*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: Fri, 03 Dec 2010 12:47:09 +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/03/t1291380395kfxagoxbc8jpeu8.htm/, Retrieved Fri, 03 Dec 2010 13:46:45 +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/03/t1291380395kfxagoxbc8jpeu8.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:

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4 4 5 4 4 4 4 4 4 4 4 3 4 4 5 5 4 4 5 5 4 3 3 2 3 4 4 3 2 3 2 3 2 4 3 5 4 3 3 4 5 4 4 3 3 3 3 4 4 2 3 4 4 2 4 2 4 4 3 4 4 5 3 4 3 2 3 2 2 3 4 3 2 4 4 4 4 2 3 2 4 2 3 2 5 4 2 5 5 5 4 3 4 2 3 3 4 4 4 3 4 4 4 4 4 4 3 3 4 4 5 4 3 2 3 3 3 3 3 4 4 4 4 4 4 4 2 3 2 2 2 4 2 4 2 4 4 3 4 4 3 3 2 4 4 4 3 3 2 4 4 2 3 4 4 4 2 4 4 4 4 4 4 3 4 4 4 4 4 4 4 4 4 4 4 4 3 3 4 3 4 3 5 4 4 4 4 4 4 3 4 3 2 4 4 4 1 4 4 4 4 4 4 4 2 4 4 4 3 4 4 2 4 4 4 4 4 3 4 3 2 4 4 4 3 2 4 4 4 3 4 4 5 4 4 5 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 5 3 2 3 3 5 4 4 4 2 4 4 4 4 4 3 3 3 3 4 4 4 4 3 4 3 4 4 3 3 4 4 3 3 3 4 4 4 4 3 4 4 2 3 2 3 2 3 2 2 2 4 2 2 5 2 4 3 4 4 4 5 4 4 4 4 4 2 4 4 5 4 4 4 4 5 5 4 3 2 4 4 4 4 4 3 3 4 3 4 3 4 4 2 4 4 4 4 5 4 2 4 4 4 4 3 3 4 3 3 4 3 2 2 4 2 1 4 4 4 4 4 4 4 4 4 4 4 3 4 4 4 3 2 3 4 4 2 4 3 2 2 5 2 2 4 2 4 4 4 4 4 4 4 4 3 4 4 4 4 4 4 3 4 4 3 4 4 3 4 4 4 3 4 4 2 3 2 3 1 4 3 4 4 4 4 4 4 4 5 3 4 4 2 4 4 4 4 3 4 4 4 4 5 4 4 5 5 5 5 4 4 2 4 3 4 4 3 3 2 3 3 4 3 3 3 2 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 y[t] = + 0.85901483403914 + 0.00480364594500278x1[t] + 0.248974358803874x2[t] + 0.147059243206037x3[t] + 0.162154471874077x4[t] + 0.163836595619903x5[t] + 0.0504204407030673x6[t] -0.00332137712527254t + 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) 0.85901483403914 0.411478 2.0876 0.038592 0.019296 x1 0.00480364594500278 0.061118 0.0786 0.937463 0.468732 x2 0.248974358803874 0.071657 3.4745 0.000676 0.000338 x3 0.147059243206037 0.06461 2.2761 0.024315 0.012158 x4 0.162154471874077 0.082937 1.9551 0.052503 0.026251 x5 0.163836595619903 0.073467 2.2301 0.02729 0.013645 x6 0.0504204407030673 0.061045 0.826 0.410197 0.205098 t -0.00332137712527254 0.00124 -2.6794 0.008234 0.004117 Multiple Linear Regression - Regression Statistics Multiple R 0.585208926340266 R-squared 0.342469487468327 Adjusted R-squared 0.310506198664704 F-TEST (value) 10.7144633824260 F-TEST (DF numerator) 7 F-TEST (DF denominator) 144 p-value 7.9982798162348e-11 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.630641441916382 Sum Squared Residuals 57.2700424697817 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 4 4.21366284032564 -0.213662840325641 2 4 3.79921263252237 0.200787367477632 3 5 4.28884044071016 0.711159559289841 4 3 3.25449230268405 -0.254492302684047 5 2 2.92686198181061 -0.926861981810613 6 5 3.71588458950534 1.28411541049466 7 4 3.38176849894109 0.618231501058912 8 2 3.51148537054551 -1.51148537054551 9 4 3.80255926063250 0.197440739367505 10 4 2.58258190494444 1.41741809505556 11 4 3.42872234671624 0.571277653283762 12 2 2.83641454881677 -0.836414548816773 13 5 3.89993354911071 1.10006645088929 14 3 3.11434814620531 -0.114348146205308 15 4 3.9133855558229 0.0866144441771042 16 4 3.82492641551365 0.175073584486348 17 3 3.12949404542039 -0.129494045420389 18 4 3.90822507039208 0.0917749296079187 19 2 2.68288301814769 -0.682883018147693 20 4 3.72982055237745 