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 09:26:04 +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/t1291283274dpjzh2q7wwj1p7q.htm/, Retrieved Thu, 02 Dec 2010 10:48:09 +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/t1291283274dpjzh2q7wwj1p7q.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 clu data

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

2 5 2 2 1 1 1 4 1 3 1 4 1 7 3 3 1 5 1 7 2 2 1 2 2 5 2 1 1 1 2 5 1 1 1 1 1 4 1 3 1 2 2 4 3 3 2 1 1 6 1 1 1 1 2 5 1 1 1 1 1 1 1 1 1 3 2 5 1 1 1 1 1 4 2 1 2 1 2 6 3 1 1 1 2 7 2 2 1 2 2 7 3 3 1 4 1 2 2 1 1 1 1 6 1 1 1 1 1 3 1 1 1 2 2 6 1 1 1 3 2 6 1 3 1 1 1 5 1 1 1 1 2 6 3 2 1 1 2 4 1 3 2 1 2 3 3 1 2 2 2 4 1 1 1 1 2 5 1 1 2 1 2 6 1 1 2 1 1 6 3 3 2 1 1 4 1 1 1 1 2 6 1 3 1 1 1 6 1 1 1 1 2 5 1 3 1 1 2 6 3 1 1 1 2 4 1 1 1 1 1 6 1 1 1 1 2 7 1 3 1 1 1 5 2 3 1 1 1 6 1 3 1 1 2 6 1 1 2 1 1 5 2 2 2 4 2 7 2 3 1 1 2 6 2 2 1 1 1 3 1 1 1 4 1 4 1 1 1 2 2 5 2 3 1 2 2 4 2 3 2 1 1 3 1 1 1 1 2 5 3 1 1 2 2 5 1 1 1 1 1 4 1 2 1 1 1 5 1 1 1 1 2 1 2 2 1 1 2 2 1 1 2 1 2 3 3 3 1 1 1 4 2 2 1 2 1 3 3 3 1 1 1 7 1 1 1 1 1 2 1 1 1 1 1 4 3 1 1 2 1 2 1 1 1 1 2 5 1 1 1 2 2 6 1 2 1 4 2 6 1 2 1 1 2 6 1 1 1 1 1 6 2 2 1 1 2 6 3 3 1 2 2 6 1 1 1 3 1 6 1 3 1 1 1 4 2 2 1 1 1 4 2 2 1 1 2 5 3 3 1 1 1 6 2 3 1 1 1 6 1 1 1 1 1 7 3 2 1 1 1 6 2 3 1 1 2 6 1 3 2 1 1 6 1 2 1 2 2 3 2 1 1 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 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation Member[t] = + 1.04782670721478 + 0.0729570089347279Provison[t] + 0.0654005174473116Mother[t] + 0.00562364643803958Father[t] + 0.063112559403901Illness[t] -0.0432767813249698Tobacco[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) 1.04782670721478 0.223746 4.6831 6e-06 3e-06 Provison 0.0729570089347279 0.027802 2.6242 0.009578 0.004789 Mother 0.0654005174473116 0.053932 1.2127 0.227156 0.113578 Father 0.00562364643803958 0.049886 0.1127 0.910395 0.455197 Illness 0.063112559403901 0.11783 0.5356 0.593006 0.296503 Tobacco -0.0432767813249698 0.04231 -1.0229 0.308012 0.154006 Multiple Linear Regression - Regression Statistics Multiple R 0.256259646347524 R-squared 0.0656690063461582 Adjusted R-squared 0.0347308939735144 F-TEST (value) 2.12259253425637 F-TEST (DF numerator) 5 F-TEST (DF denominator) 151 p-value 0.0657160719619755 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.489914985929934 Sum Squared Residuals 36.2425207092478 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 2 1.57449585773801 0.42550414226199 2 1 1.31193163381913 -0.311931633819132 3 1 1.61832691419297 -0.618326914192972 4 1 1.67713309428253 -0.677133094282532 5 2 1.56887221130001 0.431127788699995 6 2 1.50347169385269 0.496528306147307 7 1 1.39848519646908 -0.398485196469075 8 2 1.63567557209257 0.364324427907431 9 1 1.57642870278742 -0.576428702787422 10 2 1.50347169385269 0.496528306147306 11 1 1.12509009546384 -0.125090095463842 12 2 1.50347169385269 0.496528306147306 13 1 1.55902776176918 -0.559027761769178 14 2 1.70722973768204 0.292770262317955 15 2 1.67713309428253 0.322866905717469 16 2 1.66160369551794 0.338396304482057 17 1 1.35000118449582 -0.350001184495821 18 1 1.57642870278742 -0.576428702787422 19 1 1.31428089465827 -0.314280894658268 20 2 1.48987514013748 0.510124859862518 21 2 1.5876759956635 0.412324004336499 22 1 1.50347169385269 -0.503471693852694 23 2 1.71285338412008 0.287146615879916 24 2 1.50487453719795 0.495125462802054 25 2 1.50819448895679 0.491805511043208 26 2 1.43051468491797 0.569485315082034 27 2 1.56658425325660 0.433415746743405 28 2 1.63954126219132 0.360458737808677 29 1 1.78158958996203 -0.781589589962025 30 1 1.43051468491797 -0.430514684917966 31 2 1.5876759956635 0.412324004336499 32 1 1.57642870278742 -0.576428702787422 33 2 1.51471898672877 0.485281013271227 34 2 1.70722973768204 0.292770262317955 35 2 1.43051468491797 0.569485315082034 36 1 1.57642870278742 -0.576428702787422 37 2 1.66063300459823 0.339366995401771 38 1 1.58011950417608 -0.580119504176085 39 1 1.5876759956635 -0.587675995663501 40 2 1.63954126219132 0.360458737808677 41 1 1.50777807316704 -0.507778073167037 42 2 1.72603352204554 0.273966477954459 43 2 1.64745286667277 0.352547133327227 44 1 1.22772733200833 -0.227727332008328 45 1 1.38723790359300 -0.387237903592996 46 2 1.53684272285112 0.463157277148885 47 2 1.57027505464526 0.429724945354742 48 1 1.35755767598324 -0.357557675983238 49 2 1.59099594742235 0.409004052577653 50 2 1.50347169385269 0.496528306147306 51 1 1.43613833135601 -0.436138331356005 52 1 1.50347169385269 -0.503471693852694 53 2 1.28266782199913 0.717332178000867 54 2 1.34771322645241 0.652286773547589 55 2 1.49960600375394 0.50039399624606 56 1 1.45826206747835 -0.458262067478347 57 1 1.49960600375394 -0.49960600375394 58 1 1.64938571172215 -0.64938571172215 59 1 1.28460066704851 -0.284600667048510 60 1 1.51803893848762 -0.518038938487619 61 1 1.28460066704851 -0.284600667048510 62 2 1.46019491252772 0.539805087472276 63 2 1.45222200525055 0.547777994749448 64 2 1.58205234922546 0.417947650774538 65 2 1.57642870278742 0.423571297212578 66 1 1.64745286667277 -0.647452866672773 67 2 1.67520024923315 0.324799750766846 68 2 1.48987514013748 0.510124859862518 69 1 1.5876759956635 -0.587675995663501 70 1 1.50153884880332 -0.501538848803317 71 1 1.50153884880332 -0.501538848803317 72 2 1.64552002162340 0.354479978376604 73 1 1.65307651311081 -0.653076513110813 74 1 1.57642870278742 -0.576428702787422 75 1 1.78581039305481 -0.785810393054812 76 1 1.65307651311081 -0.653076513110813 77 2 1.65078855506740 0.349211444932598 78 1 1.53877556790049 -0.538775567900492 79 2 1.42295819343055 0.577041806569451 80 2 1.58011950417608 0.419880495823915 81 2 1.65307651311081 0.346923486889187 82 2 1.50716249524136 0.492837504758643 83 1 1.64552002162340 -0.645520021623396 84 2 1.71285338412008 0.287146615879916 85 2 1.64745286667277 0.352547133327227 86 1 1.36880496885932 -0.368804968859317 87 2 1.60979973178584 0.390200268214157 88 2 1.50347169385269 0.496528306147306 89 1 1.57642870278742 -0.576428702787422 90 1 1.43051468491797 -0.430514684917966 91 2 1.71478622916946 0.285213770830539 92 2 1.57449585773805 0.425504142261955 93 2 1.60417608534780 0.395823914652197 94 1 1.64745286667277 -0.647452866672773 95 2 1.47996938781093 0.520030612189066 96 1 1.71249827112605 -0.712498271126051 97 2 1.65307651311081 0.346923486889187 98 1 1.64745286667277 -0.647452866672773 99 1 1.67520024923315 -0.675200249233154 100 2 1.57642870278742 0.423571297212578 101 2 1.19804710439857 0.80195289560143 102 1 1.43051468491797 -0.430514684917966 103 2 1.57256301268867 0.427436987311332 104 2 1.65307651311081 