multiple regression Q3

*Unverified author*

R Software Module: rwasp_multipleregression.wasp (opens new window with default values)

Title produced by software: Multiple Regression

Date of computation: Thu, 27 Nov 2008 07:10:07 -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/27/t12277952426hqwhs8qxfyorov.htm/, Retrieved Thu, 27 Nov 2008 14:14:02 +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/27/t12277952426hqwhs8qxfyorov.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]  test Post a new message

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

540 0 522 0 526 0 527 0 516 0 503 0 489 0 479 0 475 0 524 0 552 0 532 0 511 0 492 0 492 0 493 0 481 0 462 0 457 0 442 0 439 0 488 0 521 0 501 0 485 0 464 0 460 0 467 0 460 0 448 0 443 0 436 0 431 0 484 0 510 0 513 0 503 0 471 0 471 0 476 0 475 0 470 0 461 0 455 0 456 1 517 1 525 1 523 1 519 1 509 1 512 1 519 1 517 1 510 1 509 1 501 1 507 1 569 1 580 1 578 1 565 1 547 1 555 1 562 1 561 1 555 1 544 1 537 1 543 1 594 1 611 1 613 1 611 1 594 1 595 1 591 1 589 1 584 1 573 1 567 1 569 1 621 1 629 1 628 1 612 1 595 1 597 1 593 1 590 1 580 1 574 1 573 1 573 1 620 1 626 1 620 1 588 1 566 1 557 1 561 1 549 1 532 1 526 1 511 1 499 1 555 1 565 1 542 1 527 1 510 1 514 1 517 1 508 1 493 1 490 1 469 1 478 1 528 1 534 1 518 1 506 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 Input view raw input (R code) Raw Output view raw output of R engine Computing time 9 seconds R Server 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 Multiple Linear Regression - Estimated Regression Equation X[t] = + 517.321472019465 + 84.0926022477117Y[t] -10.4627657352109M1[t] -24.3280569862687M2[t] -23.1343252651647M3[t] -20.1405935440607M4[t] -25.8468618229567M5[t] -36.4531301018527M6[t] -43.2593983807487M7[t] -52.5656666596448M8[t] -60.6811951633119M9[t] -7.38746344220796M10[t] + 8.20626827889602M11[t] -0.293731721103984t + 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) 517.321472019465 12.090161 42.7886 0 0 Y 84.0926022477117 11.508382 7.3071 0 0 M1 -10.4627657352109 14.651775 -0.7141 0.476723 0.238362 M2 -24.3280569862687 15.016191 -1.6201 0.10815 0.054075 M3 -23.1343252651647 15.010436 -1.5412 0.126216 0.063108 M4 -20.1405935440607 15.00635 -1.3421 0.182392 0.091196 M5 -25.8468618229567 15.003935 -1.7227 0.087837 0.043918 M6 -36.4531301018527 15.003191 -2.4297 0.016776 0.008388 M7 -43.2593983807487 15.004119 -2.8832 0.00476 0.00238 M8 -52.5656666596448 15.006718 -3.5028 0.000673 0.000337 M9 -60.6811951633119 14.997216 -4.0462 9.9e-05 4.9e-05 M10 -7.38746344220796 14.993034 -0.4927 0.623216 0.311608 M11 8.20626827889602 14.990525 0.5474 0.585223 0.292612 t -0.293731721103984 0.158366 -1.8548 0.066383 0.033191 Multiple Linear Regression - Regression Statistics Multiple R 0.775370732714189 R-squared 0.601199773149738 Adjusted R-squared 0.552747409139894 F-TEST (value) 12.4080586249121 F-TEST (DF numerator) 13 F-TEST (DF denominator) 107 p-value 4.44089209850063e-16 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 33.5179620946964 Sum Squared Residuals 120209.554779021 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 540 506.564974563149 33.4350254368507 2 522 492.405951590988 29.594048409012 3 526 493.305951590988 32.6940484090119 4 527 496.005951590988 30.9940484090119 5 516 490.005951590988 25.9940484090119 6 503 479.105951590988 23.8940484090119 7 489 472.005951590988 16.9940484090119 8 479 462.405951590988 16.5940484090119 9 475 453.996691366217 21.0033086337831 10 524 506.996691366217 17.0033086337831 11 552 522.296691366217 29.7033086337831 12 532 513.796691366217 18.2033086337831 13 511 503.040193909902 7.95980609009801 14 492 488.88117093774 3.11882906225970 15 492 489.78117093774 2.21882906225971 16 493 492.48117093774 0.518829062259712 17 481 486.48117093774 -5.48117093774029 18 462 475.58117093774 -13.5811709377403 19 457 468.48117093774 -11.4811709377403 20 442 458.88117093774 -16.8811709377403 21 439 450.471910712969 -11.4719107129691 22 488 503.471910712969 -15.4719107129691 23 521 518.771910712969 2.22808928703088 24 501 510.271910712969 -9.2719107129691 25 485 499.515413256654 -14.5154132566542 26 464 485.356390284492 -21.3563902844925 27 460 486.256390284492 -26.2563902844925 28 467 488.956390284492 -21.9563902844925 29 460 482.956390284492 -22.9563902844925 30 448 472.056390284492 -24.0563902844925 31 443 464.956390284492 -21.9563902844925 32 436 455.356390284492 -19.3563902844925 33 431 446.947130059721 -15.9471300597213 34 484 499.947130059721 -15.9471300597213 35 510 515.247130059721 -5.2471300597213 36 513 506.747130059721 6.2528699402787 