0.270179447622548 21 3 3.34508813476045 -0.345088134760445 22 3 3.39718673063293 -0.397186730632927 23 4 3.39366946715797 0.60633053284203 24 4 3.63932244883657 0.360677551163428 25 4 3.88497543051517 0.115024569484827 26 4 3.41530113606388 0.584698863936121 27 5 3.87833267626463 1.12166732373537 28 3 3.33191845392341 -0.331918453923407 29 1 3.87168992201408 -2.87168992201408 30 4 3.6949246573789 0.305075342621098 31 4 3.85543987587353 0.144560124126468 32 3 3.31863294542232 -0.318632945422317 33 3 3.68496052600308 -0.684960526003084 34 4 4.0220411542068 -0.0220411542068012 35 4 3.85176165926245 0.148238340737552 36 4 3.89886072284024 0.101139277159757 37 3 3.60163248298606 -0.601632482986063 38 4 3.83219023599662 0.167809764003376 39 3 3.43763890280644 -0.437638902806443 40 4 3.63287144378198 0.367128556218022 41 3 3.35878308581080 -0.358783085810795 42 4 3.58061189477337 0.419388105226632 43 3 2.68182196063430 0.318178039365705 44 2 2.86428334174944 -0.864283341749444 45 3 3.9807023598838 -0.9807023598838 46 4 3.57152846517544 0.428471534824557 47 4 4.13789620125316 -0.137896201253158 48 3 3.7989764647439 -0.798976464743899 49 3 3.48956289473769 -0.489562894737689 50 4 3.84275415119642 0.157245848803579 51 4 3.73859189266501 0.261408107334986 52 3 3.13458716909687 -0.134587169096866 53 2 2.85285042378168 -0.852850423781682 54 4 3.78865549388227 0.211344506117730 55 4 3.51585299378596 0.484147006214043 56 3 3.22321677619361 -0.223216776193613 57 2 2.66375461319183 -0.663754613191827 58 4 3.77536998538118 0.224630014618820 59 3 3.77204860825591 -0.772048608255907 60 3 3.57124754722153 -0.57124754722153 61 4 3.51750572939319 0.48249427060681 62 3 2.89848850094819 0.101511499051806 63 4 3.80918354045788 0.190816459542116 64 3 3.46132323621747 -0.46132323621747 65 4 3.79773714026234 0.202262859737664 66 4 4.47082363788289 -0.470823637882891 67 4 3.53839061545462 0.461609384545384 68 3 3.12225828390557 -0.122258283905566 69 3 2.69630703678334 0.303692963216657 70 3 3.68509301917484 -0.685093019174842 71 4 2.76058516489075 1.23941483510925 72 3 2.52899207947845 0.471007920521548 73 2 2.54578120064939 -0.54578120064939 74 4 3.92519557206396 0.0748044279360424 75 4 3.90677896627064 0.0932210337293552 76 4 4.04637991056526 -0.0463799105652571 77 3 2.48078939357036 0.519210606429637 78 5 4.01983828170167 0.980161718298331 79 3 3.35147484674531 -0.351474846745308 80 2 2.92024728652822 -0.920247286528218 81 3 3.28616735707613 -0.286167357076134 82 3 3.29962333236473 -0.299623332364727 83 4 3.34779663013422 0.652203369865776 84 4 3.12914398249428 0.87085601750572 85 3 3.37669071160187 -0.376690711601873 86 2 2.35554405481481 -0.355544054814809 87 4 3.49666559350721 0.503334406492789 88 4 3.11212906223989 0.887870937760112 89 3 2.7405392912572 0.259460708742799 90 4 3.46199894157335 0.538001058426653 91 3 3.12267169503124 -0.122671695031237 92 2 3.03253043097617 -1.03253043097617 93 3 3.44006110372867 -0.440061103728667 94 3 3.04550977053849 -0.0455097705384864 95 3 2.7618141206773 0.238185879322702 96 4 3.23154305425204 0.768456945747957 97 4 3.68055359997645 0.319446400023546 98 4 2.97030278201533 1.02969721798467 99 3 3.00928079109926 -0.00928079109925973 100 4 3.69718573658768 0.302814263412324 101 4 3.06787692541964 0.932123074580357 102 3 2.50948899660956 0.490511003390441 103 4 