Workshop 10 (2)

*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: Sun, 12 Dec 2010 10:42:03 +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/12/t1292150871zrpy0qij51kw5cp.htm/, Retrieved Sun, 12 Dec 2010 11:48:02 +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/12/t1292150871zrpy0qij51kw5cp.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 «

13 15 42 14 13 12 18 51 8 13 15 11 42 12 16 12 16 46 7 12 10 12 41 10 11 12 17 49 7 12 15 15 47 16 18 9 19 33 11 11 12 16 33 14 14 11 18 47 6 9 11 10 42 16 14 11 14 32 11 12 15 18 53 16 11 7 18 41 12 12 11 14 41 7 13 11 14 33 13 11 10 12 37 11 12 14 16 43 15 16 10 15 45 7 9 6 13 33 9 11 11 16 49 7 13 15 14 42 14 15 11 9 43 15 10 12 9 37 7 11 14 17 43 15 13 15 13 42 17 16 9 15 43 15 15 13 17 46 14 14 13 16 33 14 14 16 12 42 8 14 13 11 40 8 8 12 16 44 14 13 14 17 42 14 15 11 17 52 8 13 9 16 44 11 11 16 13 45 16 15 12 12 46 10 15 10 12 36 8 9 13 16 45 14 13 16 14 49 16 16 14 12 43 13 13 15 12 43 5 11 5 14 37 8 12 8 8 32 10 12 11 15 45 8 12 16 14 45 13 14 17 11 45 15 14 9 13 45 6 8 9 14 31 12 13 13 15 33 16 16 10 16 44 5 13 6 10 49 15 11 12 11 44 12 14 8 12 41 8 13 14 14 44 13 13 12 15 38 14 13 11 16 33 12 12 16 9 47 16 16 8 11 37 10 15 15 15 48 15 15 7 15 40 8 12 16 13 50 16 14 14 17 54 19 12 16 17 43 14 15 9 15 54 6 12 14 13 44 13 13 11 15 47 15 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 10 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 R Framework error message The field 'Names of X columns' contains a hard return which cannot be interpreted. Please, resubmit your request without hard returns in the 'Names of X columns'. Multiple Linear Regression - Estimated Regression Equation Y1[t] = -0.996170178492618 -0.0268429787707296X1[t] + 0.0790401730395211X2[t] + 0.323763854841615X3[t] + 0.474394463844188`X4 `[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) -0.996170178492618 1.607037 -0.6199 0.536284 0.268142 X1 -0.0268429787707296 0.077845 -0.3448 0.730712 0.365356 X2 0.0790401730395211 0.025026 3.1584 0.001921 0.000961 X3 0.323763854841615 0.058811 5.5052 0 0 `X4 ` 0.474394463844188 0.093995 5.047 1e-06 1e-06 Multiple Linear Regression - Regression Statistics Multiple R 0.6876699174452 R-squared 0.472889915359088 Adjusted R-squared 0.458739309060003 F-TEST (value) 33.4183500949828 F-TEST (DF numerator) 4 F-TEST (DF denominator) 149 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 2.16086383895017 Sum Squared Residuals 695.730547041885 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 13 12.6206944053634 0.37930559463656 2 12 11.3089438973572 0.691056102642809 3 15 13.5037220022956 1.49627799770435 4 12 10.1692706710153 1.83072932898474 5 10 10.3783388215812 -0.378338821581222 6 12 10.3795482113631 1.62045178863692 7 15 16.0353952994652 -1.03539529946516 8 9 9.88188044071155 -0.881880440711552 9 12 12.3568843330811 -0.35688433308115 10 11 8.44767764013913 2.55232235986087 11 11 13.8768314727444 -2.87683147274445 12 11 10.4114496253699 0.588550374630133 13 15 13.1083461544808 1.89165384551922 14 7 11.3392031224843 -4.33920312248425 15 11 10.3021502272033 0.697849772796714 16 11 10.6636230442484 0.336376955751568 17 10 10.8603364481089 -0.860336448108933 18 14 14.4198388460064 -0.419838846006353 19 10 8.69389008521389 1.30610991478611 20 6 9.3954106036527 -3.3954106036527 21 11 10.880785653978 0.119214346022004 22 15 13.5963263118225 1.40367368817751 23 11 11.7613729143363 -0.761372914336336 