Personal Standards (Yt)

*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, 23 Nov 2010 14:52:31 +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/23/t12905239438aje5a7e91dr965.htm/, Retrieved Tue, 23 Nov 2010 15:52:44 +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/23/t12905239438aje5a7e91dr965.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 24 14 11 12 25 25 11 7 8 30 17 6 17 8 19 18 12 10 8 22 18 8 12 9 22 16 10 12 7 25 20 10 11 4 23 16 11 11 11 17 18 16 12 7 21 17 11 13 7 19 23 13 14 12 19 30 12 16 10 15 23 8 11 10 16 18 12 10 8 23 15 11 11 8 27 12 4 15 4 22 21 9 9 9 14 15 8 11 8 22 20 8 17 7 23 31 14 17 11 23 27 15 11 9 21 34 16 18 11 19 21 9 14 13 18 31 14 10 8 20 19 11 11 8 23 16 8 15 9 25 20 9 15 6 19 21 9 13 9 24 22 9 16 9 22 17 9 13 6 25 24 10 9 6 26 25 16 18 16 29 26 11 18 5 32 25 8 12 7 25 17 9 17 9 29 32 16 9 6 28 33 11 9 6 17 13 16 12 5 28 32 12 18 12 29 25 12 12 7 26 29 14 18 10 25 22 9 14 9 14 18 10 15 8 25 17 9 16 5 26 20 10 10 8 20 15 12 11 8 18 20 14 14 10 32 33 14 9 6 25 29 10 12 8 25 23 14 17 7 23 26 16 5 4 21 18 9 12 8 20 20 10 12 8 15 11 6 6 4 30 28 8 24 20 24 26 13 12 8 26 22 10 12 8 24 17 8 14 6 22 12 7 7 4 14 14 15 13 8 24 17 9 12 9 24 21 10 13 6 24 19 12 14 7 24 18 13 8 9 19 10 10 11 5 31 29 11 9 5 22 31 8 11 8 27 19 9 13 8 19 9 13 10 6 25 20 11 11 8 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 11 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation PS[t] = + 16.7814871438007 + 0.361040957079362CM[t] -0.331410467693096D[t] + 0.152692331465191PE[t] -0.0951446605742276PC[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) 16.7814871438007 1.649635 10.1728 0 0 CM 0.361040957079362 0.060414 5.9761 0 0 D -0.331410467693096 0.11701 -2.8323 0.005239 0.00262 PE 0.152692331465191 0.110431 1.3827 0.168762 0.084381 PC -0.0951446605742276 0.138765 -0.6857 0.493964 0.246982 Multiple Linear Regression - Regression Statistics Multiple R 0.487604702873295 R-squared 0.237758346264154 Adjusted R-squared 0.217959861751535 F-TEST (value) 12.0089164457315 F-TEST (DF numerator) 4 F-TEST (DF denominator) 154 p-value 1.61012581045838e-08 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 3.72918444517006 Sum Squared Residuals 2141.64976041915 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 24 21.3446032852283 2.65539671477173 2 25 22.4696849618232 2.5303150381768 3 30 22.7653329583057 7.23466704169429 4 19 20.0690647889702 -1.06906478897016 5 22 21.6049466620987 0.395053337901304 6 22 20.4103331337022 1.58966686629777 7 25 21.9872386122772 3.01276138772283 8 23 19.5456516922470 3.45434830775297 9 17 19.1439522417024 -2.14395224170238 10 21 20.5926559545537 0.407344045446312 11 19 21.7730497902377 -2.77304979023772 12 19 25.1274209415652 -6.12742094156519 13 15 23.1623144554561 -8.16231445545609 14 16 20.0690647889702 -4.06906478897015 15 23 19.4700447168904 3.52995528310965 16 27 21.6981430876616 5.30185691233838 17 22 21.8985820712481 0.101417928751890 18 14 20.4642761199696 -6.46427611996964 19 22 23.2807795547318 -1.28077955473183 20 23 24.8831886341493 -1.88318863414932 21 23 22.3817496704961 0.618250329503914 22 21 25.4561829014664 -4.45618290146640 23 19 22.2814650862772 -3.28146508627715 24 18 24.0997762956157 -6.09977629561567 25 20 20.9142085452078 -0.914208545207802 26 23 21.3409417423355 1.65905825766446 27 25 22.7391290846826 2.26087091531742 28 19 22.5093513971089 -3.50935139710887 29 24 23.3284693485838 0.671530651416192 30 22 21.3506215505141 0.649378449485892 31 25 