*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: Sat, 13 Nov 2010 14:53:28 +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/13/t1289659933htnkew0gw6hiqvd.htm/, Retrieved Sat, 13 Nov 2010 15:52:13 +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/13/t1289659933htnkew0gw6hiqvd.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 12 25 8 17 8 18 8 18 9 16 7 20 4 16 11 18 7 17 7 23 12 30 10 23 10 18 8 15 8 12 4 21 9 15 8 20 7 31 11 27 9 34 11 21 13 31 8 19 8 16 9 20 6 21 9 22 9 17 6 24 6 25 16 26 5 25 7 17 9 32 6 33 6 13 5 32 12 25 7 29 10 22 9 18 8 17 5 20 8 15 8 20 10 33 6 29 8 23 7 26 4 18 8 20 8 11 4 28 20 26 8 22 8 17 6 12 4 14 8 17 9 21 6 19 7 18 9 10 5 29 5 31 8 19 8 9 6 20 8 28 7 19 7 30 9 29 11 26 6 23 8 13 6 21 9 19 8 28 6 23 10 18 8 21 8 20 10 23 5 21 7 21 5 15 8 28 14 19 7 26 8 10 6 16 5 22 6 19 10 31 12 31 9 29 12 19 7 22 8 23 10 15 6 20 10 18 10 23 10 25 5 21 7 24 10 25 11 17 6 13 7 28 12 21 11 25 11 9 11 16 5 19 8 17 6 25 9 20 4 29 4 14 7 22 11 15 6 19 7 20 8 15 4 20 8 18 9 33 8 22 11 16 8 17 5 16 4 21 8 26 10 18 6 18 9 17 9 22 13 30 9 30 10 24 20 21 5 21 11 29 6 31 9 20 7 16 9 22 10 20 9 28 8 38 7 22 6 20 13 17 6 28 8 22 10 31 16

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 7 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Multiple Linear Regression - Estimated Regression Equation PC[t] = + 4.85862517933143 + 0.145941427970896CM[t] + 0.00272072450394541t + 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) 4.85862517933143 0.863572 5.6262 0 0 CM 0.145941427970896 0.036 4.0539 7.9e-05 4e-05 t 0.00272072450394541 0.004474 0.6081 0.544037 0.272019 Multiple Linear Regression - Regression Statistics Multiple R 0.314293021849479 R-squared 0.0987801035832768 Adjusted R-squared 0.087226002347165 F-TEST (value) 8.54935416997593 F-TEST (DF numerator) 2 F-TEST (DF denominator) 156 p-value 0.000299778271357409 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 2.58630095079213 Sum Squared Residuals 1043.47660685865 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 12 8.36394017513689 3.63605982486311 2 8 8.51260232761174 -0.512602327611737 3 8 7.34779162834851 0.652208371651492 4 8 7.49645378082335 0.50354621917665 5 9 7.4991745053273 1.50082549467270 6 7 7.21001237388945 -0.210012373889448 7 4 7.79649881027698 -3.79649881027698 8 11 7.21545382289734 3.78454617710266 9 7 7.51005740334308 -0.510057403343077 10 7 7.36683669987613 -0.366836699876126 11 12 8.24520599220545 3.75479400779455 12 10 9.26951671250567 0.730483287494329 13 10 8.25064744121334 1.74935255878666 14 8 7.5236610258628 0.476338974137196 15 8 7.08855746645406 0.91144253354594 16 4 6.65345390704532 -2.65345390704532 17 9 7.96964748328733 1.03035251671267 18 8 7.0967196399659 0.903280360034103 19 7 7.82914750432432 -0.829147504324324 20 11 9.43722393650813 1.56277606349187 21 9 8.8561789491285 0.143821050871509 22 11 9.88048966942871 1.11951033057129 23 13 7.985971830311 5.014028169689 24 8 9.44810683452391 -1.44810683452391 25 8 7.6995304233771 0.300469576622900 26 9 7.26442686396836 1.73557313603164 27 6 7.85091330035589 -1.85091330035589 28 9 7.99957545283073 1.00042454716927 29 9 8.14823760530557 0.851762394694429 30 6 7.42125118995503 -1.42125118995503 31 6 8.44556191025526 -2.44556191025526 32 16 8.5942240627301 7.4057759372699 33 5 8.74288621520494 -3.74288621520494 34 7 8.59966551173799 -1.59966551173799 35 9 7.43485481247476 1.56514518752524 36 6 9.62669695654215 -3.62669695654215 37 6 9.775359109017 -3.77535910901700 