37 503 495.990632603406 7.00936739659362 38 471 481.831609631245 -10.8316096312447 39 471 482.731609631245 -11.7316096312447 40 476 485.431609631245 -9.43160963124468 41 475 479.431609631245 -4.43160963124468 42 470 468.531609631245 1.46839036875533 43 461 461.431609631245 -0.431609631244671 44 455 451.831609631245 3.16839036875533 45 456 527.514951654185 -71.5149516541852 46 517 580.514951654185 -63.5149516541852 47 525 595.814951654185 -70.8149516541852 48 523 587.314951654185 -64.3149516541852 49 519 576.55845419787 -57.5584541978703 50 509 562.399431225709 -53.3994312257086 51 512 563.299431225709 -51.2994312257086 52 519 565.999431225709 -46.9994312257086 53 517 559.999431225709 -42.9994312257086 54 510 549.099431225709 -39.0994312257086 55 509 541.999431225709 -32.9994312257086 56 501 532.399431225709 -31.3994312257086 57 507 523.990171000937 -16.9901710009374 58 569 576.990171000937 -7.99017100093741 59 580 592.290171000937 -12.2901710009374 60 578 583.790171000937 -5.79017100093741 61 565 573.033673544623 -8.03367354462249 62 547 558.874650572461 -11.8746505724608 63 555 559.774650572461 -4.77465057246079 64 562 562.474650572461 -0.474650572460784 65 561 556.474650572461 4.52534942753921 66 555 545.574650572461 9.42534942753921 67 544 538.474650572461 5.52534942753922 68 537 528.874650572461 8.12534942753922 69 543 520.46539034769 22.5346096523104 70 594 573.46539034769 20.5346096523104 71 611 588.76539034769 22.2346096523104 72 613 580.26539034769 32.7346096523104 73 611 569.508892891375 41.4911071086253 74 594 555.349869919213 38.650130080787 75 595 556.249869919213 38.750130080787 76 591 558.949869919213 32.050130080787 77 589 552.949869919213 36.050130080787 78 584 542.049869919213 41.950130080787 79 573 534.949869919213 38.050130080787 80 567 525.349869919213 41.650130080787 81 569 516.940609694442 52.0593903055582 82 621 569.940609694442 51.0593903055582 83 629 585.240609694442 43.7593903055582 84 628 576.740609694442 51.2593903055582 85 612 565.984112238127 46.0158877618731 86 595 551.825089265965 43.1749107340348 87 597 552.725089265965 44.2749107340348 88 593 555.425089265965 37.5749107340348 89 590 549.425089265965 40.5749107340348 90 580 538.525089265965 41.4749107340348 91 574 531.425089265965 42.5749107340348 92 573 521.825089265965 51.1749107340348 93 573 513.415829041194 59.584170958806 94 620 566.415829041194 53.584170958806 95 626 581.715829041194 44.284170958806 96 620 573.215829041194 46.784170958806 97 588 562.459331584879 25.5406684151209 98 566 548.300308612717 17.6996913872826 99 557 549.200308612717 7.79969138728264 100 561 551.900308612717 9.09969138728264 101 549 545.900308612717 3.09969138728263 102 532 535.000308612717 -3.00030861271737 103 526 527.900308612717 -1.90030861271737 104 511 518.300308612717 -7.30030861271736 105 499 509.891048387946 -10.8910483879462 106 555 562.891048387946 -7.89104838794618 107 565 578.191048387946 -13.1910483879462 108 542 569.691048387946 -27.6910483879462 109 527 558.934550931631 -31.9345509316313 110 510 544.77552795947 -34.7755279594696 111 514 545.67552795947 -31.6755279594696 112 517 548.37552795947 -31.3755279594696 113 508 542.37552795947 -34.3755279594696 114 493 531.47552795947 -38.4755279594696 115 490 524.37552795947 -34.3755279594696 116 469 514.77552795947 -45.7755279594696 117 478 506.366267734698 -28.3662677346984 118 528 559.366267734698 -31.3662677346984 119 534 574.666267734698 -40.6662677346984 120 518 566.166267734698 -48.1662677346984 121 506 555.409770278383 -49.4097702783835 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.000362125628865381 0.000724251257730762 0.999637874371135 18 0.000179069196139966 0.000358138392279933 0.99982093080386 19 1.58348655857727e-05 3.16697311715453e-05 0.999984165134414 20 1.64488225837173e-06 3.28976451674345e-06 0.999998355117742 21 1.37243133551571e-07 2.74486267103142e-07 0.999999862756866 22 1.07413174293717e-08 2.14826348587435e-08 0.999999989258683 23 1.09756886957076e-09 2.19513773914153e-09 0.999999998902431 24 1.03566174008632e-10 2.07132348017264e-10 0.999999999896434 25 2.04316051288401e-10 4.08632102576801e-10 0.999999999795684 26 4.00234116636033e-11 8.00468233272066e-11 0.999999999959977 27 3.68742714822614e-12 7.37485429645228e-12 0.999999999996313 28 6.10756866347773e-13 1.22151373269555e-12 0.99999999999939 29 3.66700729465308e-13 7.33401458930615e-13 0.999999999999633 30 5.58905476382539e-13 1.11781095276508e-12 0.999999999999441 31 1.71685112903875e-12 3.4337022580775e-12 0.999999999998283 32 9.67044724244734e-12 1.93408944848947e-11 0.99999999999033 33 