W7-model4

*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: Sun, 21 Nov 2010 20:43:25 +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/21/t1290372129yq0tf8ipixwd836.htm/, Retrieved Sun, 21 Nov 2010 21:42:20 +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/21/t1290372129yq0tf8ipixwd836.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 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 X1[t] = + 7.28456727859203 + 0.247876363312639YT[t] -0.106836322758769X2[t] + 0.148172353972168X3[t] -0.191083348051682X4[t] + 0.113319775964761`X5 `[t] + 0.00141604344161365t + 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) 7.28456727859203 1.697185 4.2921 3.1e-05 1.6e-05 YT 0.247876363312639 0.040274 6.1547 0 0 X2 -0.106836322758769 0.074214 -1.4396 0.152043 0.076022 X3 0.148172353972168 0.093171 1.5903 0.11384 0.05692 X4 -0.191083348051682 0.05704 -3.35 0.001019 0.00051 `X5 ` 0.113319775964761 0.057918 1.9566 0.052231 0.026115 t 0.00141604344161365 0.004447 0.3184 0.750623 0.375311 Multiple Linear Regression - Regression Statistics Multiple R 0.489953106743654 R-squared 0.240054046807758 Adjusted R-squared 0.210056180234380 F-TEST (value) 8.00237064261089 F-TEST (DF numerator) 6 F-TEST (DF denominator) 152 p-value 1.63423508947602e-07 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 2.48907037510704 Sum Squared Residuals 941.711642499795 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 14 12.1981985606998 1.80180143930024 2 11 11.7511041666546 -0.751104166654634 3 6 7.97236888767856 -1.97236888767856 4 12 10.8447928303832 1.15520716961683 5 8 9.75417943426532 -1.75417943426532 6 10 10.0966958027849 -0.0966958027849393 7 10 9.72540741230528 0.274592587694715 8 11 9.70141207254584 1.29858792745416 9 16 10.7588749682401 5.24112503175986 10 11 9.9812042612979 1.01879573870210 11 13 12.3727508518560 0.627249148143973 12 12 12.9193654292357 -0.919365429235675 13 8 12.9374410393484 -4.93744103934843 14 12 10.5256451012363 1.47435489876373 15 11 9.13225072737275 1.86774927262725 16 4 7.28558823753454 -3.28558823753454 17 9 10.9486297897437 -1.94862978974368 18 8 9.72305123051512 -1.72305123051512 19 8 10.0058293271588 -2.00582932715883 20 14 12.6822123310174 1.31778766898258 21 15 12.1501159257815 2.84988407421849 22 16 13.7040038811832 2.29599611881684 23 9 11.702203672608 -2.702203672608 24 14 14.2865897703314 -0.286589770331441 25 11 11.3910853149831 -0.391085314983056 26 8 9.34317018340976 -1.34317018340976 27 9 9.50940792208206 -0.509407922082058 28 9 11.5633901245804 -2.56339012458045 29 9 10.4234370468352 -1.42343704683522 30 9 9.4436298761768 -0.443629876176804 31 10 11.7141943654755 -1.71419436547548 32 16 11.7260011792470 4.27399882075298 33 11 9.0922289923638 1.90777100763619 34 8 10.0031197045880 -2.00311970458801 35 9 8.66799226818173 0.332007731818266 36 16 12.5999927690837 3.40000723091634 37 11 12.5870894200305 -1.58708942003055 38 16 9.2642137035394 6.7357862964606 39 12 12.2695523626052 -0.269552362605226 40 12 10.3582264574632 1.64177354253678 41 14 12.5211355554276 1.47886444457235 42 9 10.4644349090421 -1.46443490904205 43 10 10.6413349952821 -0.64133499528211 44 9 8.42152311795587 0.578476882044125 45 10 10.0610199017528 -0.0610199017528414 46 12 10.0893574461121 1.91064255388790 47 14 11.5748379659235 2.42516203407645 48 14 12.0649720576111 1.93502794238891 49 10 12.2749820478672 -2.27498204786719 50 14 9.88014639173744 4.11985360826256 51 16 12.1848363603033 3.81516363969666 52 9 10.4302433499245 -1.43024334992449 53 10 11.5717745719021 -1.57177457190211 54 6 8.98621129487519 -2.98621129487519 55 8 11.2362582516123 -3.23625825161234 56 13 12.4122672658608 0.587732734139183 57 10 10.8133716080190 -0.813371608018989 58 8 8.88095629771509 -0.880956297715092 59 7 9.15658542785248 -2.15658542785248 60 15 9.77425515009176 5.22574484990824 61 9 9.88335346336826 -0.883353463368259 62 10 10.2116017994204 -0.211601799420394 63 12 10.2118802513092 1.78811974869083 64 13 10.4495034720761 2.55049652792395 65 10 8.39680718914522 1.60319281085478 66 11 11.8217850361777 -0.82178503617766 67 8 13.5896296993201 -5.58962969932009 68 9 9.1074806693398 -0.107480669339806 69 13 8.6362432282595 4.3637567717405 70 11 10.4073075650156 0.592692434984383 71 8 12.7521832505915 -4.75218325059153 72 9 10.7654574204088 -1.76545742040878 73 9 12.3422994712653 -3.34229947126534 74 15 12.4960489553748 2.50395104462521 75 9 11.1779559631201 -2.17795596312011 76 10 11.5547342292438 -1.55473422924381 77 14 8.9364013646633 5.0635986353367 78 12 10.9541059297473 1.04589407025269 79 12 11.1144577153987 0.885542284601323 80 11 11.5545022245767 -0.55450222457671 81 14 11.4758247471676 2.52417525283239 82 6 11.5705339200679 -5.57053392006792 83 12 11.2664606079675 0.733539392032494 84 8 10.0759754913839 -2.07597549138394 85 14 12.4213088531772 1.57869114682285 86 11 10.8375836199217 0.162416380078289 87 10 9.93033648090274 0.0696635190972592 88 14 10.2425329758814 3.75746702411859 89 12 12.0499497829489 -0.0499497829489087 90 10 11.0081310743587 -1.00813107435873 91 14 13.0191406973377 0.980859302662273 92 5 9.01704146028203 -4.01704146028203 93 11 10.5195539270071 0.480446072992858 94 10 10.2200064995915 -0.220006499591453 95 9 11.4821499398239 -2.48214993982391 96 10 11.4708272188406 -1.47082721884057 97 16 13.7641775122808 2.23582248771919 98 13 12.8337334961195 0.166266503880472 99 9 10.8297921172816 -1.82979211728157 100 10 11.3895337299450 -1.38953372994498 101 10 10.9927210107971 -0.99272101079714 102 7 9.503279092332 -2.503279092332 103 9 9.83122988103862 -0.831229881038616 104 8 10.2530737966269 -2.25307379662691 105 14 12.9055387274718 1.09446127252820 106 14 11.6486189083262 2.35138109167375 107 8 11.0972667330982 -3.09726673309825 108 9 11.5485970601368 -2.54859706013678 109 14 11.8390577869792 2.16094221302082 110 14 10.7746935586969 3.22530644130308 111 8 9.8972202989823 -1.89722029898230 112 8 13.7325637585563 -5.73256375855635 113 8 10.9987479719796 -2.99874797197956 114 7 8.58826640738003 -1.58826640738003 115 6 7.51844260950576 -1.51844260950576 116 8 9.4737640188872 -1.47376401888721 117 6 8.33844977129384 -2.33844977129384 118 11 9.9244745823182 1.07552541768180 119 14 11.8968328413453 2.10316715865474 120 11 11.1390921545270 -0.139092154526987 121 11 12.0140262495521 -1.01402624955210 122 11 9.24746376810336 1.75253623189664 123 14 10.4222000318981 3.57779996810195 124 8 10.4376457404075 -2.43764574040748 125 20 11.5561502936060 8.44384970639404 126 11 10.3832819014706 0.616718098529425 127 8 9.22271739968478 -1.22271739968478 128 11 10.7938412086457 0.206158791354348 129 10 10.7004179553129 -0.700417955312895 130 14 13.5235795465251 0.476420453474937 131 11 10.6181282742767 0.381871725723348 132 9 10.6632315109924 -1.66323151099243 133 9 9.80385862205098 -0.80385862205098 134 8 10.2383560060895 -2.23835600608945 135 10 12.13350100981 -2.13350100980999 136 13 10.7917997392074 2.20820026079259 137 13 10.1831499267616 2.81685007323836 138 12 9.3468415815043 2.65315841849570 139 8 10.4537351200044 -2.45373512000441 140 13 11.0762610641634 1.92373893583664 141 14 12.4841044424773 1.51589555752272 142 12 11.7527330227464 0.247266977253558 143 14 10.9559169940413 3.04408300595869 144 15 11.3938129883682 3.60618701163180 145 13 10.6070936800223 2.39290631997775 146 16 11.9539829563795 4.04601704362046 147 9 12.0702186680899 -3.07021866808989 148 9 10.5673211118722 -1.56732111187224 149 9 11.0754184840640 -2.07541848406404 150 8 11.3809973670726 -3.38099736707262 151 7 10.1391367618125 -3.13913676181253 152 16 12.0500159920221 3.94998400797787 153 11 13.4590238403895 -2.45902384038951 154 9 10.078497265284 -1.078497265284 155 11 9.93149059081258 1.06850940918742 156 9 9.96866184204565 -0.968661842045649 157 14 12.5912778230240 1.40872217697596 158 13 11.1299622476729 1.87003775232708 159 16 14.5527315820551 1.44726841794489 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 10 0.347422791072967 0.694845582145934 0.652577208927033 11 0.465041872361142 0.930083744722283 0.534958127638858 12 0.346495884723839 0.692991769447679 0.653504115276161 13 0.824763500488143 