22.9357284565158 2.06427154348422 32 26 21.731090984881 4.26890901511899 33 29 24.7957755467424 4.20422445325765 34 32 24.3225226828027 7.67747731719732 35 25 21.6759568946522 3.32404310534781 36 29 23.8355933069921 5.1644066930079 37 28 25.8536866025369 2.14631339746306 38 17 17.5290367774540 -0.529036777454021 39 28 25.9645981975058 2.03540180249416 40 29 22.9968808120303 6.0031191879697 41 26 24.408943712030 1.59105628796999 42 25 23.0230846856534 1.97691531434657 43 14 21.4953473816823 -7.4953473816823 44 25 21.9038432054839 3.09615679451609 45 26 21.4539676385151 4.54603236148493 46 20 19.1386342491973 0.861365750802742 47 18 20.548805772455 -2.54880577245499 48 32 24.8594551994577 7.14054480054234 49 25 25.0087209151597 -0.00872091515971016 50 25 22.3754396198113 2.62456038018867 51 23 21.2488675598036 1.75113244019638 52 21 21.3686808549798 -0.368680854979824 53 20 21.7593523014455 -1.75935230144545 54 15 19.3000502120093 -4.30005021200934 55 30 26.0010729441581 3.9989270558419 56 24 22.9313666408423 1.06863335915767 57 26 22.4814342156042 3.51856578439582 58 24 21.8347243496724 2.16527565032760 59 22 19.4823730328608 2.5176269671392 60 14 18.088746551969 -4.08874655196899 61 24 20.9124952373262 3.08750476267377 62 24 22.4633749111385 1.53662508886154 63 24 21.1360197324845 2.86398026751549 64 24 19.3371249977724 4.66287500222755 65 19 18.2816843809093 0.718315619090677 66 31 24.5046674347937 6.49533256520628 67 22 26.2409314332394 -4.24093143323944 68 27 21.8824141435244 5.11758585647562 69 19 16.6785750287113 2.32142497128875 70 25 21.2752495022872 3.72475049771284 71 20 25.4056455540408 -5.40564555404077 72 21 21.3667894782378 -0.366789478237841 73 27 26.0641046737535 0.935895326246486 74 23 23.9823885837627 -0.98238858376269 75 25 24.9053748271587 0.094625172841252 76 20 22.8424751726835 -2.84247517268354 77 21 18.2494053837312 2.75059461626882 78 22 21.6678123254948 0.332187674505225 79 23 20.4301057460495 2.56989425395049 80 25 24.6592511430009 0.340748856999103 81 25 21.4792363122279 3.52076368777211 82 17 22.2102199265939 -5.21021992659392 83 19 21.6102646546038 -2.61026465460381 84 25 22.8426532415440 2.15734675845605 85 19 21.1914979577731 -2.19149795777307 86 20 22.4948967772667 -2.49489677726671 87 26 22.2531349087823 3.74686509121769 88 23 18.1704286508807 4.82957134911932 89 27 24.0247603851096 2.97523961489045 90 17 21.4934560049403 -4.49345600494032 91 17 22.9053408360796 -5.90534083607962 92 19 19.385515064405 -0.385515064405005 93 17 19.811134992762 -2.81113499276202 94 22 23.1298005311482 -1.12980053114820 95 21 21.3867401594455 -0.38674015944554 96 32 26.7244551702082 5.27554482979176 97 21 23.952580025516 -2.95258002551601 98 21 24.5500648585747 -3.55006485857466 99 18 21.8248664726334 -3.82486647263341 100 18 22.6341265470694 -4.63412654706937 101 23 23.1102628459307 -0.110262845930655 102 19 21.1386682402764 -2.13866824027639 103 20 22.9693197682464 -2.96931976824643 104 21 21.9678789959200 -0.967878995920038 105 20 21.1738516492975 -1.17385164929751 106 17 22.3716568663274 -5.37165686632737 107 18 22.5729741915549 -4.57297419155485 108 19 23.4973296077727 -4.49732960777273 109 22 22.4115582287428 -0.411558228742766 110 15 19.5408768805834 -4.54087688058343 111 14 19.9900311978503 -5.99003119785034 112 18 25.5406915770304 -7.5406915770304 113 24 22.0397032177928 1.96029678220725 114 35 25.18950849699 9.81049150300998 115 29 18.2173403367614 10.7826596632386 116 21 21.4161357217021 -0.41613572170207 117 