W7 - model 4

*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: Mon, 22 Nov 2010 19:23:10 +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/22/t129045371808w5pgn250hf6pa.htm/, Retrieved Mon, 22 Nov 2010 20:22:10 +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/22/t129045371808w5pgn250hf6pa.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 «

24 14 11 12 24 26 25 11 7 8 25 23 17 6 17 8 30 25 18 12 10 8 19 23 18 8 12 9 22 19 16 10 12 7 22 29 20 10 11 4 25 25 16 11 11 11 23 21 18 16 12 7 17 22 17 11 13 7 21 25 23 13 14 12 19 24 30 12 16 10 19 18 23 8 11 10 15 22 18 12 10 8 16 15 15 11 11 8 23 22 12 4 15 4 27 28 21 9 9 9 22 20 15 8 11 8 14 12 20 8 17 7 22 24 31 14 17 11 23 20 27 15 11 9 23 21 34 16 18 11 21 20 21 9 14 13 19 21 31 14 10 8 18 23 19 11 11 8 20 28 16 8 15 9 23 24 20 9 15 6 25 24 21 9 13 9 19 24 22 9 16 9 24 23 17 9 13 6 22 23 24 10 9 6 25 29 25 16 18 16 26 24 26 11 18 5 29 18 25 8 12 7 32 25 17 9 17 9 25 21 32 16 9 6 29 26 33 11 9 6 28 22 13 16 12 5 17 22 32 12 18 12 28 22 25 12 12 7 29 23 29 14 18 10 26 30 22 9 14 9 25 23 18 10 15 8 14 17 17 9 16 5 25 23 20 10 10 8 26 23 15 12 11 8 20 25 20 14 14 10 18 24 33 14 9 6 32 24 29 10 12 8 25 23 23 14 17 7 25 21 26 16 5 4 23 24 18 9 12 8 21 24 20 10 12 8 20 28 11 6 6 4 15 16 28 8 24 20 30 20 26 13 12 8 24 29 22 10 12 8 26 27 17 8 14 6 24 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 10 seconds R Server 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation YT[t] = -2.70676782746942 + 0.80482569659637X1[t] + 0.246618734551964X2[t] + 0.190858166207394X3[t] + 0.568212974041801X4[t] -0.100756792404193X5[t] + 0.00564436253658337t + 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) -2.70676782746942 3.230753 -0.8378 0.403451 0.201726 X1 0.80482569659637 0.130765 6.1547 0 0 X2 0.246618734551964 0.133141 1.8523 0.06592 0.03296 X3 0.190858166207394 0.168568 1.1322 0.25932 0.12966 X4 0.568212974041801 0.096019 5.9177 0 0 X5 -0.100756792404193 0.105352 -0.9564 0.340397 0.170199 t 0.00564436253658337 0.008004 0.7052 0.481742 0.240871 Multiple Linear Regression - Regression Statistics Multiple R 0.639616097712746 R-squared 0.409108752453280 Adjusted R-squared 0.385784097944857 F-TEST (value) 17.5397561539675 F-TEST (DF numerator) 6 F-TEST (DF denominator) 152 p-value 2.22044604925031e-15 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 4.48508352276095 Sum Squared Residuals 3057.62807933355 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 24 24.5869751364713 -0.586975136471266 2 25 21.2987181574354 3.70128184256465 3 17 22.3859726679103 -5.38597266791033 4 18 19.4454109385100 -1.44541093850996 5 18 19.0235142417146 -1.0235142417146 6 16 19.2495257409872 -3.24952574098717 7 20 20.5436429620918 -0.543642962091784 8 16 21.9567214062097 -5.95672140620966 9 18 21.9596456847955 -3.95964568479549 10 17 20.1583618178568 -3.15836181785681 11 23 21.9388979834957 1.06110201650434 12 30 21.8557785405502 8.14422145944983 13 23 14.7331473781575 8.26685262184252 14 18 18.6032699809839 -0.603269980983944 15 15 21.3229006529394 -6.32290065293937 16 12 17.5861185544217 -5.58611855442169 17 21 19.0554592926898 1.94454070731015 18 15 14.8190078084257 0.180992191574261 19 20 19.4501286955508 0.549871304449198 20 31 26.0194000461538 4.98059995384625 21 27 24.8676845731559 2.13231542684406 22 34 26.750532950888 7.24946704911197 23 21 19.2804560909692 1.71954390903085 24 31 20.5997366083926 10.4002633916074 25 19 19.0701646017546 -0.0701646017546488 26 16 