WS7 lineaire trend?

*The author of this computation has been verified*

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

Title produced by software: Multiple Regression

Date of computation: Tue, 30 Nov 2010 17:05:31 +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/Nov/30/t1291136661ykd7dwqmu3sjd3r.htm/, Retrieved Tue, 30 Nov 2010 18:04:21 +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/Nov/30/t1291136661ykd7dwqmu3sjd3r.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 «

1 24 14 11 12 24 26 1 25 11 7 8 25 23 1 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 2 17 11 13 7 21 25 2 23 13 14 12 19 24 2 30 12 16 10 19 18 2 23 8 11 10 15 22 2 18 12 10 8 16 15 2 15 11 11 8 23 22 2 12 4 15 4 27 28 2 21 9 9 9 22 20 2 15 8 11 8 14 12 2 20 8 17 7 22 24 3 31 14 17 11 23 20 3 27 15 11 9 23 21 3 34 16 18 11 21 20 3 21 9 14 13 19 21 3 31 14 10 8 18 23 3 19 11 11 8 20 28 3 16 8 15 9 23 24 3 20 9 15 6 25 24 3 21 9 13 9 19 24 3 22 9 16 9 24 23 3 17 9 13 6 22 23 3 24 10 9 6 25 29 3 25 16 18 16 26 24 3 26 11 18 5 29 18 3 25 8 12 7 32 25 3 17 9 17 9 25 21 3 32 16 9 6 29 26 3 33 11 9 6 28 22 3 13 16 12 5 17 22 3 32 12 18 12 28 22 3 25 12 12 7 29 23 3 29 14 18 10 26 30 3 22 9 14 9 25 23 3 18 10 15 8 14 17 3 17 9 16 5 25 23 3 20 10 10 8 26 23 3 15 12 11 8 20 25 3 20 14 14 10 18 24 3 33 14 9 6 32 24 3 29 10 12 8 25 23 3 23 14 17 7 25 21 3 26 16 5 4 23 24 3 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 7 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Multiple Linear Regression - Estimated Regression Equation PStandards[t] = + 9.08042770775861 -0.59742840663213Week[t] + 0.334373957930553Consern[t] -0.360543884942166Doubts[t] + 0.194459349122136PExpect[t] + 0.0119042895646442PCritisism[t] + 0.390931450917962Organisation[t] + 0.00518174230172207t + 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) 9.08042770775861 2.675944 3.3934 0.000882 0.000441 Week -0.59742840663213 0.654515 -0.9128 0.362813 0.181407 Consern 0.334373957930553 0.055969 5.9743 0 0 Doubts -0.360543884942166 0.107471 -3.3548 0.001004 0.000502 PExpect 0.194459349122136 0.101631 1.9134 0.057591 0.028795 PCritisism 0.0119042895646442 0.129376 0.092 0.926809 0.463405 Organisation 0.390931450917962 0.074053 5.2791 0 0 t 0.00518174230172207 0.011773 0.4402 0.660454 0.330227 Multiple Linear Regression - Regression Statistics Multiple R 0.610183506023453 R-squared 0.372323911023073 Adjusted R-squared 0.343226343984408 F-TEST (value) 12.7957059271767 F-TEST (DF numerator) 7 F-TEST (DF denominator) 151 p-value 7.55950857467269e-13 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 3.41748962153724 Sum Squared Residuals 1763.56453231053 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 24 23.9116636835574 0.0883363164425639 2 25 23.3346021311152 1.66539786888483 3 30 25.1939680277406 4.80603197225942 4 19 21.227182072629 -2.22718207262898 5 22 21.5116365388364 0.488363461163561 6 22 24.0124885254431 -2.01248852544306 7 25 23.5612680779791 1.43873192202093 8 23 20.3880143268971 2.61198567310293 9 17 19.7969982021306 -2.79699820213059 10 21 22.0403507064565 -1.04035070645649 11 19 23.1937377724846 -4.19373777248459 12 19 23.9196025188496 -4.91960251884957 13 15 23.6177711534672 -8.61777115346725 14 16 17.5541194816704 -1.55411948167037 15 23 19.8477027406705 3.15229725932953 16 27 24.4493787475134 2.55062125248656 17 22 21.426520432226 0.573479567773982 18 14 17.0355651132225 -3.03556511322252 19 22 24.5586458613607 -2.55864586136073 20 23 23.9651407792001 -0.965140779200138 21 23 21.4726495818933 1.52735041810667 