Meervoudige lineaire regressie

*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, 22 Dec 2010 18:52:01 +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/22/t1293043898d1zfrxes0un84qm.htm/, Retrieved Wed, 22 Dec 2010 19:51:38 +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/22/t1293043898d1zfrxes0un84qm.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:

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24 14 12 24 25 11 8 25 17 6 8 30 18 12 8 19 18 8 9 22 16 10 7 22 20 10 4 25 16 11 11 23 18 16 7 17 17 11 7 21 23 13 12 19 30 12 10 19 23 8 10 15 18 12 8 16 15 11 8 23 12 4 4 27 21 9 9 22 15 8 8 14 20 8 7 22 31 14 11 23 27 15 9 23 34 16 11 21 21 9 13 19 31 14 8 18 19 11 8 20 16 8 9 23 20 9 6 25 21 9 9 19 22 9 9 24 17 9 6 22 24 10 6 25 25 16 16 26 26 11 5 29 25 8 7 32 17 9 9 25 32 16 6 29 33 11 6 28 13 16 5 17 32 12 12 28 25 12 7 29 29 14 10 26 22 9 9 25 18 10 8 14 17 9 5 25 20 10 8 26 15 12 8 20 20 14 10 18 33 14 6 32 29 10 8 25 23 14 7 25 26 16 4 23 18 9 8 21 20 10 8 20 11 6 4 15 28 8 20 30 26 13 8 24 22 10 8 26 17 8 6 24 12 7 4 22 14 15 8 14 17 9 9 24 21 10 6 24 19 12 7 24 18 13 9 24 10 10 5 19 29 11 5 31 31 8 8 22 19 9 8 27 9 13 6 19 20 11 8 25 28 8 7 20 19 9 7 21 30 9 9 27 29 15 11 23 26 9 6 25 23 10 8 20 13 14 6 21 21 12 9 22 19 12 8 23 28 11 6 25 23 14 10 25 18 6 8 17 21 12 8 19 20 8 10 25 23 14 5 19 21 11 7 20 21 10 5 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 8 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Multiple Linear Regression - Estimated Regression Equation PS[t] = + 17.7328206986877 + 0.380763089814471CM[t] -0.358122279733057DA[t] + 0.0114452394212943PC[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) 17.7328206986877 1.503706 11.7927 0 0 CM 0.380763089814471 0.058879 6.4669 0 0 DA -0.358122279733057 0.115743 -3.0941 0.002342 0.001171 PC 0.0114452394212943 0.115721 0.0989 0.921343 0.460671 Multiple Linear Regression - Regression Statistics Multiple R 0.47780279837152 R-squared 0.228295514131655 Adjusted R-squared 0.213359298276139 F-TEST (value) 15.2846956913347 F-TEST (DF numerator) 3 F-TEST (DF denominator) 155 p-value 9.22506182554628e-09 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 3.74013733053778 Sum Squared Residuals 2168.23722394876 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 24 21.9947658110277 2.00523418897227 2 25 23.4041147823562 1.59588521764384 3 30 22.1486214625057 7.85137853749432 4 19 20.3806508739218 -1.38065087392180 5 22 21.8245852322753 0.175414767724672 6 22 20.3239240143377 1.67607598566232 7 25 21.8126406553317 3.18735934466832 8 23 20.0115826922898 2.9884173077102 9 17 18.9367165155683 -1.93671651556828 10 21 20.3465648244191 0.653435175580904 11 19 21.9721250009463 -2.97212500094628 12 19 24.9726984305380 -5.97269843053804 13 15 23.739845920769 -8.73984592076898 14 16 20.3806508739218 -4.3806508739218 15 23 19.5964838842114 3.40351611578855 16 27 20.9152696152143 6.08473038478574 17 22 22.6087522219857 -0.608752221985684 18 14 20.6708507234106 -6.67085072341062 19 22 22.5632209330617 -0.563220933061682 20 23 24.6486622003077 -1.64866220030769 21 23 22.7445970824742 0.255402917525836 22 21 25.074706910285 -4.07470691028499 23 19 22.6545331796709 -3.65453317967086 24 18 24.6143264820438 -6.61432648204381 25 20 21.1195362434693 -1.11953624346933 26 23 21.0630590526464 1.93694094735361 27 25 22.1936534139073 2.80634658609267 28 19 22.6087522219857 -3.60875222198568 29 24 22.9895153118002 1.01048468819985 30 22 21.0513641444639 0.948635855536083 31 25 23.3585834934322 1.64141650656784 32 26 21.7050652990612 4.29493470093878 33 29 23.7505421539067 5.24945784609326 34 32 24.4670363821340 7.53296361786596 35 25 