Personal Standards (Yt)

*The author of this computation has been verified*

R Software Module: /rwasp_multipleregression.wasp (opens new window with default values)

Title produced by software: Multiple Regression

Date of computation: Tue, 23 Nov 2010 16:42:52 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Nov/23/t1290530539uqzymgn7wdm6up0.htm/, Retrieved Tue, 23 Nov 2010 17:42:22 +0100

BibTeX entries for LaTeX users:

@Manual{KEY, author = {{YOUR NAME}}, publisher = {Office for Research Development and Education}, title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2010/Nov/23/t1290530539uqzymgn7wdm6up0.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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24 24 14 11 12 25 25 11 7 8 30 17 6 17 8 19 18 12 10 8 22 18 8 12 9 22 16 10 12 7 25 20 10 11 4 23 16 11 11 11 17 18 16 12 7 21 17 11 13 7 19 23 13 14 12 19 30 12 16 10 15 23 8 11 10 16 18 12 10 8 23 15 11 11 8 27 12 4 15 4 22 21 9 9 9 14 15 8 11 8 22 20 8 17 7 23 31 14 17 11 23 27 15 11 9 21 34 16 18 11 19 21 9 14 13 18 31 14 10 8 20 19 11 11 8 23 16 8 15 9 25 20 9 15 6 19 21 9 13 9 24 22 9 16 9 22 17 9 13 6 25 24 10 9 6 26 25 16 18 16 29 26 11 18 5 32 25 8 12 7 25 17 9 17 9 29 32 16 9 6 28 33 11 9 6 17 13 16 12 5 28 32 12 18 12 29 25 12 12 7 26 29 14 18 10 25 22 9 14 9 14 18 10 15 8 25 17 9 16 5 26 20 10 10 8 20 15 12 11 8 18 20 14 14 10 32 33 14 9 6 25 29 10 12 8 25 23 14 17 7 23 26 16 5 4 21 18 9 12 8 20 20 10 12 8 15 11 6 6 4 30 28 8 24 20 24 26 13 12 8 26 22 10 12 8 24 17 8 14 6 22 12 7 7 4 14 14 15 13 8 24 17 9 12 9 24 21 10 13 6 24 19 12 14 7 24 18 13 8 9 19 10 10 11 5 31 29 11 9 5 22 31 8 11 8 27 19 9 13 8 19 9 13 10 6 25 20 11 11 8 etc...

Output produced by software:

Enter (or paste) a matrix (table) containing all data (time) series. Every column represents a different variable and must be delimited by a space or Tab. Every row represents a period in time (or category) and must be delimited by hard returns. The easiest way to enter data is to copy and paste a block of spreadsheet cells. Please, do not use commas or spaces to seperate groups of digits! Summary of computational transaction Raw Input view raw input (R code) Raw Output view raw output of R engine Computing time 8 seconds R Server 'RServer@AstonUniversity' @ vre.aston.ac.uk Multiple Linear Regression - Estimated Regression Equation PS[t] = + 15.4323237613405 + 0.364294694129429CM[t] -0.321728388550003D[t] + 0.142655035713217PE[t] -0.0849617358950159PC[t] + 1.18753715676232M1[t] + 0.582940513559847M2[t] + 1.4142918417762M3[t] + 1.37572882776538M4[t] + 1.13169308310493M5[t] + 1.21435808901099M6[t] + 1.63067391786142M7[t] + 2.61302398862814M8[t] + 2.20955916043914M9[t] + 1.17050255859489M10[t] + 0.130689993576573M11[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) 15.4323237613405 2.046627 7.5404 0 0 CM 0.364294694129429 0.064801 5.6217 0 0 D -0.321728388550003 0.126426 -2.5448 0.011995 0.005997 PE 0.142655035713217 0.116233 1.2273 0.221719 0.110859 PC -0.0849617358950159 0.148896 -0.5706 0.569159 0.28458 M1 1.18753715676232 1.467547 0.8092 0.419745 0.209873 M2 0.582940513559847 1.492804 0.3905 0.696748 0.348374 M3 1.4142918417762 1.47771 0.9571 0.34014 0.17007 M4 1.37572882776538 1.510899 0.9105 0.364072 0.182036 M5 1.13169308310493 1.518284 0.7454 0.457268 0.228634 M6 1.21435808901099 1.52834 0.7946 0.428186 0.214093 M7 1.63067391786142 1.532172 1.0643 0.288992 0.144496 M8 2.61302398862814 1.511423 1.7289 0.085994 0.042997 M9 2.20955916043914 1.498284 1.4747 0.142484 0.071242 M10 1.17050255859489 1.495098 0.7829 