Workshop 7 – Multiple Linear Regression

*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 10:02:20 +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/t129128496843dqvpta3ouos1w.htm/, Retrieved Thu, 02 Dec 2010 11:16:27 +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/t129128496843dqvpta3ouos1w.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:

Member of sports club data ( Provision, Illness & Tobacco)

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

2 5 1 1 1 4 1 4 1 7 1 5 1 7 1 2 2 5 1 1 2 5 1 1 1 4 1 2 2 4 2 1 1 6 1 1 2 5 1 1 1 1 1 3 2 5 1 1 1 4 2 1 2 6 1 1 2 7 1 2 2 7 1 4 1 2 1 1 1 6 1 1 1 3 1 2 2 6 1 3 2 6 1 1 1 5 1 1 2 6 1 1 2 4 2 1 2 3 2 2 2 4 1 1 2 5 2 1 2 6 2 1 1 6 2 1 1 4 1 1 2 6 1 1 1 6 1 1 2 5 1 1 2 6 1 1 2 4 1 1 1 6 1 1 2 7 1 1 1 5 1 1 1 6 1 1 2 6 2 1 1 5 2 4 2 7 1 1 2 6 1 1 1 3 1 4 1 4 1 2 2 5 1 2 2 4 2 1 1 3 1 1 2 5 1 2 2 5 1 1 1 4 1 1 1 5 1 1 2 1 1 1 2 2 2 1 2 3 1 1 1 4 1 2 1 3 1 1 1 7 1 1 1 2 1 1 1 4 1 2 1 2 1 1 2 5 1 2 2 6 1 4 2 6 1 1 2 6 1 1 1 6 1 1 2 6 1 2 2 6 1 3 1 6 1 1 1 4 1 1 1 4 1 1 2 5 1 1 1 6 1 1 1 6 1 1 1 7 1 1 1 6 1 1 2 6 2 1 1 6 1 2 2 3 1 1 2 5 1 1 2 6 1 1 2 4 1 1 1 5 1 1 2 6 1 1 2 6 1 1 1 3 1 1 2 6 1 2 2 5 1 1 1 6 1 1 1 4 1 1 2 7 1 1 2 5 1 1 2 6 1 2 1 6 1 1 2 6 1 5 1 7 2 1 2 6 1 1 1 6 1 1 1 6 1 2 2 6 1 1 2 2 1 3 1 4 1 1 2 4 1 1 2 6 1 1 1 5 1 3 1 6 1 1 1 6 1 1 1 2 2 1 2 7 1 1 1 1 1 1 1 4 1 1 1 1 1 2 1 6 1 2 2 6 1 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 14 seconds R Server 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation Member[t] = + 1.13063229552587 + 0.0785437330394767Provision[t] + 0.0679185931028256Illness[t] -0.0381110070875364Tobacco[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) 1.13063229552587 0.208643 5.419 0 0 Provision 0.0785437330394767 0.027454 2.8609 0.004815 0.002408 Illness 0.0679185931028256 0.11738 0.5786 0.563697 0.281848 Tobacco -0.0381110070875364 0.041979 -0.9079 0.365382 0.182691 Multiple Linear Regression - Regression Statistics Multiple R 0.233300950142260 R-squared 0.0544293333372814 Adjusted R-squared 0.0358887320301693 F-TEST (value) 2.93568328425262 F-TEST (DF numerator) 3 F-TEST (DF denominator) 153 p-value 0.0352584502761568 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.489621071820791 Sum Squared Residuals 36.6785054775539 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 2 1.55315854673851 0.446841453261493 2 1 1.36028179243645 -0.360281792436451 3 1 1.55780198446735 -0.557801984467352 4 1 1.67213500572996 -0.672135005729958 5 2 1.55315854673854 0.446841453261459 6 2 1.55315854673854 0.446841453261459 7 1 1.43650380661153 -0.436503806611528 8 2 1.54253340680189 0.457466593198111 9 1 1.63170227977802 -0.631702279778018 10 2 1.55315854673854 0.446841453261459 11 1 1.16276160040556 -0.162761600405560 12 2 1.55315854673854 0.446841453261459 13 1 1.54253340680189 -0.542533406801889 14 2 1.63170227977802 0.368297720221982 15 2 1.67213500572996 0.327864994270041 16 2 1.59591299155489 0.404087008445114 17 1 1.31752734762011 -0.31752734762011 18 1 1.63170227977802 -0.631702279778018 19 1 1.35796007357205 -0.357960073572051 20 2 1.55548026560295 0.444519734397055 21 2 1.63170227977802 0.368297720221982 22 1 1.55315854673854 -0.553158546738541 23 2 1.63170227977802 0.368297720221982 24 2 1.54253340680189 0.457466593198111 25 2 1.42587866667488 0.574121333325124 26 2 1.47461481369906 0.525385186300936 27 2 1.62107713984137 0.378922860158634 