21.0856998627278 3.9143001372722 36 29 24.2559545335496 4.74404546645042 37 28 26.4273290220293 1.57267097797066 38 17 17.0100105876533 -0.0100105876533363 39 28 25.7571150890096 2.24288491099043 40 29 23.0345472632018 5.96545273679819 41 26 23.8756907812575 2.12430921874254 42 25 22.9895153118002 2.01048468819985 43 14 21.0968954333879 -7.09689543338792 44 25 21.0399189050426 3.96008109495738 45 26 21.8584216130169 4.14157838698314 46 20 19.2383616044784 0.761638395521609 47 18 20.4488229729272 -2.44882297292722 48 32 25.3529621828302 6.64703781716984 49 25 25.2852894213471 -0.285289421347099 50 25 21.5567765241067 3.44322347589325 51 23 21.9484855158202 1.05151448417984 52 21 21.4550177131210 -0.455017713120977 53 20 21.8584216130169 -1.85842161301686 54 15 19.8182619659337 -4.81826196593367 55 30 25.7581137640543 4.24188623594573 56 24 23.0686333127045 0.931366687295486 57 26 22.6199477926458 3.3800522073542 58 24 21.4094864241970 2.59051357580303 59 22 19.8409027760151 2.15909722398491 60 14 17.7832316754647 -3.78323167546475 61 24 21.0856998627278 2.9143001372722 62 24 22.2162942239887 1.78370577601126 63 24 20.749968724315 3.25003127568502 64 24 20.0339738336100 3.96602616638996 65 19 18.0164549966083 0.983545003391731 66 31 24.8928314233502 6.10716857664984 67 22 26.7630601604422 -4.76306016044216 68 27 21.8357808029354 5.16421919706455 69 19 16.5727703070159 2.42722969298408 70 25 21.5002993332838 3.49970066671620 71 20 25.6093256515774 -5.60932565157745 72 21 21.8243355635142 -0.824335563514153 73 27 26.0356200303159 0.964379969684079 74 23 23.5290137409457 -0.529013740945694 75 25 24.4782319527942 0.521768047205845 76 20 23.0007108824603 -3.00071088246027 77 21 17.7377003865407 3.26229961345925 78 22 21.5343853827865 0.465614617213489 79 23 20.7614139637363 2.23858603626373 80 25 24.523513572957 0.476486427043018 81 25 21.5911122423706 3.40888775762937 82 17 22.5293845523201 -5.52938455232015 83 19 21.5229401433652 -2.52294014336522 84 25 22.5975566513256 2.40244334867443 85 19 21.5338860452642 -2.53388604526416 86 20 21.869617183677 -1.86961718367698 87 26 22.2048489845674 3.79515101543255 88 23 18.5221170450123 4.47788295498772 89 27 24.2569532085943 2.74304679140572 90 17 21.4662132837811 -4.46621328378109 91 17 22.7105110329715 -5.71051103297146 92 19 19.8185116346949 -0.81851163469485 93 17 19.9429112557620 -2.94291125576204 94 22 22.5970573138032 -0.597057313803214 95 21 21.8586712817780 -0.858671281778036 96 32 26.0925965586612 5.90740344133878 97 21 23.909527161999 -2.90952716199899 98 21 24.2567035398331 -3.25670353983310 99 18 21.8243355635142 -3.82433556351415 100 18 22.6199477926458 -4.6199477926458 101 23 23.0236013613029 -0.0236013613028622 102 19 21.0060825243011 -2.00608252430109 103 20 22.2394343715925 -2.23943437159251 104 21 21.8360304716966 -0.836030471696623 105 20 21.5911122423706 -1.59111224237063 106 17 22.2954122248931 -5.2954122248931 107 18 22.9439840228762 -4.94398402287615 108 19 23.7624867308504 -4.76248673085039 109 22 22.3640836614209 -0.364083661420868 110 15 19.2607527457986 -4.26075274579863 111 14 19.8978793043604 -5.89787930436039 112 18 25.6665518486839 -7.66655184868392 113 24 22.9897649805613 1.01023501943867 114 35 24.8709396195523 10.1290603804477 115 29 19.1368524622538 9.8631475377462 116 21 21.0172780949612 -0.0172780949612091 117 25 22.9101476421346 2.08985235786538 118 20 20.3351195849978 -0.335119584997802 119 22 22.3411931825783 -0.341193182578279 120 13 21.4545183755986 -8.45451837559863 121 26 24.8813861839289 1.11861381607114 122 17 19.2042755549757 -2.20427555497568 123 25 21.2217943919775 3.77820560802254 124 20 20.6479602445680 -0.647960244568033 125 19 