24 12 9.17141550121048 2.82858449878953 25 14 12.9698124757031 1.03018752429694 26 15 15.0688553189623 -0.0688553189622511 27 9 13.9722873609329 -4.9722873609329 28 13 13.3575636038242 -0.357563603824196 29 13 12.3568843330811 0.64311566691885 30 16 11.2330346764701 4.76696532352993 31 13 8.25543052609663 4.74456947390337 32 12 12.7519317726717 -0.751931772671696 33 14 13.5157973755103 0.484202624489701 34 11 11.4148270491674 -0.414827049167445 35 9 10.8318512804585 -1.83185128045848 36 16 14.5078175193950 1.49218248060499 37 12 12.6711175421556 -0.671117542155571 38 10 8.386821319012 1.61317868098800 39 13 12.8309719457112 0.169028054288782 40 16 15.2715296966266 0.728470303373445 41 14 12.4564996598735 1.54350034012652 42 15 8.91759989345218 6.08240010654782 43 5 9.83535892604263 -4.83535892604263 44 8 10.2487436431526 -2.24874364315263 45 11 10.4408373315881 0.559162668411931 46 16 13.0352885122552 2.96471148774475 47 17 13.7633451582507 3.23665484174933 48 9 7.94941772406955 1.05058227593045 49 9 11.1305677710161 -2.13056777101615 50 13 13.9800439492235 -0.980043949223485 51 10 9.83805707909716 0.161942920902841 52 6 12.6831654376469 -6.68316543764692 53 12 12.7130134206863 -0.713013420686302 54 8 10.6796000395864 -2.67960003958636 55 14 12.4818538753715 1.51814612462846 56 12 12.3045337132053 -0.304533713205298 57 11 10.7605676957095 0.239432304290455 58 16 15.2476642444012 0.752335755598839 59 8 11.9865989635706 -3.98659896357061 60 15 14.3674882261305 0.632511773869499 61 7 10.0456364663905 -3.04563646639046 62 16 14.4286239207484 1.57137607925157 63 14 14.6599153346601 -0.659915334660067 64 16 13.5948375485498 2.40516245145018 65 9 10.5046711792605 -1.50467117926053 66 14 12.5086968541423 1.49130314585773 67 11 12.8652646615584 -1.86526466155842 68 13 9.22227735781366 3.77772264218634 69 15 12.5340510696403 2.46594893035967 70 5 5.01075348269169 -0.0107534826916893 71 15 12.7787747514424 2.22122524855757 72 13 12.7189743944901 0.281025605509896 73 11 12.3609178238013 -1.36091782380129 74 11 14.5704694550089 -3.57046945500892 75 12 11.3154910958659 0.684508904134079 76 12 13.2382422634104 -1.23824226341036 77 12 11.4886243417050 0.511375658295036 78 12 12.6130912426799 -0.613091242679853 79 14 11.6013925628969 2.39860743710305 80 6 9.45015252536896 -3.45015252536896 81 7 6.53342271119727 0.466577288802734 82 14 11.8493790654483 2.15062093455169 83 14 13.8796830514060 0.120316948593959 84 10 11.4404606381563 -1.44046063815631 85 13 9.54858594010274 3.45141405989726 86 12 11.0513741723696 0.948625827630432 87 9 9.36229979986405 -0.362299799864049 88 12 12.7831150933767 -0.783115093376685 89 16 13.9646841982494 2.03531580175064 90 10 10.6094983668960 -0.609498366895977 91 14 13.1440232427271 0.855976757272909 92 10 13.5081942128268 -3.50819421282677 93 16 15.0597633930061 0.940236606993947 94 15 13.6112257859754 1.38877421402457 95 12 11.4911690691524 0.508830930847565 96 10 9.22823833161746 0.77176166838254 97 8 8.56878867432662 -0.568788674326625 98 8 9.35171911063518 -1.35171911063518 99 11 13.8066038521703 -2.80660385217032 100 13 12.2026840521152 0.797315947884813 101 16 14.9744553949486 1.02554460505139 102 14 13.5405559036547 0.459444096345263 103 11 10.4703784634133 0.529621536586671 104 4 7.3558828231419 -3.3558828231419 105 14 13.0634943064149 0.936505693585098 106 9 10.9648842622536 -1.96488426225358 107 14 14.0781705127431 -0.0781705127431459 108 