38 5 6.85925127410301 -1.85925127410301 39 12 9.63485913005399 2.36514086994601 40 7 8.61598985876166 -1.61598985876166 41 10 9.2024762951492 0.797523704850808 42 9 8.18360702385686 0.816392976143138 43 8 7.60256203647722 0.397437963522779 44 5 7.45934133301027 -2.45934133301027 45 8 7.8998863414269 0.100113658573095 46 8 7.17289992607637 0.827100073923632 47 10 7.9053277904348 2.09467220956520 48 6 9.8052870785604 -3.80528707856039 49 8 9.22424209118076 -1.22424209118076 50 7 8.35131424785932 -1.35131424785932 51 4 8.79185925627596 -4.79185925627596 52 8 7.62704855701273 0.37295144298727 53 8 7.92165213745847 0.0783478625415317 54 4 6.61090001022434 -2.61090001022434 55 20 9.09462501023353 10.9053749897665 56 8 8.80546287879568 -0.805462878795684 57 8 8.22441789141604 -0.224417891416043 58 6 7.4974314760655 -1.49743147606551 59 4 6.77044506071497 -2.77044506071497 60 8 7.06504864116071 0.934951358839293 61 9 7.50559364957734 1.49440635042266 62 6 8.09208008596487 -2.09208008596487 63 7 7.80291795452703 -0.802917954527026 64 9 7.65969725106008 1.34030274893993 65 5 6.49488655179685 -1.49488655179685 66 5 9.27049440774783 -4.27049440774783 67 8 9.56509798819357 -1.56509798819357 68 8 7.81652157704675 0.183478422953247 69 6 6.35982802184173 -0.359828021841734 70 8 7.96790445402554 0.0320955459744598 71 7 9.13815660229666 -2.13815660229666 72 7 7.82740447506253 -0.827404475062535 73 9 9.43548090724634 -0.435480907246341 74 11 9.29226020377939 1.70773979622061 75 6 8.85715664437065 -2.85715664437065 76 8 8.4220530849619 -0.422053084961902 77 6 6.96535952975688 -0.965359529756883 78 9 8.135611678028 0.864388321972 79 8 7.84644954659015 0.153550453409848 80 6 9.16264312283216 -3.16264312283217 81 10 8.43565670748163 1.56434329251837 82 8 7.7086702921311 0.291329707868908 83 8 8.14921530054773 -0.149215300547727 84 10 8.00599459708078 1.99400540291922 85 5 8.44653960549741 -3.44653960549741 86 7 8.15737747405956 -1.15737747405956 87 5 8.16009819856351 -3.16009819856351 88 8 7.28717035524208 0.712829644757925 89 14 9.18712964336768 4.81287035663232 90 7 7.87637751613355 -0.876377516133552 91 8 8.90068823643377 -0.900688236433773 92 6 6.56834611340337 -0.568346113403374 93 5 7.4467154057327 -2.4467154057327 94 6 8.32508469806202 -2.32508469806202 95 10 7.88998113865328 2.11001886134672 96 12 9.64399899880798 2.35600100119202 97 9 9.64671972331193 -0.646719723311928 98 12 9.35755759187408 2.64244240812592 99 7 7.90086403666906 -0.90086403666906 100 8 8.3414090450857 -0.341409045085695 101 10 8.49007119756054 1.50992880243946 102 6 7.32526049829731 -1.32526049829731 103 10 8.05768836265574 1.94231163734426 104 10 7.76852623121789 2.23147376878211 105 10 8.50095409557632 1.49904590442368 106 5 8.79555767602206 -3.79555767602206 107 7 8.21451268864242 -1.21451268864242 108 10 8.65505769705905 1.34494230294095 109 11 8.8037198495339 2.19628015046611 110 6 7.63890915027067 -1.63890915027067 111 7 7.05786416289103 -0.0578641628910268 112 12 9.24970630695842 2.75029369304158 113 11 8.23083703566609 2.76916296433391 114 11 8.81732347205362 2.18267652794638 115 11 6.48498134902322 4.51501865097678 116 5 7.50929206932344 -2.50929206932344 117 8 7.94983707774008 0.0501629222599221 118 6 7.66067494630223 -1.66067494630223 119 9 8.83092709457335 0.169072905426652 120 4 8.10394067922281 -4.10394067922281 121 4 9.42013425546482 -5.42013425546482 122 7 7.23373356040532 -0.233733560405323 123 11 8.40398570867644 2.59601429132356 124 6 7.38511643738411 -1.38511643738411 125 7 7.97160287377164 -0.971602873771641 126 8 8.12026502624648 -0.120265026246483 127 4 7.39327861089595 -3.39327861089595 128 8 8.12570647525437 -0.125706475254374 129 9 7.83654434381653 1.16345565618347 130 8 10.0283864878839 -2.02838648788392 131 11 8.425751504708 2.574248495292 132 8 7.55282366138657 0.44717633861343 133 5 7.70148581386141 -2.70148581386141 134 4 7.55826511039446 -3.55826511039446 135 8 8.29069297475289 -0.290692974752888 136 10 9.02312083911132 0.976879160888684 137 6 7.85831013984809 -1.85831013984809 138 9 7.86103086435203 1.13896913564796 139 9 7.71781016088508 1.28218983911492 140 13 8.45023802524351 4.54976197475649 141 9 9.62049017351463 -0.620490173514629 142 10 9.62321089801857 0.376789101981426 143 20 8.75028305469714 11.2497169453029 144 5 8.3151794952884 -3.31517949528840 145 11 8.31790021979234 2.68209978020766 146 6 9.48815236806346 -3.48815236806346 147 9 9.7827559485092 -0.782755948509198 148 7 8.18012096533328 -1.18012096533328 149 9 7.59907597795364 1.40092402204636 150 10 8.47744527028297 1.52255472971703 151 9 8.18828313884512 0.811716861154882 152 8 9.35853528711623 -1.35853528711624 153 7 10.8206702913291 -3.82067029132915 154 6 8.48832816829875 -2.48832816829875 155 13 8.1991660368609 4.8008339631391 156 6 7.76406247745216 -1.76406247745216 157 8 9.37213890963596 -1.37213890963596 158 10 8.49921106631453 1.50078893368547 159 16 9.81540464255654 6.18459535744346 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 6 0.253759145761716 0.507518291523431 0.746240854238284 7 0.175099049994234 0.350198099988468 0.824900950005766 8 0.619260981164875 0.761478037670249 0.380739018835125 9 0.495543449528653 0.991086899057306 0.504456550471347 10 0.380626711177762 0.761253422355524 0.619373288822238 11 0.529682367057293 0.940635265885414 0.470317632942707 12 0.436112808259226 0.872225616518452 0.563887191740774 13 0.35207400531553 0.70414801063106 0.64792599468447 14 0.268211898168846 0.536423796337692 0.731788101831154 15 0.198921500132268 0.397843000264537 0.801078499867732 16 0.206676995870443 0.413353991740886 0.793323004129557 17 0.153267477045751 0.306534954091503 0.846732522954249 18 0.115524096838496 0.231048193676993 0.884475903161504 19 0.0892584859730937 0.178516971946187 0.910741514026906 20 0.061914557457564 0.123829114915128 0.938085442542436 21 0.0430973191230179 0.0861946382460357 0.956902680876982 22 0.028596546743604 0.057193093487208 0.971403453256396 23 0.0920204852020142 0.184040970404028 0.907979514797986 24 0.100928002785122 0.201856005570245 0.899071997214878 25 0.07342883840776 0.14685767681552 0.92657116159224 26 0.059366667696362 0.118733335392724 0.940633332303638 27 0.058687232285215 0.11737446457043 0.941312767714785 28 0.0430789076007752 0.0861578152015503 0.956921092399225 29 0.0306353565483506 0.0612707130967012 0.96936464345165 30 0.0248154362680004 0.0496308725360007 0.975184563732 31 0.0271540802440993 0.0543081604881986 0.9728459197559 32 0.23633240116975 0.4726648023395 0.76366759883025 33 0.329082647866499 0.658165295732998 0.670917352133501 34 0.300287390166585 0.60057478033317 0.699712609833415 35 0.276881648811195 0.55376329762239 0.723118351188805 36 0.327579112346369 0.655158224692738 0.672420887653631 37 0.358352001092069 0.716704002184137 0.641647998907931 38 0.320933257542302 0.641866515084604 0.679066742457698 39 0.34214880595717 0.68429761191434 0.65785119404283 40 0.300568949445150 0.601137898890301 0.69943105055485 41 