25 23.4874148724644 1.51258512753557 118 20 20.0770312892672 -0.0770312892671516 119 22 22.6018475498912 -0.601847549891221 120 13 21.1977511501885 -8.1977511501885 121 26 24.2944274324376 1.70557256756243 122 17 19.3568407518504 -2.35684075185041 123 25 21.1757430260395 3.82425697396051 124 20 19.8911037837921 0.108896216207855 125 19 17.5685820021486 1.43141799785141 126 21 22.1914034910783 -1.19140349107831 127 22 20.6921624308014 1.30783756919864 128 24 21.2752495022872 2.72475049771284 129 21 21.2475103896429 -0.247510389642882 130 26 24.9745505412396 1.02544945876042 131 24 22.0172820976536 1.98271790234641 132 16 20.6465989408211 -4.6465989408211 133 23 21.1403815481580 1.85961845184205 134 18 20.9005110564155 -2.90051105641553 135 16 22.1203932585248 -6.12039325852481 136 26 23.9626159714154 2.03738402858459 137 19 20.2333283053559 -1.23332830535589 138 21 20.4319971227915 0.568002877208502 139 21 21.2439057050193 -0.243905705019331 140 22 21.0114795096537 0.988520490346251 141 23 23.4908983464969 -0.490898346496886 142 29 24.9747286101 4.0252713899 143 21 22.5684463096821 -1.56844630968207 144 21 19.9853132444561 1.01468675554394 145 23 21.6041895310488 1.39581046895120 146 27 23.0578550986844 3.94214490131560 147 25 26.7305302937633 -1.73053029376326 148 21 22.0332150982476 -1.03321509824759 149 10 20.5514542802469 -10.5514542802469 150 20 23.2593504927723 -3.25935049277230 151 26 22.5057467124853 3.49425328751468 152 24 23.2699864777825 0.730013522217467 153 29 29.3960547049418 -0.396054704941817 154 19 23.3085186673761 -4.30851866737611 155 24 22.1737571826027 1.82624281739725 156 19 21.3506215505141 -2.35062155051411 157 24 23.1693457558428 0.830654244157229 158 22 21.754990485772 0.245009514227996 159 17 24.0500290588224 -7.05002905882237 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 8 0.275441261197073 0.550882522394146 0.724558738802927 9 0.167885047016958 0.335770094033915 0.832114952983042 10 0.0917864556637122 0.183572911327424 0.908213544336288 11 0.198715480347544 0.397430960695088 0.801284519652456 12 0.262816787288933 0.525633574577865 0.737183212711067 13 0.778217356105258 0.443565287789485 0.221782643894742 14 0.803783803894903 0.392432392210194 0.196216196105097 15 0.747840013773307 0.504319972453385 0.252159986226693 16 0.687242253481719 0.625515493036563 0.312757746518281 17 0.606076313835612 0.787847372328776 0.393923686164388 18 0.841792245364849 0.316415509270303 0.158207754635151 19 0.801448990308278 0.397102019383444 0.198551009691722 20 0.758304903384561 0.483390193230879 0.241695096615439 21 0.726149834695106 0.547700330609789 0.273850165304894 22 0.678493622133082 0.643012755733836 0.321506377866918 23 0.628153528786932 0.743692942426136 0.371846471213068 24 0.626593209637993 0.746813580724013 0.373406790362007 25 0.563327249595646 0.873345500808708 0.436672750404354 26 0.500188852265284 0.999622295469433 0.499811147734716 27 0.44756441279041 0.89512882558082 0.55243558720959 28 0.423852618369006 0.847705236738013 0.576147381630994 29 0.3677059630596 0.7354119261192 0.6322940369404 30 0.312035229145453 0.624070458290906 0.687964770854547 31 0.294447322209546 0.588894644419091 0.705552677790454 32 0.388346072317424 0.776692144634848 0.611653927682576 33 0.398270409343616 0.796540818687232 0.601729590656384 34 0.646005059678999 0.707989880642002 0.353994940321001 35 0.611260062761475 0.77747987447705 0.388739937238525 36 0.698848599259737 0.602302801480526 0.301151400740263 37 0.669996751413746 