28 2 1.69962087288084 0.300379127119157 29 1 1.69962087288084 -0.699620872880843 30 1 1.47461481369906 -0.474614813699064 31 2 1.63170227977802 0.368297720221982 32 1 1.63170227977802 -0.631702279778018 33 2 1.55315854673854 0.446841453261459 34 2 1.63170227977802 0.368297720221982 35 2 1.47461481369906 0.525385186300936 36 1 1.63170227977802 -0.631702279778018 37 2 1.71024601281749 0.289753987182505 38 1 1.55315854673854 -0.553158546738541 39 1 1.63170227977802 -0.631702279778018 40 2 1.69962087288084 0.300379127119157 41 1 1.50674411857876 -0.506744118578757 42 2 1.71024601281749 0.289753987182505 43 2 1.63170227977802 0.368297720221982 44 1 1.28173805939698 -0.281738059396978 45 1 1.43650380661153 -0.436503806611528 46 2 1.51504753965100 0.484952460348995 47 2 1.54253340680189 0.457466593198111 48 1 1.39607108065959 -0.396071080659587 49 2 1.51504753965100 0.484952460348995 50 2 1.55315854673854 0.446841453261459 51 1 1.47461481369906 -0.474614813699064 52 1 1.55315854673854 -0.553158546738541 53 2 1.23898361458063 0.761016385419367 54 2 1.38544594072294 0.614554059277065 55 2 1.39607108065959 0.603928919340413 56 1 1.43650380661153 -0.436503806611528 57 1 1.39607108065959 -0.396071080659587 58 1 1.71024601281749 -0.710246012817495 59 1 1.31752734762011 -0.31752734762011 60 1 1.43650380661153 -0.436503806611528 61 1 1.31752734762011 -0.31752734762011 62 2 1.51504753965100 0.484952460348995 63 2 1.51736925851541 0.482630741484591 64 2 1.63170227977802 0.368297720221982 65 2 1.63170227977802 0.368297720221982 66 1 1.63170227977802 -0.631702279778018 67 2 1.59359127269048 0.406408727309518 68 2 1.55548026560295 0.444519734397055 69 1 1.63170227977802 -0.631702279778018 70 1 1.47461481369906 -0.474614813699064 71 1 1.47461481369906 -0.474614813699064 72 2 1.55315854673854 0.446841453261459 73 1 1.63170227977802 -0.631702279778018 74 1 1.63170227977802 -0.631702279778018 75 1 1.71024601281749 -0.710246012817495 76 1 1.63170227977802 -0.631702279778018 77 2 1.69962087288084 0.300379127119157 78 1 1.59359127269048 -0.593591272690482 79 2 1.39607108065959 0.603928919340413 80 2 1.55315854673854 0.446841453261459 81 2 1.63170227977802 0.368297720221982 82 2 1.47461481369906 0.525385186300936 83 1 1.55315854673854 -0.553158546738541 84 2 1.63170227977802 0.368297720221982 85 2 1.63170227977802 0.368297720221982 86 1 1.39607108065959 -0.396071080659587 87 2 1.59359127269048 0.406408727309518 88 2 1.55315854673854 0.446841453261459 89 1 1.63170227977802 -0.631702279778018 90 1 1.47461481369906 -0.474614813699064 91 2 1.71024601281749 0.289753987182505 92 2 1.55315854673854 0.446841453261459 93 2 1.59359127269048 0.406408727309518 94 1 1.63170227977802 -0.631702279778018 95 2 1.47925825142787 0.520741748572128 96 1 1.77816460592032 -0.77816460592032 97 2 1.63170227977802 0.368297720221982 98 1 1.63170227977802 -0.631702279778018 99 1 1.59359127269048 -0.593591272690482 100 2 1.63170227977802 0.368297720221982 101 2 1.24130533344504 0.758694666554963 102 1 1.47461481369906 -0.474614813699064 103 2 1.47461481369906 0.525385186300936 104 2 1.63170227977802 0.368297720221982 105 1 1.47693653256347 -0.476936532563468 106 1 1.63170227977802 -0.631702279778018 107 1 1.63170227977802 -0.631702279778018 108 1 1.38544594072294 -0.385445940722935 109 2 1.71024601281749 0.289753987182505 110 1 1.23898361458063 -0.238983614580633 111 1 1.47461481369906 -0.474614813699064 112 