0.434984 0.217492 M11 0.130689993576573 1.544946 0.0846 0.932704 0.466352 Multiple Linear Regression - Regression Statistics Multiple R 0.516397323766253 R-squared 0.266666195992948 Adjusted R-squared 0.189743069698502 F-TEST (value) 3.46665832291065 F-TEST (DF numerator) 15 F-TEST (DF denominator) 143 p-value 4.76876238936219e-05 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 3.79586465897246 Sum Squared Residuals 2060.42815682077 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 24 21.4084006996143 2.59159930038574 2 25 21.9025107169184 3.0974892830816 3 30 22.8546967919815 7.1453032080185 4 19 20.2514728908076 -1.25147289080757 5 22 21.4946990358786 0.505300964121442 6 22 20.3752413482158 1.62475865178422 7 25 22.3609661255558 2.63903387444424 8 23 20.9696768799896 2.03032312001035 9 17 20.1686614766028 -3.16866147660277 10 21 20.5166071590923 0.483392840907681 11 19 20.7369523379887 -1.73695233798871 12 19 23.9332871350846 -4.93328713508462 13 15 23.1443998085749 -8.14439980857486 14 16 19.458684576602 -3.45868457660204 15 23 19.6615352466933 3.33846475330668 16 27 21.6926539565772 5.30734604342283 17 22 21.8378896225772 0.162110377422807 18 14 20.4267866595781 -6.42678665957812 19 22 23.60546790925 -1.60546790925002 20 23 26.3248423405604 -3.32484234056038 21 23 23.4564636048144 -0.456463604814387 22 21 25.4744032515286 -4.47440325152863 23 19 21.2103147680349 -2.21031476803485 24 18 22.9681183096248 -4.96811830962476 25 20 20.8919593381972 -0.891959338197159 26 23 20.6453221852143 2.35467781478574 27 25 22.8670091090834 2.13299089091662 28 19 22.6525455100905 -3.65254551009051 29 24 23.2007695666991 0.79923043330086 30 22 21.2888812025034 0.711118797496557 31 25 23.362911358857 1.63708864114299 32 26 23.2134637549219 2.78653624507807 33 29 25.7175146584576 3.28248534154245 34 32 24.2534948420646 7.74650515793545 35 25 20.5209480422368 4.47905195776315 36 29 22.716224662731 6.28377533726899 37 28 25.8766984563728 2.12330154362723 38 17 16.8904928308664 0.109507169133642 39 28 26.1915549647561 1.80844503524392 40 29 23.171807557035 5.82819244296497 41 26 24.3425388183865 1.65746118161345 42 25 22.9981245011788 2.00187549882124 43 14 21.8631499365697 -7.8631499365697 44 25 23.2004739451553 1.79952605484474 45 26 22.4573493888402 3.5426506111598 46 20 19.096017574962 0.903982425037993 47 18 19.4922633388405 -1.49226333884045 48 32 23.7239761339604 8.27602386603956 49 25 24.9992897037547 0.00071029624532456 50 25 21.7202482560367 3.27975174396329 51 23 21.5440516686678 1.45594833133221 52 21 21.501968127884 -0.501968127884017 53 20 21.6647933829324 -1.66479338293243 54 15 19.2396364251744 -4.23963642517439 55 30 26.4139081456428 3.58609185435724 56 24 24.3667072875822 -0.3667072875822 57 26 23.4712488485255 2.52875115147451 58 24 21.7094090963506 2.29059090364944 59 22 18.3411896710326 3.65881032896738 60 14 16.8813452280141 -2.88134522801411 61 24 20.8645200268565 3.13547997314349 62 24 21.79291401502 2.20708598497998 63 24 21.3099124776957 2.6900875223043 64 24 19.5594726949361 4.44052730506388 65 19 18.13407661361 0.86592338639004 66 31 24.5313023479987 6.46869765200126 67 22 26.6718175944994 -4.67181759449943 68 27 23.2462130185894 3.75378698141058 69 19 17.6548460595565 1.34515394044351 70 25 21.2392194341592 3.76078056584084 71 20 24.3065663594345 -4.30656635943452 72 21 20.1475306230034 0.85246937699657 73 27 26.0283161576787 0.971683842321257 74 23 23.3870961243964 -0.387096124396441 75 25 25.05277727386 -0.0527772738599558 76 20 23.0017132099812 -3.00171320998116 77 21 18.1403954773297 