0.660006497172508 0.330003248586254 38 0.635586221314849 0.728827557370303 0.364413778685151 39 0.605084040624764 0.789831918750471 0.394915959375236 40 0.664375278266519 0.671249443466962 0.335624721733481 41 0.61966193291391 0.76067613417218 0.38033806708609 42 0.577046242520197 0.845907514959606 0.422953757479803 43 0.750546489529458 0.498907020941083 0.249453510470542 44 0.726548557200373 0.546902885599255 0.273451442799627 45 0.740281182625302 0.519437634749395 0.259718817374698 46 0.69838791365095 0.6032241726981 0.30161208634905 47 0.66958999588127 0.660820008237460 0.330410004118730 48 0.746055214168608 0.507889571662784 0.253944785831392 49 0.707653242128953 0.584693515742095 0.292346757871047 50 0.679801539648594 0.640396920702812 0.320198460351406 51 0.63841186434782 0.723176271304359 0.361588135652180 52 0.592685823345909 0.814628353308183 0.407314176654091 53 0.559602329788992 0.880795340422015 0.440397670211007 54 0.598174835562952 0.803650328874096 0.401825164437048 55 0.625224968294607 0.749550063410787 0.374775031705393 56 0.580502754348768 0.838994491302464 0.419497245651232 57 0.569036881884801 0.861926236230398 0.430963118115199 58 0.534469603005607 0.931060793988785 0.465530396994393 59 0.506775770025468 0.986448459949063 0.493224229974532 60 0.505943177386198 0.988113645227604 0.494056822613802 61 0.491651474847936 0.983302949695872 0.508348525152064 62 0.452395390662483 0.904790781324966 0.547604609337517 63 0.431616127144229 0.863232254288458 0.568383872855771 64 0.473794868965236 0.947589737930471 0.526205131034764 65 0.429684350994259 0.859368701988518 0.570315649005741 66 0.507992162575337 0.984015674849325 0.492007837424663 67 0.553378994908333 0.893242010183335 0.446621005091668 68 0.592219381630387 0.815561236739226 0.407780618369613 69 0.566995157239773 0.866009685520454 0.433004842760227 70 0.566944766010946 0.866110467978108 0.433055233989054 71 0.637909769776444 0.724180460447113 0.362090230223556 72 0.594954529426399 0.810090941147202 0.405045470573601 73 0.553953769290983 0.892092461418033 0.446046230709017 74 0.51321374515888 0.97357250968224 0.48678625484112 75 0.476886326325576 0.953772652651152 0.523113673674424 76 0.460773269511319 0.921546539022638 0.539226730488681 77 0.446852468859923 0.893704937719847 0.553147531140077 78 0.403072197761031 0.806144395522063 0.596927802238969 79 0.381078125225718 0.762156250451436 0.618921874774282 80 0.343744482567191 0.687488965134383 0.656255517432809 81 0.340738292745476 0.681476585490952 0.659261707254524 82 0.384310557023628 0.768621114047255 0.615689442976372 83 0.363667587726375 0.727335175452750 0.636332412273625 84 0.337581318089245 0.67516263617849 0.662418681910755 85 0.312596530038129 0.625193060076258 0.687403469961871 86 0.294142915070660 0.588285830141321 0.70585708492934 87 0.306025289718595 0.61205057943719 0.693974710281405 88 0.344884659721588 0.689769319443175 0.655115340278412 89 0.32686642327144 0.65373284654288 0.67313357672856 90 0.342807301539907 0.685614603079814 0.657192698460093 91 0.40462072611797 0.80924145223594 0.59537927388203 92 0.361280312192969 0.722560624385938 0.638719687807031 93 0.338514904711895 0.67702980942379 0.661485095288105 94 0.302704396471844 0.605408792943688 0.697295603528156 95 0.263039719702253 0.526079439404507 0.736960280297747 96 0.309513757811717 0.619027515623434 0.690486242188283 97 0.291886641657221 0.583773283314442 0.708113358342779 98 0.285690953668172 0.571381907336343 0.714309046331828 99 