17.8849904864505 1.11500951354948 126 21 21.5002993332838 -0.500299333283803 127 22 20.6250697657254 1.37493023427456 128 24 21.5002993332838 2.49970066671620 129 21 21.1083406728092 -0.108340672809213 130 26 25.3758526616728 0.624147338327247 131 24 22.2961612311766 1.70383876882337 132 16 20.6934915334920 -4.69349153349203 133 23 21.0399189050426 1.96008109495738 134 18 21.0058328555399 -3.00583285553992 135 16 22.2391847028313 -6.23918470283133 136 26 23.0915237915471 2.9084762084529 137 19 19.9996381153462 -0.999638115346158 138 21 20.3920961133431 0.607903886656902 139 21 21.4438221424609 -0.443822142460858 140 22 21.6028071505531 0.397192849446898 141 23 24.2450086316506 -1.24500863165063 142 29 24.9726984305380 4.02730156946196 143 21 22.0863277263980 -1.08632772639805 144 21 20.4142375859022 0.585762414097839 145 23 21.1991535818960 1.80084641810396 146 27 23.1136652641062 3.88633473589383 147 25 26.4163831201304 -1.41638312013039 148 21 22.2050986533286 -1.20509865332862 149 10 20.7049367729133 -10.7049367729133 150 20 23.3590828309545 -3.35908283095451 151 26 22.9442336916373 3.05576630836267 152 24 22.7557926531343 1.24420734686572 153 29 28.342589710523 0.657410289477015 154 19 22.9551795935363 -3.95517959353627 155 24 21.5575255303903 2.44247446960973 156 19 21.0513641444639 -2.05136414446392 157 24 23.4720372126004 0.527962787399602 158 22 21.5684714322892 0.431528567710781 159 17 23.9896438379481 -6.98964383794805 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 7 0.424069508813318 0.848139017626636 0.575930491186682 8 0.308069590692805 0.61613918138561 0.691930409307195 9 0.188102622113152 0.376205244226305 0.811897377886848 10 0.107395084813335 0.21479016962667 0.892604915186665 11 0.125378615563952 0.250757231127903 0.874621384436048 12 0.205873748311742 0.411747496623483 0.794126251688258 13 0.703630806595517 0.592738386808966 0.296369193404483 14 0.747480884927987 0.505038230144025 0.252519115072013 15 0.685461636905196 0.629076726189609 0.314538363094804 16 0.625349313441963 0.749301373116074 0.374650686558037 17 0.54401674659295 0.9119665068141 0.45598325340705 18 0.821134401995371 0.357731196009258 0.178865598004629 19 0.769348277971074 0.461303444057853 0.230651722028927 20 0.742614931389853 0.514770137220294 0.257385068610147 21 0.704803810144013 0.590392379711973 0.295196189855987 22 0.653588358191672 0.692823283616656 0.346411641808328 23 0.602652744057837 0.794694511884326 0.397347255942163 24 0.631622934154607 0.736754131690787 0.368377065845393 25 0.572325403291603 0.855349193416793 0.427674596708397 26 0.517238663246799 0.965522673506403 0.482761336753201 27 0.477125685867837 0.954251371735674 0.522874314132163 28 0.456587043324632 0.913174086649264 0.543412956675368 29 0.410767272414993 0.821534544829986 0.589232727585007 30 0.353055178025407 0.706110356050814 0.646944821974593 31 0.311083175269629 0.622166350539257 0.688916824730371 32 0.474809864060373 0.949619728120745 0.525190135939627 33 0.569010769850264 0.861978460299473 0.430989230149736 34 0.737696754805493 0.524606490389013 0.262303245194507 35 0.72801083096519 0.543978338069619 0.271989169034809 36 0.76591269812486 0.468174603750281 0.234087301875140 37 0.727578130854861 0.544843738290278 0.272421869145139 38 0.68829248293675 0.6234150341265 0.31170751706325 39 0.67870305126001 0.642593897479979 0.321296948739989 40 0.728858930953957 0.542282138092087 0.271141069046043 41 0.702640986890983 0.594718026218034 0.297359013109017 42 0.6646722962701 0.6706554074598 0.3353277037299 43 0.791507827938292 0.416984344123416 0.208492172061708 44 0.777739653643486 0.444520692713027 0.222260346356514 45 0.776666221717857 0.446667556564286 