2.85960452267035 78 22 21.6686446413993 0.33135535860068 79 23 20.870712675033 2.12928732496696 80 25 26.0513319604443 -1.05133196044432 81 25 22.5213615523781 2.47863844762191 82 17 22.1192719886503 -5.11927198865032 83 19 20.5272832461467 -1.5272832461467 84 25 21.5772537479903 3.42274625200966 85 19 21.2108730496103 -2.21087304961026 86 20 21.8141889977146 -1.81418899771465 87 26 22.423917007705 3.57608299229505 88 23 18.3724769956061 4.62752300439394 89 27 23.9965438863506 3.00345611364937 90 17 21.4681254306041 -4.46812543060407 91 17 23.3479388996919 -6.3479388996919 92 19 20.7111226188485 -1.71112261884852 93 17 20.7906723957443 -3.79067239574431 94 22 23.0300808256109 -1.03008082561092 95 21 20.3086454803214 0.69135451967861 96 32 25.4843903130901 6.5156096869099 97 21 23.9978570962449 -2.99785709624493 98 21 23.9455911656014 -2.94559116560143 99 18 21.9897875719193 -3.98978757191928 100 18 22.7800735515649 -4.78007355156495 101 23 23.0157191006703 -0.0157191006703341 102 19 21.0610935556314 -2.06109355563137 103 20 23.3141643844414 -3.3141643844414 104 21 23.3190333126464 -2.3190333126464 105 20 22.2360514809517 -2.23605148095166 106 17 22.3503929468413 -5.35039294684134 107 18 21.4711934291021 -3.47119342910208 108 19 22.2847390288184 -3.2847390288184 109 22 22.4282772724915 -0.428277272491546 110 15 18.9061666485891 -3.90616664858907 111 14 20.1257477956927 -6.12574779569271 112 18 25.6974166570011 -7.69741665700112 113 24 21.9896945393372 2.01030546066284 114 35 25.1351620317299 9.8648379682701 115 29 18.6179407859273 10.3820592140727 116 21 22.7299425324362 -1.72994253243619 117 25 24.3785534989033 0.6214465010967 118 20 20.0309487521345 -0.0309487521344678 119 22 21.5413535810958 0.458646418904167 120 13 19.9805987120047 -6.98059871200469 121 26 24.3041330802187 1.69586691978135 122 17 18.6935059959558 -1.69350599595577 123 25 21.4194928394039 3.58050716059607 124 20 20.0448056915565 -0.0448056915564629 125 19 17.5975563963451 1.40244360365489 126 21 22.1390051788546 -1.13900517885456 127 22 21.0402943962954 0.959705603704602 128 24 22.6817408641924 1.31825913580759 129 21 22.2144184075392 -1.21441840753919 130 26 25.0098652921917 0.990134707808268 131 24 20.9584211211411 3.04157887885891 132 16 19.3976499118598 -3.39764991185978 133 23 21.0617119347234 1.93828806527665 134 18 20.21420065041 -2.21420065041004 135 16 22.3116868357331 -6.31168683573312 136 26 24.1007289406351 1.89927105936486 137 19 20.1409423008136 -1.14094230081359 138 21 20.4331055232978 0.566894476702186 139 21 21.6293851765056 -0.629385176505612 140 22 22.4847198315894 -0.484719831589402 141 23 24.5857660043262 -1.58576600432624 142 29 24.9611346579663 4.03886534203371 143 21 21.5263751135402 -0.526375113540181 144 21 18.8303630803259 2.16963691967413 145 23 21.5781369559503 1.42186304404974 146 27 22.491591165329 4.508408834671 147 25 26.9046756082485 -1.90467560824849 148 21 22.1728642163247 -1.17286421632468 149 10 20.4443812590697 -10.4443812590697 150 20 23.2348911538338 -3.23489115383375 151 26 22.9013426117307 3.09865738826931 152 24 24.7007316530439 -0.700731653043916 153 29 30.3470926233603 -1.34709262336033 154 19 23.2091541784477 -4.20915417844771 155 24 21.0584935110847 2.94150648891528 156 19 20.0745231134925 -1.07452311349246 157 24 23.205426419712 0.794573580287986 158 22 21.1374866713458 0.862513328654194 159 17 24.3431548085598 -7.34315480855979 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 19 0.608608438383602 0.782783123232795 0.391391561616398 20 0.95934633517793 0.08130732964414 0.04065366482207 