0.280912009482282 0.561824018964563 0.719087990517718 100 0.295270979459725 0.590541958919449 0.704729020540275 101 0.255536246776235 0.51107249355247 0.744463753223765 102 0.226681819685379 0.453363639370758 0.773318180314621 103 0.207622264891015 0.415244529782029 0.792377735108985 104 0.175742459968953 0.351484919937906 0.824257540031047 105 0.148645499158014 0.297290998316028 0.851354500841986 106 0.169872366856523 0.339744733713046 0.830127633143477 107 0.180577068463133 0.361154136926267 0.819422931536867 108 0.194978649597026 0.389957299194052 0.805021350402974 109 0.16268754260881 0.32537508521762 0.83731245739119 110 0.165619789638499 0.331239579276998 0.834380210361501 111 0.205106692346030 0.410213384692059 0.79489330765397 112 0.346994694559925 0.69398938911985 0.653005305440075 113 0.307741661935481 0.615483323870962 0.692258338064519 114 0.593722213662134 0.812555572675732 0.406277786337866 115 0.912773517322604 0.174452965354793 0.0872264826773963 116 0.890416699018795 0.219166601962410 0.109583300981205 117 0.88535492981686 0.229290140366279 0.114645070183140 118 0.856957112349121 0.286085775301758 0.143042887650879 119 0.824060433727061 0.351879132545877 0.175939566272939 120 0.937356764063886 0.125286471872227 0.0626432359361137 121 0.919592521555085 0.160814956889830 0.0804074784449148 122 0.902024645941713 0.195950708116573 0.0979753540582866 123 0.90841898732261 0.183162025354780 0.0915810126773901 124 0.884194579195529 0.231610841608943 0.115805420804471 125 0.853881313581813 0.292237372836374 0.146118686418187 126 0.817323941957247 0.365352116085506 0.182676058042753 127 0.792392094284788 0.415215811430424 0.207607905715212 128 0.78791475494656 0.424170490106881 0.212085245053440 129 0.74465396367805 0.5106920726439 0.25534603632195 130 0.690993731665014 0.618012536669972 0.309006268334986 131 0.677735948372697 0.644528103254605 0.322264051627303 132 0.661957166491105 0.67608566701779 0.338042833508895 133 0.642110932678119 0.715778134643761 0.357889067321881 134 0.587562579877123 0.824874840245755 0.412437420122877 135 0.653021174498156 0.693957651003688 0.346978825501844 136 0.616141694991803 0.767716610016393 0.383858305008197 137 0.550415670346104 0.899168659307792 0.449584329653896 138 0.484647340502401 0.969294681004802 0.515352659497599 139 0.423112214395295 0.846224428790589 0.576887785604705 140 0.370425192629626 0.740850385259253 0.629574807370374 141 0.301378550810284 0.602757101620569 0.698621449189716 142 0.329950922886958 0.659901845773917 0.670049077113042 143 0.276289656748082 0.552579313496165 0.723710343251918 144 0.207395547590653 0.414791095181305 0.792604452409347 145 0.183284724632027 0.366569449264054 0.816715275367973 146 0.160697616498246 0.321395232996492 0.839302383501754 147 0.1076820192251 0.2153640384502 0.8923179807749 148 0.0670292662369072 0.134058532473814 0.932970733763093 149 0.324259393837284 0.648518787674567 0.675740606162716 150 0.259745772735067 0.519491545470135 0.740254227264933 151 0.333331829101967 0.666663658203934 0.666668170898033 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 0 0 OK 5% type I error level 0 0 OK 10% type I error level 0 0 OK

Charts produced by software:

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Parameters (Session):

par1 = 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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Software written by Ed van Stee & Patrick Wessa

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