453 57 789.8 779.55198794382 10.2480120561797 58 684 696.88114727294 -12.8811472729401 59 639 651.619626020473 -12.6196260204732 60 768.5 753.97325706769 14.5267429323093 61 643.8 707.274962523194 -63.4749625231937 62 623 722.411133361621 -99.4111333616214 63 692.8 726.798111422639 -33.9981114226389 64 936.5 775.991130664743 160.508869335257 65 795.9 784.475573299328 11.4244267006723 66 695.7 749.21825126544 -53.5182512654406 67 648.3 806.340130526526 -158.040130526526 68 675.2 830.150154942765 -154.950154942765 69 826.5 898.127654632522 -71.6276546325215 70 742.4 835.571640050063 -93.1716400500627 71 793.9 1115.39337957581 -321.493379575812 72 685.3 876.806029806852 -191.506029806852 73 756.1 728.735397435787 27.3646025642133 74 704 766.008519736604 -62.0085197366041 75 860.6 796.04456175164 64.5554382483598 76 795.9 794.737660470168 1.16233952983195 77 816.7 830.999720084001 -14.2997200840012 78 777.9 782.864652247474 -4.96465224747415 79 746.4 718.712222896093 27.687777103907 80 694.7 742.681888789224 -47.9818887892243 81 909.2 795.706303476742 113.493696523258 82 783.6 730.542811438377 53.0571885616234 83 730.4 758.397086602552 -27.9970866025523 84 847.7 802.85407536352 44.8459246364799 85 758.7 751.845460942933 6.85453905706722 86 839.2 798.909927159807 40.2900728401929 87 784.8 840.493369336715 -55.6933693367149 88 906.1 814.814535916362 91.2854640836383 89 838.2 870.286786582894 -32.0867865828936 90 729 811.934664225264 -82.9346642252636 91 768.1 813.554523353482 -45.4545233534823 92 710.5 833.160655544893 -122.660655544893 93 863 832.332678694097 30.6673213059029 94 778.3 797.713922567779 -19.4139225677791 95 827.7 809.657263868362 18.0427361316379 96 853.1 895.514608970049 -42.4146089700489 97 859.3 877.126069661108 -17.8260696611080 98 779.2 855.172204034907 -75.9722040349069 99 724.6 841.945405812148 -117.345405812148 100 829.2 869.852894801954 -40.6528948019543 101 862.9 930.274031252146 -67.3740312521455 102 601.6 839.940399690438 -238.340399690438 103 964.9 870.189297007997 94.7107029920027 104 766.3 863.986723768497 -97.6867237684967 105 847.8 895.19346994741 -47.3934699474092 106 992.7 868.450360014441 124.249639985559 107 865.3 864.855264230847 0.444735769152932 108 1054.1 983.226256792919 70.8737432070812 109 972.5 999.799200923376 -27.2992009233765 110 857.4 906.432381300717 -49.0323813007168 111 1043.3 968.024221914784 75.2757780852157 112 1061 1012.32156919886 48.6784308011401 113 989.4 1041.24012087565 -51.8401208756504 114 963.2 982.08979113356 -18.8897911335591 115 1181.9 1125.57770939334 56.322290606658 116 1256.4 1188.23382652002 68.1661734799757 117 1492.7 1217.57808880186 275.121911198139 118 1360.8 1214.83441422836 145.965585771641 119 1342.8 1201.34154687745 141.458453122554 120 1464 1360.79361282645 103.206387173548 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 6 0.0482969383243491 0.0965938766486982 0.95170306167565 7 0.0131112783144921 0.0262225566289843 0.986888721685508 8 0.00694115232480782 0.0138823046496156 0.993058847675192 9 0.00184702905241157 0.00369405810482313 0.998152970947588 10 0.00054915889029487 0.00109831778058974 0.999450841109705 11 0.000237341331530692 0.000474682663061384 0.99976265866847 12 6.52204849877258e-05 0.000130440969975452 0.999934779515012 13 5.99641144538465e-05 0.000119928228907693 0.999940035885546 14 0.00424114022511286 0.00848228045022573 0.995758859774887 15 0.00260652466488635 0.00521304932977270 0.997393475335114 16 0.00228794050717802 0.00457588101435604 0.997712059492822 17 0.00119438242176369 0.00238876484352738 0.998805617578236 18 0.000660808454100489 0.00132161690820098 0.9993391915459 19 0.000351521762927541 0.000703043525855082 0.999648478237072 20 0.00018681373453912 0.00037362746907824 0.999813186265461 21 0.000120173088176547 0.000240346176353094 0.999879826911823 22 5.80579087332107e-05 0.000116115817466421 0.999941942091267 23 3.91642662870171e-05 7.83285325740342e-05 0.999960835733713 