22 21 24.4519977168330 -3.45199771683305 23 19 22.2710278341914 -3.27102783419144 24 18 23.7617337886120 -5.76173378861203 25 20 22.9851762942856 -2.98517629428555 26 23 22.2948837000035 0.705116299996546 27 25 23.2413045203913 1.75869547960871 28 19 23.2276543910732 -4.22765439107323 29 24 23.7596566877539 0.240343312246051 30 22 21.4738777243426 0.526122275657438 31 25 25.0268845962352 -0.02688459623522 32 26 23.1176967699704 2.88230323002964 33 29 22.7834360041946 6.2165639958054 34 32 25.1294480842145 6.87055191578552 35 25 21.5314737991977 3.46852620080227 36 29 24.3917273087814 4.60827269121863 37 28 24.9702766300526 3.02972336994737 38 17 17.0567335468342 -0.0567335468342179 39 28 26.1072821512704 1.89271784872955 40 29 22.9365000964202 6.06349990357978 41 26 27.4970790204123 -1.49707902041231 42 25 23.4381006394321 1.56189936056794 43 14 19.5822090191191 -5.58220901911912 44 25 22.1178958743684 2.88210412563156 45 26 21.6346123794808 4.36538762051923 46 20 20.2231588132035 -0.223158813203450 47 18 21.3953777508513 -3.39537775085134 48 32 24.727507042381 7.272492957619 49 25 25.0536236683069 -0.0536236683069085 50 25 21.7889156774668 3.21108432253324 51 23 20.8797008182701 2.12029918172988 52 21 22.1425306938361 -1.14253069383611 53 20 24.0196422707286 -4.01964227072863 54 15 16.5520832674171 -1.55208326741709 55 30 26.7749972455585 3.2250027544415 56 24 25.3507310413086 -1.35073104130858 57 26 24.3181857048787 1.68181429512134 58 24 21.7830382919371 2.21696170806288 59 22 21.4374588120518 0.562541187948228 60 14 15.7502332326531 -1.75023323265312 61 24 22.2576281571037 1.74237184289633 62 24 23.0075768756957 0.992423124304322 63 24 23.3930123746106 0.60698762538941 64 24 19.9966029547642 4.00339704523579 65 19 18.5532541266379 0.446745873362123 66 31 26.8985986428594 4.10140135714059 67 22 26.7332028172792 -4.73320281727917 68 27 21.5814775249625 5.41852247503753 69 19 17.7572833253661 1.24271667463385 70 25 22.3799343030397 2.62006569696029 71 20 25.1515000704160 -5.15150007041597 72 21 21.5943257099521 -0.594325709952094 73 27 27.6409800161059 -0.640980016105898 74 23 24.5829167645659 -1.58291676456588 75 25 25.8872033493752 -0.887203349375234 76 20 22.4054240610342 -2.40542406103416 77 21 19.3590672579264 1.64093274207362 78 22 22.5995692004550 -0.599569200454967 79 23 23.1009185954322 -0.100918595432204 80 25 24.2990591558625 0.700940844137541 81 25 23.5530138665333 1.44698613346670 82 17 23.9670181704281 -6.96701817042806 83 19 21.6372513714409 -2.63725137144087 84 25 24.1392842239123 0.860715776087671 85 19 21.9444942356742 -2.94449423567416 86 20 22.7692487362938 -2.76924873629376 87 26 22.1388690387977 3.86113096120232 88 23 20.2970829187869 2.70291708121311 89 27 24.0663349088872 2.93366509111278 90 17 20.5311399253393 -3.53113992533928 91 17 23.008381173949 -6.00838117394901 92 19 19.7179098799793 -0.717909879979271 93 17 19.3576956688508 -2.35769566885085 94 22 21.7355310752216 0.264468924778369 95 21 23.1044347468696 -2.10443474686963 96 32 28.3390307188285 3.66096928117148 97 21 24.3930893880104 -3.39308938801039 98 21 24.0609793307881 -3.06097933078813 99 18 20.9383194909969 -2.93831949099694 100 18 21.010579958999 -3.01057995899902 101 23 22.5447258384408 0.455274161559222 102 19 20.3255523664996 -1.32555236649959 103 20 20.7356914760935 -0.735691476093464 104 21 22.0004204964955 -1.00042049649547 105 20 23.4728914787342 -3.47289147873415 106 17 18.6142593762223 -1.61425937622229 107 18 20.0564207282979 -2.05642072829787 108 19 20.5414084736735 -1.54140847367351 109 