*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: Tue, 14 Dec 2010 18:33:47 +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/14/t12923516463zt49k1lrv4oacb.htm/, Retrieved Tue, 14 Dec 2010 19:34:06 +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/2010/Dec/14/t12923516463zt49k1lrv4oacb.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 «

6 4 15 10 4 4 1 11 9 9 19 7 7 1 9 9 12 15 4 4 1 14 6 16 12 5 4 1 12 8 16 14 5 6 1 18 11 15 13 4 4 1 15 10 16 11 4 5 1 12 13 13 18 5 5 1 15 10 18 12 5 4 1 13 6 17 15 3 4 1 10 8 14 15 7 7 1 13 5 13 9 4 5 1 17 9 15 11 6 5 1 15 11 15 16 5 4 1 13 11 13 17 7 7 1 17 9 13 11 5 5 1 21 7 16 13 5 5 1 12 6 14 9 4 4 1 15 6 18 11 4 4 1 16 10 16 12 7 7 1 11 4 17 13 5 8 1 9 9 15 13 2 2 1 14 10 11 13 4 3 1 14 13 11 14 5 7 1 12 8 15 9 4 5 1 15 10 15 9 4 4 1 11 5 12 15 4 4 1 11 8 17 10 4 4 1 13 9 14 15 5 6 1 12 7 17 13 4 6 1 24 20 10 24 4 4 1 11 8 15 13 4 4 1 12 7 7 22 2 4 1 13 6 9 9 5 5 1 11 10 14 12 5 7 1 14 11 11 16 7 8 1 16 12 15 10 7 7 1 12 7 16 13 4 4 1 21 12 17 11 4 4 1 6 6 15 13 4 2 1 14 9 15 10 2 4 1 16 5 16 11 5 4 1 18 11 16 9 4 4 1 13 10 12 14 2 4 1 11 7 15 11 4 5 1 16 8 17 10 4 5 1 11 9 19 11 5 5 1 11 8 15 12 1 1 1 20 13 14 14 4 5 1 10 7 16 21 5 7 1 12 7 15 13 5 7 1 14 9 12 12 7 7 1 12 9 18 12 4 4 1 12 8 13 11 4 4 1 12 7 14 14 4 4 1 13 10 15 12 2 2 1 12 7 11 12 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 7 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Multiple Linear Regression - Estimated Regression Equation Ha[t] = + 20.6116433791875 + 0.0922363853607814PE[t] -0.121308271780651PC[t] -0.406200063771142De[t] -0.153397692032067DM[t] + 0.108700153383175DV[t] -0.98972587899186Geslacht[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) 20.6116433791875 1.271197 16.2144 0 0 PE 0.0922363853607814 0.059039 1.5623 0.120559 0.060279 PC -0.121308271780651 0.075033 -1.6167 0.108269 0.054135 De -0.406200063771142 0.051139 -7.943 0 0 DM -0.153397692032067 0.176284 -0.8702 0.385751 0.192876 DV 0.108700153383175 0.145222 0.7485 0.455454 0.227727 Geslacht -0.98972587899186 0.352609 -2.8069 0.005744 0.002872 Multiple Linear Regression - Regression Statistics Multiple R 0.600441188248882 R-squared 0.360529620545729 Adjusted R-squared 0.332108714792206 F-TEST (value) 12.685367020755 F-TEST (DF numerator) 6 F-TEST (DF denominator) 135 p-value 2.54611887129386e-11 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 1.93658428066618 Sum Squared Residuals 506.298421276653 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 15 15.4493119329308 -0.449311932930813 2 9 11.5140593109445 -2.51405931094449 3 12 13.0884794112542 -1.08847941125417 4 16 14.9787886526814 1.02121134731861 5 16 13.9566995176226 2.04330048237741 6 15 14.4883904634822 0.511609536517817 7 16 15.2540898601059 0.745910139894052 8 13 11.6166577502516 1.38334224974841 9 18 14.5857919509196 3.41420804908043 10 17 13.9747474600713 3.02525253992869 11 14 13.1679314524489 0.832068547551073 12 13 16.4885585758299 -3.48855857582992 13 15 15.2530755185440 -0.253075518544029 14 15 12.8396834240543 2.16031657594565 15 13 12.2683156656470 0.731684334352964 16 13 15.4064732105761 -2.40647321057609 17 16 15.2056351680382 0.794364831961761 18 14 16.1663137653053 -2.16631376530531 19 18 15.6306227938454 2.36937720615462 20 16 14.6973334123657 1.30266658763426 21 17 14.9732965899219 2.02670341007810 22 15 13.9902746160942 1.00972538390576 23 11 14.1320530404365 -3.13205304043653 24 11 13.6433310828241 -2.64333108282407 25 15 16.0323973751272 -1.03239737512719 26 15 15.9577898342651 -0.957789834265056 27 12 13.7581852690983 -1.75818526909834 28 17 15.4252607726121 1.57473922738791 29 14 13.5214275674316 0.478572432568422 30 17 14.6376055452064 2.36239445479355 31 10 9.48183362813846 0.51816637186154 32 15 14.2066605812987 0.793339418701334 33 7 11.0712000485640 -4.07120004856396 34 9 16.2138526120172 -7.2138526120172 35 14 14.5429468696260 -0.542946869625965 36 11 12.8754522681621 -1.87545226816213 37 15 15.2671169963467 -0.26711699634672 38 16 14.4202052384401 1.5797947615599 39 17 15.4561914753262 1.54380852467384 40 15 13.7706948912897 1.22930510871029 41 15 15.8874570409779 -0.887457040977917 42 16 15.6907697589547 0.309230241045258 43 16 16.1131907185667 -0.113190718566750 44 12 14.0491121287519 -2.04911212875192 45 15 15.2490691340048 -0.249069134004775 46 17 15.9951428527992 1.00485714720083 47 19 14.8530548984114 4.14694510158859 48 15 14.7469532610165 0.253046738983518 49 14 14.1327467802545 -0.132746780254479 50 16 11.1588347256669 4.84116527433314 51 15 14.5929080065576 0.407091993442444 52 12 14.6341689134248 -2.63416891342483 53 18 14.5837887586499 3.41621124135006 54 13 15.1112970942017 -2.11129709420173 55 14 14.0140051746690 -0.0140051746689567 56 15 14.6441119495279 0.355888050472148 57 11 14.6730076101792 -3.67300761017917 58 15 14.9558962099000 0.0441037900999627 59 14 13.4283530662774 0.571646933722574 60 16 15.1112970942017 0.88870290579827 61 14 11.7331422883433 2.26685771165673 62 18 16.1320767768088 1.86792322319115 63 14 15.2220004398545 -1.22200043985453 64 13 12.7536264823321 0.246373517667913 65 14 15.1112970942017 -1.11129709420173 66 17 15.7735599357250 1.22644006427498 67 12 13.8017495009573 -1.80174950095731 68 16 14.0674028632754 1.93259713672461 69 15 15.2122336295201 -0.212233629520055 70 16 15.5700567307859 0.429943269214065 71 14 14.2439151036267 -0.243915103626682 72 17 15.6901999260903 1.30980007390967 73 14 14.8983222699247 -0.89832226992471 74 16 13.5787332244779 2.42126677552206 75 12 14.9057906969930 -2.90579069699302 76 13 13.3751777808306 -0.375177780830625 77 19 16.0078287007591 2.99217129924090 78 11 12.7663330969357 -1.76633309693566 79 15 13.9892602745323 1.01073972546768 80 12 13.2938414324875 -1.29384143248746 81 14 14.4961540815470 -0.496154081547034 82 11 13.4459819107761 -2.44598191077607 83 15 14.4120226025320 0.587977397468048 84 12 12.4317230401951 -0.431723040195107 85 14 14.0430770610888 -0.0430770610888261 86 13 16.0105922792596 -3.01059227925965 87 9 10.3053490308667 -1.30534903086673 88 12 12.6945455890623 -0.694545589062288 89 15 14.6362952065956 0.363704793404361 90 17 15.4777672205578 1.52223277944221 91 14 12.9029710238964 1.09702897610355 92 11 9.18600914328489 1.81399085671511 93 13 14.0759370645615 -1.07593706456151 94 10 14.4708847198847 -4.47088471988472 95 12 14.8217823188791 -2.82178231887912 96 15 13.6832817311873 1.31671826881269 97 13 14.4355348936202 -1.43553489362023 98 13 13.8376682739271 -0.837668273927086 99 12 13.0242792956771 -1.02427929567710 100 9 10.1346494550189 -1.13464945501890 101 16 16.2362062656749 -0.236206265674917 102 17 14.2063645842498 2.79363541575023 103 13 14.4564241441320 -1.45642414413195 104 10 12.4626783476043 -2.46267834760426 105 13 13.8260744970915 -0.826074497091531 106 16 15.3610606570350 0.638939342964982 107 15 13.3837786285297 1.61622137147028 108 16 14.8499175932995 1.15008240670048 109 11 13.6138392924018 -2.61383929240178 110 15 14.1162298873647 0.883770112635278 111 17 14.5217680611110 2.47823193888896 112 14 12.9947883914139 1.00521160858607 113 18 15.8221440876328 2.17785591236718 114 14 13.1506082935589 0.849391706441079 115 14 14.2683037192404 -0.268303719240363 116 12 14.0293348298491 -2.02933482984909 117 11 13.2750784751465 -2.27507847514654 118 14 13.4088504893492 0.591149510650755 119 16 12.4594179415912 3.54058205840881 120 17 13.9206346764659 3.07936532353409 121 14 13.3673148605073 0.632685139492674 122 14 13.3091710876676 0.690828912332412 123 12 13.5308983807172 -1.53089838071717 124 12 13.3775006886851 -1.3775006886851 125 11 11.5238048462047 -0.523804846204728 126 15 13.2382429706618 1.76175702933818 127 14 12.6553337542340 1.34466624576603 128 10 11.9193014876419 -1.91930148764192 129 13 13.9370984444883 -0.937098444488308 130 15 14.5518224392997 0.448177560700292 131 15 13.7452811536520 1.25471884634803 132 16 