0.350472999023714 0.175236499511857 14 0.763354260090481 0.473291479819038 0.236645739909519 15 0.718744309474746 0.562511381050507 0.281255690525254 16 0.708150237717604 0.583699524564792 0.291849762282396 17 0.627597296515271 0.744805406969458 0.372402703484729 18 0.60762898183664 0.784742036326721 0.392371018163361 19 0.527654175358379 0.944691649283241 0.472345824641621 20 0.603166637349695 0.79366672530061 0.396833362650305 21 0.645419942939278 0.709160114121444 0.354580057060722 22 0.615939756294849 0.768120487410302 0.384060243705151 23 0.602276298133152 0.795447403733696 0.397723701866848 24 0.539311343789138 0.921377312421723 0.460688656210862 25 0.469216085532377 0.938432171064754 0.530783914467623 26 0.40152750166815 0.8030550033363 0.59847249833185 27 0.337268442473763 0.674536884947527 0.662731557526237 28 0.307244107150903 0.614488214301806 0.692755892849097 29 0.253129386908026 0.506258773816053 0.746870613091974 30 0.208754774148877 0.417509548297755 0.791245225851123 31 0.172485114148519 0.344970228297038 0.827514885851481 32 0.283646954044087 0.567293908088173 0.716353045955913 33 0.260965529500715 0.521931059001429 0.739034470499286 34 0.245875295479550 0.491750590959101 0.75412470452045 35 0.203782546742186 0.407565093484372 0.796217453257814 36 0.236741271399709 0.473482542799419 0.763258728600291 37 0.226864980606658 0.453729961213316 0.773135019393342 38 0.622454999031607 0.755090001936786 0.377545000968393 39 0.572585885382941 0.854828229234118 0.427414114617059 40 0.53279055288848 0.93441889422304 0.46720944711152 41 0.488404341259092 0.976808682518183 0.511595658740908 42 0.464353158177256 0.928706316354511 0.535646841822744 43 0.421950903327067 0.843901806654135 0.578049096672933 44 0.370677273648956 0.741354547297911 0.629322726351044 45 0.321173805064289 0.642347610128577 0.678826194935712 46 0.293700682184349 0.587401364368699 0.706299317815651 47 0.274735888909326 0.549471777818652 0.725264111090674 48 0.248703826667464 0.497407653334928 0.751296173332536 49 0.262400120042446 0.524800240084892 0.737599879957554 50 0.318058927221605 0.636117854443209 0.681941072778395 51 0.354276298514595 0.70855259702919 0.645723701485405 52 0.343450108094828 0.686900216189656 0.656549891905172 53 0.329578392359388 0.659156784718775 0.670421607640612 54 0.357196996842139 0.714393993684278 0.642803003157861 55 0.377281299813075 0.754562599626149 0.622718700186925 56 0.33309578046658 0.66619156093316 0.66690421953342 57 0.293836699820083 0.587673399640165 0.706163300179917 58 0.256772929702072 0.513545859404144 0.743227070297928 59 0.241500743747312 0.483001487494623 0.758499256252688 60 0.389632517162628 0.779265034325257 0.610367482837372 61 0.346380163860732 0.692760327721463 0.653619836139268 62 0.304515135660015 0.609030271320031 0.695484864339985 63 0.283713788924071 0.567427577848142 0.716286211075929 64 0.293322515690081 0.586645031380161 0.70667748430992 65 0.268656534924105 0.53731306984821 0.731343465075895 66 0.237316280441396 0.474632560882791 0.762683719558604 67 0.420683729416001 0.841367458832003 0.579316270583999 68 0.375232450563049 0.750464901126098 0.624767549436951 69 0.472991813953995 0.94598362790799 0.527008186046005 70 0.430997600320869 0.861995200641738 0.569002399679131 71 0.549600984681515 0.90079803063697 0.450399015318485 72 0.522549725628376 0.954900548743248 0.477450274371624 73 0.546092264407328 0.907815471185344 0.453907735592672 74 0.554439826195076 0.891120347609848 0.445560173804924 75 0.536062212806981 0.927875574386038 0.463937787193019 76 0.502930770526699 0.994138458946602 0.497069229473301 77 0.667100569889284 0.665798860221431 0.332899430110716 78 0.636120975879089 0.727758048241822 0.363879024120911 79 0.600095752996245 0.79980849400751 0.399904247003755 80 0.554795417000603 0.890409165998793 0.445204582999397 81 0.564703287448629 0.870593425102742 0.435296712551371 82 0.719496806813411 0.561006386373178 0.280503193186589 83 0.685993833657444 0.628012332685113 0.314006166342556 84 0.663091280054384 0.673817439891231 0.336908719945616 85 0.640261757803718 