19.9463310706595 -3.94633107065954 27 20 21.3206525792539 -1.32065257925392 28 21 17.9963561270580 3.00364387294205 29 22 21.6836783558636 0.316321644136378 30 17 19.2404660680385 -2.24046606803853 31 24 20.1645593566639 3.83544064333613 32 25 30.1993051078831 -5.19930510788305 33 26 26.390560835707 -0.390560835707015 34 25 23.8830734088535 1.11692659114646 35 17 22.7338898244853 -5.73388982448527 36 32 27.5968576223048 4.40314237769521 37 33 23.4131876974345 9.5868123025655 38 13 21.7416158659416 -8.74161586594162 39 32 27.5940197273161 4.40598027268393 40 25 25.6331170331415 -0.633117033141505 41 29 26.8907632258500 2.10923677414995 42 22 21.8320305737771 0.167969426222923 43 18 17.0524592412200 0.947540758780045 44 17 21.5731241031246 -4.5731241031246 45 20 22.0446692276097 -2.04466922760975 46 15 20.2957922888318 -5.29579228883185 47 20 21.9969914249524 -1.99699142495244 48 33 27.9610910864848 5.03890891351517 49 29 21.9922711728182 7.00772882718179 50 23 26.4609674131011 -3.46096741310109 51 26 23.1055675302885 2.89443246971152 52 18 18.8307698752602 -0.830769875260195 53 20 18.6699997907346 1.33000020926542 54 11 11.5812129333856 -0.581212933385631 55 28 28.8095440113788 -0.809544011378844 56 26 23.2735050718964 2.72649492810355 57 22 22.2026118775359 -0.202611877535904 58 17 20.0774839975063 -3.07748399750625 59 12 15.4292884866592 -3.42928848665917 60 14 20.780061210624 -6.78006121062399 61 17 20.6763094340180 -3.67630943401805 62 21 21.261580521485 -0.261580521484977 63 19 22.9113260083569 -3.91132600835689 64 18 23.0268271622096 -5.02682716220961 65 10 17.8541098959786 -7.8541098959786 66 29 24.2846006276799 4.71539937232013 67 31 18.4322038562024 12.5677961437976 68 19 22.8792466318609 -3.87924663186087 69 9 20.0338902827611 -11.0338902827611 70 20 22.4674961633225 -2.46749616332248 71 28 17.5756295114181 10.4243704885819 72 19 18.1136995485328 0.886300451467232 73 30 23.0877801178341 6.91221988216585 74 29 27.073369677065 1.92663032293499 75 26 21.4908251886057 4.50917481139427 76 23 19.5051176759053 3.49488232409466 77 13 22.7601530313896 -9.76015303138962 78 21 22.6443090003536 -1.64430900035360 79 19 21.5370492704958 -2.53704927049576 80 28 22.9377313025900 5.06226869740997 81 23 25.6175014577243 -2.61750145772434 82 18 13.8646394460410 4.13536055395897 83 21 20.7319285749601 0.268071425039861 84 20 21.8476069466243 -1.84760694662434 85 23 20.0434165598231 2.95658344017692 86 21 20.8597333926554 0.140266607344566 87 21 21.8550198976718 -0.855019897671838 88 15 22.9508811919658 -7.95088119196579 89 28 27.1965037434143 0.803496256585704 90 19 17.6886416630847 1.31135833691528 91 26 21.2954140701055 4.70458592989447 92 10 13.3326243716318 -3.3326243716318 93 16 17.1873143264118 -1.18731432641177 94 22 21.2020388132927 0.797961186707256 95 19 18.9063046849835 0.093695315016476 96 31 28.9157779289149 2.08422207108510 97 31 25.3018849084882 5.69811509151183 98 29 24.8551287876824 4.14487121231755 99 19 17.5028282033594 1.49717179664060 100 22 18.9522887480601 3.04771125193990 101 23 22.472438197516 0.527561802483991 102 15 16.2874647056108 -1.28746470561081 103 20 21.4645212040962 -1.46452120409623 104 18 19.6425371514452 -1.64253715144523 105 23 22.217150234481 0.782849765518977 106 25 20.9744599375139 4.02554006248606 107 21 16.6529471075685 4.34705289243146 108 24 19.5455744278297 4.45442557217025 109 25 25.3595410763598 -0.359541076359750 110 17 19.6935475859109 -2.69354758591087 111 13 14.6943965458432 -1.69439654584321 112 28 18.4098746117709 9.59012538822914 113 21 20.3106346801039 0.68936531989613 114 25 28.2836350486841 -3.28363504868414 115 9 21.0044477704288 -12.0044477704288 116 16 18.0612276169349 -2.06122761693494 117 19 21.2966898433180 -2.29668984331795 118 17 19.6269476477759 -2.62694764777592 119 25 24.7319979920982 0.268002007901782 120 20 15.6369512420149 4.36304875798511 121 29 21.8759344009052 7.12406559909482 122 14 19.1778709228727 -5.17787092287272 123 22 27.0980959242537 -5.09809592425374 124 15 15.9019397751253 -0.901939775125261 125 19 25.6813751580878 -6.6813751580878 126 20 22.1919545613241 -2.19195456132412 127 15 17.7608142090159 -2.76081420901587 128 20 22.1258994239983 -2.12589942399832 129 18 20.5527935376764 -2.55279353767642 130 33 25.7888479793484 7.21115202065161 131 22 24.0146988185677 -2.01469881856772 132 16 16.7435243851904 -0.743524385190442 133 17 19.4036823708245 -2.40368237082452 134 16 15.381610908457 0.618389091543015 135 21 17.3637695845882 3.63623041541182 136 26 27.9214437785666 -1.92144377856657 137 18 21.4147283663736 -3.41472836637364 138 18 23.2764637604010 -5.27646376040095 139 17 18.7078618855540 -1.70786188555397 140 22 24.9760915015815 -2.97609150158152 141 30 24.952242458675 5.04775754132501 142 30 27.6220295065553 2.37797049344472 143 24 30.0288532518421 -6.02885325184213 144 21 22.3733372368221 -1.37333723682208 145 21 25.7186060818219 -4.71860608182192 146 29 27.7760626071577 1.22393739284233 147 31 23.567572013391 7.432427986609 148 20 19.3381789476296 0.661821052370389 149 16 14.4271132095025 1.57288679049751 150 22 19.2888597043427 2.71114029565732 151 20 20.7667282598620 -0.766728259862024 152 28 27.7200998654264 0.279900134573619 153 38 27.0811321597216 10.9188678402784 154 22 19.5906715514476 2.40932844855245 155 20 26.0566974089159 -6.05669740891588 156 17 18.4485304103310 -1.44853041033102 157 28 24.9055766121567 3.09442338784327 158 22 24.5396741854444 -2.53967418544438 159 31 26.4518682878217 4.54813171217832 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 10 0.0986137661024836 0.197227532204967 0.901386233897516 11 0.354975571887273 0.709951143774547 0.645024428112727 12 0.749205672924374 0.501588654151253 0.250794327075626 13 0.743994274618463 0.512011450763075 0.256005725381537 14 0.72714235157568 0.545715296848641 0.272857648424320 15 0.689806032322999 0.620387935354002 0.310193967677001 16 0.607520523040911 0.784958953918178 0.392479476959089 17 0.552963977005477 0.894072045989047 0.447036022994523 18 0.524489297213625 0.95102140557275 0.475510702786375 19 0.469705119785149 0.939410239570298 0.530294880214851 20 0.498689321613759 0.997378643227517 0.501310678386241 21 0.431176180699656 0.862352361399312 0.568823819300344 22 0.419451092528739 0.838902185057479 0.58054890747126 23 0.376937483513751 0.753874967027501 0.62306251648625 24 0.530934349054126 0.938131301891747 0.469065650945874 25 0.488778271623548 0.977556543247095 0.511221728376452 26 0.50572430443727 0.98855139112546 0.49427569556273 27 0.438393462196286 0.876786924392572 0.561606537803714 28 0.379359317119068 0.758718634238136 0.620640682880932 29 0.317823247581353 0.635646495162706 0.682176752418647 30 0.278075108364166 0.556150216728331 0.721924891635834 31 0.269604109958725 0.539208219917449 0.730395890041275 32 0.399006591421526 0.798013182843052 0.600993408578474 33 0.343222070528927 0.686444141057854 0.656777929471073 34 0.313641715491667 0.627283430983334 0.686358284508333 