Multiple Regression Analysis

*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, 14 Dec 2010 23:59:54 +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/15/t1292372543zotmtd6eb8h5a8j.htm/, Retrieved Wed, 15 Dec 2010 01:24:35 +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/15/t1292372543zotmtd6eb8h5a8j.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 «

13 26 9 15 6 25 25 16 20 9 15 6 25 24 19 21 9 14 13 19 21 15 31 14 10 8 18 23 14 21 8 10 7 18 17 13 18 8 12 9 22 19 19 26 11 18 5 29 18 15 22 10 12 8 26 27 14 22 9 14 9 25 23 15 29 15 18 11 23 23 16 15 14 9 8 23 29 16 16 11 11 11 23 21 16 24 14 11 12 24 26 17 17 6 17 8 30 25 15 19 20 8 7 19 25 15 22 9 16 9 24 23 20 31 10 21 12 32 26 18 28 8 24 20 30 20 16 38 11 21 7 29 29 16 26 14 14 8 17 24 19 25 11 7 8 25 23 16 25 16 18 16 26 24 17 29 14 18 10 26 30 17 28 11 13 6 25 22 16 15 11 11 8 23 22 15 18 12 13 9 21 13 14 21 9 13 9 19 24 15 25 7 18 11 35 17 12 23 13 14 12 19 24 14 23 10 12 8 20 21 16 19 9 9 7 21 23 14 18 9 12 8 21 24 7 18 13 8 9 24 24 10 26 16 5 4 23 24 14 18 12 10 8 19 23 16 18 6 11 8 17 26 16 28 14 11 8 24 24 16 17 14 12 6 15 21 14 29 10 12 8 25 23 20 12 4 15 4 27 28 14 25 12 12 7 29 23 14 28 12 16 14 27 22 11 20 14 14 10 18 24 15 17 9 17 9 25 21 16 17 9 13 6 22 23 14 20 10 10 8 26 23 16 31 14 17 11 23 20 14 21 10 12 8 16 23 12 19 9 13 8 27 21 16 23 1 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 Learning[t] = + 12.3256161875859 + 0.00618479983854838Concern[t] -0.278785234171933Doubts[t] + 0.103632621238310Expectations[t] + 0.0086704709418611Criticism[t] + 0.0271802218699456Standards[t] + 0.157965607370892Organization[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) 12.3256161875859 1.462481 8.4279 0 0 Concern 0.00618479983854838 0.037772 0.1637 0.870167 0.435083 Doubts -0.278785234171933 0.069179 -4.0299 9e-05 4.5e-05 Expectations 0.103632621238310 0.06296 1.646 0.101959 0.05098 Criticism 0.0086704709418611 0.079066 0.1097 0.912831 0.456416 Standards 0.0271802218699456 0.049093 0.5536 0.580686 0.290343 Organization 0.157965607370892 0.049734 3.1762 0.001828 0.000914 Multiple Linear Regression - Regression Statistics Multiple R 0.455226373457424 R-squared 0.207231051091198 Adjusted R-squared 0.173968018269849 F-TEST (value) 6.23007084784512 F-TEST (DF numerator) 6 F-TEST (DF denominator) 143 p-value 7.8201096992414e-06 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 2.06577475960640 Sum Squared Residuals 610.241826112041 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 13 16.2125117510879 -3.21251175108787 2 16 16.0174373446854 -0.0174373446853516 3 19 15.3437046665463 3.65629533345371 4 15 13.8424946472814 1.15750535271862 5 14 14.4968939387603 -0.49689393876028 6 13 15.1275978258265 -2.12759782582654 7 19 14.9601303114003 4.03986968859972 8 15 15.9585418323419 -0.958541832341931 9 14 15.7942201285788 -1.79422012857883 10 15 14.5423133055141 0.457686694485855 11 16 14.7235999822014 1.27640001779863 12 16 14.5356922808908 1.46430771910921 13 16 14.5744937067496 1.42550629325035 14 17 17.3537115487665 -0.353711548766472 15 15 12.2227413673804 2.77725863261955 16 15 15.9743051491855 -0.974305149185507 17 20 16.9866962296499 3.01330377035011 18 18 16.9038198417627 1.09618015823732 19 16 17.1002083961413 -1.10020839614133 20 16 14.3568865185428 1.64311348145717 21 19 14.5211052401406 4.47889475985942 22 16 14.5216474996781 1.47835250032195 23 17 15.9997279859503 1.00027201404970 24 17 14.9861488178315 2.01385118216853 25 16 14.6614616755976 1.33853832440245 26 15 13.1411156442818 1.85888435571818 27 14 15.6792869836532 -1.67928698365319 28 15 16.1262249977494 -1.12622499774941 29 12 14.7061596807064 -2.70615968070645 30 14 14.8538516567355 -0.853851656735453 