8 11.8268764286118 -3.82687642861184 109 8 13.0050292871282 -5.00502928712819 110 11 12.4475611595243 -1.44756115952434 111 12 13.2874619311338 -1.28746193113381 112 11 10.4333875945116 0.566612405488402 113 14 13.5618801703682 0.438119829631772 114 15 13.7915509524103 1.20844904758968 115 16 12.4642562481641 3.53574375183593 116 16 13.8571588575594 2.14284114244061 117 14 13.4725386815906 0.527461318409354 118 14 11.5778124048755 2.42218759512451 119 12 12.1312470417592 -0.131247041759196 120 14 13.7676639431747 0.232336056825257 121 8 10.5304581938565 -2.53045819385646 122 13 13.2607723779701 -0.260772377970143 123 16 13.7350134162073 2.26498658379273 124 12 11.3475769551387 0.652423044861346 125 16 14.6776879444848 1.32231205551522 126 12 13.0488526487426 -1.04885264874258 127 11 11.3541241536474 -0.354124153647380 128 4 5.60295304595373 -1.60295304595373 129 16 14.3093300580579 1.69066994194209 130 15 12.2893273878382 2.71067261216176 131 10 12.2847292294234 -2.28472922942336 132 13 13.4944766507324 -0.494476650732376 133 15 13.0889744697967 1.91102553020329 134 12 11.5029591481632 0.497040851836835 135 14 13.7350134162073 0.264986583792729 136 7 12.8232153574206 -5.82321535742063 137 19 14.2616050743203 4.73839492567975 138 12 13.2009720210178 -1.20097202101782 139 12 13.0594333379714 -1.05943333797145 140 13 13.4917784976778 -0.491778497677845 141 15 14.8864767215599 0.113523278440050 142 8 7.8736403717793 0.126359628220702 143 12 11.774525808736 0.225474191264012 144 10 9.8319426796863 0.168057320313702 145 8 11.1793487189286 -3.17934871892861 146 10 14.7358461125574 -4.73584611255738 147 15 13.7948137731596 1.20518622684041 148 16 13.1605649057598 2.83943509424024 149 13 12.0805386107631 0.919461389236928 150 16 15.1326891666347 0.867310833365288 151 9 11.4759627437854 -2.47596274378538 152 14 12.8966014078705 1.10339859212953 153 14 12.8308185201042 1.16918147989584 154 12 12.8888448195799 -0.888844819579876 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 8 0.122295528643141 0.244591057286282 0.877704471356859 9 0.0480362566872007 0.0960725133744013 0.9519637433128 10 0.0397219524321037 0.0794439048642075 0.960278047567896 11 0.0410006855100272 0.0820013710200545 0.958999314489973 12 0.0182749768316880 0.0365499536633759 0.981725023168312 13 0.0518876561373771 0.103775312274754 0.948112343862623 14 0.350265460647852 0.700530921295705 0.649734539352148 15 0.262635888502977 0.525271777005953 0.737364111497023 16 0.211599397603859 0.423198795207719 0.78840060239614 17 0.159451252941621 0.318902505883242 0.840548747058379 18 0.111887894198079 0.223775788396159 0.88811210580192 19 0.0760020904624192 0.152004180924838 0.92399790953758 20 0.133114101885191 0.266228203770382 0.866885898114809 21 0.106130865003053 0.212261730006106 0.893869134996947 22 0.103622766471158 0.207245532942315 0.896377233528842 23 0.0736758489767836 0.147351697953567 0.926324151023216 24 0.0941172663080095 0.188234532616019 0.90588273369199 25 0.0824674982851736 0.164934996570347 0.917532501714826 26 0.0601833469515753 0.120366693903151 0.939816653048425 27 0.202952211524517 0.405904423049033 0.797047788475483 28 0.158389011064893 0.316778022129786 0.841610988935107 29 0.151701962357905 0.303403924715811 0.848298037642095 30 0.278195983767821 0.556391967535642 0.721804016232179 31 0.398535105750248 0.797070211500495 0.601464894249752 32 0.342933830852711 0.685867661705422 0.657066169147289 