3.77845519472799 0.221544805272014 104 3 3.68329866104475 -0.683298661044747 105 4 3.43748869480643 0.562511305193571 106 4 3.98755174562014 0.0124482543798581 107 3 3.46075961709178 -0.460759617091784 108 3 3.43585724160764 -0.435857241607643 109 3 3.39889277619317 -0.398892776193169 110 3 3.34515095836483 -0.345150958364829 111 3 2.8536840418715 0.146315958128501 112 2 2.47627522535683 -0.476275225356834 113 4 3.51411865127695 0.485881348723046 114 2 2.68016009567596 -0.680160095675958 115 3 3.04295864402470 -0.0429586440246957 116 3 3.26703062734443 -0.267030627344429 117 3 3.01473489141528 -0.0147348914152821 118 4 3.59286471027869 0.407135289721308 119 4 2.95935382020749 1.04064617979251 120 3 2.85290787088842 0.147092129111576 121 4 3.51089913984094 0.489100860159061 122 3 2.84794724038370 0.152052759616296 123 3 3.40761758308742 -0.407617583087424 124 3 3.32227996497736 -0.322279964977358 125 4 3.60934766251086 0.390652337489141 126 2 2.78797070293285 -0.787970702932848 127 4 3.36273627430461 0.637263725695393 128 3 3.33578661081299 -0.335786610812991 129 3 2.90287692685008 0.0971230731499242 130 4 3.48268886945931 0.517311130540689 131 4 2.96991773540729 1.03008226459271 132 4 3.47436399146294 0.525636008537059 133 3 2.9925201041931 0.00747989580690048 134 2 1.96547982993585 0.0345201700641528 135 4 3.51962394673519 0.480376053264806 136 2 3.41546168820379 -1.41546168820379 137 3 3.11214394452973 -0.112143944529734 138 4 3.47433460332435 0.525665396675651 139 3 3.07302071964316 -0.0730207196431601 140 3 2.79798136770197 0.202018632298028 141 3 3.15515675686842 -0.155156756868416 142 3 3.33253771123838 -0.332537711238383 143 4 3.49305292973301 0.506947070266987 144 3 3.48012426071773 -0.480124260717735 145 3 3.40066452274437 -0.400664522744374 146 2 2.69996216206853 -0.699962162068528 147 2 3.47976742123192 -1.47976742123192 148 3 2.89499484811797 0.105005151882032 149 4 3.41309693438830 0.586903065611695 150 3 3.01854560119812 -0.0185456011981236 151 4 3.36023581833786 0.639764181662143 152 3 4.18998885105445 -1.18998885105446 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 11 0.171952217541052 0.343904435082104 0.828047782458948 12 0.122609118576654 0.245218237153309 0.877390881423346 13 0.0884975763171005 0.176995152634201 0.9115024236829 14 0.864129903246083 0.271740193507834 0.135870096753917 15 0.812716356780949 0.374567286438103 0.187283643219051 16 0.739543708471578 0.520912583056843 0.260456291528422 17 0.652891574501867 0.694216850996266 0.347108425498133 18 0.60224129147102 0.795517417057959 0.397758708528979 19 0.529346735804414 0.941306528391173 0.470653264195586 20 0.50818580142493 0.98362839715014 0.49181419857507 21 0.474390299473599 0.948780598947198 0.525609700526401 22 0.412646721492868 0.825293442985736 0.587353278507132 23 0.351690068910916 0.703380137821833 0.648309931089084 24 0.288544200715735 0.57708840143147 0.711455799284265 25 0.228119103657113 0.456238207314227 0.771880896342887 26 0.357174673592138 0.714349347184275 0.642825326407862 27 0.407080731445707 0.814161462891415 0.592919268554293 28 0.489657432809911 0.979314865619823 0.510342567190089 29 0.998661607589402 0.00267678482119516 0.00133839241059758 30 0.997995973661821 0.00400805267635788 0.00200402633817894 31 0.996982898656564 0.00603420268687135 0.00301710134343568 32 