1 1.20087260749310 -0.200872607493097 113 1 1.59359127269048 -0.593591272690482 114 2 1.51736925851541 0.482630741484591 115 1 1.51736925851541 -0.517369258515409 116 2 1.71024601281749 0.289753987182505 117 1 1.63170227977802 -0.631702279778018 118 2 1.47461481369906 0.525385186300936 119 2 1.47461481369906 0.525385186300936 120 1 1.51736925851541 -0.517369258515409 121 1 1.62107713984137 -0.621077139841366 122 2 1.71024601281749 0.289753987182505 123 2 1.47461481369906 0.525385186300936 124 1 1.47461481369906 -0.474614813699064 125 2 1.55548026560295 0.444519734397055 126 2 1.71024601281749 0.289753987182505 127 2 1.55315854673854 0.446841453261459 128 2 1.63170227977802 0.368297720221982 129 1 1.58528785161823 -0.585287851618234 130 2 1.51736925851541 0.482630741484591 131 2 1.55315854673854 0.446841453261459 132 2 1.67213500572996 0.327864994270041 133 2 1.47461481369906 0.525385186300936 134 1 1.59359127269048 -0.593591272690482 135 1 1.63170227977802 -0.631702279778018 136 2 1.63402399864242 0.365976001357578 137 2 1.59359127269048 0.406408727309518 138 2 1.59359127269048 0.406408727309518 139 2 1.55315854673854 0.446841453261459 140 1 1.55315854673854 -0.553158546738541 141 2 1.51504753965100 0.484952460348995 142 2 1.63170227977802 0.368297720221982 143 2 1.66150986579331 0.338490134206693 144 1 1.74005359883278 -0.740053598832784 145 1 1.47461481369906 -0.474614813699064 146 2 1.63170227977802 0.368297720221982 147 2 1.59359127269048 0.406408727309518 148 2 1.71024601281749 0.289753987182505 149 1 1.59359127269048 -0.593591272690482 150 2 1.71024601281749 0.289753987182505 151 2 1.54253340680189 0.457466593198111 152 2 1.63170227977802 0.368297720221982 153 1 1.47461481369906 -0.474614813699064 154 1 1.47461481369906 -0.474614813699064 155 2 1.71024601281749 0.289753987182505 156 1 1.47461481369906 -0.474614813699064 157 2 1.77816460592032 0.22183539407968 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 7 0.62645683767383 0.74708632465234 0.37354316232617 8 0.46372923352297 0.92745846704594 0.53627076647703 9 0.566706716998540 0.866586566002919 0.433293283001460 10 0.504438669545157 0.991122660909686 0.495561330454843 11 0.428535580203182 0.857071160406364 0.571464419796818 12 0.37081384961609 0.74162769923218 0.62918615038391 13 0.488149021590964 0.976298043181929 0.511850978409036 14 0.421006119291285 0.84201223858257 0.578993880708715 15 0.404251305389171 0.808502610778342 0.595748694610829 16 0.522662591136375 0.95467481772725 0.477337408863625 17 0.493926673077888 0.987853346155777 0.506073326922112 18 0.59997128935593 0.80005742128814 0.40002871064407 19 0.545222956337152 0.909554087325696 0.454777043662848 20 0.55479409018234 0.89041181963532 0.44520590981766 21 0.500862199324698 0.998275601350604 0.499137800675302 22 0.537882959206856 0.924234081586289 0.462117040793144 23 0.49004826361884 0.98009652723768 0.50995173638116 24 0.469935043855374 0.939870087710748 0.530064956144626 25 0.47580459146412 0.95160918292824 0.52419540853588 26 0.478457001241127 0.956914002482254 0.521542998758873 27 0.42274859268998 0.84549718537996 0.57725140731002 28 0.367346543948423 0.734693087896847 0.632653456051577 29 0.515366152818336 0.969267694363329 0.484633847181664 30 0.520065989954053 0.959868020091894 0.479934010045947 31 0.482927284453509 0.965854568907018 0.517072715546491 32 0.535906628779538 0.928186742440923 0.464093371220462 33 