31 16 15.1314407935081 0.86855920649187 32 14 15.6027899356973 -1.60278993569727 33 7 14.163329650608 -7.16332965060799 34 10 12.9950219065064 -2.99502190650639 35 14 14.3468429395941 -0.346842939594062 36 16 16.5427233442368 -0.542723344236757 37 16 14.2486198075946 1.75138019240539 38 16 13.5483598697830 2.45164013021702 39 14 15.3427927798583 -1.34279277985826 40 20 18.0307670481764 1.96923295182363 41 14 14.8605335286981 -0.860533528698117 42 14 15.1419856586492 -1.14198565864925 43 11 14.3642988832652 -3.3642988832652 44 15 15.7582627783592 -0.758262778359236 45 16 15.5521114297124 0.447888570287641 46 14 15.1070445607046 -1.10704456070464 47 16 14.2559386960122 1.74406130398781 48 14 15.0486923843204 -1.04869238432036 49 12 15.4017918658811 -3.40179186588112 50 16 14.9433790367448 1.05662096325517 51 9 13.6735393075749 -4.67353930757492 52 14 14.2848213877727 -0.284821387772669 53 16 15.5916412607011 0.408358739298907 54 16 14.9806224045578 1.01937759544224 55 15 15.0448667768714 -0.0448667768714398 56 16 14.7144347348262 1.28556526517378 57 12 13.4044584111642 -1.40445841116418 58 16 16.4306176266659 -0.430617626665932 59 16 16.1199728896308 -0.119972889630781 60 14 16.3731463457375 -2.37314634573747 61 16 12.4555583401581 3.54444165984192 62 17 15.9959388519617 1.00406114803827 63 18 14.5810078196535 3.41899218034646 64 18 15.4095422711377 2.59045772886225 65 12 14.4918698578981 -2.49186985789814 66 16 15.8447818797813 0.155218120218692 67 10 14.3109847797333 -4.31098477973325 68 14 12.5549855404930 1.44501445950697 69 18 15.3546694865409 2.64533051345908 70 18 16.2294492664044 1.77055073359564 71 16 15.5103914460054 0.489608553994597 72 16 15.4647462910473 0.535253708952651 73 16 14.7382625863182 1.26173741368180 74 13 14.6840829976808 -1.68408299768081 75 16 15.0649213546218 0.935078645378235 76 16 14.7750325979285 1.22496740207154 77 20 15.9965798782939 4.0034201217061 78 16 15.2636311279439 0.736368872056057 79 15 12.6533132422704 2.34668675772957 80 15 15.3514283261438 -0.351428326143807 81 16 15.8558716296856 0.144128370314401 82 14 14.1055970151842 -0.105597015184237 83 15 13.2179707233303 1.78202927666970 84 12 14.8618911097905 -2.86189110979051 85 17 16.0544395351271 0.945560464872856 86 16 15.2206429406429 0.77935705935714 87 15 13.0015774150171 1.99842258498291 88 13 14.3841044646471 -1.38410446464714 89 16 15.9358794880953 0.0641205119047345 90 16 15.2919624251822 0.708037574817808 91 16 16.2431343485888 -0.243134348588786 92 16 15.8855251684020 0.114474831598036 93 14 15.5962077967892 -1.59620779678920 94 16 14.2092124454423 1.79078755455770 95 16 15.2034992041161 0.79650079588393 96 20 16.4345370838630 3.56546291613696 97 15 15.5524538535673 -0.55245385356726 98 16 14.1423500400052 1.85764995999478 99 13 14.3388817605544 -1.3388817605544 100 17 15.9410565088161 1.05894349118395 101 16 14.2723793973866 1.72762060261342 102 12 13.3820911668385 -1.38209116683846 103 16 15.0376186150971 0.962381384902888 104 16 15.3838293804663 0.616170619533714 105 17 15.5289187613571 1.47108123864287 106 13 13.1697057822538 -0.16970578225384 107 12 15.8938827607261 -3.89388276072607 108 18 15.8372527602765 2.1627472397235 109 14 13.7614338628154 0.238566137184593 110 14 14.5518760110905 -0.551876011090541 111 13 13.7840851839024 -0.78408518390235 112 16 15.4718779022302 0.528122097769778 113 13 12.5921019758257 0.407898024174267 114 16 15.3796806277726 0.620319372227447 115 13 14.8709940137106 -1.87099401371062 116 16 15.8840608409725 0.115939159027488 117 15 14.7888071465404 0.211192853459580 118 16 15.4084961001822 0.591503899817782 119 15 14.9325562176423 0.0674437823577326 120 17 15.6482538659794 1.35174613402057 121 15 15.8977377480297 -0.897737748029724 122 12 13.6393640506104 -1.63936405061043 123 16 14.4292540962851 1.57074590371489 124 10 14.2187822446243 -4.2187822446243 125 16 14.3125682379591 1.68743176204089 126 14 14.7389013208296 -0.738901320829561 127 15 16.4755884143781 -1.47558841437810 128 13 14.5183295954537 -1.51832959545375 129 15 15.4177865658512 -0.417786565851156 130 11 13.7857724701193 -2.78577247011932 131 12 14.2703691701158 -2.27036917011577 132 8 14.5989059202342 -6.59890592023418 133 16 16.3110948713655 -0.311094871365533 134 15 14.9161438996603 0.0838561003397311 135 17 15.3471949437459 1.65280505625411 136 16 15.4424536590105 0.55754634098952 137 10 15.0704011970605 -5.07040119706048 138 18 13.8675057034538 4.13249429654624 139 13 13.9430146783361 -0.943014678336107 140 15 14.3333497221560 0.66665027784403 141 16 14.6614616755976 1.33853832440245 142 16 15.0281045679855 0.97189543201446 143 14 13.4712432005434 0.528756799456632 144 10 13.1612303086049 -3.16123030860495 145 17 16.0544395351271 0.945560464872856 146 13 14.3803771702264 -1.38037717022638 147 15 15.8977377480297 -0.897737748029724 148 16 15.9468267786048 0.0531732213951709 149 12 15.284119549729 -3.28411954972900 150 13 13.5624866853128 -0.562486685312814 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 10 0.929162373438926 0.141675253122148 0.0708376265610739 11 0.875870946955373 0.248258106089254 0.124129053044627 12 0.7996737902567 0.400652419486599 0.200326209743300 13 0.708217239792919 0.583565520414162 0.291782760207081 14 0.629047374120305 0.74190525175939 0.370952625879695 15 0.548864341338667 0.902271317322666 0.451135658661333 16 0.464611610485308 0.929223220970616 0.535388389514692 17 0.449457278230867 0.898914556461734 0.550542721769133 18 0.454543000516936 0.909086001033872 0.545456999483064 19 0.369873988664769 0.739747977329538 0.63012601133523 20 0.316560039137521 0.633120078275041 0.683439960862479 21 0.460315115703017 0.920630231406034 0.539684884296983 22 0.443775719823656 0.887551439647311 0.556224280176344 23 0.385096523482664 0.770193046965327 0.614903476517336 24 0.32686103611583 0.65372207223166 0.67313896388417 25 0.269433446887484 0.538866893774967 0.730566553112516 26 0.229734477608571 0.459468955217142 0.770265522391429 27 0.184083380379199 0.368166760758399 0.8159166196208 28 0.265619833359865 0.53123966671973 0.734380166640135 29 0.364042808127576 0.728085616255151 0.635957191872424 30 0.314639268966104 0.629278537932207 0.685360731033896 31 0.272602529830838 0.545205059661676 0.727397470169162 32 0.232648668348641 0.465297336697282 0.767351331651359 33 0.922042137744413 0.155915724511174 0.0779578622555869 34 0.951904667869728 0.096190664260543 0.0480953321302715 35 0.935643945586828 0.128712108826344 0.0643560544131718 36 0.921317933203207 0.157364133593586 0.078682066796793 37 0.909587680384306 0.180824639231387 0.0904123196156936 38 0.903693994938545 0.192612010122909 0.0963060050614546 39 0.885550454617984 0.228899090764033 0.114449545382016 40 0.903639792137163 0.192720415725673 0.0963602078628366 41 0.882266554727474 0.235466890545053 0.117733445272526 42 0.863983570508731 0.272032858982537 0.136016429491269 43 0.920262077983152 0.159475844033697 0.0797379220168483 44 0.905332014136677 0.189335971726646 0.0946679858633232 45 0.881839474717711 0.236321050564578 0.118160525282289 46 0.858321134333488 0.283357731333023 0.141678865666512 47 0.839956308015503 0.320087383968994 0.160043691984497 48 0.813600732135474 0.372798535729052 0.186399267864526 49 0.859695206715183 0.280609586569634 0.140304793284817 50 0.837036356118637 0.325927287762726 0.162963643881363 51 0.925516539703982 0.148966920592035 0.0744834602960177 52 0.90706086188471 0.185878276230579 