0.99543792770544 0.00912414458911856 0.00456207229455928 33 0.995419718137902 0.0091605637241967 0.00458028186209835 34 0.993334758378006 0.0133304832439876 0.0066652416219938 35 0.991612878733668 0.0167742425326644 0.0083871212663322 36 0.987915226609526 0.0241695467809488 0.0120847733904744 37 0.985895165266602 0.0282096694667962 0.0141048347333981 38 0.98346462926298 0.0330707414740427 0.0165353707370213 39 0.977973517389443 0.0440529652211136 0.0220264826105568 40 0.987544593616975 0.0249108127660503 0.0124554063830252 41 0.983614645702218 0.0327707085955645 0.0163853542977823 42 0.98982576289816 0.0203484742036824 0.0101742371018412 43 0.98887567309613 0.0222486538077394 0.0111243269038697 44 0.993153669777963 0.0136926604440741 0.00684633022203705 45 0.994843843211456 0.0103123135770884 0.00515615678854418 46 0.99413759961897 0.0117248007620601 0.00586240038103003 47 0.991573215597037 0.0168535688059254 0.0084267844029627 48 0.99165275804185 0.0166944839163013 0.00834724195815066 49 0.989637084013514 0.0207258319729718 0.0103629159864859 50 0.986277479025604 0.0274450419487917 0.0137225209743958 51 0.984620675116844 0.030758649766313 0.0153793248831565 52 0.980283129338784 0.0394337413224317 0.0197168706612159 53 0.981626092849136 0.0367478143017269 0.0183739071508635 54 0.977454785925086 0.0450904281498283 0.0225452140749141 55 0.977416470880393 0.0451670582392141 0.0225835291196071 56 0.971817047208265 0.0563659055834709 0.0281829527917355 57 0.970165735799063 0.0596685284018733 0.0298342642009366 58 0.963200628062671 0.0735987438746578 0.0367993719373289 59 0.96588616624384 0.0682276675123207 0.0341138337561604 60 0.963935117981077 0.0721297640378458 0.0360648820189229 61 0.962592942371315 0.0748141152573708 0.0374070576286854 62 0.955487125469417 0.0890257490611663 0.0445128745305831 63 0.945650881430078 0.108698237139844 0.0543491185699219 64 0.940785548401206 0.118428903197587 0.0592144515987936 65 0.927727199357135 0.144545601285730 0.0722728006428651 66 0.922103371436918 0.155793257126164 0.0778966285630821 67 0.915270336887834 0.169459326224332 0.084729663112166 68 0.896446753257752 0.207106493484497 0.103553246742248 69 0.885043623417094 0.229912753165812 0.114956376582906 70 0.895866796891912 0.208266406216176 0.104133203108088 71 0.944346857519497 0.111306284961007 0.0556531424805034 72 0.939315032681565 0.121369934636869 0.0606849673184345 73 0.9368375942779 0.126324811444198 0.0631624057220992 74 0.920435886468814 0.159128227062372 0.079564113531186 75 0.901180182233299 0.197639635533403 0.0988198177667015 76 0.880336791234615 0.239326417530771 0.119663208765385 77 0.866903824514382 0.266192350971235 0.133096175485618 78 0.88911984389774 0.22176031220452 0.11088015610226 79 0.8771983865038 0.245603226992400 0.122801613496200 80 0.9171747202338 0.1656505595324 0.0828252797662 81 0.905600523837011 0.188798952325978 0.0943994761629891 82 0.894719874006029 0.210560251987942 0.105280125993971 83 0.891156264943364 0.217687470113271 0.108843735056636 84 0.90107892622924 0.197842147541522 0.098921073770761 85 0.895943496259109 0.208113007481783 0.104056503740891 86 0.889225849796188 0.221548300407623 0.110774150203811 87 0.877374326325982 0.245251347348036 0.122625673674018 88 0.888462564619943 0.223074870760115 0.111537435380057 89 0.864547738287824 0.270904523424351 