ws 7 1

*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, 24 Nov 2010 12:56:28 +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/24/t1290603356ktlv39ri6882aj2.htm/, Retrieved Wed, 24 Nov 2010 13:55:56 +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/24/t1290603356ktlv39ri6882aj2.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 «

26 24 14 11 12 24 23 25 11 7 8 25 25 17 6 17 8 30 23 18 12 10 8 19 19 18 8 12 9 22 29 16 10 12 7 22 25 20 10 11 4 25 21 16 11 11 11 23 22 18 16 12 7 17 25 17 11 13 7 21 24 23 13 14 12 19 18 30 12 16 10 19 22 23 8 11 10 15 15 18 12 10 8 16 22 15 11 11 8 23 28 12 4 15 4 27 20 21 9 9 9 22 12 15 8 11 8 14 24 20 8 17 7 22 20 31 14 17 11 23 21 27 15 11 9 23 20 34 16 18 11 21 21 21 9 14 13 19 23 31 14 10 8 18 28 19 11 11 8 20 24 16 8 15 9 23 24 20 9 15 6 25 24 21 9 13 9 19 23 22 9 16 9 24 23 17 9 13 6 22 29 24 10 9 6 25 24 25 16 18 16 26 18 26 11 18 5 29 25 25 8 12 7 32 21 17 9 17 9 25 26 32 16 9 6 29 22 33 11 9 6 28 22 13 16 12 5 17 22 32 12 18 12 28 23 25 12 12 7 29 30 29 14 18 10 26 23 22 9 14 9 25 17 18 10 15 8 14 23 17 9 16 5 25 23 20 10 10 8 26 25 15 12 11 8 20 24 20 14 14 10 18 24 33 14 9 6 32 23 29 10 12 8 25 21 23 14 17 7 25 24 26 16 5 4 23 24 18 9 12 8 21 28 20 10 12 8 20 16 11 6 6 4 15 20 28 8 24 20 30 29 26 13 12 8 24 27 22 10 12 8 26 22 17 8 14 6 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 O[t] = + 16.1634772168084 -0.0705105327835315CM[t] + 0.215960321376021D[t] -0.149741441133531PE[t] -0.254410995984344PC[t] + 0.422488248372724PS[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) 16.1634772168084 2.00169 8.0749 0 0 CM -0.0705105327835315 0.063068 -1.118 0.265316 0.132658 D 0.215960321376021 0.112996 1.9112 0.057846 0.028923 PE -0.149741441133531 0.10427 -1.4361 0.153017 0.076509 PC -0.254410995984344 0.130432 -1.9505 0.05294 0.02647 PS 0.422488248372724 0.075659 5.5841 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.471036638254722 R-squared 0.221875514578309 Adjusted R-squared 0.196446609825966 F-TEST (value) 8.7253272108728 F-TEST (DF numerator) 5 F-TEST (DF denominator) 153 p-value 2.66656804082110e-07 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 3.50047733459247 Sum Squared Residuals 1874.76126020933 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 26 22.9342990859323 3.06570091406767 2 23 24.2550055858650 -1.25500558586496 3 25 24.3543150717814 0.645684928218581 4 23 21.9803858230888 1.01961417691123 5 19 21.8301154044514 -2.83011540445145 6 29 22.9118791047392 6.08812089526076 7 25 24.8102761478099 0.189723852190148 8 21 22.6824251316841 -1.68242513168414 9 22 21.9541787255647 0.0458212744353119 10 25 22.4850992038255 2.51490079617452 11 24 20.2271837320756 3.77281626792437 12 18 19.7269887909165 -1.72698879091652 13 22 18.4154754470739 3.58452455292609 14 15 20.7129210779706 -5.7129210779706 15 22 23.5161686524207 -1.51616865242071 16 28 24.3246092140333 3.6753907859667 17 20 22.2837684508775 -2.28376845087747 18 12 19.0658934529381 -7.06589345293813 19 24 21.4492091251854 2.55079087481458 20 20 21.3741994572580 -1.37419945725805 21 21 23.2794725485381 -2.27947254853807 22 20 20.5998705637805 -0.599870563780518 23 21 19.2499525161543 1.75004748384574 24 23 21.0731812912822 1.92681870871782 25 28 21.9666617761684 6.03333822383159 26 24 21.9444003949906 2.05559960500936 27 24 23.486528069931 0.51347193006898 28 24 20.4173379412252 3.58266205877483 29 23 22.0100443269047 0.989955673095331 30 23 22.7300778054305 0.269922194569496 31 29 24.3188949069741 4.6811050930259 32 24 22.0748516207742 1.9251483792258 33 18 24.9905251820565 -6.99052518205652 34 25 26.0702461506627 -1.07024615066266 35 21 22.6353437980615 -1.63534379806152 36 26 26.7405255664529 -0.74052556645287 37 22 25.1677251784165 -3.16772517841651 38 22 22.8155533814510 -0.815553381451035 39 22 22.5800570864682 -0.580057086468219 40 23 25.6666226910486 -2.66662269104857 41 30 22.8873548227941 7.1126451772059 42 23 22.7320154575445 0.267984542455546 43 17 18.6873167328055 -1.68731673280545 44 23 23.8027292231324 -0.802729223132429 45 23 24.3648618533787 -1.36486185337873 46 25 22.4646642286786 2.53533577132144 47 24 20.7410093953982 3.25899060460179 48 24 27.5055591360355 -3.50555913603547 49 23 23.0082959276872 -0.00829592768716035 50 21 23.8009042002091 -2.80090420020913 51 24 25.7364470294205 -1.73644702942053 52 24 21.8779984734391 2.12200152656091 53 28 21.5304494808753 6.46955051912468 54 16 21.1048543792980 -5.10485437929796 55 20 19.9094978141678 0.0905021858322328 56 29 23.4452202417931 5.5547797582069 57 27 23.9243579055446 3.07564209445539 58 22 23.2093525396664 -1.2093525396664 59 28 24.057980465366 3.94201953463401 60 16 20.3486433530867 -4.34864335308675 61 25 22.9615627553565 2.03843724464355 62 24 23.5089724924178 0.491027507582153 63 28 23.6777617636191 4.32223823638092 64 24 24.3538592726111 -0.353859272611125 65 23 22.7260409894245 0.27395901057552 66 30 26.9716430506531 3.02835694934685 67 24 21.3176309153834 2.68236908461659 68 21 24.1926759897584 -3.19267598975837 69 25 23.3397629314853 1.66023706851474 70 25 24.0085924852485 0.991407514751505 71 22 20.7888555718394 1.21114442816063 72 23 22.5111232600405 0.488876739959505 73 26 22.8631662508881 3.13683374911188 74 23 21.5814394030676 1.41856059693240 75 25 23.0634648732298 1.93653512677017 76 21 21.3189178825247 -0.31891788252473 77 25 23.669433295072 1.33056670492799 78 24 22.1829422093379 1.81705779066212 79 29 23.5998282837961 5.40017171620387 80 22 23.6538473326819 -1.65384733268187 81 27 23.6366369767902 3.36336302320978 82 26 19.6899059569537 6.31009404304634 83 22 21.3196299013376 0.680370098662419 84 24 22.1031823234841 1.89681767651591 85 27 23.1224696721432 3.87753032785675 86 24 21.3313445009180 2.66865549908196 87 24 24.9078428674147 -0.9078428674147 88 29 24.4635324988158 4.53646750118417 89 22 22.230271859528 -0.230271859527993 90 21 20.5879062645250 0.412093735474971 91 24 20.404279942293 3.59572005770701 92 24 21.8410527099606 2.15894729003938 93 23 21.9734444996209 1.02655550037907 94 20 22.2940025806218 -2.29400258062181 95 27 21.4484073898204 5.5515926101796 96 26 23.45937564659 2.54062435340999 97 25 21.9191899186339 3.08081008136608 98 21 20.0501312675858 0.949868732414233 99 21 20.7944341915217 0.205565808478268 100 19 20.3947104774293 -1.39471047742928 101 21 21.6283363122736 -0.628336312273621 102 21 21.3214549242609 -0.321454924260883 103 16 19.7574770795959 -3.7574770795959 104 22 20.7039918366938 1.29600816330621 105 29 21.8236786171937 7.17632138280634 106 15 21.6872477864301 -6.68724778643014 107 17 20.7369356868457 -3.73693568684571 108 15 19.9513953468902 -4.95139534689023 109 21 21.6742572878536 -0.674257287853575 110 21 21.0022031148351 -0.00220311483507387 111 19 19.311584073356 -0.311584073356004 112 24 18.0728583306381 5.92714166936192 113 20 22.4039626342782 -2.40396263427820 114 17 25.2056579436662 -8.20565794366624 115 23 25.0803510679257 -2.08035106792569 116 24 22.4165507644496 1.58344923555036 117 14 22.1008527643507 -8.10085276435074 118 19 22.9159877159712 -3.91598771597122 119 24 22.1830792798223 1.81692072017774 120 13 20.4056018121138 -7.40560181211378 121 22 25.4130956870409 -3.41309568704094 122 16 21.1564192498187 -5.15641924981871 123 19 23.3029950724559 -4.30299507245587 124 25 22.8583521408108 2.14164785918919 125 25 