*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: Wed, 01 Dec 2010 09:37:13 +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/01/t1291196394fc0h0ycukk3keej.htm/, Retrieved Wed, 01 Dec 2010 10:39:54 +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/01/t1291196394fc0h0ycukk3keej.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 «

4 4 3 3 2 2 2 2 2 4 2 4 2 3 1 1 2 3 3 2 2 1 2 2 5 4 4 3 4 3 2 2 4 4 4 2 2 1 1 2 4 4 4 4 2 3 3 3 4 4 4 4 4 4 2 2 1 1 2 3 4 4 2 3 3 2 3 3 4 4 3 4 1 2 2 2 2 3 2 2 1 3 1 2 4 3 4 3 4 3 4 4 1 2 2 2 4 4 4 3 5 4 4 4 4 4 4 3 4 4 3 3 4 4 3 3 2 2 2 2 2 2 2 2 4 4 2 4 4 3 4 3 2 2 1 3 3 2 4 2 4 4 4 4 3 3 1 3 2 2 2 2 4 4 3 3 4 4 4 4 3 3 3 4 1 1 1 2 2 2 3 1 4 2 2 2 2 2 1 3 3 4 3 3 4 3 4 4 1 2 1 2 3 2 4 3 4 4 4 4 1 1 1 2 4 5 4 2 3 2 4 3 1 3 2 2 1 4 4 4 4 4 3 3 4 3 2 3 4 4 4 4 2 2 2 4 4 3 4 4 2 2 2 2 4 4 4 4 5 5 5 4 3 3 4 4 2 1 1 2 4 3 3 3 4 4 4 3 2 2 1 2 3 3 3 4 1 1 1 1 4 3 4 3 4 2 4 3 4 3 2 2 4 4 4 2 3 3 3 3 4 4 4 3 3 4 4 3 3 3 4 3 2 2 1 3 1 1 2 2 2 2 1 2 4 3 3 3 3 4 3 3 5 1 3 2 1 1 1 2 3 3 3 3 2 2 2 2 3 2 3 3 4 3 4 3 3 2 2 2 3 2 2 3 4 3 3 3 4 4 4 4 4 4 4 4 2 2 4 3 2 2 2 2 1 1 1 1 1 2 2 2 4 3 4 3 2 3 3 3 4 4 4 5 3 4 4 4 5 4 3 5 1 NA 2 2 1 1 1 1 2 3 2 3 4 2 2 3 4 3 4 4 3 3 2 2 4 2 1 2 4 3 2 3 5 2 4 4 1 2 2 2 4 3 3 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 6 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 R Framework error message The field 'Names of X columns' contains a hard return which cannot be interpreted. Please, resubmit your request without hard returns in the 'Names of X columns'. Multiple Linear Regression - Estimated Regression Equation Q4 [t] = + 1.07639616086863 + 0.15332101187467Q1[t] + 0.230797317115352Q2[t] + 0.247490376625303Q3[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) 1.07639616086863 0.169658 6.3445 0 0 Q1 0.15332101187467 0.064714 2.3692 0.0191 0.00955 Q2 0.230797317115352 0.072552 3.1812 0.001783 0.000891 Q3 0.247490376625303 0.068065 3.6361 0.00038 0.00019 Multiple Linear Regression - Regression Statistics Multiple R 0.679846065001826 R-squared 0.462190672098467 Adjusted R-squared 0.451434485540436 F-TEST (value) 42.9697523006786 F-TEST (DF numerator) 3 F-TEST (DF denominator) 150 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.638029844270637 Sum Squared Residuals 61.062312327002 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 3 3.35534060670463 -0.355340606704631 2 2 2.33961357209929 -0.339613572099286 3 4 2.80120820632999 1.19879179367001 4 1 2.32292051258934 -1.32292051258934 5 2 2.81790126583994 -0.817901265839942 6 2 2.10881625498393 -0.108816254983934 7 3 3.75615199520461 -0.756151995204607 8 2 2.87705291296398 -0.877052912963978 9 2 3.60283098332994 -1.60283098332994 10 2 1.86132587835863 0.138674121641370 11 4 3.60283098332994 0.397169016670063 12 3 2.81790126583994 0.182098734160058 13 4 3.60283098332994 0.397169016670063 14 2 3.10785023007933 -1.10785023007933 15 3 1.95549524310926 1.04450475689074 16 3 3.10785023007933 -0.107850230079330 17 3 2.74042496059926 0.259575039400741 18 4 3.35534060670463 0.644659393295366 19 2 2.18629256022462 -0.186292560224616 20 2 2.57041088921464 -0.570410889214638 21 2 2.16959950071466 -0.169599500714665 22 3 3.37203366621458 -0.372033666214585 23 4 3.37203366621458 0.627966333785415 24 2 2.18629256022462 -0.186292560224616 25 3 3.60283098332994 -0.602830983329937 26 4 3.75615199520461 0.243848004795393 27 3 3.60283098332994 -0.602830983329937 28 3 3.35534060670463 -0.355340606704634 29 3 3.35534060670463 -0.355340606704634 30 2 2.33961357209929 -0.339613572099286 31 2 2.33961357209929 -0.339613572099286 32 4 3.10785023007933 0.89214976992067 33 3 3.37203366621458 -0.372033666214585 34 3 2.09212319547398 0.907876804526017 35 2 2.98791533722456 -0.987915337224563 36 4 3.60283098332994 0.397169016670063 37 3 2.47624152446400 0.523758475535995 38 2 2.33961357209929 -0.339613572099286 39 3 3.35534060670463 -0.355340606704634 40 4 3.60283098332994 0.397169016670063 41 4 2.97122227771461 1.02877772228539 42 2 1.70800486648396 0.29199513351604 43 1 2.58710394872459 -1.58710394872459 44 2 2.64625559584863 -0.646255595848626 45 3 2.09212319547398 0.907876804526017 46 3 3.20201959482996 -0.202019594829964 47 4 3.37203366621458 0.627966333785415 48 2 1.93880218359931 0.0611978164006874 49 3 2.98791533722456 0.0120846627754373 50 4 3.60283098332994 0.397169016670063 51 2 1.70800486648396 0.29199513351604 52 2 3.83362830044529 -1.83362830044529 53 3 2.98791533722456 0.0120846627754373 54 2 2.41708987733997 -0.417089877339968 55 4 3.14286794770593 0.857132052294073 56 3 3.35534060670463 -0.355340606704634 57 3 2.87705291296398 0.122947087036022 58 4 3.60283098332994 0.397169016670063 59 4 2.33961357209929 1.66038642790071 60 4 3.37203366621458 0.627966333785415 61 2 2.33961357209929 -0.339613572099286 62 4 3.60283098332994 0.397169016670063 63 4 4.23443968894526 -0.234439688945263 64 4 3.21871265433992 0.781287345660085 65 2 1.86132587835863 0.138674121641370 66 3 3.12454328958928 -0.124543289589282 67 3 3.60283098332994 -0.602830983329937 68 2 2.09212319547398 -0.0921231954739826 69 4 2.97122227771461 1.02877772228539 70 1 1.70800486648396 -0.70800486648396 71 3 3.37203366621458 -0.372033666214585 72 3 3.14123634909923 -0.141236349099233 73 2 2.87705291296398 -0.877052912963978 74 2 3.60283098332994 -1.60283098332994 75 3 2.97122227771461 0.0287777222853885 76 3 3.60283098332994 -0.602830983329937 77 3 3.44950997145527 -0.449509971455267 78 3 3.21871265433991 -0.218712654339915 79 3 2.09212319547398 0.907876804526017 80 2 1.95549524310926 0.0445047568907363 81 2 2.09212319547398 -0.0921231954739826 82 3 3.12454328958928 -0.124543289589282 83 3 3.20201959482996 -0.202019594829964 84 2 2.81626966723325 -0.816269667233247 85 2 1.70800486648396 0.29199513351604 86 3 2.97122227771461 0.0287777222853885 87 2 2.33961357209929 -0.339613572099286 88 3 2.74042496059926 0.259575039400741 89 3 3.37203366621458 -0.372033666214585 90 2 2.49293458397396 -0.492934583973956 91 3 2.49293458397396 0.507065416026044 92 3 3.12454328958928 -0.124543289589282 93 4 3.60283098332994 0.397169016670063 94 4 3.60283098332994 0.397169016670063 95 3 2.83459432534989 0.165405674650107 96 2 2.33961357209929 -0.339613572099286 97 1 1.70800486648396 -0.70800486648396 98 2 2.18629256022462 -0.186292560224616 99 3 3.37203366621458 -0.372033666214585 100 3 2.81790126583994 0.182098734160058 101 5 3.60283098332994 1.39716901667006 102 4 3.44950997145527 0.550490028544733 103 5 3.50866161857930 1.49133838142070 104 2 2.70800486648396 -0.70800486648396 105 1 0.570410889214638 0.429589110785362 106 3 2.64625559584863 0.353744404151374 107 3 2.37203366621458 0.627966333785415 108 4 4.72373190108931 -0.723731901089308 109 2 2.39876521922332 -0.398765219223323 110 2 1.87705291296398 0.122947087036022 111 3 2.29455736097390 0.705442639026097 112 4 4.18629256022462 -0.186292560224616 113 2 2.12454328958928 -0.124543289589282 114 3 2.89374597247393 0.106254027526071 115 3 2.12454328958928 0.875456710410718 116 4 3.2961889595806 0.703811040419403 117 4 4.33961357209929 -0.339613572099286 118 2 2.60283098332994 -0.602830983329937 119 3 4.21871265433991 -1.21871265433991 120 2 1.97122227771461 0.0287777222853885 121 3 2.60283098332994 0.397169016670063 122 4 4.58710394872459 -0.58710394872459 123 2 1.37203366621458 0.627966333785415 