24 0.000201620736895328 0.000403241473790655 0.999798379263105 25 0.000115365034704946 0.000230730069409893 0.999884634965295 26 7.39834310907211e-05 0.000147966862181442 0.99992601656891 27 3.47716427367558e-05 6.95432854735115e-05 0.999965228357263 28 0.000127442505536665 0.000254885011073330 0.999872557494463 29 7.13613674250322e-05 0.000142722734850064 0.999928638632575 30 4.22318871063767e-05 8.44637742127535e-05 0.999957768112894 31 4.22761034192644e-05 8.45522068385288e-05 0.99995772389658 32 2.04252209052502e-05 4.08504418105004e-05 0.999979574779095 33 1.86962480364268e-05 3.73924960728535e-05 0.999981303751964 34 1.75035743914682e-05 3.50071487829363e-05 0.999982496425609 35 8.42158648904236e-06 1.68431729780847e-05 0.99999157841351 36 5.78830673002131e-06 1.15766134600426e-05 0.99999421169327 37 6.18319614534959e-06 1.23663922906992e-05 0.999993816803855 38 3.13157578148031e-06 6.26315156296063e-06 0.999996868424219 39 1.98495320834875e-06 3.96990641669749e-06 0.999998015046792 40 3.50940531517262e-06 7.01881063034524e-06 0.999996490594685 41 1.72172743621085e-06 3.44345487242169e-06 0.999998278272564 42 2.20538759850763e-06 4.41077519701526e-06 0.999997794612401 43 2.43312394403445e-06 4.8662478880689e-06 0.999997566876056 44 1.23854610755725e-06 2.47709221511449e-06 0.999998761453892 45 1.41000497269454e-06 2.82000994538909e-06 0.999998589995027 46 8.74758698595195e-07 1.74951739719039e-06 0.999999125241301 47 1.05965728917715e-06 2.11931457835431e-06 0.99999894034271 48 1.09661722792096e-06 2.19323445584192e-06 0.999998903382772 49 5.83672091453394e-06 1.16734418290679e-05 0.999994163279085 50 3.68821031203128e-06 7.37642062406255e-06 0.999996311789688 51 2.54721112262536e-06 5.09442224525073e-06 0.999997452788877 52 1.78793511501615e-06 3.5758702300323e-06 0.999998212064885 53 1.18749628052936e-06 2.37499256105871e-06 0.99999881250372 54 9.71036115575942e-07 1.94207223115188e-06 0.999999028963884 55 1.58530341336100e-05 3.17060682672199e-05 0.999984146965866 56 9.87652389175888e-06 1.97530477835178e-05 0.999990123476108 57 6.7230009628663e-06 1.34460019257326e-05 0.999993276999037 58 5.00767098244217e-06 1.00153419648843e-05 0.999994992329018 59 5.00140162200815e-06 1.00028032440163e-05 0.999994998598378 60 3.39087726827611e-06 6.78175453655223e-06 0.999996609122732 61 4.48877385642188e-06 8.97754771284376e-06 0.999995511226144 62 9.5674389812725e-06 1.9134877962545e-05 0.999990432561019 63 6.65410746920935e-06 1.33082149384187e-05 0.99999334589253 64 0.000198417837595922 0.000396835675191844 0.999801582162404 65 0.000164384807496668 0.000328769614993336 0.999835615192503 66 0.000146853745884525 0.000293707491769050 0.999853146254115 67 0.000438720507934309 0.000877441015868618 0.999561279492066 68 0.000790695625055718 0.00158139125011144 0.999209304374944 69 0.00049493147994228 0.00098986295988456 0.999505068520058 70 0.000374213032274554 0.000748426064549108 0.999625786967725 71 0.0144716128544935 0.028943225708987 0.985528387145507 72 0.0922024104862427 0.184404820972485 0.907797589513757 73 0.0746711257540403 0.149342251508081 0.92532887424596 74 0.0784264657484766 0.156852931496953 0.921573534251523 75 0.0724411096068096 0.144882219213619 0.92755889039319 76 0.0561233674800129 0.112246734960026 0.943876632519987 77 0.0473790932451497 0.0947581864902993 0.95262090675485 78 0.0365464826476332 0.0730929652952663 0.963453517352367 79 0.0309062125388938 0.0618124250777876 0.969093787461106 80 0.0307126128491256 0.0614252256982512 0.969287387150874 81 0.0452549196908142 0.0905098393816283 0.954745080309186 82 0.0471610866599937 0.0943221733199874 0.952838913340006 83 0.0401631443861017 0.0803262887722035 0.959836855613898 84 0.0356566432537477 0.0713132865074954 0.964343356746252 85 0.0322889898180621 0.0645779796361242 0.967711010181938 86 0.0317968513986253 0.0635937027972507 0.968203148601375 87 0.025158795018496 0.050317590036992 0.974841204981504 88 