24.1914517395648 0.808548260435188 126 23 21.4201908449564 1.57980915504358 127 24 23.6131848649908 0.386815135009174 128 26 23.5861042368758 2.41389576312423 129 26 21.5400649165637 4.45993508343629 130 25 24.1623247715634 0.837675228436626 131 18 22.3823673010886 -4.38236730108861 132 21 19.9065782971425 1.09342170285747 133 26 23.7064599320546 2.29354006794537 134 23 22.0024627798499 0.99753722015007 135 23 19.7699859546009 3.2300140453991 136 22 22.5834432175016 -0.583443217501609 137 20 22.4056852541664 -2.40568525416642 138 13 22.1217270004493 -9.12172700044928 139 24 21.4781376888623 2.52186231113774 140 15 21.6102308962601 -6.61023089626005 141 14 23.1514635110785 -9.15146351107852 142 22 24.1016127157773 -2.10161271577729 143 10 17.6849076382035 -7.68490763820351 144 24 24.4741689969653 -0.47416899696531 145 22 21.8633444637173 0.136655536282658 146 24 25.8075977857910 -1.80759778579096 147 19 21.8641566604681 -2.8641566604681 148 20 22.1411298449899 -2.14112984498990 149 13 17.1172378109218 -4.11723781092184 150 20 20.1492028983205 -0.149202898320468 151 22 23.3128284521328 -1.31282845213279 152 24 23.3531143758200 0.646885624180027 153 29 23.1863524732849 5.81364752671514 154 12 20.9603189552611 -8.96031895526115 155 20 20.9663762867523 -0.966376286752273 156 21 21.4626130603123 -0.462613060312332 157 24 23.6699009387356 0.330099061264416 158 22 21.9242395608125 0.0757604391875075 159 20 17.6996527475850 2.30034725241504 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 9 0.725054619727416 0.549890760545168 0.274945380272584 10 0.598321151527414 0.803357696945171 0.401678848472586 11 0.488975851591454 0.977951703182909 0.511024148408546 12 0.444478150610061 0.888956301220122 0.555521849389939 13 0.452507565329431 0.905015130658863 0.547492434670569 14 0.692944455991945 0.614111088016111 0.307055544008055 15 0.624361545721041 0.751276908557917 0.375638454278959 16 0.57234025674681 0.855319486506379 0.427659743253190 17 0.506313500320501 0.987372999358998 0.493686499679499 18 0.636441549701062 0.727116900597877 0.363558450298938 19 0.561381672166246 0.877236655667508 0.438618327833754 20 0.566462604627629 0.867074790744743 0.433537395372371 21 0.518595053226336 0.962809893547328 0.481404946773664 22 0.449441536747204 0.898883073494408 0.550558463252796 23 0.390420051333630 0.780840102667259 0.60957994866637 24 0.391051795869886 0.782103591739773 0.608948204130114 25 0.534775205525779 0.930449588948442 0.465224794474221 26 0.472150175187517 0.944300350375035 0.527849824812483 27 0.408598228529319 0.817196457058637 0.591401771470681 28 0.401847030917499 0.803694061834999 0.5981529690825 29 0.340959709734207 0.681919419468414 0.659040290265793 30 0.284307128687356 0.568614257374712 0.715692871312644 31 0.308442849647593 0.616885699295186 0.691557150352407 32 0.259940453152262 0.519880906304525 0.740059546847738 33 0.484013786847129 0.968027573694258 0.515986213152871 34 0.437627659905406 0.875255319810813 0.562372340094594 35 0.402858138041794 0.805716276083588 0.597141861958206 36 0.347214242721731 0.694428485443462 0.652785757278269 37 0.3245861755392 0.6491723510784 0.6754138244608 38 0.275314516733695 0.55062903346739 0.724685483266305 39 0.230568769234332 0.461137538468663 0.769431230765668 40 0.207289923443625 0.41457984688725 0.792710076556375 41 0.358628733812652 0.717257467625304 0.641371266187348 42 0.308567712697564 0.617135425395128 0.691432287302436 43 0.276851864283789 0.553703728567578 0.723148135716211 44 0.235041754442239 0.470083508884477 0.764958245557761 45 0.20251404922081 0.40502809844162 0.79748595077919 46 0.181691105623728 0.363382211247456 0.818308894376272 47 