Workshop 10 - multiple regression

*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: Sat, 11 Dec 2010 13:56:28 +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/11/t1292075738j619b1wbs22l2ye.htm/, Retrieved Sat, 11 Dec 2010 14:55:48 +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/11/t1292075738j619b1wbs22l2ye.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 «

0 24 14 11 12 24 26 0 25 11 7 8 25 23 0 17 6 17 8 30 25 1 18 12 10 8 19 23 1 18 8 12 9 22 19 1 16 10 12 7 22 29 1 20 10 11 4 25 25 1 16 11 11 11 23 21 1 18 16 12 7 17 22 1 17 11 13 7 21 25 0 23 13 14 12 19 24 0 30 12 16 10 19 18 1 23 8 11 10 15 22 1 18 12 10 8 16 15 1 15 11 11 8 23 22 1 12 4 15 4 27 28 0 21 9 9 9 22 20 1 15 8 11 8 14 12 1 20 8 17 7 22 24 0 31 14 17 11 23 20 0 27 15 11 9 23 21 1 34 16 18 11 21 20 1 21 9 14 13 19 21 1 31 14 10 8 18 23 1 19 11 11 8 20 28 0 16 8 15 9 23 24 1 20 9 15 6 25 24 1 21 9 13 9 19 24 1 22 9 16 9 24 23 1 17 9 13 6 22 23 1 24 10 9 6 25 29 0 25 16 18 16 26 24 0 26 11 18 5 29 18 1 25 8 12 7 32 25 1 17 9 17 9 25 21 1 32 16 9 6 29 26 1 33 11 9 6 28 22 1 13 16 12 5 17 22 1 32 12 18 12 28 22 1 25 12 12 7 29 23 1 29 14 18 10 26 30 1 22 9 14 9 25 23 1 18 10 15 8 14 17 1 17 9 16 5 25 23 0 20 10 10 8 26 23 1 15 12 11 8 20 25 1 20 14 14 10 18 24 1 33 14 9 6 32 24 0 29 10 12 8 25 23 1 23 14 17 7 25 21 0 26 16 5 4 23 24 1 18 9 12 8 21 2 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 9 seconds R Server 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation Gender[t] = + 3.88078900333712 + 0.0273651683211434Concernovermistakes[t] + 0.421293104886232Doubtsaboutactions[t] + 0.00115024260981116Parentalexpectations[t] + 0.481242912513191Parentalcritism[t] + 0.0710155481385383Personalstandars[t] -0.598935405599315organization[t] + 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) 3.88078900333712 2.723801 1.4248 0.156274 0.078137 Concernovermistakes 0.0273651683211434 0.088653 0.3087 0.757991 0.378995 Doubtsaboutactions 0.421293104886232 0.120879 3.4852 0.000643 0.000321 Parentalexpectations 0.00115024260981116 0.127276 0.009 0.992801 0.496401 Parentalcritism 0.481242912513191 0.101519 4.7404 5e-06 2e-06 Personalstandars 0.0710155481385383 0.090677 0.7832 0.434747 0.217374 organization -0.598935405599315 0.083351 -7.1857 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.921794407753777 R-squared 0.849704930166137 Adjusted R-squared 0.843772230041116 F-TEST (value) 143.223981030584 F-TEST (DF numerator) 6 F-TEST (DF denominator) 152 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 4.28063629106381 Sum Squared Residuals 2785.22475256862 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 0 2.35527674006072 -2.35527674006072 2 0 1.05701173816767 -1.05701173816767 3 0 -2.09966577724043 2.09966577724043 4 1 0.86410610380411 0.135893896195891 5 1 2.27126534880483 -1.27126534880483 6 1 -3.8927186590845 4.8927186590845 7 1 -2.61934869913644 3.61934869913644 8 1 3.31489464617775 -2.31489464617775 9 1 2.52724040537770 -1.52724040537770 10 1 -1.11818406900859 2.11818406900859 11 0 2.75286226518875 -2.75286226518875 12 0 5.15655243233965 -5.15655243233965 13 1 0.594268806546253 0.405731193453747 14 1 5.44254270418301 -4.44254270418301 15 1 1.24486533471772 -0.244865334717718 16 1 -7.01620282510459 8.0162028251046 17 0 2.17226782522578 -2.17226782522578 18 1 5.33120014280533 -4.33120014280533 19 1 -1.62541595452675 2.62541595452675 20 0 5.59508834691179 -5.59508834691179 21 0 4.33859809222888 -4.33859809222888 22 1 6.37888920798041 -5.37888920798041 23 1 3.29100863831267 -2.29100863831267 24 1 1.99142395361289 -0.991423953612893 25 1 -2.45233307000921 3.45233307000921 26 0 -0.703675739866027 0.703675739866027 27 1 -1.47461960295772 2.47461960295772 28 1 -0.431919471147852 1.43191947114785 29 1 0.552909571294732 0.447090428705268 30 1 -1.17312683195707 2.17312683195707 31 1 -3.94544430844236 4.94544430844236 32 0 6.4981533739515 -6.4981533739515 33 0 2.93204005820789 -2.93204005820789 34 1 -1.38312125018402 2.38312125018402 35 1 1.68612033163599 -0.686120331635993 36 1 0.882104076796281 0.117895923203719 37 1 1.12772979494499 -0.127729794944994 38 1 1.42792873874559 -0.427928738745594 39 1 4.41946739007753 -3.41946739007753 40 1 1.28687533614392 -0.286875336143922 41 1 -0.716042071211423 1.71604207121142 42 1 0.621624634213648 0.378375365786352 43 1 3.26580579998389 -2.26580579998389 44 1 -1.43787237222522 2.43787237222522 45 0 0.573359067643694 -0.573359067643694 46 1 -0.343694421609612 1.34369442160961 47 1 2.05855849194662 -1.05855849194662 48 1 1.47780049095921 -0.47780049095921 49 0 0.750930519615074 -0.750930519615074 50 1 2.99429104096763 -1.99429104096763 51 0 0.522603793771192 -0.522603793771192 52 1 -0.854377034957211 1.85437703495721 53 0 -2.84511076396449 2.84511076396449 54 11 14.3332966653358 -3.33329666533579 55 28 29.4924126519392 -1.49241265193924 56 26 22.9105361873595 3.08946381264054 57 22 23.0499600055460 -1.04996000554602 58 17 23.1168872333368 -6.11688723333682 59 12 19.0028419037980 -7.00284190379797 60 14 17.0519929723558 -3.05199297235575 61 17 21.9192281585312 -4.91922815853123 62 21 22.2934201557706 -1.29342015577064 63 19 23.0546560324631 -4.05465603246312 64 18 20.8714362697317 -2.87143626973166 65 10 19.5713889982832 -9.57138899828318 66 29 24.4292563383606 4.57074366163939 67 31 21.0348536751484 9.96514632485156 68 19 23.4990375657931 -4.49903756579307 69 9 18.7764373316480 -9.77643733164795 70 20 22.0327580601907 -2.03275806019067 71 28 20.3504796161214 7.6495203838786 72 19 19.6662239304356 -0.66622393043558 73 30 25.2967871644674 4.70321283553265 74 29 24.5891396798042 4.41086032019585 75 26 24.259835063473 1.740164936527 76 23 19.7364092416356 3.26359075836436 77 13 21.0301676396542 -8.03016763965417 78 21 21.8104085001022 -0.810408500102204 79 19 20.9604064911534 -1.96040649115335 80 28 22.6599971403279 5.34000285967211 81 23 23.1017713564233 -0.101771356423261 82 18 18.7159398722173 -0.715939872217272 83 21 19.8022053187895 1.19779468121049 84 20 23.9884130167395 -3.98841301673948 85 23 18.1020971438639 4.8979028561361 86 21 21.6608432313075 -0.660843231307518 87 21 22.4121695284147 -1.41216952841474 88 15 20.5938437229094 -5.59384372290941 89 28 24.9229293892126 3.07707061078740 90 19 18.2915302614863 0.708469738513742 91 26 19.4577740315687 6.54222596843127 92 10 18.2428496327671 -8.24284963276712 93 16 17.1947467262062 -1.19474672620616 94 22 21.8894583479626 0.110541652037439 95 19 20.1973876549923 -1.19738765499231 96 31 30.2615762525013 0.738423747498724 97 31 21.5096418090121 9.49035819098787 98 29 23.4310426644682 5.56895733553179 99 19 18.7454080056783 0.254591994321693 100 22 19.0531854252184 2.94681457478158 101 23 23.0452531846529 -0.0452531846528508 102 15 19.7697057445387 -4.76970574453872 103 20 22.3053185520451 -2.30531855204505 104 18 21.5001171655234 -3.50011716552340 105 23 19.9950016803619 3.00499831963808 106 25 17.5513040558338 7.44869594416625 107 21 17.5913944350305 3.40860556496945 108 24 19.2253014620759 4.77469853792407 