124 4 3.35534060670463 0.644659393295366 125 4 3.95549524310926 0.0445047568907363 126 2 2.35534060670463 -0.355340606704634 127 3 3.60283098332994 -0.602830983329937 128 3 2.49293458397396 0.507065416026044 129 3 1.70800486648396 1.29199513351604 130 3 2.10785023007933 0.89214976992067 131 4 3.98791533722456 0.0120846627754373 132 3 3.33961357209929 -0.339613572099286 133 2 1.72373190108931 0.276268098910692 134 3 3.12454328958928 -0.124543289589282 135 3 2.33961357209929 0.660386427900714 136 3 2.37203366621458 0.627966333785415 137 4 4.12454328958928 -0.124543289589282 138 3 2.44950997145527 0.550490028544733 139 4 3.12454328958928 0.875456710410718 140 4 3.60283098332994 0.397169016670063 141 4 4.37203366621458 -0.372033666214585 142 3 3.35534060670463 -0.355340606704634 143 3 3.72373190108931 -0.723731901089308 144 2 1.49293458397396 0.507065416026044 145 3 3.70800486648396 -0.70800486648396 146 1 1.33961357209929 -0.339613572099286 147 2 1.35534060670463 0.644659393295366 148 4 3.60283098332994 0.397169016670063 149 4 3.97122227771461 0.0287777222853885 150 3 2.97122227771461 0.0287777222853885 151 3 2.37203366621458 0.627966333785415 152 4 4.49293458397396 -0.492934583973956 153 2 2.35534060670463 -0.355340606704634 154 4 3.64625559584863 0.353744404151374 155 3 NA NA 156 3 NA NA Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 7 0.953640409640161 0.0927191807196777 0.0463595903598389 8 0.911404157858794 0.177191684282412 0.0885958421412058 9 0.952578596116796 0.094842807766408 0.047421403883204 10 0.934594316485384 0.130811367029232 0.0654056835146162 11 0.960230221152465 0.0795395576950707 0.0397697788475354 12 0.937245261420702 0.125509477158596 0.0627547385792978 13 0.940246095777792 0.119507808444416 0.0597539042222079 14 0.927681586456393 0.144636827087214 0.0723184135436072 15 0.934566782839005 0.130866434321989 0.0654332171609947 16 0.932281051856716 0.135437896286569 0.0677189481432844 17 0.912188834346024 0.175622331307951 0.0878111656539755 18 0.943052175647028 0.113895648705943 0.0569478243529717 19 0.92942504622922 0.141149907541559 0.0705749537707797 20 0.917914700991134 0.164170598017732 0.0820852990088658 21 0.88857856748649 0.222842865027022 0.111421432513511 22 0.857257951703201 0.285484096593597 0.142742048296799 23 0.862112552417483 0.275774895165034 0.137887447582517 24 0.83086652144435 0.338266957111301 0.169133478555650 25 0.810744589784024 0.378510820431951 0.189255410215976 26 0.793287639791108 0.413424720417784 0.206712360208892 27 0.772649796026682 0.454700407946637 0.227350203973318 28 0.727869019815989 0.544261960368022 0.272130980184011 29 0.680144282781603 0.639711434436794 0.319855717218397 30 0.634280291990666 0.731439416018668 0.365719708009334 31 0.586143634878096 0.827712730243807 0.413856365121904 32 0.733871276782383 0.532257446435233 0.266128723217617 33 0.69284535057358 0.61430929885284 0.30715464942642 34 0.752466991191753 0.495066017616493 0.247533008808247 35 0.787451636797771 0.425096726404458 0.212548363202229 36 0.779489503371634 0.441020993256731 0.220510496628366 37 0.767180192312907 0.465639615374186 0.232819807687093 38 0.732461287618452 0.535077424763095 0.267538712381548 39 0.69355851269896 0.612882974602079 0.306441487301040 40 0.681890182425455 0.63621963514909 0.318109817574545 41 0.765440997391671 0.469118005216658 0.234559002608329 42 0.730081573913542 0.539836852172916 0.269918426086458 43 0.879950138780336 0.240099722439327 0.120049861219664 44 0.872828148351847 0.254343703296307 0.127171851648153 45 0.895131549166631 0.209736901666738 0.104868450833369 46 0.871711962037091 0.256576075925818 0.128288037962909 47 0.88260956490517 0.23478087018966 