0.223333778282143 46 0.737492246096005 0.525015507807991 0.262507753903995 47 0.708421651007161 0.583156697985678 0.291578348992839 48 0.764172442260706 0.471655115478587 0.235827557739294 49 0.72918806407741 0.541623871845181 0.270811935922591 50 0.713294523368543 0.573410953262913 0.286705476631457 51 0.677503229158655 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0.639148279220678 0.721703441558645 0.360851720779322 70 0.633918038177971 0.732163923644057 0.366081961822029 71 0.703655980737834 0.592688038524333 0.296344019262166 72 0.667976513236278 0.664046973527443 0.332023486763722 73 0.629370987828687 0.741258024342627 0.370629012171313 74 0.585752446844604 0.828495106310792 0.414247553155396 75 0.546787483372415 0.90642503325517 0.453212516627585 76 0.533553349445452 0.932893301109095 0.466446650554548 77 0.525291309327731 0.949417381344538 0.474708690672269 78 0.480874683892416 0.961749367784833 0.519125316107584 79 0.45419292496664 0.90838584993328 0.54580707503336 80 0.414194456013572 0.828388912027144 0.585805543986428 81 0.409387092722121 0.818774185444242 0.590612907277879 82 0.465708317369663 0.931416634739326 0.534291682630337 83 0.441941235708254 0.883882471416508 0.558058764291746 84 0.41723657187385 0.8344731437477 0.58276342812615 85 0.396685286478233 0.793370572956466 0.603314713521767 86 0.364579028732814 0.729158057465628 0.635420971267186 87 0.377959820833922 0.755919641667845 0.622040179166078 88 0.4104775587816 0.8209551175632 0.5895224412184 89 0.38946831186415 0.7789366237283 0.61053168813585 90 0.405457524936549 0.810915049873097 0.594542475063451 91 0.460388382310146 0.920776764620293 0.539611617689854 92 0.418936041686251 0.837872083372502 0.581063958313749 93 0.398012397585423 0.796024795170846 0.601987602414577 94 0.35629009080971 0.71258018161942 0.64370990919029 95 0.315310625776684 0.630621251553369 0.684689374223316 96 0.381079365171529 0.762158730343059 0.61892063482847 97 0.359842474344666 0.719684948689333 0.640157525655334 98 0.34753056848786 0.69506113697572 0.65246943151214 99 0.34223567936202 0.68447135872404 0.65776432063798 100 0.356899538425401 0.713799076850803 0.643100461574599 101 0.313633726684461 0.627267453368922 0.686366273315539 102 0.280817284184814 0.561634568369628 0.719182715815186 103 0.252749444419388 0.505498888838775 0.747250555580612 104 0.216770774343925 0.433541548687849 0.783229225656075 105 0.187410191708177 0.374820383416354 0.812589808291823 106 0.210050311151338 0.420100622302676 0.789949688848662 107 0.226955464683005 0.45391092936601 0.773044535316995 108 0.245478275651018 0.490956551302035 0.754521724348982 109 0.208370174403684 0.416740348807367 0.791629825596316 110 0.209509538915398 0.419019077830796 0.790490461084602 111 0.254257997920659 0.508515995841318 0.745742002079341 112 0.408075901513757 0.816151803027514 0.591924098486243 113 0.361170388604549 0.722340777209097 0.638829611395451 114 0.656468077750697 0.687063844498606 0.343531922249303 115 0.92317512825355 0.153649743492900 0.0768248717464501 116 0.904168081875677 0.191663836248646 0.0958319181243228 117 0.904684551587235 0.190630896825529 0.0953154484127646 118 0.879821220321148 0.240357559357703 0.120178779678852 119 0.850229793596483 0.299540412807034 0.149770206403517 120 0.951917954099575 0.096164091800849 0.0480820459004245 121 0.936432246534011 0.127135506931977 0.0635677534659887 122 0.920911073749128 0.158177852501744 0.079088926250872 123 0.926073217286187 0.147853565427626 0.0739267827138132 124 0.904006912661264 0.191986174677472 0.095993087338736 125 0.877487073845235 0.245025852309531 0.122512926154765 126 0.844102009329085 0.31179598134183 0.155897990670915 