0.135452261712176 90 0.84781372100652 0.304372557986959 0.152186278993480 91 0.82033631743037 0.359327365139261 0.179663682569630 92 0.88410864455302 0.231782710893959 0.115891355446980 93 0.882652288003871 0.234695423992257 0.117347711996129 94 0.861214312182143 0.277571375635714 0.138785687817857 95 0.832893053920462 0.334213892159077 0.167106946079538 96 0.829339954685078 0.341320090629844 0.170660045314922 97 0.798449094193552 0.403101811612897 0.201550905806448 98 0.84999423586624 0.300011528267519 0.150005764133759 99 0.819639922118308 0.360720155763383 0.180360077881691 100 0.789569321314826 0.420861357370347 0.210430678685174 101 0.826105384703389 0.347789230593222 0.173894615296611 102 0.821049605887552 0.357900788224896 0.178950394112448 103 0.79111239990415 0.417775200191698 0.208887600095849 104 0.78671647085539 0.426567058289219 0.213283529144610 105 0.772546098194831 0.454907803610338 0.227453901805169 106 0.729961771146403 0.540076457707193 0.270038228853597 107 0.705757445696397 0.588485108607205 0.294242554303603 108 0.68071270500046 0.63857458999908 0.31928729499954 109 0.669802369439678 0.660395261120644 0.330197630560322 110 0.663896381707675 0.67220723658465 0.336103618292325 111 0.616641466935771 0.766717066128458 0.383358533064229 112 0.585890483406649 0.828219033186703 0.414109516593351 113 0.541355109894088 0.917289780211824 0.458644890105912 114 0.590340185612371 0.819319628775258 0.409659814387629 115 0.538605179695526 0.922789640608947 0.461394820304474 116 0.508221205461786 0.983557589076429 0.491778794538214 117 0.457974135171095 0.91594827034219 0.542025864828905 118 0.407186029530148 0.814372059060296 0.592813970469852 119 0.448410465601944 0.896820931203889 0.551589534398056 120 0.399981239234595 0.79996247846919 0.600018760765405 121 0.359704156419390 0.719408312838779 0.64029584358061 122 0.306576000530677 0.613152001061353 0.693423999469323 123 0.301254374127556 0.602508748255112 0.698745625872444 124 0.292515562329718 0.585031124659436 0.707484437670282 125 0.238150959045272 0.476301918090543 0.761849040954728 126 0.370560505698418 0.741121011396837 0.629439494301582 127 0.311506905993472 0.623013811986943 0.688493094006528 128 0.412566145678119 0.825132291356239 0.58743385432188 129 0.409913423612080 0.819826847224159 0.59008657638792 130 0.378498118893802 0.756996237787604 0.621501881106198 131 0.445274956058693 0.890549912117387 0.554725043941307 132 0.40386260923388 0.80772521846776 0.59613739076612 133 0.41056489854262 0.82112979708524 0.58943510145738 134 0.328452171705213 0.656904343410427 0.671547828294787 135 0.430818719684303 0.861637439368607 0.569181280315697 136 0.42622873063782 0.85245746127564 0.57377126936218 137 0.33029339348261 0.66058678696522 0.66970660651739 138 0.266262642864930 0.532525285729861 0.73373735713507 139 0.185401881327281 0.370803762654562 0.814598118672719 140 0.134363826447379 0.268727652894757 0.865636173552621 141 0.0807869459053985 0.161573891810797 0.919213054094602 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 5 0.0381679389312977 NOK 5% type I error level 27 0.206106870229008 NOK 10% type I error level 34 0.259541984732824 NOK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 1 ; 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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