21 0.946385770088966 0.107228459822069 0.0536142299110343 22 0.914331835385903 0.171336329228195 0.0856681646140974 23 0.865323332375598 0.269353335248805 0.134676667624402 24 0.821406039795468 0.357187920409063 0.178593960204532 25 0.750097172192068 0.499805655615865 0.249902827807932 26 0.697155990382783 0.605688019234435 0.302844009617217 27 0.656418216644454 0.687163566711092 0.343581783355546 28 0.622696906864119 0.754606186271762 0.377303093135881 29 0.541877742132009 0.916244515735981 0.458122257867991 30 0.481020670707198 0.962041341414395 0.518979329292802 31 0.417653022865185 0.835306045730369 0.582346977134815 32 0.422132157568433 0.844264315136866 0.577867842431567 33 0.416922054809742 0.833844109619484 0.583077945190258 34 0.593028032550688 0.813943934898624 0.406971967449312 35 0.58569258102303 0.828614837953941 0.41430741897697 36 0.750827369987106 0.498345260025788 0.249172630012894 37 0.697547742023785 0.60490451595243 0.302452257976215 38 0.655638208292424 0.688723583415152 0.344361791707576 39 0.60675013403792 0.786499731924161 0.393249865962081 40 0.656625280309514 0.686749439380971 0.343374719690486 41 0.609593922562435 0.78081215487513 0.390406077437565 42 0.600041122326102 0.799917755347796 0.399958877673898 43 0.675821309567245 0.64835738086551 0.324178690432755 44 0.672355216880823 0.655289566238353 0.327644783119177 45 0.66129623133333 0.67740753733334 0.33870376866667 46 0.606582840439208 0.786834319121584 0.393417159560792 47 0.561371956046201 0.877256087907597 0.438628043953799 48 0.68690285340554 0.62619429318892 0.31309714659446 49 0.634500073007418 0.730999853985164 0.365499926992582 50 0.615328223892246 0.769343552215507 0.384671776107754 51 0.636646161716862 0.726707676566276 0.363353838283138 52 0.586846381024557 0.826307237950887 0.413153618975443 53 0.55187244596643 0.896255108067141 0.448127554033571 54 0.589529149170756 0.820941701658488 0.410470850829244 55 0.676821401432472 0.646357197135056 0.323178598567528 56 0.63470801358738 0.73058397282524 0.36529198641262 57 0.596419646568122 0.807160706863755 0.403580353431878 58 0.556681671808855 0.88663665638229 0.443318328191145 59 0.53717567644293 0.925648647114141 0.46282432355707 60 0.499697825945402 0.999395651890805 0.500302174054598 61 0.49800147973507 0.99600295947014 0.501998520264929 62 0.462541750120747 0.925083500241493 0.537458249879253 63 0.440134007209294 0.880268014418587 0.559865992790706 64 0.470302875299826 0.940605750599652 0.529697124700174 65 0.426179543813603 0.852359087627205 0.573820456186397 66 0.516180291180141 0.967639417639717 0.483819708819859 67 0.560395270686864 0.879209458626273 0.439604729313136 68 0.548480462503033 0.903039074993935 0.451519537496967 69 0.508971703441287 0.982056593117425 0.491028296558713 70 0.50264406016146 0.994711879677081 0.49735593983854 71 0.548963457060948 0.902073085878104 0.451036542939052 72 0.500292604081047 0.999414791837907 0.499707395918953 73 0.45123762374089 0.90247524748178 0.54876237625911 74 0.403507695523349 0.807015391046698 0.596492304476651 75 0.400447073382302 0.800894146764603 0.599552926617698 76 0.393013085788849 0.786026171577699 0.606986914211151 77 0.39019227676727 0.780384553534541 0.60980772323273 78 0.344284747493176 0.688569494986351 0.655715252506824 79 0.320079951974776 0.640159903949551 0.679920048025224 80 0.289845559831988 0.579691119663977 0.710154440168012 81 0.266092260563939 0.532184521127879 0.733907739436061 82 0.316256440885889 0.632512881771778 0.683743559114111 83 0.277060993555666 0.554121987111332 0.722939006444334 84 