0.719476484392564 0.359738242196282 86 0.599769561197095 0.80046087760581 0.400230438802905 87 0.556792418080184 0.886415163839631 0.443207581919816 88 0.643990001517281 0.712019996965437 0.356009998482719 89 0.599323784913762 0.801352430172476 0.400676215086238 90 0.557347941379364 0.885304117241272 0.442652058620636 91 0.52409170982396 0.95181658035208 0.47590829017604 92 0.568690576851452 0.862618846297097 0.431309423148548 93 0.531795352860464 0.936409294279073 0.468204647139537 94 0.487758435786491 0.975516871572982 0.512241564213509 95 0.470415441779975 0.940830883559951 0.529584558220024 96 0.428997611948209 0.857995223896418 0.571002388051791 97 0.429175251009558 0.858350502019117 0.570824748990442 98 0.384951293972488 0.769902587944975 0.615048706027512 99 0.351427769012601 0.702855538025202 0.648572230987399 100 0.31259722908763 0.62519445817526 0.68740277091237 101 0.271954782992968 0.543909565985936 0.728045217007032 102 0.253815637205803 0.507631274411607 0.746184362794197 103 0.216229941209856 0.432459882419712 0.783770058790144 104 0.196794686286367 0.393589372572734 0.803205313713633 105 0.172795891011543 0.345591782023087 0.827204108988457 106 0.180614394305868 0.361228788611736 0.819385605694132 107 0.181112308474927 0.362224616949854 0.818887691525073 108 0.174047285739055 0.34809457147811 0.825952714260945 109 0.171234747955927 0.342469495911855 0.828765252044073 110 0.216696832843942 0.433393665687885 0.783303167156058 111 0.187801050813564 0.375602101627128 0.812198949186436 112 0.372995938390879 0.745991876781759 0.62700406160912 113 0.435238415283698 0.870476830567397 0.564761584716302 114 0.404244467365098 0.808488934730197 0.595755532634902 115 0.398446967554107 0.796893935108215 0.601553032445893 116 0.357669114568711 0.715338229137422 0.642330885431289 117 0.360939665071490 0.721879330142979 0.63906033492851 118 0.318232055027942 0.636464110055884 0.681767944972058 119 0.288946862886554 0.577893725773109 0.711053137113446 120 0.243442507634524 0.486885015269048 0.756557492365476 121 0.229367516485238 0.458735032970476 0.770632483514762 122 0.206018284049764 0.412036568099528 0.793981715950236 123 0.210554273751277 0.421108547502555 0.789445726248722 124 0.228042572649675 0.45608514529935 0.771957427350325 125 0.759383385644503 0.481233228710993 0.240616614355497 126 0.719767488508598 0.560465022982804 0.280232511491402 127 0.667858760188057 0.664282479623885 0.332141239811943 128 0.607909482311448 0.784181035377103 0.392090517688552 129 0.545356821886809 0.909286356226382 0.454643178113191 130 0.482711159143575 0.96542231828715 0.517288840856425 131 0.427479618508462 0.854959237016923 0.572520381491538 132 0.374550231740534 0.749100463481069 0.625449768259466 133 0.314915845176699 0.629831690353398 0.685084154823301 134 0.283249568823146 0.566499137646292 0.716750431176854 135 0.285747013310789 0.571494026621577 0.714252986689211 136 0.241391632009783 0.482783264019566 0.758608367990217 137 0.250219105481734 0.500438210963467 0.749780894518266 138 0.257509634397614 0.515019268795228 0.742490365602386 139 0.287491053870267 0.574982107740534 0.712508946129733 140 0.227100084665721 0.454200169331442 0.772899915334279 141 0.173073945472057 0.346147890944114 0.826926054527943 142 0.131854645128240 0.263709290256480 0.86814535487176 143 0.137043520783235 0.27408704156647 0.862956479216765 144 0.127500947505422 0.255001895010845 0.872499052494577 145 0.144170433053289 0.288340866106577 0.855829566946711 146 0.415726473492409 0.831452946984817 0.584273526507591 147 0.305219608063006 0.610439216126011 0.694780391936994 148 0.211738084905967 0.423476169811933 0.788261915094033 149 0.123447710862182 0.246895421724363 0.876552289137818 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 0 0 OK

Charts produced by software:

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Parameters (Session):

par1 = 2 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 2 ; 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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