22 21.8246564425116 0.175343557488359 110 15 18.5119470261793 -3.51194702617930 111 14 18.5729376341405 -4.57293763414053 112 18 26.3857448443021 -8.38574484430213 113 24 21.1134633439985 2.88653665600147 114 35 23.3940245923100 11.6059754076900 115 29 18.8107621069514 10.1892378930486 116 21 21.7272762440235 -0.72727624402346 117 25 20.3609033860040 4.63909661399597 118 20 18.2697916702172 1.73020832978275 119 22 23.0254596391535 -1.02545963915346 120 13 16.7194203948531 -3.71942039485315 121 26 23.0578914676694 2.94210853233062 122 17 16.7098847498096 0.290115250190359 123 25 19.9177567099860 5.08224329001397 124 20 20.4759765211343 -0.475976521134335 125 19 17.8929504636612 1.10704953633881 126 21 22.4575766582009 -1.45757665820091 127 22 20.8546191144808 1.14538088551920 128 24 22.4739784008254 1.52602159917458 129 21 22.7662384491393 -1.76623844913926 130 26 25.3586402327816 0.641359767218398 131 24 20.4554515031862 3.54454849681380 132 16 20.1180994027268 -4.11809940272676 133 23 22.1821401397328 0.817859860267226 134 18 20.6398744684833 -2.63987446848331 135 16 22.2268334361784 -6.22683343617845 136 26 24.0108052344949 1.98919476550514 137 19 18.9558404602806 0.0441595397194419 138 21 16.8152181489148 4.18478185108522 139 21 22.0339880840301 -1.03398808403006 140 22 18.4375542912706 3.56244570872936 141 23 19.7352571555317 3.26474284446833 142 29 24.7676386593589 4.23236134064111 143 21 19.2234885109231 1.77651148907692 144 21 19.8536715287965 1.14632847120354 145 23 21.8140973677558 1.18590263224418 146 27 22.9682244779554 4.03177552204464 147 25 25.4137730395503 -0.413773039550292 148 21 20.9412080216718 0.0587919783282198 149 10 17.0906417040770 -7.09064170407698 150 20 22.5999542231388 -2.59995422313884 151 26 22.4835124994265 3.51648750057351 152 24 23.6610462985751 0.338953701424892 153 29 31.7277367555290 -2.72773675552905 154 19 19.0850685418013 -0.085068541801287 155 24 22.0779523273866 1.92204767261340 156 19 20.7474859458915 -1.74748594589149 157 24 23.4357460343574 0.564253965642631 158 22 21.8150109877998 0.184989012200154 159 17 23.8153269286905 -6.81532692869054 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 11 0.45330165034606 0.90660330069212 0.54669834965394 12 0.348817051836565 0.697634103673131 0.651182948163435 13 0.461664840572019 0.923329681144038 0.538335159427981 14 0.373255236166306 0.746510472332611 0.626744763833694 15 0.633768216198002 0.732463567603996 0.366231783801998 16 0.566200127021235 0.86759974595753 0.433799872978765 17 0.571086172781664 0.857827654436673 0.428913827218336 18 0.546604481746558 0.906791036506884 0.453395518253442 19 0.458956640215519 0.917913280431037 0.541043359784481 20 0.572015782557865 0.855968434884269 0.427984217442135 21 0.612999741971446 0.774000516057107 0.387000258028554 22 0.54749609814778 0.90500780370444 0.45250390185222 23 0.483379063869196 0.966758127738393 0.516620936130804 24 0.47582933437832 0.95165866875664 0.52417066562168 25 0.416347724308251 0.832695448616503 0.583652275691749 26 0.372959935178656 0.745919870357311 0.627040064821344 27 0.357107794410066 0.714215588820132 0.642892205589934 28 0.324354572922373 0.648709145844746 0.675645427077627 29 0.303420222453375 0.60684044490675 0.696579777546625 30 0.254891602776697 0.509783205553393 0.745108397223303 31 0.222883491383068 0.445766982766135 0.777116508616932 32 0.257429546700414 0.514859093400827 0.742570453299586 33 0.359917141578272 0.719834283156545 0.640082858421728 34 0.480774513980847 0.961549027961693 0.519225486019154 35 0.430664622805647 