0.11739043509483 48 0.855909643413307 0.288180713173386 0.144090356586693 49 0.827951704900328 0.344096590199344 0.172048295099672 50 0.814125145328291 0.371749709343418 0.185874854671709 51 0.78574851447763 0.428502971044741 0.214251485522370 52 0.93970033207259 0.120599335854819 0.0602996679274097 53 0.92420137592457 0.151597248150859 0.0757986240754297 54 0.912214617881641 0.175570764236718 0.087785382118359 55 0.931541509012683 0.136916981974634 0.0684584909873169 56 0.91943586665333 0.161128266693340 0.0805641333466699 57 0.901856638916617 0.196286722166767 0.0981433610833833 58 0.89231720519143 0.21536558961714 0.10768279480857 59 0.971693338249056 0.0566133235018884 0.0283066617509442 60 0.972282704315376 0.0554345913692477 0.0277172956846238 61 0.966455609513124 0.0670887809737518 0.0335443904868759 62 0.961384812462658 0.0772303750746847 0.0386151875373424 63 0.953090128881763 0.0938197422364734 0.0469098711182367 64 0.958630682899012 0.0827386342019754 0.0413693171009877 65 0.947891045211729 0.104217909576542 0.0521089547882711 66 0.934800903799464 0.130398192401071 0.0651990962005357 67 0.933980117039374 0.132039765921252 0.0660198829606259 68 0.91788880491181 0.164222390176380 0.0821111950881902 69 0.942383570724387 0.115232858551226 0.057616429275613 70 0.945271596904096 0.109456806191809 0.0547284030959045 71 0.93605611176071 0.127887776478579 0.0639438882392895 72 0.920508073989695 0.158983852020610 0.0794919260103051 73 0.936654170436566 0.126691659126869 0.0633458295634343 74 0.986798069335282 0.0264038613294368 0.0132019306647184 75 0.982303706710571 0.0353925865788578 0.0176962932894289 76 0.983586386693701 0.0328272266125972 0.0164136133062986 77 0.982505121806679 0.0349897563866428 0.0174948781933214 78 0.977853885116912 0.0442922297661763 0.0221461148830881 79 0.984664317607383 0.0306713647852348 0.0153356823926174 80 0.98030197127581 0.0393960574483806 0.0196980287241903 81 0.974005000038767 0.0519899999224661 0.0259949999612331 82 0.96716971175935 0.0656605764812994 0.0328302882406497 83 0.96098539000444 0.0780292199911187 0.0390146099955593 84 0.967462660789194 0.0650746784216112 0.0325373392108056 85 0.963666271528989 0.0726674569420221 0.0363337284710111 86 0.953281100855389 0.0934377982892223 0.0467188991446111 87 0.943605388187049 0.112789223625902 0.056394611812951 88 0.931669266846843 0.136661466306314 0.0683307331531572 89 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0.193577332364482 0.096788666182241 107 0.896118616900545 0.207762766198911 0.103881383099455 108 0.907742913888804 0.184514172222391 0.0922570861111957 109 0.906512999874817 0.186974000250366 0.0934870001251832 110 0.883832379550567 0.232335240898867 0.116167620449433 111 0.878755641924758 0.242488716150484 0.121244358075242 112 0.85065022285205 0.298699554295902 0.149349777147951 113 0.823086009940657 0.353827980118686 0.176913990059343 114 0.785493786256711 0.429012427486578 0.214506213743289 115 0.804477020146362 0.391045959707277 0.195522979853638 116 0.843334196470653 0.313331607058694 0.156665803529347 117 0.817865233916009 0.364269532167983 0.182134766083991 118 0.819342842123326 0.361314315753347 0.180657157876674 119 0.911346730830036 0.177306538339928 0.0886532691699638 120 0.88491325707545 0.230173485849100 0.115086742924550 121 0.860414917308698 0.279170165382605 0.139585082691302 122 0.863115706754717 0.273768586490566 0.136884293245283 123 0.849087003225375 0.301825993549249 0.150912996774625 124 0.840803257980424 0.318393484039152 0.159196742019576 125 0.798851971875008 0.402296056249983 0.201148028124992 126 0.77885964506833 0.442280709863339 0.221140354931669 127 0.804239530132885 