parent expectations

*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: Thu, 02 Dec 2010 11:21:28 +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/Dec/02/t12912888355d0a8wxmtxde9ku.htm/, Retrieved Thu, 02 Dec 2010 12:20:53 +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/02/t12912888355d0a8wxmtxde9ku.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 «

4 2 1 2 1 2 1 1 5 4 2 4 3 2 1 2 3 3 2 2 3 4 1 2 2 3 3 2 3 3 1 2 4 3 1 1 4 2 1 4 4 4 2 2 2 4 4 3 2 3 2 2 2 3 1 2 4 4 1 1 4 4 3 3 3 3 2 1 2 3 2 2 5 3 3 4 4 4 3 4 3 2 1 3 4 5 2 2 3 4 2 3 2 2 2 2 2 3 2 2 3 4 3 3 4 4 2 3 4 3 2 2 5 4 2 4 4 4 2 2 3 1 2 2 4 4 3 3 4 5 2 5 4 2 2 2 5 4 2 3 2 3 2 1 2 2 2 2 4 4 1 2 5 5 2 4 3 4 1 2 5 4 2 4 2 4 2 3 4 3 2 2 4 4 2 4 2 2 2 2 2 2 3 2 4 4 2 2 2 2 2 2 2 4 2 2 4 4 4 3 1 1 1 1 2 4 2 2 4 2 2 2 1 1 1 1 5 4 5 5 4 3 2 2 4 2 2 2 4 4 2 2 1 3 1 1 4 2 2 2 4 2 2 2 4 3 2 2 4 2 2 4 2 1 2 2 4 3 1 1 3 2 1 2 2 3 2 2 4 3 2 2 4 3 1 1 3 2 2 2 3 3 2 2 2 2 1 2 4 4 3 3 4 4 3 3 4 4 3 2 4 2 2 2 4 3 2 3 4 4 2 2 2 3 1 2 2 4 4 2 4 2 3 2 2 3 2 2 4 3 2 1 5 4 2 3 2 2 1 2 4 4 2 4 2 2 3 2 4 2 1 1 4 4 2 4 2 3 2 3 4 4 2 2 1 2 1 3 2 2 1 2 5 3 2 3 2 3 2 2 5 5 4 5 4 2 2 3 4 3 4 4 2 4 1 2 2 3 3 2 4 4 2 2 2 3 2 3 4 3 4 4 4 2 3 3 2 3 2 2 4 2 1 2 2 3 1 3 4 2 2 2 4 4 3 2 4 2 2 2 3 4 1 2 3 4 2 3 2 1 2 2 5 5 2 4 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 15 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation best[t] = + 1.22151640213814 + 0.231803248360643standards[t] + 0.0583245373239288performance[t] + 0.467278936963013excellence[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) 1.22151640213814 0.284986 4.2862 3.2e-05 1.6e-05 standards 0.231803248360643 0.088029 2.6333 0.009314 0.004657 performance 0.0583245373239288 0.109204 0.5341 0.594046 0.297023 excellence 0.467278936963013 0.102773 4.5467 1.1e-05 5e-06 Multiple Linear Regression - Regression Statistics Multiple R 0.536873098061071 R-squared 0.288232723421692 Adjusted R-squared 0.274456582584693 F-TEST (value) 20.9226028415423 F-TEST (DF numerator) 3 F-TEST (DF denominator) 155 p-value 1.95858884666222e-11 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.963925850954448 Sum Squared Residuals 144.018722151430 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 4 2.67800531010939 1.32199468989061 2 1 2.21072637314639 -1.21072637314639 3 5 4.13449421808062 0.86550578191938 4 3 2.67800531010939 0.321994689890611 5 3 2.96813309579396 0.0318669042060444 6 3 3.14161180683067 -0.141611806830668 7 2 3.02645763311788 -1.02645763311788 8 3 2.90980855847003 0.0901914415299734 9 4 2.44252962150701 1.55747037849299 10 4 3.61256318403541 0.387436815964589 11 4 3.1999363441546 0.800063655845403 12 2 3.78386435576547 -1.78386435576547 13 2 2.96813309579396 -0.968133095793956 14 2 2.90980855847003 -0.909808558470027 15 4 2.67433286986766 1.32566713013234 16 4 3.72553981844154 0.274460181558461 17 3 2.50085415883094 0.499145841169057 18 2 2.96813309579396 -0.968133095793956 19 5 3.96101550704391 1.03898449295609 20 4 4.19281875540455 -0.192818755404552 21 3 3.1452842470724 -0.145284247072398 22 4 3.43173959251524 0.568260407484761 23 3 3.66721528111761 -0.66721528111761 24 2 2.73632984743331 -0.736329847433314 25 2 2.96813309579396 -0.968133095793956 26 3 3.72553981844154 -0.725539818441539 27 4 3.66721528111761 0.33278471888239 28 4 2.96813309579396 1.03186690420604 29 5 4.13449421808062 0.865505781919377 30 4 3.1999363441546 0.800063655845403 31 3 