109 25 22.0756857824347 2.92431421756527 110 17 17.4373548671346 -0.437354867134640 111 13 16.6510400910273 -3.65104009102732 112 28 21.2209485199661 6.77905148003393 113 21 20.2752064200783 0.724793579921674 114 25 29.7190399945621 -4.71903999456207 115 9 22.4184441855314 -13.4184441855314 116 16 20.7938108389790 -4.79381083897896 117 19 23.6425198183784 -4.64251981837842 118 17 18.3555635138014 -1.35556351380140 119 25 22.2864319416307 2.71356805836928 120 20 14.1371762472720 5.86282375272803 121 29 20.6111809383041 8.38881906169592 122 14 17.9638176891147 -3.96381768911471 123 22 22.956090318811 -0.956090318810997 124 15 18.0346173886098 -3.03461738860982 125 19 18.1265575427333 0.873442457266693 126 20 23.0924493487775 -3.09244934877753 127 15 20.0100241942237 -5.01002419422365 128 20 21.622530695816 -1.62253069581602 129 18 21.4164663472238 -3.4164663472238 130 33 22.5960964776673 10.4039035223327 131 22 21.9004432483096 0.0995567516903947 132 16 17.7840724232617 -1.78407242326173 133 17 21.0831067188311 -4.0831067188311 134 16 18.1916792967454 -2.19167929674543 135 21 18.5524040934593 2.44759590654073 136 26 26.1496230941262 -0.149623094126236 137 18 19.2639458007277 -1.26394580072772 138 18 20.1267014531789 -2.12670145317886 139 17 20.3771187045320 -3.37711870453198 140 22 20.3606484958433 1.63935150415672 141 30 20.1286961490405 9.87130385095954 142 30 25.4595211389135 4.54047886108649 143 24 24.615261967862 -0.615261967861999 144 21 18.4576083879096 2.54239161209042 145 21 23.4431652845378 -2.44316528453778 146 29 23.0587536934646 5.94124630653539 147 31 24.0808433066443 6.91915669335565 148 20 20.2957634957924 -0.295763495792428 149 16 14.9285762112834 1.07142378871659 150 22 20.4555500518469 1.54444994815310 151 20 22.1926438976135 -2.19264389761348 152 28 23.7237909655758 4.27620903442419 153 38 29.0525081146494 8.9474918853506 154 22 19.4289469521073 2.57105304789269 155 20 25.5927619696092 -5.59276196960924 156 17 19.6467937804679 -2.64679378046792 157 28 21.5625951045024 6.43740489549763 158 22 22.7171213252416 -0.717121325241629 159 31 21.9430450465658 9.05695495343418 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 10 0.000407290955334972 0.000814581910669945 0.999592709044665 11 2.21216285477553e-05 4.42432570955105e-05 0.999977878371452 12 2.39273947302360e-06 4.78547894604719e-06 0.999997607260527 13 1.28786390163766e-07 2.57572780327531e-07 0.99999987121361 14 2.12200797744121e-08 4.24401595488241e-08 0.99999997877992 15 1.16750403185834e-09 2.33500806371668e-09 0.999999998832496 16 9.03007723211601e-11 1.80601544642320e-10 0.9999999999097 17 6.34810879683548e-11 1.26962175936710e-10 0.999999999936519 18 9.90855974658904e-12 1.98171194931781e-11 0.999999999990091 19 1.28329333087353e-12 2.56658666174706e-12 0.999999999998717 20 1.64055353635786e-13 3.28110707271571e-13 0.999999999999836 21 1.26466847709161e-14 2.52933695418322e-14 0.999999999999987 22 7.55567739798786e-14 1.51113547959757e-13 0.999999999999925 23 1.48946437617379e-14 2.97892875234758e-14 0.999999999999985 24 2.9687809724021e-15 5.9375619448042e-15 0.999999999999997 25 2.79786605926472e-16 5.59573211852944e-16 1 26 1.33664934149003e-16 2.67329868298007e-16 1 27 1.73201706905090e-17 3.46403413810179e-17 1 28 1.70133811953406e-18 3.40267623906812e-18 1 29 3.15072064864349e-19 6.30144129728698e-19 1 30 3.05351684333925e-20 6.1070336866785e-20 1 31 4.93302545509385e-21 9.8660509101877e-21 1 32 6.35950858808717e-22 1.27190171761743e-21 1 33 7.84623206141659e-23 