0.346923486889187 105 1 1.55896645897346 -0.558966458973456 106 1 1.70722973768204 -0.707229737682045 107 1 1.58205234922546 -0.582052349225461 108 1 1.34771322645241 -0.347713226452411 109 2 1.7204098756075 0.279590124392499 110 1 1.21726730455182 -0.217267304551821 111 1 1.43051468491797 -0.430514684917966 112 1 1.24501468711220 -0.245014687112202 113 1 1.60417608534780 -0.604176085347803 114 2 1.51762252269786 0.482377477302136 115 1 1.52324616913590 -0.523246169135903 116 2 1.7204098756075 0.279590124392499 117 1 1.5876759956635 -0.587675995663501 118 2 1.43051468491797 0.569485315082034 119 2 1.57256301268867 0.427436987311332 120 1 1.44659835881251 -0.446598358812513 121 1 1.69738528815122 -0.697385288151218 122 2 1.64938571172215 0.35061428827785 123 2 1.43051468491797 0.569485315082034 124 1 1.50153884880332 -0.501538848803317 125 2 1.56089930402283 0.439100695977166 126 2 1.78018674661677 0.219813253383227 127 2 1.50347169385269 0.496528306147306 128 2 1.71285338412008 0.287146615879916 129 1 1.58073508210176 -0.580735082101765 130 2 1.58864668658321 0.411353313416785 131 2 1.58011950417608 0.419880495823915 132 2 1.60610893039718 0.39389106960282 133 2 1.57256301268867 0.427436987311332 134 1 1.59855243890976 -0.598552438909764 135 1 1.71847703055812 -0.718477030558124 136 2 1.63385631295756 0.366143687042438 137 2 1.67520024923315 0.324799750766846 138 2 1.67520024923315 0.324799750766846 139 2 1.50909534029073 0.490904659709266 140 1 1.56887221130001 -0.568872211300005 141 2 1.46019491252772 0.539805087472276 142 2 1.65307651311081 0.346923486889187 143 2 1.72706551576098 0.272934484239024 144 1 1.68046878267716 -0.68046878267716 145 1 1.43613833135601 -0.436138331356005 146 2 1.64745286667277 0.352547133327227 147 2 1.60417608534780 0.395823914652197 148 2 1.64938571172215 0.35061428827785 149 1 1.53315192146245 -0.533151921462452 150 2 1.65500935816019 0.34499064183981 151 2 1.49925089075991 0.500749109240094 152 2 1.58205234922546 0.417947650774538 153 1 1.57256301268867 -0.572563012688668 154 1 1.43051468491797 -0.430514684917966 155 2 1.78018674661677 0.219813253383227 156 1 1.43613833135601 -0.436138331356005 157 2 1.84329930602067 0.156700693979326 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 9 0.259412884927412 0.518825769854825 0.740587115072588 10 0.204708323978147 0.409416647956294 0.795291676021853 11 0.525192110391727 0.949615779216545 0.474807889608273 12 0.477197214714661 0.954394429429322 0.522802785285339 13 0.471278075579662 0.942556151159323 0.528721924420338 14 0.383237304985793 0.766474609971586 0.616762695014207 15 0.387121238321916 0.774242476643833 0.612878761678084 16 0.436827899554817 0.873655799109634 0.563172100445183 17 0.555123002192842 0.889753995614316 0.444876997807158 18 0.580854972716702 0.838290054566596 0.419145027283298 19 0.505268920935858 0.989462158128285 0.494731079064142 20 0.622269849617579 0.755460300764842 0.377730150382421 21 0.574557316881648 0.850885366236704 0.425442683118352 22 0.584214403626372 0.831571192747257 0.415785596373628 23 0.513391637198033 0.973216725603933 0.486608362801967 24 0.513244357879264 0.973511284241472 0.486755642120736 25 0.513078670592997 0.973842658814006 0.486921329407003 26 0.52649363936254 0.94701272127492 0.47350636063746 27 0.484139746833141 