2.50452659907267 0.495473400927328 32 4 3.72553981844154 0.274460181558461 33 4 4.83357640340428 -0.833576403404278 34 4 2.73632984743331 1.26367015256669 35 5 3.66721528111761 1.33278471888239 36 2 2.50085415883094 -0.500854158830943 37 2 2.73632984743331 -0.736329847433314 38 4 3.14161180683067 0.858388193169332 39 5 4.36629746644127 0.633702533558735 40 3 3.14161180683067 -0.141611806830668 41 5 4.13449421808062 0.865505781919377 42 2 3.66721528111761 -1.66721528111761 43 4 2.96813309579396 1.03186690420604 44 4 4.13449421808062 -0.134494218080623 45 2 2.73632984743331 -0.736329847433314 46 2 2.79465438475724 -0.794654384757243 47 4 3.1999363441546 0.800063655845403 48 2 2.73632984743331 -0.736329847433314 49 2 3.1999363441546 -1.19993634415460 50 4 3.78386435576547 0.216135644234532 51 1 1.97892312478573 -0.97892312478573 52 2 3.1999363441546 -1.19993634415460 53 4 2.73632984743331 1.26367015256669 54 1 1.97892312478573 -0.97892312478573 55 5 4.77674676701542 0.223253232984577 56 4 2.96813309579396 1.03186690420604 57 4 2.73632984743331 1.26367015256669 58 4 3.1999363441546 0.800063655845403 59 1 2.44252962150701 -1.44252962150701 60 4 2.73632984743331 1.26367015256669 61 4 2.73632984743331 1.26367015256669 62 4 2.96813309579396 1.03186690420604 63 4 3.67088772135934 0.32911227864066 64 2 2.50452659907267 -0.504526599072672 65 4 2.44252962150701 1.55747037849299 66 3 2.67800531010939 0.321994689890615 67 2 2.96813309579396 -0.968133095793956 68 4 2.96813309579396 1.03186690420604 69 4 2.44252962150701 1.55747037849299 70 3 2.73632984743331 0.263670152566686 71 3 2.96813309579396 0.0318669042060444 72 2 2.67800531010939 -0.678005310109385 73 4 3.72553981844154 0.274460181558461 74 4 3.72553981844154 0.274460181558461 75 4 3.25826088147853 0.741739118521474 76 4 2.73632984743331 1.26367015256669 77 4 3.43541203275697 0.564587967243031 78 4 3.1999363441546 0.800063655845403 79 2 2.90980855847003 -0.909808558470027 80 2 3.31658541880245 -1.31658541880245 81 4 2.79465438475724 1.20534561524276 82 2 2.96813309579396 -0.968133095793956 83 4 2.50085415883094 1.49914584116906 84 5 3.66721528111761 1.33278471888239 85 2 2.67800531010939 -0.678005310109385 86 4 4.13449421808062 -0.134494218080623 87 2 2.79465438475724 -0.794654384757243 88 4 2.21072637314637 1.78927362685363 89 4 4.13449421808062 -0.134494218080623 90 2 3.43541203275697 -1.43541203275697 91 4 3.1999363441546 0.800063655845403 92 1 3.1452842470724 -2.1452842470724 93 2 2.67800531010939 -0.678005310109385 94 5 3.43541203275697 1.56458796724303 95 2 2.96813309579396 -0.968133095793956 96 5 4.95022547805214 0.049774521947864 97 4 3.20360878439633 0.796391215603673 98 4 4.01934004436784 -0.0193400443678395 99 2 3.14161180683067 -1.14161180683067 100 2 3.02645763311788 -1.02645763311788 101 4 3.1999363441546 0.800063655845403 102 2 3.43541203275697 -1.43541203275697 103 4 4.01934004436784 -0.0193400443678395 104 4 3.26193332172026 0.738066678279744 105 2 2.96813309579396 -0.968133095793956 106 4 2.67800531010939 1.32199468989062 107 2 3.37708749543304 -1.37708749543304 108 4 2.73632984743331 1.26367015256669 109 4 3.25826088147853 0.741739118521474 110 4 2.73632984743331 1.26367015256669 111 3 3.14161180683067 -0.141611806830668 112 3 3.66721528111761 -0.66721528111761 113 2 2.50452659907267 -0.504526599072672 114 5 4.36629746644127 0.633702533558735 115 3 2.21072637314637 0.789273626853628 116 4 2.96813309579396 1.03186690420604 