0.268801657678454 0.537603315356909 0.731198342321546 42 0.239209289470449 0.478418578940897 0.760790710529551 43 0.205042424344915 0.410084848689830 0.794957575655085 44 0.187697314819163 0.375394629638326 0.812302685180837 45 0.157340141026845 0.31468028205369 0.842659858973155 46 0.137590762713211 0.275181525426421 0.86240923728679 47 0.14023444114193 0.28046888228386 0.85976555885807 48 0.157695580226085 0.315391160452171 0.842304419773915 49 0.129785780823983 0.259571561647966 0.870214219176017 50 0.106309649661291 0.212619299322582 0.893690350338709 51 0.144791521713059 0.289583043426117 0.855208478286941 52 0.123876404560876 0.247752809121752 0.876123595439124 53 0.103007007307302 0.206014014614604 0.896992992692698 54 0.0939925662875196 0.187985132575039 0.90600743371248 55 0.853869207956358 0.292261584087284 0.146130792043642 56 0.825104378466584 0.349791243066831 0.174895621533416 57 0.793311046824918 0.413377906350163 0.206688953175082 58 0.76203576578517 0.475928468429659 0.237964234214830 59 0.748453672760372 0.503092654479256 0.251546327239628 60 0.724977429485394 0.550045141029212 0.275022570514606 61 0.711517117711482 0.576965764577036 0.288482882288518 62 0.683389429590913 0.633221140818174 0.316610570409087 63 0.640591249948601 0.718817500102798 0.359408750051399 64 0.621998052467982 0.756003895064036 0.378001947532018 65 0.581842902558841 0.836314194882319 0.418157097441159 66 0.622146282684343 0.755707434631314 0.377853717315657 67 0.582116304826336 0.835767390347328 0.417883695173664 68 0.542101770977091 0.915796458045817 0.457898229022908 69 0.496679004288636 0.993358008577271 0.503320995711364 70 0.454464589723721 0.908929179447443 0.545535410276279 71 0.423038527652897 0.846077055305794 0.576961472347103 72 0.379051398369631 0.758102796739261 0.62094860163037 73 0.337558200688153 0.675116401376306 0.662441799311847 74 0.332309392145118 0.664618784290235 0.667690607854882 75 0.321169752739571 0.642339505479143 0.678830247260429 76 0.282214431474977 0.564428862949954 0.717785568525023 77 0.245812617512743 0.491625235025486 0.754187382487257 78 0.22315827848454 0.44631655696908 0.77684172151546 79 0.193604957048783 0.387209914097565 0.806395042951217 80 0.193711896750252 0.387423793500504 0.806288103249748 81 0.185122746917699 0.370245493835399 0.8148772530823 82 0.159507069428879 0.319014138857759 0.84049293057112 83 0.134235296890293 0.268470593780585 0.865764703109707 84 0.133487859423458 0.266975718846916 0.866512140576542 85 0.140559847073964 0.281119694147928 0.859440152926036 86 0.118440847521695 0.236881695043389 0.881559152478305 87 0.120816172152303 0.241632344304607 0.879183827847697 88 0.104114387186656 0.208228774373312 0.895885612813344 89 0.184987080767466 0.369974161534931 0.815012919232534 90 0.156844226719310 0.313688453438619 0.84315577328069 91 0.131940771179665 0.263881542359330 0.868059228820335 92 0.109156318364677 0.218312636729354 0.890843681635323 93 0.101774398321916 0.203548796643832 0.898225601678084 94 0.0940894563808676 0.188178912761735 0.905910543619132 95 0.0923164252504717 0.184632850500943 0.907683574749528 96 0.0943146374354298 0.188629274870860 0.90568536256457 97 0.0765627202240654 0.153125440448131 0.923437279775935 98 0.0824113110161566 0.164822622032313 0.917588688983843 99 0.066820814825244 0.133641629650488 0.933179185174756 100 0.0530073831972465 0.106014766394493 0.946992616802753 101 0.0470781871651358 0.0941563743302715 0.952921812834864 102 0.0382232509462555 