0.0929391381152894 53 0.88873846953627 0.222523060927462 0.111261530463731 54 0.873342869630429 0.253314260739143 0.126657130369571 55 0.846049711150487 0.307900577699025 0.153950288849513 56 0.836177509932676 0.327644980134648 0.163822490067324 57 0.818158112056372 0.363683775887257 0.181841887943628 58 0.784575454520599 0.430849090958803 0.215424545479402 59 0.746504785040901 0.506990429918198 0.253495214959099 60 0.747689730142498 0.504620539715004 0.252310269857502 61 0.808046936221255 0.38390612755749 0.191953063778745 62 0.785016094851123 0.429967810297755 0.214983905148877 63 0.838099976729959 0.323800046540083 0.161900023270041 64 0.861276231987536 0.277447536024928 0.138723768012464 65 0.874240469927597 0.251519060144806 0.125759530072403 66 0.848267861542842 0.303464276914315 0.151732138457158 67 0.92192778985214 0.156144420295718 0.078072210147859 68 0.910606855801358 0.178786288397284 0.0893931441986421 69 0.92904362527955 0.141912749440902 0.0709563747204508 70 0.927587191922801 0.144825616154397 0.0724128080771987 71 0.910140526533317 0.179718946933367 0.0898594734666833 72 0.890053387826172 0.219893224347656 0.109946612173828 73 0.877193303737536 0.245613392524928 0.122806696262464 74 0.868054195463885 0.263891609072230 0.131945804536115 75 0.847315636723818 0.305368726552363 0.152684363276182 76 0.82822318285658 0.343553634286841 0.171776817143420 77 0.905192887252466 0.189614225495067 0.0948071127475335 78 0.886357642425335 0.227284715149330 0.113642357574665 79 0.8917025296548 0.216594940690400 0.108297470345200 80 0.867585415187782 0.264829169624435 0.132414584812218 81 0.840002736394346 0.319994527211308 0.159997263605654 82 0.813029993269397 0.373940013461206 0.186970006730603 83 0.81425290053609 0.371494198927819 0.185747099463909 84 0.843184105538536 0.313631788922927 0.156815894461464 85 0.818549507039875 0.362900985920249 0.181450492960125 86 0.79090305072174 0.418193898556519 0.209096949278260 87 0.798941938223149 0.402116123553703 0.201058061776851 88 0.782523102918616 0.434953794162767 0.217476897081384 89 0.749892094612542 0.500215810774915 0.250107905387457 90 0.713760960340097 0.572478079319806 0.286239039659903 91 0.671722914803435 0.65655417039313 0.328277085196565 92 0.626715103595145 0.746569792809709 0.373284896404854 93 0.618457537577178 0.763084924845643 0.381542462422822 94 0.621006722995939 0.757986554008122 0.378993277004061 95 0.578027973963577 0.843944052072846 0.421972026036423 96 0.66516199519547 0.669676009609061 0.334838004804530 97 0.61902895107147 0.761942097857059 0.380971048928530 98 0.648268161742614 0.703463676514772 0.351731838257386 99 0.61868524487181 0.76262951025638 0.38131475512819 100 0.598207740127297 0.803584519745405 0.401792259872703 101 0.611116753004157 0.777766493991686 0.388883246995843 102 0.577771961648272 0.844456076703456 0.422228038351728 103 0.532397374481144 0.935205251037712 0.467602625518856 104 0.511121393731048 0.977757212537904 0.488878606268952 105 0.503979906422163 0.992040187155675 0.496020093577837 106 0.450171137067422 0.900342274134844 0.549828862932578 107 0.586603688736935 0.82679262252613 0.413396311263065 108 0.590006146434476 0.819987707131048 0.409993853565524 109 0.586449884188445 0.82710023162311 0.413550115811555 110 0.53551944028606 0.92896111942788 0.46448055971394 111 0.48143837919943 0.96287675839886 0.51856162080057 112 0.429516570395245 0.85903314079049 0.570483429604755 113 0.397817595745914 0.795635191491827 0.602182404254086 114 0.360257186196027 0.720514372392054 0.639742813803973 115 0.343794789294001 0.687589578588002 0.656205210705999 116 0.290258690871178 0.580517381742355 0.709741309128822 117 0.264786817476584 0.529573634953167 