0.268075594860185 0.536151189720369 0.731924405139815 85 0.240923909643306 0.481847819286611 0.759076090356694 86 0.214780938206791 0.429561876413583 0.785219061793209 87 0.259589489984524 0.519178979969049 0.740410510015476 88 0.306271985878659 0.612543971757317 0.693728014121341 89 0.285726905496725 0.571453810993451 0.714273094503275 90 0.302898301376723 0.605796602753447 0.697101698623277 91 0.412150537496999 0.824301074993998 0.587849462503001 92 0.37502210939285 0.7500442187857 0.62497789060715 93 0.367417383538672 0.734834767077344 0.632582616461328 94 0.326517579364397 0.653035158728794 0.673482420635603 95 0.283109647006484 0.566219294012967 0.716890352993516 96 0.407235572856445 0.81447114571289 0.592764427143555 97 0.405724641482921 0.811449282965841 0.59427535851708 98 0.389495648219371 0.778991296438741 0.610504351780629 99 0.394187094206399 0.788374188412798 0.6058129057936 100 0.406878201669573 0.813756403339146 0.593121798330427 101 0.370189415239293 0.740378830478585 0.629810584760708 102 0.33960019820761 0.67920039641522 0.66039980179239 103 0.362611253843539 0.725222507687078 0.637388746156461 104 0.324747767764176 0.649495535528351 0.675252232235824 105 0.297057687241027 0.594115374482054 0.702942312758973 106 0.342609400519543 0.685218801039086 0.657390599480457 107 0.342711920399037 0.685423840798075 0.657288079600963 108 0.317356514824533 0.634713029649066 0.682643485175467 109 0.278276529384782 0.556553058769565 0.721723470615218 110 0.280427513151955 0.56085502630391 0.719572486848045 111 0.295487955854742 0.590975911709484 0.704512044145258 112 0.44033713952287 0.88067427904574 0.55966286047713 113 0.447785838380425 0.89557167676085 0.552214161619575 114 0.848912948522607 0.302174102954786 0.151087051477393 115 0.973413767817784 0.0531724643644324 0.0265862321822162 116 0.962352363986002 0.0752952720279959 0.037647636013998 117 0.964904683514543 0.0701906329709143 0.0350953164854572 118 0.950445699965474 0.0991086000690527 0.0495543000345263 119 0.950692614008457 0.0986147719830853 0.0493073859915426 120 0.98177993798644 0.0364401240271208 0.0182200620135604 121 0.972940938981177 0.0541181220376453 0.0270590610188226 122 0.96312094696173 0.0737581060765401 0.0368790530382701 123 0.989342927390955 0.021314145218091 0.0106570726090455 124 0.982545718635904 0.0349085627281916 0.0174542813640958 125 0.977426903714553 0.0451461925708941 0.0225730962854471 126 0.964740299145436 0.0705194017091277 0.0352597008545638 127 0.952095437105497 0.095809125789005 0.0479045628945025 128 0.940856017016032 0.118287965967935 0.0591439829839676 129 0.939212304227733 0.121575391544535 0.0607876957722674 130 0.914638256735996 0.170723486528008 0.085361743264004 131 0.874731281039574 0.250537437920852 0.125268718960426 132 0.824944303145245 0.35011139370951 0.175055696854755 133 0.781960662863033 0.436078674273935 0.218039337136967 134 0.713349765858321 0.573300468283358 0.286650234141679 135 0.6378199510814 0.724360097837199 0.362180048918599 136 0.54947368894526 0.90105262210948 0.45052631105474 137 0.664138690909855 0.67172261818029 0.335861309090145 138 0.71445060665474 0.57109878669052 0.28554939334526 139 0.58399847012426 0.83200305975148 0.41600152987574 140 0.415003606844583 0.830007213689165 0.584996393155417 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 4 0.0327868852459016 OK 10% type I error level 14 0.114754098360656 NOK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Include Monthly 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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