0.518838543672837 0.962322912654326 0.481161456327163 34 0.484406016127814 0.968812032255627 0.515593983872186 35 0.481154228362557 0.962308456725114 0.518845771637443 36 0.533568127437889 0.932863745124222 0.466431872562111 37 0.491234310237415 0.982468620474829 0.508765689762585 38 0.514339976667321 0.971320046665358 0.485660023332679 39 0.553246364240873 0.893507271518253 0.446753635759127 40 0.511169919594611 0.977660160810778 0.488830080405389 41 0.502684871213568 0.994630257572865 0.497315128786432 42 0.464708587822664 0.929417175645328 0.535291412177336 43 0.436869026377662 0.873738052755323 0.563130973622338 44 0.395212997601153 0.790425995202305 0.604787002398847 45 0.379493674597652 0.758987349195303 0.620506325402348 46 0.384640433237877 0.769280866475755 0.615359566762123 47 0.369393752358338 0.738787504716677 0.630606247641662 48 0.354390075248079 0.708780150496159 0.645609924751921 49 0.358613731975989 0.717227463951977 0.641386268024011 50 0.346159296114005 0.692318592228011 0.653840703885995 51 0.347037767614241 0.694075535228482 0.652962232385759 52 0.364664901750202 0.729329803500404 0.635335098249798 53 0.433203490180666 0.866406980361332 0.566796509819334 54 0.452773783487201 0.905547566974402 0.547226216512799 55 0.470352094110396 0.94070418822079 0.529647905889604 56 0.459672340712046 0.919344681424093 0.540327659287954 57 0.449825563571665 0.89965112714333 0.550174436428335 58 0.504495305307686 0.991009389384628 0.495504694692314 59 0.480859039895579 0.961718079791158 0.519140960104421 60 0.467230789186636 0.934461578373272 0.532769210813364 61 0.440936749710354 0.881873499420707 0.559063250289646 62 0.446390554116382 0.892781108232763 0.553609445883618 63 0.460713668706242 0.921427337412485 0.539286331293757 64 0.439213374641528 0.878426749283055 0.560786625358472 65 0.417460294957286 0.834920589914572 0.582539705042714 66 0.450275717777236 0.900551435554472 0.549724282222764 67 0.436393502834517 0.872787005669034 0.563606497165483 68 0.429641582979285 0.85928316595857 0.570358417020715 69 0.461542189197704 0.923084378395408 0.538457810802296 70 0.457198221804159 0.914396443608318 0.542801778195841 71 0.452590136185087 0.905180272370175 0.547409863814913 72 0.444858166159639 0.889716332319279 0.55514183384036 73 0.474921330680983 0.949842661361966 0.525078669319017 74 0.504392619072382 0.991214761855237 0.495607380927618 75 0.554429219742922 0.891141560514157 0.445570780257078 76 0.583883499278719 0.832233001442563 0.416116500721281 77 0.56655599135304 0.86688801729392 0.43344400864696 78 0.589187890560262 0.821624218879477 0.410812109439738 79 0.615967926245901 0.768064147508198 0.384032073754099 80 0.609981680136643 0.780036639726714 0.390018319863357 81 0.591050190875237 0.817899618249525 0.408949809124763 82 0.600390928470538 0.799218143058923 0.399609071529462 83 0.612369995615271 0.775260008769458 0.387630004384729 84 0.592868956025806 0.814262087948388 0.407131043974194 85 0.572858478496362 0.854283043007277 0.427141521503638 86 0.554690782442183 0.890618435115634 0.445309217557817 87 0.539349627122904 0.921300745754192 0.460650372877096 88 0.531871458175423 0.936257083649154 0.468128541824577 89 0.564800597403182 0.870398805193637 0.435199402596818 90 0.561191050533171 0.877617898933659 0.438808949466829 91 0.529237130725644 0.941525738548712 0.470762869274356 92 0.520783975918509 0.958432048162982 0.479216024081491 93 0.503995369407431 