1.56924641228332e-22 1 34 8.48732009581346e-23 1.69746401916269e-22 1 35 1.40143590689700e-23 2.80287181379401e-23 1 36 3.70687078747777e-24 7.41374157495554e-24 1 37 6.720108001447e-25 1.3440216002894e-24 1 38 6.92851755772221e-26 1.38570351154444e-25 1 39 6.01649224281799e-26 1.20329844856360e-25 1 40 9.28337847888918e-27 1.85667569577784e-26 1 41 1.25408906199576e-27 2.50817812399151e-27 1 42 1.64846677782877e-28 3.29693355565754e-28 1 43 1.75810544072036e-29 3.51621088144072e-29 1 44 2.07765787871273e-30 4.15531575742545e-30 1 45 6.0193853697616e-31 1.20387707395232e-30 1 46 7.93640272171126e-32 1.58728054434225e-31 1 47 8.2464631947364e-33 1.64929263894728e-32 1 48 1.54419615383412e-33 3.08839230766824e-33 1 49 7.92515739829067e-34 1.58503147965813e-33 1 50 1.06847272408618e-34 2.13694544817236e-34 1 51 1.18180445461706e-34 2.36360890923413e-34 1 52 1.24300706698948e-35 2.48601413397896e-35 1 53 1.9680276145169e-35 3.9360552290338e-35 1 54 8.23459297625284e-20 1.64691859525057e-19 1 55 3.97127543886718e-10 7.94255087773436e-10 0.999999999602872 56 5.61442384398846e-09 1.12288476879769e-08 0.999999994385576 57 2.50928254760876e-09 5.01856509521752e-09 0.999999997490717 58 6.60710071924501e-09 1.32142014384900e-08 0.9999999933929 59 8.91369180537533e-08 1.78273836107507e-07 0.999999910863082 60 1.28204226659671e-07 2.56408453319341e-07 0.999999871795773 61 8.33016391299592e-08 1.66603278259918e-07 0.99999991669836 62 5.67988494893083e-08 1.13597698978617e-07 0.99999994320115 63 3.40644055530201e-08 6.81288111060403e-08 0.999999965935594 64 2.66609803815739e-08 5.33219607631478e-08 0.99999997333902 65 5.14659591533309e-07 1.02931918306662e-06 0.999999485340408 66 3.13711131503367e-06 6.27422263006735e-06 0.999996862888685 67 0.00150386185794496 0.00300772371588992 0.998496138142055 68 0.00121016335806792 0.00242032671613583 0.998789836641932 69 0.00670133734955046 0.0134026746991009 0.99329866265045 70 0.00486529037489766 0.00973058074979533 0.995134709625102 71 0.0379677761655389 0.0759355523310778 0.962032223834461 72 0.0299728855099968 0.0599457710199935 0.970027114490003 73 0.0475796512703207 0.0951593025406414 0.95242034872968 74 0.0813284772101544 0.162656954420309 0.918671522789846 75 0.0709978249904691 0.141995649980938 0.929002175009531 76 0.0818647199498573 0.163729439899715 0.918135280050143 77 0.180662380652447 0.361324761304894 0.819337619347553 78 0.154899336959468 0.309798673918936 0.845100663040532 79 0.132475541281848 0.264951082563697 0.867524458718152 80 0.181286480738198 0.362572961476395 0.818713519261802 81 0.157924800336725 0.315849600673450 0.842075199663275 82 0.138951548832335 0.277903097664671 0.861048451167665 83 0.125466059342716 0.250932118685432 0.874533940657284 84 0.115333993971884 0.230667987943768 0.884666006028116 85 0.133159855218402 0.266319710436805 0.866840144781598 86 0.110802607792049 0.221605215584099 0.88919739220795 87 0.0912565302442524 0.182513060488505 0.908743469755748 88 0.130253129038377 0.260506258076753 0.869746870961623 89 0.134557639255736 0.269115278511471 0.865442360744264 90 0.115664902304152 0.231329804608303 0.884335097695848 91 0.165267377963370 0.330534755926739 0.83473262203663 92 0.231848273352477 0.463696546704954 0.768151726647523 93 0.201350590612640 0.402701181225279 0.79864940938736 94 0.171289486132615 0.342578972265229 0.828710513867385 95 0.145098207875747 0.290196415751495 0.854901792124253 96 0.120210264617028 0.240420529234056 0.879789735382972 97 0.236495489880832 0.472990979761663 