0.0506309756728946 0.101261951345789 0.949369024327105 89 0.0373738686854182 0.0747477373708364 0.962626131314582 90 0.0361799442420293 0.0723598884840586 0.96382005575797 91 0.0292015402184211 0.0584030804368423 0.970798459781579 92 0.0387085759409324 0.0774171518818649 0.961291424059068 93 0.0376886396965243 0.0753772793930486 0.962311360303476 94 0.0328046735358659 0.0656093470717319 0.967195326464134 95 0.0380187277175276 0.0760374554350552 0.961981272282472 96 0.0271794906956656 0.0543589813913312 0.972820509304335 97 0.0221924722041526 0.0443849444083053 0.977807527795847 98 0.0170726279288523 0.0341452558577046 0.982927372071148 99 0.0171245387814764 0.0342490775629529 0.982875461218524 100 0.0116926753530876 0.0233853507061751 0.988307324646912 101 0.00766437809354823 0.0153287561870965 0.992335621906452 102 0.139444270544404 0.278888541088807 0.860555729455596 103 0.185707371572141 0.371414743144281 0.81429262842786 104 0.205117077130152 0.410234154260304 0.794882922869848 105 0.193490596313687 0.386981192627374 0.806509403686313 106 0.350854682792999 0.701709365585997 0.649145317207001 107 0.28506086379761 0.57012172759522 0.71493913620239 108 0.297983186584334 0.595966373168668 0.702016813415666 109 0.228328596767070 0.456657193534141 0.77167140323293 110 0.167973640855358 0.335947281710716 0.832026359144642 111 0.173068908286844 0.346137816573688 0.826931091713156 112 0.145698785261421 0.291397570522842 0.854301214738579 113 0.119960669113158 0.239921338226317 0.880039330886841 114 0.0989935958174117 0.197987191634823 0.901006404182588 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 62 0.568807339449541 NOK 5% type I error level 70 0.642201834862385 NOK 10% type I error level 90 0.825688073394495 NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Nov/27/t1259329132deia2e6by501j6a/10xal11259329055.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/27/t1259329132deia2e6by501j6a/10xal11259329055.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/27/t1259329132deia2e6by501j6a/1azqg1259329055.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/27/t1259329132deia2e6by501j6a/1azqg1259329055.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/27/t1259329132deia2e6by501j6a/2s2in1259329055.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/27/t1259329132deia2e6by501j6a/2s2in1259329055.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/27/t1259329132deia2e6by501j6a/3tffq1259329055.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/27/t1259329132deia2e6by501j6a/3tffq1259329055.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/27/t1259329132deia2e6by501j6a/4kl181259329055.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/27/t1259329132deia2e6by501j6a/4kl181259329055.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/27/t1259329132deia2e6by501j6a/5bde41259329055.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/27/t1259329132deia2e6by501j6a/5bde41259329055.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/27/t1259329132deia2e6by501j6a/6mmqy1259329055.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/27/t1259329132deia2e6by501j6a/6mmqy1259329055.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/27/t1259329132deia2e6by501j6a/77wxl1259329055.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/27/t1259329132deia2e6by501j6a/77wxl1259329055.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/27/t1259329132deia2e6by501j6a/8m8ny1259329055.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/27/t1259329132deia2e6by501j6a/8m8ny1259329055.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/27/t1259329132deia2e6by501j6a/9hfho1259329055.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/27/t1259329132deia2e6by501j6a/9hfho1259329055.ps (open in new window)

Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Do not include Seasonal 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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