0.992009261185138 0.496004630592569 94 0.538591435031343 0.922817129937314 0.461408564968657 95 0.54056980132145 0.9188603973571 0.45943019867855 96 0.594904497456596 0.810191005086808 0.405095502543404 97 0.571600714760841 0.856798570478317 0.428399285239159 98 0.609105063675345 0.781789872649309 0.390894936324655 99 0.63680067928576 0.72639864142848 0.36319932071424 100 0.612469757784858 0.775060484430285 0.387530242215142 101 0.705132290497748 0.589735419004503 0.294867709502252 102 0.701220987467545 0.59755802506491 0.298779012532455 103 0.711452150600653 0.577095698798694 0.288547849399347 104 0.687675561805332 0.624648876389335 0.312324438194668 105 0.680253170984343 0.639493658031314 0.319746829015657 106 0.725503141393031 0.548993717213939 0.274496858606969 107 0.773739871587255 0.452520256825491 0.226260128412745 108 0.74749819847666 0.50500360304668 0.25250180152334 109 0.712590980044614 0.574818039910771 0.287409019955386 110 0.67140421492735 0.657191570145299 0.328595785072650 111 0.67083760587364 0.658324788252720 0.329162394126360 112 0.62504168968033 0.749916620639339 0.374958310319669 113 0.666716504825728 0.666566990348543 0.333283495174272 114 0.672791268267025 0.654417463465951 0.327208731732975 115 0.67368003239049 0.65263993521902 0.32631996760951 116 0.630751298539954 0.738497402920091 0.369248701460046 117 0.705250075458013 0.589499849083974 0.294749924541987 118 0.710427385678797 0.579145228642405 0.289572614321203 119 0.722679818988398 0.554640362023204 0.277320181011602 120 0.74182192071415 0.516356158571699 0.258178079285849 121 0.743440810909422 0.513118378181155 0.256559189090578 122 0.699840845375477 0.600318309249045 0.300159154624523 123 0.718294979244808 0.563410041510383 0.281705020755192 124 0.709593774271303 0.580812451457394 0.290406225728697 125 0.687622873023524 0.624754253952951 0.312377126976476 126 0.636647599020927 0.726704801958145 0.363352400979073 127 0.618310205439537 0.763379589120926 0.381689794560463 128 0.575189592227741 0.849620815544517 0.424810407772259 129 0.609358068221478 0.781283863557043 0.390641931778522 130 0.577498220733769 0.845003558532462 0.422501779266231 131 0.565949188614186 0.868101622771628 0.434050811385814 132 0.51028686823872 0.97942626352256 0.48971313176128 133 0.561361453492364 0.877277093015272 0.438638546507636 134 0.623288713075943 0.753422573848115 0.376711286924057 135 0.706517638403433 0.586964723193134 0.293482361596567 136 0.646421378391728 0.707157243216544 0.353578621608272 137 0.607650512655615 0.78469897468877 0.392349487344385 138 0.581340411840271 0.837319176319459 0.418659588159729 139 0.579422048518308 0.841155902963383 0.420577951481692 140 0.592350071128314 0.815299857743373 0.407649928871686 141 0.714876169175005 0.57024766164999 0.285123830824995 142 0.659485711299403 0.681028577401194 0.340514288700597 143 0.692041301661876 0.615917396676248 0.307958698338124 144 0.870605019548125 0.25878996090375 0.129394980451875 145 0.816525831316093 0.366948337367815 0.183474168683907 146 0.771340123241979 0.457319753516043 0.228659876758021 147 0.91634101049127 0.16731797901746 0.08365898950873 148 0.846522152539057 0.306955694921887 0.153477847460943 149 0.734674029332063 0.530651941335873 0.265325970667937 150 0.578858261777207 0.842283476445587 0.421141738222793 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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