0.861329245611295 0.569335377194353 36 0.396868841903905 0.79373768380781 0.603131158096095 37 0.344425349856268 0.688850699712536 0.655574650143732 38 0.337727445906457 0.675454891812915 0.662272554093543 39 0.307087504028610 0.614175008057221 0.69291249597139 40 0.304673961414871 0.609347922829741 0.69532603858513 41 0.384617901632646 0.769235803265293 0.615382098367354 42 0.350636520363868 0.701273040727735 0.649363479636132 43 0.586158212972036 0.827683574055927 0.413841787027964 44 0.548911709284171 0.902176581431658 0.451088290715829 45 0.52436379089627 0.95127241820746 0.47563620910373 46 0.49311984723313 0.98623969446626 0.50688015276687 47 0.538729570985174 0.922540858029651 0.461270429014826 48 0.590908702717332 0.818182594565336 0.409091297282668 49 0.583667818062155 0.83266436387569 0.416332181937845 50 0.552334091479206 0.895331817041589 0.447665908520794 51 0.51565376399874 0.96869247200252 0.48434623600126 52 0.503619914705028 0.992760170589945 0.496380085294973 53 0.587049095699573 0.825901808600855 0.412950904300427 54 0.561088262702726 0.877823474594549 0.438911737297274 55 0.55129422676115 0.8974115464777 0.44870577323885 56 0.543651514782118 0.912696970435764 0.456348485217882 57 0.498347469244222 0.996694938488444 0.501652530755778 58 0.460303928865576 0.920607857731153 0.539696071134424 59 0.413985463926883 0.827970927853767 0.586014536073117 60 0.382785975455276 0.765571950910552 0.617214024544724 61 0.340946971339271 0.681893942678543 0.659053028660729 62 0.307687224549679 0.615374449099358 0.692312775450321 63 0.27197597395141 0.54395194790282 0.72802402604859 64 0.279919341555579 0.559838683111157 0.720080658444421 65 0.242324751997316 0.484649503994632 0.757675248002684 66 0.245397761647327 0.490795523294653 0.754602238352673 67 0.359264860320586 0.718529720641171 0.640735139679414 68 0.407183535358206 0.814367070716413 0.592816464641794 69 0.366917630995067 0.733835261990134 0.633082369004933 70 0.344145064074794 0.688290128149587 0.655854935925206 71 0.453144848051643 0.906289696103286 0.546855151948357 72 0.411635243123268 0.823270486246536 0.588364756876732 73 0.379160923730190 0.758321847460381 0.62083907626981 74 0.352387917314153 0.704775834628307 0.647612082685847 75 0.325586740813563 0.651173481627126 0.674413259186437 76 0.304480381064307 0.608960762128615 0.695519618935693 77 0.280680293450984 0.561360586901968 0.719319706549016 78 0.244761065769667 0.489522131539333 0.755238934230334 79 0.211968339694138 0.423936679388276 0.788031660305862 80 0.189143062476510 0.378286124953019 0.81085693752349 81 0.176937131330905 0.35387426266181 0.823062868669095 82 0.259925787376070 0.519851574752139 0.74007421262393 83 0.242015348617196 0.484030697234391 0.757984651382804 84 0.208745812990384 0.417491625980767 0.791254187009616 85 0.202003787515489 0.404007575030978 0.797996212484511 86 0.189144997109618 0.378289994219236 0.810855002890382 87 0.209201275156253 0.418402550312507 0.790798724843747 88 0.205337819342912 0.410675638685824 0.794662180657088 89 0.202580446196324 0.405160892392649 0.797419553803676 90 0.196103230361503 0.392206460723005 0.803896769638497 91 0.251531488708055 0.50306297741611 0.748468511291945 92 0.215090706641149 0.430181413282298 0.784909293358851 93 0.190901902146039 0.381803804292077 0.809098097853961 94 0.163258885820493 0.326517771640986 0.836741114179507 95 0.142769049032862 0.285538098065725 0.857230950967138 96 0.158851186659358 0.317702373318716 0.841148813340642 97 0.148961384154724 0.297922768309449 0.851038615845276 98 0.135164020949581 