35 0.356773406558775 0.71354681311755 0.643226593441225 36 0.323998275685864 0.647996551371729 0.676001724314136 37 0.438555192615725 0.87711038523145 0.561444807384275 38 0.745624437903074 0.508751124193852 0.254375562096926 39 0.7299817348089 0.540036530382199 0.270018265191100 40 0.693934084025519 0.612131831948961 0.306065915974481 41 0.656722991738823 0.686554016522355 0.343277008261177 42 0.609635486056108 0.780729027887784 0.390364513943892 43 0.559432351693985 0.88113529661203 0.440567648306015 44 0.552798911731338 0.894402176537324 0.447201088268662 45 0.540193248509558 0.919613502980884 0.459806751490442 46 0.584175010022566 0.831649979954868 0.415824989977434 47 0.547117591212125 0.90576481757575 0.452882408787875 48 0.537011624774238 0.925976750451523 0.462988375225762 49 0.589669637022596 0.820660725954807 0.410330362977404 50 0.56842203322175 0.8631559335565 0.43157796677825 51 0.538178226534435 0.92364354693113 0.461821773465565 52 0.491057984345915 0.98211596869183 0.508942015654085 53 0.445536972695212 0.891073945390424 0.554463027304788 54 0.404935211723215 0.80987042344643 0.595064788276785 55 0.366544629337198 0.733089258674396 0.633455370662802 56 0.335762606108049 0.671525212216098 0.664237393891951 57 0.292733820431059 0.585467640862119 0.70726617956894 58 0.267371541827075 0.53474308365415 0.732628458172925 59 0.249510500844237 0.499021001688475 0.750489499155763 60 0.308670878298285 0.617341756596571 0.691329121701715 61 0.294097713731881 0.588195427463762 0.70590228626812 62 0.255099579665819 0.510199159331638 0.744900420334181 63 0.239430065579774 0.478860131159548 0.760569934420226 64 0.265644227426384 0.531288454852768 0.734355772573616 65 0.330364327637465 0.66072865527493 0.669635672362535 66 0.338966844575652 0.677933689151305 0.661033155424348 67 0.683800498206363 0.632399003587274 0.316199501793637 68 0.673315481045092 0.653369037909817 0.326684518954908 69 0.841190161183829 0.317619677632342 0.158809838816171 70 0.819138327521373 0.361723344957254 0.180861672478627 71 0.930851738061275 0.13829652387745 0.069148261938725 72 0.914656901731174 0.170686196537652 0.0853430982688258 73 0.938282933785067 0.123434132429866 0.061717066214933 74 0.926386103955744 0.147227792088512 0.0736138960442558 75 0.927628103388979 0.144743793222042 0.0723718966110212 76 0.921532903260819 0.156934193478363 0.0784670967391814 77 0.969328781764506 0.0613424364709885 0.0306712182354943 78 0.961667340439294 0.0766653191214129 0.0383326595607064 79 0.95410748689714 0.0917850262057185 0.0458925131028593 80 0.956601951586903 0.0867960968261944 0.0433980484130972 81 0.94866640143641 0.102667197127179 0.0513335985635893 82 0.947674557240554 0.104650885518891 0.0523254427594454 83 0.93387686395165 0.132246272096699 0.0661231360483494 84 0.920778464987115 0.158443070025771 0.0792215350128854 85 0.911255843490231 0.177488313019537 0.0887441565097685 86 0.893685955156079 0.212628089687843 0.106314044843921 87 0.871647292220025 0.256705415559949 0.128352707779975 88 0.919379775763868 0.161240448472264 0.0806202242361318 89 0.902611562542193 0.194776874915614 0.097388437457807 90 0.88176524363347 0.236469512733059 0.118234756366529 91 0.88139741398992 0.237205172020159 0.118602586010079 92 0.871398039668186 0.257203920663629 0.128601960331814 93 0.849132483499532 0.301735033000937 0.150867516500468 94 0.820422351999575 0.359155296000851 0.179577648000425 95 0.787017743228047 0.425964513543906 0.212982256771953 96 