117 3 4.19281875540455 -1.19281875540455 118 2 2.50452659907267 -0.504526599072672 119 4 3.43173959251524 0.568260407484761 120 2 2.44252962150701 -0.442529621507014 121 1 2.44252962150701 -1.44252962150701 122 2 3.43541203275697 -1.43541203275697 123 4 3.43541203275697 0.564587967243031 124 1 2.21072637314637 -1.21072637314637 125 1 2.2690509104703 -1.2690509104703 126 4 3.72553981844154 0.274460181558461 127 3 2.67433286986766 0.325667130132345 128 2 2.96813309579396 -0.968133095793956 129 3 3.43541203275697 -0.435412032756969 130 2 2.96813309579396 -0.968133095793956 131 3 3.1999363441546 -0.199936344154597 132 4 2.96813309579396 1.03186690420604 133 2 3.14161180683067 -1.14161180683067 134 1 3.14161180683067 -2.14161180683067 135 4 2.73632984743331 1.26367015256669 136 4 4.25114329272848 -0.251143292728481 137 4 2.73632984743331 1.26367015256669 138 3 3.1999363441546 -0.199936344154597 139 2 3.43541203275697 -1.43541203275697 140 2 2.96813309579396 -0.968133095793956 141 2 2.73632984743331 -0.736329847433314 142 5 3.67088772135934 1.32911227864066 143 5 4.54127107841305 0.458728921586948 144 2 2.21072637314637 -0.210726373146372 145 3 3.78386435576547 -0.783864355765468 146 2 2.96813309579396 -0.968133095793956 147 4 3.96101550704391 0.0389844929560892 148 2 2.96813309579396 -0.968133095793956 149 2 2.50085415883094 -0.500854158830943 150 4 3.1999363441546 0.800063655845403 151 2 3.14161180683067 -1.14161180683067 152 5 3.66721528111761 1.33278471888239 153 5 4.77674676701542 0.223253232984577 154 4 3.1999363441546 0.800063655845403 155 4 4.42462200376519 -0.424622003765194 156 4 2.96813309579396 1.03186690420604 157 2 2.96813309579396 -0.968133095793956 158 4 3.66721528111761 0.33278471888239 159 3 4.25114329272848 -1.25114329272848 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 7 0.348705772283607 0.697411544567213 0.651294227716393 8 0.196926117674761 0.393852235349521 0.80307388232524 9 0.649090344972348 0.701819310055305 0.350909655027653 10 0.563581108480416 0.872837783039167 0.436418891519584 11 0.495547822651428 0.991095645302857 0.504452177348572 12 0.460498102535905 0.92099620507181 0.539501897464095 13 0.418658897868757 0.837317795737515 0.581341102131243 14 0.51855254582394 0.96289490835212 0.48144745417606 15 0.486034437932817 0.972068875865634 0.513965562067183 16 0.450172255035902 0.900344510071803 0.549827744964098 17 0.428511631942873 0.857023263885745 0.571488368057127 18 0.402747700093628 0.805495400187256 0.597252299906372 19 0.516693141578095 0.96661371684381 0.483306858421905 20 0.443959681809271 0.887919363618542 0.556040318190729 21 0.385710220492061 0.771420440984122 0.614289779507939 22 0.319204145781872 0.638408291563745 0.680795854218128 23 0.32474124201608 0.64948248403216 0.67525875798392 24 0.271240687987990 0.542481375975981 0.72875931201201 25 0.255361068854513 0.510722137709027 0.744638931145487 26 0.215430613630148 0.430861227260296 0.784569386369852 27 0.170193005941472 0.340386011882943 0.829806994058528 28 0.205833480669213 0.411666961338426 0.794166519330787 29 0.175246591380767 0.350493182761533 0.824753408619233 30 0.156603356831314 0.313206713662628 0.843396643168686 31 0.174195360454385 0.34839072090877 0.825804639545615 32 0.146119857525579 0.292239715051159 0.85388014247442 33 0.182747410996591 0.365494821993182 0.817252589003409 34 0.227706476999612 0.455412953999225 0.772293523000388 35 0.260384794811586 