1.13945833940308e-11 2.27891667880617e-11 0.999999999988605 34 1.95667499747975e-11 3.91334999495951e-11 0.999999999980433 35 9.45861643856238e-12 1.89172328771248e-11 0.999999999990541 36 3.8900565826193e-10 7.7801131652386e-10 0.999999999610994 37 9.29994796044794e-09 1.85998959208959e-08 0.999999990700052 38 8.52183052814694e-09 1.70436610562939e-08 0.99999999147817 39 6.1287324437934e-09 1.22574648875868e-08 0.999999993871268 40 4.37532362971595e-09 8.7506472594319e-09 0.999999995624676 41 5.98753017467225e-09 1.19750603493445e-08 0.99999999401247 42 1.61675681100824e-08 3.23351362201649e-08 0.999999983832432 43 2.48664157750151e-08 4.97328315500303e-08 0.999999975133584 44 4.28390697418086e-08 8.56781394836173e-08 0.99999995716093 45 2.94691051908847e-08 5.89382103817694e-08 0.999999970530895 46 2.13634511755699e-08 4.27269023511399e-08 0.999999978636549 47 2.10349618990819e-08 4.20699237981639e-08 0.999999978965038 48 1.68827838282463e-08 3.37655676564925e-08 0.999999983117216 49 1.36679930358601e-08 2.73359860717202e-08 0.999999986332007 50 1.87809184552427e-08 3.75618369104854e-08 0.999999981219082 51 2.82259697213373e-08 5.64519394426746e-08 0.99999997177403 52 4.44672776843931e-08 8.89345553687862e-08 0.999999955532722 53 8.91025978805904e-08 1.78205195761181e-07 0.999999910897402 54 2.19875427748617e-07 4.39750855497234e-07 0.999999780124572 55 6.95007911561947e-07 1.39001582312389e-06 0.999999304992088 56 2.12097359419692e-06 4.24194718839384e-06 0.999997879026406 57 2.72148895824295e-05 5.44297791648589e-05 0.999972785110418 58 0.000288408891420929 0.000576817782841858 0.99971159110858 59 0.00091626740788882 0.00183253481577764 0.999083732592111 60 0.00308836005996680 0.00617672011993361 0.996911639940033 61 0.00757548956324846 0.0151509791264969 0.992424510436752 62 0.0211712397311411 0.0423424794622822 0.978828760268859 63 0.0537996065970959 0.107599213194192 0.946200393402904 64 0.111758450600637 0.223516901201274 0.888241549399363 65 0.208629935916283 0.417259871832566 0.791370064083717 66 0.342295102856735 0.68459020571347 0.657704897143265 67 0.516877496529208 0.966245006941584 0.483122503470792 68 0.698715709400773 0.602568581198454 0.301284290599227 69 0.875793336744182 0.248413326511635 0.124206663255817 70 0.966236188752098 0.0675276224958041 0.0337638112479021 71 0.99160409952821 0.0167918009435815 0.00839590047179075 72 0.997756851911337 0.00448629617732619 0.00224314808866310 73 0.99894175930789 0.00211648138422185 0.00105824069211092 74 0.999507320695514 0.000985358608971809 0.000492679304485904 75 0.99974809637548 0.000503807249038276 0.000251903624519138 76 0.999903797224478 0.000192405551044210 9.62027755221051e-05 77 0.99995677616178 8.64476764419477e-05 4.32238382209738e-05 78 0.999970750411222 5.84991775560064e-05 2.92495887780032e-05 79 0.999988866213185 2.22675736293195e-05 1.11337868146597e-05 80 0.999994511863538 1.09762729248939e-05 5.48813646244694e-06 81 0.999997601979929 4.79604014238004e-06 2.39802007119002e-06 82 0.999999127111397 1.74577720611923e-06 8.72888603059614e-07 83 0.999999775294527 4.49410946308817e-07 2.24705473154409e-07 84 0.99999978373858 4.32522839085024e-07 2.16261419542512e-07 85 0.999999724093369 5.5181326285432e-07 2.7590663142716e-07 86 0.999999402868201 1.19426359731335e-06 5.97131798656675e-07 87 0.999998466754693 3.06649061425913e-06 1.53324530712956e-06 88 0.999997371826866 5.25634626819522e-06 2.62817313409761e-06 89 0.999993470484575 1.30590308499956e-05 6.52951542499778e-06 90 0.99998179756904 3.64048619214146e-05 1.82024309607073e-05 91 0.999951913225498 9.61735490037936e-05 4.80867745018968e-05 92 0.999919763011373 0.000160473977254348 8.0236988627174e-05 93 0.99989625256267 0.000207494874660439 0.000103747437330220 94 0.999814123891112 0.000371752217775652 0.000185876108887826 95 0.999656586813197 0.000686826373605663 0.000343413186802831 96 0.999938344247124 0.000123311505752763 6.16557528763813e-05 97 0.999934060160977 0.000131879678046614 6.5939839023307e-05 98 0.99996422665661 7.15466867820589e-05 3.57733433910294e-05 99 0.999908370329565 0.000183259340869384 9.16296704346921e-05 100 0.999814734647447 0.000370530705105795 0.000185265352552897 101 0.99953828757763 0.000923424844741609 0.000461712422370804 102 0.998733051010504 0.00253389797899250 0.00126694898949625 103 0.99562911448842 0.00874177102315874 0.00437088551157937 104 0.997635025939334 0.00472994812133282 0.00236497406066641 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 77 0.875 NOK 5% type I error level 80 0.909090909090909 NOK 10% type I error level 81 0.920454545454545 NOK