0.755715717519414 0.488568564961171 0.244284282480585 97 0.773221498701842 0.453557002596317 0.226778501298158 98 0.769991622825097 0.460016754349806 0.230008377174903 99 0.734360026106278 0.531279947787445 0.265639973893722 100 0.712285342532017 0.575429314935965 0.287714657467983 101 0.673804180886968 0.652391638226063 0.326195819113032 102 0.632880695737512 0.734238608524976 0.367119304262488 103 0.591795492302649 0.816409015394702 0.408204507697351 104 0.548631219337819 0.902737561324363 0.451368780662181 105 0.506340488687243 0.987319022625515 0.493659511312757 106 0.492691634388543 0.985383268777085 0.507308365611457 107 0.500002089027186 0.999995821945628 0.499997910972814 108 0.539303621396916 0.921392757206167 0.460696378603084 109 0.501865343762256 0.996269312475489 0.498134656237744 110 0.46070428980282 0.92140857960564 0.53929571019718 111 0.413743913231612 0.827487826463224 0.586256086768388 112 0.7406188406695 0.518762318661 0.2593811593305 113 0.775579162293002 0.448841675413997 0.224420837706998 114 0.751192493702793 0.497615012594414 0.248807506297207 115 0.875459864023444 0.249080271953112 0.124540135976556 116 0.847093187395819 0.305813625208363 0.152906812604181 117 0.817630525758243 0.364738948483513 0.182369474241757 118 0.78416977850527 0.431660442989461 0.215830221494730 119 0.75623961941945 0.487520761161101 0.243760380580550 120 0.804970576588138 0.390058846823725 0.195029423411862 121 0.884059519069933 0.231880961860133 0.115940480930067 122 0.865249738023541 0.269500523952918 0.134750261976459 123 0.844910324733052 0.310179350533897 0.155089675266948 124 0.806900129855565 0.386199740288871 0.193099870144435 125 0.811564180355852 0.376871639288295 0.188435819644148 126 0.768212231461183 0.463575537077633 0.231787768538817 127 0.736867409455641 0.526265181088717 0.263132590544359 128 0.690330756079321 0.619338487841358 0.309669243920679 129 0.645015922560205 0.70996815487959 0.354984077439795 130 0.765893935019667 0.468212129960667 0.234106064980333 131 0.713580282724145 0.57283943455171 0.286419717275855 132 0.653407430680831 0.693185138638337 0.346592569319169 133 0.615380189803281 0.769239620393438 0.384619810196719 134 0.545690341410029 0.908619317179942 0.454309658589971 135 0.571000707376548 0.857998585246904 0.428999292623452 136 0.500535746389736 0.998928507220528 0.499464253610264 137 0.453408493907196 0.906816987814392 0.546591506092804 138 0.470186630788956 0.940373261577911 0.529813369211044 139 0.396281266677953 0.792562533355906 0.603718733322047 140 0.322837797121087 0.645675594242173 0.677162202878913 141 0.425940533040581 0.851881066081162 0.574059466959419 142 0.375946927934400 0.751893855868801 0.6240530720656 143 0.303350492215239 0.606700984430479 0.696649507784761 144 0.227185895699066 0.454371791398132 0.772814104300934 145 0.333525544777945 0.66705108955589 0.666474455222055 146 0.254150574218036 0.508301148436071 0.745849425781964 147 0.252870623285588 0.505741246571175 0.747129376714412 148 0.159612301285357 0.319224602570713 0.840387698714643 149 0.0863434141037005 0.172686828207401 0.9136565858963 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 0 0 OK 10% type I error level 4 0.0285714285714286 OK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 1 ; 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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Software written by Ed van Stee & Patrick Wessa

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