0.520769589623172 0.739615205188414 36 0.228456985043727 0.456913970087455 0.771543014956273 37 0.207734032365106 0.415468064730211 0.792265967634894 38 0.180456979785985 0.360913959571970 0.819543020214015 39 0.152500220353588 0.305000440707176 0.847499779646412 40 0.135356002620245 0.270712005240489 0.864643997379755 41 0.123694373734863 0.247388747469726 0.876305626265137 42 0.216588212089664 0.433176424179328 0.783411787910336 43 0.225825225214339 0.451650450428679 0.77417477478566 44 0.191388927874139 0.382777855748279 0.80861107212586 45 0.174118073807088 0.348236147614176 0.825881926192912 46 0.152198019059945 0.304396038119891 0.847801980940055 47 0.140945971578895 0.281891943157790 0.859054028421105 48 0.126043494477298 0.252086988954595 0.873956505522702 49 0.150195546811567 0.300391093623135 0.849804453188433 50 0.138416525556095 0.276833051112189 0.861583474443905 51 0.139641469679819 0.279282939359637 0.860358530320181 52 0.162163707968603 0.324327415937206 0.837836292031397 53 0.200538516362102 0.401077032724203 0.799461483637898 54 0.201318713863104 0.402637427726209 0.798681286136896 55 0.179446009136708 0.358892018273416 0.820553990863292 56 0.188492702114846 0.376985404229692 0.811507297885154 57 0.222159809915979 0.444319619831958 0.777840190084021 58 0.209746683820366 0.419493367640731 0.790253316179634 59 0.262953677341465 0.52590735468293 0.737046322658535 60 0.296995263970196 0.593990527940393 0.703004736029804 61 0.328566393896580 0.657132787793159 0.67143360610342 62 0.333840925837394 0.667681851674787 0.666159074162606 63 0.296959393841308 0.593918787682617 0.703040606158692 64 0.267914185352451 0.535828370704902 0.732085814647549 65 0.327736007503593 0.655472015007185 0.672263992496407 66 0.290495008101899 0.580990016203799 0.7095049918981 67 0.292650692468213 0.585301384936427 0.707349307531786 68 0.297630790775706 0.595261581551412 0.702369209224294 69 0.358864118834767 0.717728237669534 0.641135881165233 70 0.319195731848384 0.638391463696767 0.680804268151616 71 0.278965482800249 0.557930965600498 0.721034517199751 72 0.264501862442975 0.529003724885951 0.735498137557025 73 0.230918716016209 0.461837432032418 0.769081283983791 74 0.199862300436688 0.399724600873377 0.800137699563312 75 0.187060595360049 0.374121190720098 0.812939404639951 76 0.210798844001545 0.42159768800309 0.789201155998455 77 0.189999602716159 0.379999205432317 0.810000397283841 78 0.180272345667962 0.360544691335925 0.819727654332038 79 0.181549720305771 0.363099440611542 0.81845027969423 80 0.21093193560702 0.42186387121404 0.78906806439298 81 0.231368952933079 0.462737905866158 0.768631047066921 82 0.232760139203398 0.465520278406796 0.767239860796602 83 0.284378567596510 0.568757135193019 0.71562143240349 84 0.325903640542349 0.651807281084698 0.674096359457651 85 0.306112539447341 0.612225078894682 0.693887460552659 86 0.270407787277440 0.540815574554881 0.72959221272256 87 0.259989735597835 0.51997947119567 0.740010264402165 88 0.366827299543004 0.733654599086008 0.633172700456996 89 0.327736948427311 0.655473896854622 0.672263051572689 90 0.373887649114284 0.747775298228568 0.626112350885716 91 0.366465984010432 0.732931968020864 0.633534015989568 92 0.536615143614498 0.926769712771004 0.463384856385502 93 0.51112357704594 0.97775284590812 0.48887642295406 94 0.596723236578608 0.806553526842783 0.403276763421392 95 0.592996790894391 0.814006418211218 0.407003209105609 96 