14.1929183500589 1.80708164994107 133 8 10.3685135298076 -2.36851352980764 134 9 10.9952821690910 -1.99528216909102 135 15 14.3107377513497 0.689262248650278 136 11 12.9539987410982 -1.95399874109819 137 15 15.1765878863135 -0.176587886313455 138 16 14.6653670930155 1.33463290698449 139 16 13.7229585437350 2.27704145626497 140 15 12.8710578294136 2.12894217058642 141 13 14.4708847198847 -1.47088471988472 142 15 15.0654654427106 -0.0654654427105774 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 10 0.819993140975346 0.360013718049307 0.180006859024654 11 0.764685943793288 0.470628112413425 0.235314056206712 12 0.915189372684317 0.169621254631365 0.0848106273156826 13 0.869782340878511 0.260435318242978 0.130217659121489 14 0.80888469706828 0.382230605863439 0.191115302931719 15 0.739204828961177 0.521590342077646 0.260795171038823 16 0.778304520120106 0.443390959759787 0.221695479879894 17 0.703690144530546 0.592619710938908 0.296309855469454 18 0.676050616807482 0.647898766385035 0.323949383192518 19 0.679117931657999 0.641764136684002 0.320882068342001 20 0.685598801221023 0.628802397557955 0.314401198778977 21 0.71633708396797 0.56732583206406 0.28366291603203 22 0.649479703068981 0.701040593862038 0.350520296931019 23 0.772536811580957 0.454926376838087 0.227463188419043 24 0.802156242871797 0.395687514256405 0.197843757128203 25 0.751275938883851 0.497448122232298 0.248724061116149 26 0.694604674616533 0.610790650766934 0.305395325383467 27 0.740188879708788 0.519622240582423 0.259811120291212 28 0.744887499698441 0.510225000603117 0.255112500301559 29 0.689701224737849 0.620597550524303 0.310298775262151 30 0.693714604249984 0.612570791500032 0.306285395750016 31 0.65388799436874 0.69222401126252 0.34611200563126 32 0.60117968762429 0.797640624751421 0.398820312375710 33 0.796350199918158 0.407299600163683 0.203649800081842 34 0.992787777772855 0.0144244444542903 0.00721222222714517 35 0.989506199992083 0.0209876000158342 0.0104938000079171 36 0.988761608949256 0.0224767821014889 0.0112383910507445 37 0.98388592404454 0.0322281519109216 0.0161140759554608 38 0.98159457173855 0.0368108565229014 0.0184054282614507 39 0.978016087131857 0.0439678257362855 0.0219839128681428 40 0.972441493229139 0.0551170135417224 0.0275585067708612 41 0.963904020453423 0.072191959093154 0.036095979546577 42 0.951678272354717 0.0966434552905661 0.0483217276452831 43 0.93637951379098 0.127240972418039 0.0636204862090193 44 0.93307611193044 0.133847776139121 0.0669238880695607 45 0.914504868933692 0.170990262132615 0.0854951310663077 46 0.899264546705053 0.201470906589893 0.100735453294947 47 0.955181095941672 0.0896378081166554 0.0448189040583277 48 0.9413764886978 0.117247022604399 0.0586235113021997 49 0.924312143428659 0.151375713142682 0.0756878565713411 50 0.980708664886307 0.038582670227386 0.019291335113693 51 0.97420655131252 0.0515868973749599 0.0257934486874799 52 0.9787911461042 0.042417707791599 0.0212088538957995 53 0.988651426121447 0.0226971477571062 0.0113485738785531 54 0.988976528129713 0.0220469437405730 0.0110234718702865 55 0.984734808796393 0.0305303824072132 0.0152651912036066 56 0.979314378096749 0.0413712438065028 0.0206856219032514 57 0.990722241564786 0.0185555168704275 0.00927775843521373 58 0.987050235653956 0.0258995286920877 0.0129497643460439 59 0.982706931936772 0.0345861361264564 0.0172930680632282 60 0.97792298853944 0.0441540229211212 0.0220770114605606 61 0.980560936809389 0.0388781263812226 0.0194390631906113 62 0.980231332971776 0.0395373340564487 0.0197686670282243 63 0.975754591678643 0.0484908166427132 0.0242454083213566 64 0.968075736741943 0.0638485265161132 0.0319242632580566 65 0.961175206050035 0.0776495878999303 0.0388247939499652 66 0.954308999364696 0.0913820012706085 0.0456910006353043 67 0.948588879015504 0.102822241968992 0.051411120984496 68 0.951251459811476 0.0974970803770482 0.0487485401885241 69 0.937171707155841 0.125656585688317 