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/27/t12277952426hqwhs8qxfyorov/10p3em1227794992.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/27/t12277952426hqwhs8qxfyorov/10p3em1227794992.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/27/t12277952426hqwhs8qxfyorov/1rqhy1227794992.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/27/t12277952426hqwhs8qxfyorov/1rqhy1227794992.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/27/t12277952426hqwhs8qxfyorov/2fhes1227794992.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/27/t12277952426hqwhs8qxfyorov/2fhes1227794992.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/27/t12277952426hqwhs8qxfyorov/3utzc1227794992.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/27/t12277952426hqwhs8qxfyorov/3utzc1227794992.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/27/t12277952426hqwhs8qxfyorov/4j4951227794992.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/27/t12277952426hqwhs8qxfyorov/4j4951227794992.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/27/t12277952426hqwhs8qxfyorov/5czz91227794992.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/27/t12277952426hqwhs8qxfyorov/5czz91227794992.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/27/t12277952426hqwhs8qxfyorov/66mmv1227794992.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/27/t12277952426hqwhs8qxfyorov/66mmv1227794992.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/27/t12277952426hqwhs8qxfyorov/74v2t1227794992.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/27/t12277952426hqwhs8qxfyorov/74v2t1227794992.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/27/t12277952426hqwhs8qxfyorov/8d6xr1227794992.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/27/t12277952426hqwhs8qxfyorov/8d6xr1227794992.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/27/t12277952426hqwhs8qxfyorov/9ufih1227794992.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/27/t12277952426hqwhs8qxfyorov/9ufih1227794992.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') }