0.547071094629374 0.905857810741252 0.452928905370626 97 0.536010579309808 0.927978841380383 0.463989420690192 98 0.48931844579632 0.97863689159264 0.51068155420368 99 0.49811380485273 0.99622760970546 0.50188619514727 100 0.504141464163961 0.991717071672078 0.495858535836039 101 0.500236509943281 0.999526980113438 0.499763490056719 102 0.548313604430781 0.903372791138437 0.451686395569218 103 0.501493791646521 0.997012416706957 0.498506208353479 104 0.478291272835013 0.956582545670027 0.521708727164987 105 0.472058648936499 0.944117297872997 0.527941351063501 106 0.532616150985185 0.93476769802963 0.467383849014815 107 0.562676239339327 0.874647521321345 0.437323760660673 108 0.607690384652446 0.784619230695107 0.392309615347554 109 0.599034149372227 0.801931701255545 0.400965850627773 110 0.653449254782541 0.693101490434917 0.346550745217459 111 0.608051053143108 0.783897893713784 0.391948946856892 112 0.576033342615083 0.847933314769835 0.423966657384918 113 0.533078132389604 0.933843735220792 0.466921867610396 114 0.512724178025575 0.97455164394885 0.487275821974425 115 0.522388900885386 0.955222198229227 0.477611099114614 116 0.559654541514306 0.880690916971388 0.440345458485694 117 0.585070971788785 0.82985805642243 0.414929028211215 118 0.538647478862257 0.922705042275487 0.461352521137743 119 0.5387376614854 0.9225246770292 0.4612623385146 120 0.491828486797651 0.983656973595301 0.508171513202349 121 0.509314556472533 0.981370887054934 0.490685443527467 122 0.568048112442305 0.86390377511539 0.431951887557695 123 0.534353096385198 0.931293807229604 0.465646903614802 124 0.537000315144604 0.925999369710791 0.462999684855396 125 0.564558268178149 0.870883463643701 0.435441731821851 126 0.519027415992378 0.961945168015244 0.480972584007622 127 0.51394434533322 0.97211130933356 0.48605565466678 128 0.497710903052184 0.995421806104369 0.502289096947816 129 0.447817898449712 0.895635796899424 0.552182101550288 130 0.434072766998787 0.868145533997575 0.565927233001213 131 0.378440535255841 0.756881070511682 0.621559464744159 132 0.403964159973086 0.807928319946172 0.596035840026914 133 0.374010887043708 0.748021774087416 0.625989112956292 134 0.54356951497271 0.91286097005458 0.45643048502729 135 0.601392571207093 0.797214857585815 0.398607428792907 136 0.534972640829759 0.930054718340482 0.465027359170241 137 0.644497052479459 0.711005895041083 0.355502947520541 138 0.573818211902909 0.852363576194182 0.426181788097091 139 0.678590614944257 0.642818770111485 0.321409385055743 140 0.650921574514103 0.698156850971793 0.349078425485897 141 0.598046828558513 0.803906342882973 0.401953171441487 142 0.627367853705483 0.745264292589034 0.372632146294517 143 0.583102457586113 0.833795084827774 0.416897542413887 144 0.495282210747915 0.99056442149583 0.504717789252085 145 0.421360069250932 0.842720138501863 0.578639930749068 146 0.38338826602527 0.76677653205054 0.61661173397473 147 0.295301023728632 0.590602047457265 0.704698976271368 148 0.269961531288596 0.539923062577191 0.730038468711405 149 0.213089315525369 0.426178631050738 0.786910684474631 150 0.165155523818429 0.330311047636858 0.834844476181571 151 0.255338586963392 0.510677173926785 0.744661413036608 152 0.236826484046643 0.473652968093285 0.763173515953357 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 = 2 ; 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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