33 0.304704332912259 0.609408665824519 0.695295667087741 34 0.286798207921088 0.573596415842175 0.713201792078912 35 0.287432631573007 0.574865263146013 0.712567368426993 36 0.275241456258855 0.55048291251771 0.724758543741145 37 0.254429080914762 0.508858161829525 0.745570919085238 38 0.219460618096459 0.438921236192918 0.780539381903541 39 0.180977130327486 0.361954260654973 0.819022869672514 40 0.153109892553383 0.306219785106767 0.846890107446617 41 0.1326557916651 0.2653115833302 0.8673442083349 42 0.292963712875834 0.585927425751668 0.707036287124166 43 0.5817129369753 0.836574126049399 0.418287063024699 44 0.607652639865722 0.784694720268555 0.392347360134277 45 0.561614015547539 0.876771968904922 0.438385984452461 46 0.59866072181978 0.80267855636044 0.40133927818022 47 0.638378490082785 0.72324301983443 0.361621509917215 48 0.612648012662566 0.774703974674868 0.387351987337434 49 0.588247236376275 0.823505527247451 0.411752763623725 50 0.557381650314967 0.885236699370066 0.442618349685033 51 0.514487082754772 0.971025834490456 0.485512917245228 52 0.910659095783542 0.178681808432916 0.089340904216458 53 0.89381268654461 0.212374626910780 0.106187313455390 54 0.915186564420892 0.169626871158215 0.0848134355791076 55 0.905114543143451 0.189770913713099 0.0948854568565493 56 0.884196155100995 0.231607689798011 0.115803844899005 57 0.861807858614069 0.276384282771863 0.138192141385931 58 0.836192466996715 0.327615066006569 0.163807533003285 59 0.899065337980423 0.201869324039153 0.100934662019577 60 0.877749944340806 0.244500111318388 0.122250055659194 61 0.902236779760657 0.195526440478686 0.0977632202393432 62 0.8892069763304 0.221586047339202 0.110793023669601 63 0.869328653228496 0.261342693543009 0.130671346771504 64 0.877216306091028 0.245567387817944 0.122783693908972 65 0.88033124929142 0.239337501417159 0.119668750708580 66 0.866353436604929 0.267293126790142 0.133646563395071 67 0.861627761946789 0.276744476106422 0.138372238053211 68 0.912061630616419 0.175876738767162 0.0879383693835812 69 0.916856386836403 0.166287226327194 0.083143613163597 70 0.899848763080267 0.200302473839466 0.100151236919733 71 0.900684849228096 0.198630301543808 0.0993151507719041 72 0.878698553476471 0.242602893047057 0.121301446523529 73 0.865023676089467 0.269952647821066 0.134976323910533 74 0.909026652653155 0.18194669469369 0.0909733473468451 75 0.891686659323597 0.216626681352806 0.108313340676403 76 0.877250342467122 0.245499315065756 0.122749657532878 77 0.854780767187685 0.290438465624630 0.145219232812315 78 0.828933413710888 0.342133172578223 0.171066586289112 79 0.839268951348324 0.321462097303352 0.160731048651676 80 0.880387314475978 0.239225371048044 0.119612685524022 81 0.859770295763191 0.280459408473617 0.140229704236809 82 0.859778731714419 0.280442536571162 0.140221268285581 83 0.831603609746586 0.336792780506829 0.168396390253414 84 0.813624985259714 0.372750029480571 0.186375014740286 85 0.878717506008067 0.242564987983866 0.121282493991933 86 0.858707535497189 0.282584929005623 0.141292464502811 87 0.832994859632823 0.334010280734354 0.167005140367177 88 0.805480812887628 0.389038374224744 0.194519187112372 89 0.799626727596245 0.400746544807509 0.200373272403755 90 0.766670029623622 0.466659940752756 0.233329970376378 91 0.736710419889539 0.526579160220922 0.263289580110461 92 0.804316818760653 0.391366362478694 0.195683181239347 93 0.77383781355849 