0.391520939734229 0.195760469867115 128 0.7756534441729 0.448693111654199 0.224346555827100 129 0.952516867993328 0.0949662640133446 0.0474831320066723 130 0.968246952770584 0.0635060944588329 0.0317530472294165 131 0.958579843927095 0.0828403121458095 0.0414201560729047 132 0.941976274509904 0.116047450980192 0.0580237254900962 133 0.933189527800162 0.133620944399676 0.0668104721998381 134 0.912347219341293 0.175305561317415 0.0876527806587074 135 0.952340086498154 0.095319827003691 0.0476599135018455 136 0.930292188030068 0.139415623939864 0.0697078119699321 137 0.909595181687358 0.180809636625284 0.0904048183126422 138 0.910729929130197 0.178540141739606 0.0892700708698029 139 0.925591828833931 0.148816342332138 0.0744081711660689 140 0.891580807796973 0.216838384406055 0.108419192203027 141 0.961068389728592 0.0778632205428169 0.0389316102714084 142 0.944564795481105 0.110870409037790 0.0554352045188952 143 0.93503112063782 0.12993775872436 0.06496887936218 144 0.948029290240872 0.103941419518255 0.0519707097591276 145 0.90047880952389 0.199042380952222 0.0995211904761108 146 0.826290093983226 0.347419812033549 0.173709906016775 147 0.916336529456709 0.167326941086582 0.0836634705432912 148 0.782645537831845 0.434708924336309 0.217354462168155 149 0.527216052493395 0.94556789501321 0.472783947506605 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 7 0.048951048951049 OK 10% type I error level 27 0.188811188811189 NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/01/t1291196394fc0h0ycukk3keej/104m761291196222.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/01/t1291196394fc0h0ycukk3keej/104m761291196222.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/01/t1291196394fc0h0ycukk3keej/1f3ad1291196222.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/01/t1291196394fc0h0ycukk3keej/1f3ad1291196222.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/01/t1291196394fc0h0ycukk3keej/2f3ad1291196222.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/01/t1291196394fc0h0ycukk3keej/2f3ad1291196222.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/01/t1291196394fc0h0ycukk3keej/3f3ad1291196222.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/01/t1291196394fc0h0ycukk3keej/3f3ad1291196222.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/01/t1291196394fc0h0ycukk3keej/48u9x1291196222.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/01/t1291196394fc0h0ycukk3keej/48u9x1291196222.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/01/t1291196394fc0h0ycukk3keej/58u9x1291196222.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/01/t1291196394fc0h0ycukk3keej/58u9x1291196222.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/01/t1291196394fc0h0ycukk3keej/6j4qi1291196222.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/01/t1291196394fc0h0ycukk3keej/6j4qi1291196222.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/01/t1291196394fc0h0ycukk3keej/7tv731291196222.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/01/t1291196394fc0h0ycukk3keej/7tv731291196222.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/01/t1291196394fc0h0ycukk3keej/8tv731291196222.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/01/t1291196394fc0h0ycukk3keej/8tv731291196222.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/01/t1291196394fc0h0ycukk3keej/9tv731291196222.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/01/t1291196394fc0h0ycukk3keej/9tv731291196222.ps (open in new window)

Parameters (Session):

par1 = 4 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 4 ; 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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