0.735213182523416 118 0.267519330892590 0.535038661785179 0.73248066910741 119 0.219009383405196 0.438018766810391 0.780990616594804 120 0.187924344969432 0.375848689938865 0.812075655030568 121 0.154407350022854 0.308814700045707 0.845592649977146 122 0.140537139090532 0.281074278181063 0.859462860909468 123 0.131106195217387 0.262212390434775 0.868893804782613 124 0.177433809314216 0.354867618628432 0.822566190685784 125 0.142862714159503 0.285725428319006 0.857137285840497 126 0.110463697640415 0.220927395280831 0.889536302359585 127 0.0832675364824746 0.166535072964949 0.916732463517525 128 0.0629901080190008 0.125980216038002 0.937009891981 129 0.0443120783738492 0.0886241567476983 0.95568792162615 130 0.0363163959710087 0.0726327919420174 0.963683604028991 131 0.0269094347650174 0.0538188695300347 0.973090565234983 132 0.196173542274698 0.392347084549396 0.803826457725302 133 0.142839352985323 0.285678705970646 0.857160647014677 134 0.103272015931721 0.206544031863442 0.89672798406828 135 0.315283795191318 0.630567590382636 0.684716204808682 136 0.242588552149695 0.485177104299391 0.757411447850305 137 0.584481925157999 0.831036149684003 0.415518074842001 138 0.575405358570799 0.849189282858401 0.424594641429201 139 0.43855980269196 0.87711960538392 0.56144019730804 140 0.313208895217926 0.626417790435851 0.686791104782075 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 0.0305343511450382 OK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/15/t1292372543zotmtd6eb8h5a8j/10k4da1292371182.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/15/t1292372543zotmtd6eb8h5a8j/10k4da1292371182.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/15/t1292372543zotmtd6eb8h5a8j/1v3gg1292371182.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/15/t1292372543zotmtd6eb8h5a8j/1v3gg1292371182.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/15/t1292372543zotmtd6eb8h5a8j/2v3gg1292371182.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/15/t1292372543zotmtd6eb8h5a8j/2v3gg1292371182.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/15/t1292372543zotmtd6eb8h5a8j/36cyj1292371182.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/15/t1292372543zotmtd6eb8h5a8j/36cyj1292371182.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/15/t1292372543zotmtd6eb8h5a8j/46cyj1292371182.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/15/t1292372543zotmtd6eb8h5a8j/46cyj1292371182.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/15/t1292372543zotmtd6eb8h5a8j/56cyj1292371182.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/15/t1292372543zotmtd6eb8h5a8j/56cyj1292371182.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/15/t1292372543zotmtd6eb8h5a8j/6ymxm1292371182.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/15/t1292372543zotmtd6eb8h5a8j/6ymxm1292371182.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/15/t1292372543zotmtd6eb8h5a8j/7rvep1292371182.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/15/t1292372543zotmtd6eb8h5a8j/7rvep1292371182.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/15/t1292372543zotmtd6eb8h5a8j/8rvep1292371182.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/15/t1292372543zotmtd6eb8h5a8j/8rvep1292371182.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/15/t1292372543zotmtd6eb8h5a8j/9rvep1292371182.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/15/t1292372543zotmtd6eb8h5a8j/9rvep1292371182.ps (open in new window)

Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; 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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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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