0.169455911971035 0.338911823942069 0.830544088028965 48 0.156496159068687 0.312992318137374 0.843503840931313 49 0.127516697144460 0.255033394288920 0.87248330285554 50 0.118033713114159 0.236067426228319 0.88196628688584 51 0.0972687247136764 0.194537449427353 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0.182716649992596 0.908641675003702 70 0.0744932481640963 0.148986496328193 0.925506751835904 71 0.0605348977915152 0.121069795583030 0.939465102208485 72 0.0477996698750225 0.095599339750045 0.952200330124978 73 0.0449137264088656 0.0898274528177312 0.955086273591134 74 0.036026180648269 0.072052361296538 0.963973819351731 75 0.0300049536652854 0.0600099073305709 0.969995046334715 76 0.0230414419804431 0.0460828839608863 0.976958558019557 77 0.0180913980120979 0.0361827960241958 0.981908601987902 78 0.0144855986610463 0.0289711973220926 0.985514401338954 79 0.0217318789136061 0.0434637578272121 0.978268121086394 80 0.0173386750570144 0.0346773501140287 0.982661324942986 81 0.0169790641910422 0.0339581283820844 0.983020935808958 82 0.0304888492197468 0.0609776984394936 0.969511150780253 83 0.0235334249294142 0.0470668498588284 0.976466575070586 84 0.0196622359863707 0.0393244719727414 0.98033776401363 85 0.0216406578347216 0.0432813156694431 0.978359342165278 86 0.0192530053869049 0.0385060107738099 0.980746994613095 87 0.0146662508602832 0.0293325017205664 0.985333749139717 88 0.0192339511379366 0.0384679022758731 0.980766048862063 89 0.0151696243396934 0.0303392486793868 0.984830375660307 90 0.0113732216090305 0.022746443218061 0.98862677839097 91 0.0115021855029134 0.0230043710058269 0.988497814497087 92 0.0100640536151708 0.0201281072303417 0.98993594638483 93 0.00773952213791182 0.0154790442758236 0.992260477862088 94 0.00641618915165393 0.0128323783033079 0.993583810848346 95 0.0118044113120626 0.0236088226241252 0.988195588687937 96 0.0107451724969053 0.0214903449938105 0.989254827503095 97 0.0102827718184301 0.0205655436368602 0.98971722818157 98 0.00790205465807949 0.0158041093161590 0.99209794534192 99 0.0058516955708905 0.011703391141781 0.99414830442911 100 0.00449838975618616 0.00899677951237231 0.995501610243814 101 0.0033388359040687 0.0066776718081374 0.996661164095931 102 0.00238597195773079 0.00477194391546159 0.99761402804227 103 0.00256431583436890 0.00512863166873779 0.997435684165631 104 0.00201810772247375 0.00403621544494750 0.997981892277526 105 0.008616270214018 0.017232540428036 0.991383729785982 106 0.0193169703567745 0.038633940713549 0.980683029643226 107 0.0192672199822972 0.0385344399645944 0.980732780017703 108 0.0243956234840814 0.0487912469681627 0.975604376515919 109 0.0189388208012814 0.0378776416025629 0.981061179198719 110 0.0139242373488795 0.0278484746977591 0.98607576265112 111 0.0101459402279362 0.0202918804558724 0.989854059772064 112 0.0248323992935841 0.0496647985871683 0.975167600706416 113 0.0226463783585092 0.0452927567170183 0.97735362164149 114 0.0626716384088068 0.125343276817614 0.937328361591193 115 0.0536899234766868 0.107379846953374 0.946310076523313 116 0.0438251716511212 0.0876503433022424 0.956174828348879 117 0.127712254341788 0.255424508683576 0.872287745658212 118 0.123183619686242 0.246367239372483 0.876816380313758 119 0.110163602757869 0.220327205515739 0.88983639724213 120 0.190173466465613 0.380346932931225 0.809826533534387 121 0.182394483267425 0.364788966534850 0.817605516732575 122 0.216779914075919 0.433559828151839 0.78322008592408 123 0.210359256407196 0.420718512814392 0.789640743592804 124 0.209304463892027 0.418608927784054 0.790695536107973 125 0.193261850696199 0.386523701392397 0.806738149303801 126 0.159394279155869 