Copyright

This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa

Disclaimer

Information provided on this web site is provided "AS IS" without warranty of any kind, either express or implied, including, without limitation, warranties of merchantability, fitness for a particular purpose, and noninfringement. We use reasonable efforts to include accurate and timely information and periodically update the information, and software without notice. However, we make no warranties or representations as to the accuracy or completeness of such information (or software), and we assume no liability or responsibility for errors or omissions in the content of this web site, or any software bugs in online applications. Your use of this web site is AT YOUR OWN RISK. Under no circumstances and under no legal theory shall we be liable to you or any other person for any direct, indirect, special, incidental, exemplary, or consequential damages arising from your access to, or use of, this web site.

Privacy Policy

We may request personal information to be submitted to our servers in order to be able to:

• personalize online software applications according to your needs
• enforce strict security rules with respect to the data that you upload (e.g. statistical data)
• manage user sessions of online applications
• alert you about important changes or upgrades in resources or applications

We NEVER allow other companies to directly offer registered users information about their products and services. Banner references and hyperlinks of third parties NEVER contain any personal data of the visitor.

We do NOT sell, nor transmit by any means, personal information, nor statistical data series uploaded by you to third parties.

We carefully protect your data from loss, misuse, alteration, and destruction. However, at any time, and under any circumstance you are solely responsible for managing your passwords, and keeping them secret.

We store a unique ANONYMOUS USER ID in the form of a small 'Cookie' on your computer. This allows us to track your progress when using this website which is necessary to create state-dependent features. The cookie is used for NO OTHER PURPOSE. At any time you may opt to disallow cookies from this website - this will not affect other features of this website.

We examine cookies that are used by third-parties (banner and online ads) very closely: abuse from third-parties automatically results in termination of the advertising contract without refund. We have very good reason to believe that the cookies that are produced by third parties (banner ads) do NOT cause any privacy or security risk.

FreeStatistics.org is safe. There is no need to download any software to use the applications and services contained in this website. Hence, your system's security is not compromised by their use, and your personal data - other than data you submit in the account application form, and the user-agent information that is transmitted by your browser - is never transmitted to our servers.

As a general rule, we do not log on-line behavior of individuals (other than normal logging of webserver 'hits'). However, in cases of abuse, hacking, unauthorized access, Denial of Service attacks, illegal copying, hotlinking, non-compliance with international webstandards (such as robots.txt), or any other harmful behavior, our system engineers are empowered to log, track, identify, publish, and ban misbehaving individuals - even if this leads to ban entire blocks of IP addresses, or disclosing user's identity.

FreeStatistics.org is powered by