0.0628282928441587 70 0.922088381251404 0.155823237497192 0.0779116187485962 71 0.902110912641216 0.195778174717567 0.0978890873587837 72 0.895021822035629 0.209956355928742 0.104978177964371 73 0.87627965444001 0.247440691119980 0.123720345559990 74 0.899746955200468 0.200506089599063 0.100253044799532 75 0.915919423046853 0.168161153906294 0.0840805769531472 76 0.896365276908167 0.207269446183666 0.103634723091833 77 0.930776686785453 0.138446626429094 0.0692233132145468 78 0.92377771987421 0.152444560251580 0.0762222801257899 79 0.915860664207275 0.16827867158545 0.084139335792725 80 0.900873012341182 0.198253975317637 0.0991269876588184 81 0.878493079409112 0.243013841181775 0.121506920590888 82 0.879651067145173 0.240697865709654 0.120348932854827 83 0.863035896776579 0.273928206446842 0.136964103223421 84 0.84528849887592 0.309423002248161 0.154711501124081 85 0.848293756330775 0.303412487338451 0.151706243669225 86 0.838508714426038 0.322982571147923 0.161491285573962 87 0.805607305107952 0.388785389784097 0.194392694892048 88 0.775616410244204 0.448767179511593 0.224383589755796 89 0.74227896981148 0.51544206037704 0.25772103018852 90 0.726235176046529 0.547529647906942 0.273764823953471 91 0.69596619187901 0.608067616241979 0.304033808120989 92 0.714580093972935 0.570839812054131 0.285419906027065 93 0.694787749964385 0.61042450007123 0.305212250035615 94 0.86732942346801 0.265341153063979 0.132670576531989 95 0.912091764176052 0.175816471647895 0.0879082358239476 96 0.903419606146111 0.193160787707778 0.096580393853889 97 0.900944610548836 0.198110778902327 0.0990553894511636 98 0.875300379613685 0.249399240772631 0.124699620386315 99 0.850599283890285 0.29880143221943 0.149400716109715 100 0.822068518274965 0.355862963450070 0.177931481725035 101 0.806849922319794 0.386300155360412 0.193150077680206 102 0.846295105666798 0.307409788666404 0.153704894333202 103 0.850777713029256 0.298444573941489 0.149222286970744 104 0.862296622984455 0.27540675403109 0.137703377015545 105 0.838735968850963 0.322528062298073 0.161264031149037 106 0.808256293133071 0.383487413733858 0.191743706866929 107 0.792112788914092 0.415774422171816 0.207887211085908 108 0.75668429753811 0.48663140492378 0.24331570246189 109 0.795523552951821 0.408952894096357 0.204476447048179 110 0.750648526763773 0.498702946472454 0.249351473236227 111 0.744844519300896 0.510310961398209 0.255155480699104 112 0.705945074205278 0.588109851589443 0.294054925794722 113 0.67442961963316 0.651140760733681 0.325570380366840 114 0.623631443839538 0.752737112320924 0.376368556160462 115 0.569229855611532 0.861540288776935 0.430770144388468 116 0.608537269895157 0.782925460209687 0.391462730104844 117 0.63896773044002 0.72206453911996 0.36103226955998 118 0.572737020052852 0.854525959894296 0.427262979947148 119 0.765787693152645 0.468424613694711 0.234212306847355 120 0.85102677468803 0.29794645062394 0.14897322531197 121 0.803225021031993 0.393549957936013 0.196774978968007 122 0.750593539812435 0.498812920375129 0.249406460187564 123 0.726920096771044 0.546159806457911 0.273079903228956 124 0.694156948550353 0.611686102899294 0.305843051449647 125 0.61569196650106 0.76861606699788 0.38430803349894 126 0.611559284793958 0.776881430412084 0.388440715206042 127 0.574794239309141 0.850411521381717 0.425205760690859 128 0.510420616462203 0.979158767075594 0.489579383537797 129 0.459797529062467 0.919595058124935 0.540202470937533 130 0.342421881518417 0.684843763036833 0.657578118481583 131 0.241342343340833 0.482684686681666 0.758657656659167 132 0.159663248034030 0.319326496068061 0.84033675196597 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 0 0 OK 5% type I error level 19 0.154471544715447 NOK 10% type I error level 28 0.227642276422764 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 = 3 ; 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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