0.763504510119168 98 0.256755212594102 0.513510425188203 0.743244787405898 99 0.223079427749974 0.446158855499948 0.776920572250026 100 0.216676787838884 0.433353575677768 0.783323212161116 101 0.183491844690113 0.366983689380226 0.816508155309887 102 0.18476686458953 0.36953372917906 0.81523313541047 103 0.157053670418520 0.314107340837039 0.84294632958148 104 0.137264753379459 0.274529506758918 0.862735246620541 105 0.123639480658150 0.247278961316301 0.87636051934185 106 0.171962258438682 0.343924516877364 0.828037741561318 107 0.184741147789085 0.369482295578171 0.815258852210915 108 0.228875137540631 0.457750275081262 0.771124862459369 109 0.204965834976617 0.409931669953235 0.795034165023383 110 0.182213819648626 0.364427639297252 0.817786180351374 111 0.159483213571574 0.318966427143149 0.840516786428426 112 0.288384309698082 0.576768619396164 0.711615690301918 113 0.295441991661981 0.590883983323962 0.704558008338019 114 0.313335034929617 0.626670069859234 0.686664965070383 115 0.5759872432979 0.8480255134042 0.4240127567021 116 0.554504347412358 0.890991305175285 0.445495652587642 117 0.546933332481972 0.906133335036056 0.453066667518028 118 0.50578965918061 0.98842068163878 0.49421034081939 119 0.465838278847949 0.931676557695899 0.534161721152051 120 0.538706704594069 0.922586590811862 0.461293295405931 121 0.643710131506826 0.712579736986349 0.356289868493174 122 0.623090859738340 0.753818280523321 0.376909140261660 123 0.614202965300769 0.771594069398462 0.385797034699231 124 0.582282077085805 0.83543584582839 0.417717922914195 125 0.595852280355023 0.808295439289953 0.404147719644976 126 0.615565554089631 0.768868891820738 0.384434445910369 127 0.606006220857002 0.787987558285995 0.393993779142998 128 0.560323621264416 0.879352757471167 0.439676378735584 129 0.516564334431326 0.966871331137349 0.483435665568674 130 0.675789834562601 0.648420330874798 0.324210165437399 131 0.614217482585774 0.771565034828453 0.385782517414226 132 0.551899414772751 0.896201170454498 0.448100585227249 133 0.531872371958075 0.93625525608385 0.468127628041925 134 0.504032134107141 0.991935731785718 0.495967865892859 135 0.441594701248598 0.883189402497196 0.558405298751402 136 0.395473345701647 0.790946691403294 0.604526654298353 137 0.371026162074786 0.742052324149573 0.628973837925214 138 0.389067095186721 0.778134190373441 0.610932904813279 139 0.320387145582274 0.640774291164549 0.679612854417726 140 0.2527294301477 0.5054588602954 0.7472705698523 141 0.312664252003263 0.625328504006526 0.687335747996737 142 0.272880600970719 0.545761201941437 0.727119399029281 143 0.205692799860823 0.411385599721645 0.794307200139177 144 0.149412644731699 0.298825289463398 0.850587355268301 145 0.202278550869115 0.40455710173823 0.797721449130885 146 0.141759813199575 0.283519626399151 0.858240186800425 147 0.180817368814683 0.361634737629366 0.819182631185317 148 0.107688789096790 0.215377578193581 0.89231121090321 149 0.0577767529843776 0.115553505968755 0.942223247015622 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 60 0.428571428571429 NOK 5% type I error level 61 0.435714285714286 NOK 10% type I error level 64 0.457142857142857 NOK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

R code (references can be found in the software module):

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

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Software written by Ed van Stee & Patrick Wessa

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