0.076446501892511 0.961776749053745 103 0.0357605398537372 0.0715210797074743 0.964239460146263 104 0.0352005228218837 0.0704010456437674 0.964799477178116 105 0.0311630572007093 0.0623261144014186 0.96883694279929 106 0.0362160139186226 0.0724320278372452 0.963783986081377 107 0.0285244166704139 0.0570488333408277 0.971475583329586 108 0.0241661224040433 0.0483322448080865 0.975833877595957 109 0.0240572909255589 0.0481145818511177 0.975942709074441 110 0.0192413606394652 0.0384827212789304 0.980758639360535 111 0.0142470576288919 0.0284941152577839 0.985752942371108 112 0.0171187770718135 0.0342375541436269 0.982881222928187 113 0.0204198143152029 0.0408396286304057 0.979580185684797 114 0.0232085995384256 0.0464171990768512 0.976791400461574 115 0.0445738418154259 0.0891476836308517 0.955426158184574 116 0.0384675832501983 0.0769351665003965 0.961532416749802 117 0.0304236919669492 0.0608473839338984 0.96957630803305 118 0.0235794061435256 0.0471588122870512 0.976420593856474 119 0.0190725463097682 0.0381450926195364 0.980927453690232 120 0.0218962095751477 0.0437924191502953 0.978103790424852 121 0.0365659233834263 0.0731318467668526 0.963434076616574 122 0.0271620196488737 0.0543240392977475 0.972837980351126 123 0.0302304182712901 0.0604608365425802 0.96976958172871 124 0.0229362424691144 0.0458724849382289 0.977063757530886 125 0.0166639767583627 0.0333279535167255 0.983336023241637 126 0.0118379245613120 0.0236758491226241 0.988162075438688 127 0.0133650806846933 0.0267301613693867 0.986634919315307 128 0.00927963065578988 0.0185592613115798 0.99072036934421 129 0.0068416734278843 0.0136833468557686 0.993158326572116 130 0.00505505709551513 0.0101101141910303 0.994944942904485 131 0.00502245750904634 0.0100449150180927 0.994977542490954 132 0.00333629433820283 0.00667258867640567 0.996663705661797 133 0.00312939987166659 0.00625879974333318 0.996870600128333 134 0.00489888007898902 0.00979776015797805 0.995101119921011 135 0.00332305190829803 0.00664610381659607 0.996676948091702 136 0.00214806397773137 0.00429612795546273 0.997851936022269 137 0.00223717141482293 0.00447434282964587 0.997762828585177 138 0.00144676331188261 0.00289352662376522 0.998553236688117 139 0.000928767071760377 0.00185753414352075 0.99907123292824 140 0.00121715241698449 0.00243430483396899 0.998782847583015 141 0.000709096482137381 0.00141819296427476 0.999290903517863 142 0.000388330095370944 0.000776660190741887 0.99961166990463 143 0.274503093116913 0.549006186233825 0.725496906883087 144 0.255681483774200 0.511362967548401 0.7443185162258 145 0.321149737562519 0.642299475125038 0.678850262437481 146 0.268805315904868 0.537610631809736 0.731194684095132 147 0.216146162221212 0.432292324442423 0.783853837778788 148 0.152958171074951 0.305916342149901 0.84704182892505 149 0.115435727028784 0.230871454057568 0.884564272971216 150 0.119371038432029 0.238742076864058 0.880628961567971 151 0.128621266574994 0.257242533149989 0.871378733425006 152 0.0956560631350727 0.191312126270145 0.904343936864927 153 0.0560381739289345 0.112076347857869 0.943961826071065 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 11 0.0743243243243243 NOK 5% type I error level 30 0.202702702702703 NOK 10% type I error level 48 0.324324324324324 NOK

Charts produced by software:

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Parameters (Session):

par1 = 0 ;

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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