127 0.823801843132555 0.352396313734891 0.176198156867445 128 0.816031972101873 0.367936055796253 0.183968027898127 129 0.777814006718002 0.444371986563996 0.222185993281998 130 0.728789977354098 0.542420045291804 0.271210022645902 131 0.707582507275934 0.584834985448132 0.292417492724066 132 0.693420082521465 0.61315983495707 0.306579917478535 133 0.680523204243621 0.638953591512757 0.319476795756379 134 0.629485303626913 0.741029392746173 0.370514696373087 135 0.700238481187976 0.599523037624048 0.299761518812024 136 0.681336284146713 0.637327431706574 0.318663715853287 137 0.618222980239844 0.763554039520312 0.381777019760156 138 0.556667661999525 0.88666467600095 0.443332338000475 139 0.49526943539885 0.9905388707977 0.50473056460115 140 0.432997050361784 0.865994100723568 0.567002949638216 141 0.372685355885016 0.745370711770032 0.627314644114984 142 0.391660926433086 0.783321852866171 0.608339073566914 143 0.339283564236610 0.678567128473221 0.66071643576339 144 0.266181845820085 0.53236369164017 0.733818154179915 145 0.250405749275854 0.500811498551707 0.749594250724146 146 0.218318000396481 0.436636000792962 0.781681999603519 147 0.155233567263026 0.310467134526052 0.844766432736974 148 0.102904499345556 0.205808998691112 0.897095500654444 149 0.441085776212402 0.882171552424805 0.558914223787598 150 0.385138090128551 0.770276180257102 0.614861909871449 151 0.354215477072619 0.708430954145239 0.64578452292738 152 0.243976176395308 0.487952352790616 0.756023823604692 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 1 0.00684931506849315 OK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/22/t1293043898d1zfrxes0un84qm/10qjxp1293043909.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/22/t1293043898d1zfrxes0un84qm/10qjxp1293043909.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/22/t1293043898d1zfrxes0un84qm/1ki0w1293043909.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/22/t1293043898d1zfrxes0un84qm/1ki0w1293043909.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/22/t1293043898d1zfrxes0un84qm/2urzg1293043909.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/22/t1293043898d1zfrxes0un84qm/2urzg1293043909.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/22/t1293043898d1zfrxes0un84qm/3urzg1293043909.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/22/t1293043898d1zfrxes0un84qm/3urzg1293043909.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/22/t1293043898d1zfrxes0un84qm/4urzg1293043909.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/22/t1293043898d1zfrxes0un84qm/4urzg1293043909.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/22/t1293043898d1zfrxes0un84qm/5n1g21293043909.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/22/t1293043898d1zfrxes0un84qm/5n1g21293043909.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/22/t1293043898d1zfrxes0un84qm/6n1g21293043909.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/22/t1293043898d1zfrxes0un84qm/6n1g21293043909.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/22/t1293043898d1zfrxes0un84qm/7gaym1293043909.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/22/t1293043898d1zfrxes0un84qm/7gaym1293043909.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/22/t1293043898d1zfrxes0un84qm/8gaym1293043909.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/22/t1293043898d1zfrxes0un84qm/8gaym1293043909.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/22/t1293043898d1zfrxes0un84qm/9qjxp1293043909.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/22/t1293043898d1zfrxes0un84qm/9qjxp1293043909.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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