0.318788558311737 0.840605720844131 127 0.126401761548948 0.252803523097895 0.873598238451052 128 0.130910824939466 0.261821649878933 0.869089175060534 129 0.185787054018668 0.371574108037337 0.814212945981332 130 0.161991674654977 0.323983349309955 0.838008325345023 131 0.143573170957020 0.287146341914039 0.85642682904298 132 0.125769870175506 0.251539740351012 0.874230129824494 133 0.116506941960348 0.233013883920695 0.883493058039653 134 0.0964925681399964 0.192985136279993 0.903507431860004 135 0.130346054522817 0.260692109045634 0.869653945477183 136 0.0987358156979437 0.197471631395887 0.901264184302056 137 0.0737283865542685 0.147456773108537 0.926271613445732 138 0.180287176691590 0.360574353383181 0.81971282330841 139 0.250321998512361 0.500643997024722 0.749678001487639 140 0.231691330048748 0.463382660097497 0.768308669951252 141 0.470624131224184 0.941248262448368 0.529375868775816 142 0.422400846878156 0.844801693756312 0.577599153121844 143 0.728533458252504 0.542933083494992 0.271466541747496 144 0.679249492862061 0.641501014275878 0.320750507137939 145 0.579343023922605 0.84131395215479 0.420656976077395 146 0.508302392586352 0.983395214827295 0.491697607413648 147 0.558406818456728 0.883186363086544 0.441593181543272 148 0.431110510972315 0.86222102194463 0.568889489027685 149 0.338206148176793 0.676412296353586 0.661793851823207 150 0.242095892321836 0.484191784643673 0.757904107678164 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 5 0.0352112676056338 NOK 5% type I error level 37 0.26056338028169 NOK 10% type I error level 43 0.302816901408451 NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/24/t1290603356ktlv39ri6882aj2/104ark1290603375.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290603356ktlv39ri6882aj2/104ark1290603375.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290603356ktlv39ri6882aj2/1x9u91290603375.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290603356ktlv39ri6882aj2/1x9u91290603375.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290603356ktlv39ri6882aj2/2qicu1290603375.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290603356ktlv39ri6882aj2/2qicu1290603375.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290603356ktlv39ri6882aj2/3qicu1290603375.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290603356ktlv39ri6882aj2/3qicu1290603375.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290603356ktlv39ri6882aj2/4qicu1290603375.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290603356ktlv39ri6882aj2/4qicu1290603375.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290603356ktlv39ri6882aj2/5iabf1290603375.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290603356ktlv39ri6882aj2/5iabf1290603375.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290603356ktlv39ri6882aj2/6iabf1290603375.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290603356ktlv39ri6882aj2/6iabf1290603375.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290603356ktlv39ri6882aj2/7b1ah1290603375.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290603356ktlv39ri6882aj2/7b1ah1290603375.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290603356ktlv39ri6882aj2/8b1ah1290603375.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290603356ktlv39ri6882aj2/8b1ah1290603375.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290603356ktlv39ri6882aj2/94ark1290603375.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290603356ktlv39ri6882aj2/94ark1290603375.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') }

Copyright

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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