0.45232437288302 0.22616218644151 94 0.748934940960345 0.502130118079311 0.251065059039655 95 0.713159852468703 0.573680295062594 0.286840147531297 96 0.684206401815491 0.631587196369018 0.315793598184509 97 0.644461422331675 0.71107715533665 0.355538577668325 98 0.612525957742574 0.774948084514853 0.387474042257426 99 0.656905999815574 0.686188000368853 0.343094000184426 100 0.620471175795513 0.759057648408973 0.379528824204486 101 0.579453453522351 0.841093092955297 0.420546546477649 102 0.57028877593993 0.85942244812014 0.42971122406007 103 0.559617340682954 0.880765318634093 0.440382659317046 104 0.590525754063268 0.818948491873465 0.409474245936732 105 0.550212161228172 0.899575677543656 0.449787838771828 106 0.573334705732857 0.853330588534285 0.426665294267143 107 0.527453180966574 0.945093638066853 0.472546819033426 108 0.654462849267741 0.691074301464517 0.345537150732259 109 0.785880208043771 0.428239583912457 0.214119791956229 110 0.780924543041382 0.438150913917236 0.219075456958618 111 0.760857225765021 0.478285548469958 0.239142774234979 112 0.720792699861737 0.558414600276527 0.279207300138263 113 0.673597197000813 0.652805605998375 0.326402802999187 114 0.631283310641212 0.737433378717575 0.368716689358788 115 0.652830080565779 0.694339838868442 0.347169919434221 116 0.656938895396043 0.686122209207913 0.343061104603957 117 0.604288961811493 0.791422076377014 0.395711038188507 118 0.621730696997076 0.756538606005848 0.378269303002924 119 0.564958658661469 0.870082682677063 0.435041341338531 120 0.515103770791667 0.969792458416666 0.484896229208333 121 0.559339727688492 0.881320544623016 0.440660272311508 122 0.507994604861184 0.984010790277633 0.492005395138816 123 0.507815987971629 0.984368024056742 0.492184012028371 124 0.502394350368667 0.995211299262667 0.497605649631333 125 0.451342524516146 0.902685049032291 0.548657475483854 126 0.400905716902107 0.801811433804214 0.599094283097893 127 0.381318569120824 0.762637138241648 0.618681430879176 128 0.327962614477013 0.655925228954025 0.672037385522987 129 0.276812664913321 0.553625329826642 0.723187335086679 130 0.325668640441461 0.651337280882923 0.674331359558539 131 0.324866010870884 0.649732021741768 0.675133989129116 132 0.266426151880435 0.532852303760869 0.733573848119565 133 0.241485190543775 0.48297038108755 0.758514809456225 134 0.200894692104940 0.401789384209881 0.79910530789506 135 0.151682338169898 0.303364676339797 0.848317661830101 136 0.304318496616007 0.608636993232013 0.695681503383993 137 0.618123740907624 0.763752518184752 0.381876259092376 138 0.555618026657775 0.88876394668445 0.444381973342225 139 0.622928716664113 0.754142566671774 0.377071283335887 140 0.590192064155411 0.819615871689179 0.409807935844589 141 0.555701325198505 0.88859734960299 0.444298674801495 142 0.512178975484287 0.975642049031426 0.487821024515713 143 0.394752986446904 0.789505972893807 0.605247013553096 144 0.461618124716159 0.923236249432319 0.538381875283841 145 0.388749714177449 0.777499428354898 0.611250285822551 146 0.758901524687866 0.482196950624269 0.241098475312134 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 1 0.00719424460431655 OK 10% type I error level 4 0.0287769784172662 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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This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa

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