0.270328041899163 0.864835979050419 99 0.121488843423344 0.242977686846688 0.878511156576656 100 0.11067860150851 0.22135720301702 0.88932139849149 101 0.0909031862889883 0.181806372577977 0.909096813711012 102 0.0732307713587914 0.146461542717583 0.926769228641209 103 0.057845194213585 0.11569038842717 0.942154805786415 104 0.0455998233242062 0.0911996466484125 0.954400176675794 105 0.0464495853445728 0.0928991706891456 0.953550414655427 106 0.0372461147169879 0.0744922294339758 0.962753885283012 107 0.032697582356061 0.065395164712122 0.967302417643939 108 0.0299515060117436 0.0599030120234871 0.970048493988256 109 0.0236117662894677 0.0472235325789353 0.976388233710532 110 0.0244250123500386 0.0488500247000773 0.975574987649961 111 0.0342124629968627 0.0684249259937254 0.965787537003137 112 0.236070374008425 0.47214074801685 0.763929625991575 113 0.248487412381767 0.496974824763533 0.751512587618233 114 0.606362014104736 0.787275971790529 0.393637985895264 115 0.865538296951172 0.268923406097656 0.134461703048828 116 0.834116930171712 0.331766139656576 0.165883069828288 117 0.863453455877002 0.273093088245995 0.136546544122998 118 0.834858998849552 0.330282002300896 0.165141001150448 119 0.813301729600703 0.373396540798593 0.186698270399297 120 0.869419979961048 0.261160040077903 0.130580020038952 121 0.841827920548363 0.316344158903273 0.158172079451637 122 0.807092304550098 0.385815390899804 0.192907695449902 123 0.814538458847391 0.370923082305217 0.185461541152609 124 0.770843605539375 0.45831278892125 0.229156394460625 125 0.735905896480925 0.52818820703815 0.264094103519075 126 0.697070504839785 0.60585899032043 0.302929495160215 127 0.6481192245101 0.7037615509798 0.3518807754899 128 0.595162179873622 0.809675640252756 0.404837820126378 129 0.540291195054718 0.919417609890565 0.459708804945282 130 0.488731477759475 0.97746295551895 0.511268522240525 131 0.459190230523929 0.918380461047857 0.540809769476071 132 0.483568704051726 0.967137408103452 0.516431295948274 133 0.418495132258111 0.836990264516221 0.581504867741889 134 0.389643766766899 0.779287533533798 0.610356233233101 135 0.691552618295808 0.616894763408384 0.308447381704192 136 0.622062805228564 0.755874389542871 0.377937194771436 137 0.607927809959527 0.784144380080945 0.392072190040473 138 0.551288579810449 0.897422840379101 0.448711420189551 139 0.575083456983905 0.84983308603219 0.424916543016095 140 0.497478808790314 0.994957617580629 0.502521191209686 141 0.43440511573545 0.8688102314709 0.56559488426455 142 0.390236903892568 0.780473807785136 0.609763096107432 143 0.408535104891144 0.817070209782289 0.591464895108855 144 0.348871685720814 0.697743371441629 0.651128314279186 145 0.249788471075978 0.499576942151957 0.750211528924022 146 0.212466133782871 0.424932267565741 0.78753386621713 147 0.172160470749873 0.344320941499745 0.827839529250127 148 0.0951785911136146 0.190357182227229 0.904821408886385 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 2 0.0144927536231884 OK 10% type I error level 8 0.0579710144927536 OK

Charts produced by software:

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Parameters (Session):

par1 = 6 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 6 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ;

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

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

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

Software written by Ed van Stee & Patrick Wessa

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