0.968279493666281 0.515860253166859 28 0.428333188642814 0.856666377285628 0.571666811357186 29 0.606359056544349 0.787281886911303 0.393640943455651 30 0.60446569401692 0.79106861196616 0.39553430598308 31 0.574430171781297 0.851139656437405 0.425569828218703 32 0.611757616293592 0.776484767412816 0.388242383706408 33 0.590818050955562 0.818363898088877 0.409181949044438 34 0.546210476924343 0.907579046151314 0.453789523075657 35 0.548906995597458 0.902186008805084 0.451093004402542 36 0.5801481867163 0.8397036265674 0.4198518132837 37 0.537570941216598 0.924858117566804 0.462429058783402 38 0.583161950548487 0.833676098903025 0.416838049451513 39 0.610884610076304 0.778230779847391 0.389115389923696 40 0.574596940150516 0.850806119698969 0.425403059849484 41 0.562704427651694 0.874591144696612 0.437295572348306 42 0.521511585262234 0.956976829475533 0.478488414737766 43 0.488313902061253 0.976627804122506 0.511686097938747 44 0.441736354965111 0.883472709930223 0.558263645034889 45 0.417957294395924 0.835914588791848 0.582042705604076 46 0.412964344136113 0.825928688272225 0.587035655863887 47 0.389627879123596 0.779255758247192 0.610372120876404 48 0.370270705250082 0.740541410500164 0.629729294749918 49 0.352433399800832 0.704866799601665 0.647566600199168 50 0.348761564775214 0.697523129550428 0.651238435224786 51 0.34383744204846 0.68767488409692 0.65616255795154 52 0.350336978132839 0.700673956265677 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0.696521925315939 0.348260962657970 106 0.724690200513603 0.550619598972794 0.275309799486397 107 0.755380027256592 0.489239945486815 0.244619972743408 108 0.725579081510449 0.548841836979102 0.274420918489551 109 0.688121595039745 0.623756809920509 0.311878404960254 110 0.644399834657539 0.711200330684923 0.355600165342461 111 0.635255273357683 0.729489453284633 0.364744726642317 112 0.589154340093502 0.821691319812996 0.410845659906498 113 0.633596258547969 0.732807482904063 0.366403741452031 114 0.636787446984013 0.726425106031973 0.363212553015987 115 0.636147791820344 0.727704416359313 0.363852208179656 116 0.590086272220564 0.819827455558871 0.409913727779436 117 0.655362719065248 0.689274561869503 0.344637280934752 118 0.677724001606667 0.644551996786666 0.322275998393333 119 0.667599015819533 0.664801968360935 0.332400984180467 120 0.66948033689992 0.661039326200161 0.330519663100081 121 0.677861338354092 0.644277323291815 0.322138661645908 122 0.631930790773522 0.736138418452957 0.368069209226478 123 0.664412186339045 0.67117562732191 0.335587813660955 124 0.657088963295667 0.685822073408666 0.342911036704333 125 0.633315438319995 0.73336912336001 0.366684561680005 126 0.576296870964927 0.847406258070147 0.423703129035073 127 0.575471848680909 0.849056302638182 0.424528151319091 128 0.519837739591899 0.960324520816202 0.480162260408101 129 0.543642606529941 0.912714786940118 0.456357393470059 130 0.495766076018386 0.991532152036771 0.504233923981614 131 0.47164660296408 0.94329320592816 0.52835339703592 132 0.422887557619965 0.84577511523993 0.577112442380035 133 0.442854911645646 0.885709823291293 0.557145088354354 134 0.510490987125635 0.97901802574873 0.489509012874365 135 0.618905414544388 0.762189170911225 0.381094585455612 136 0.551668256341769 0.896663487316462 0.448331743658231 137 0.490024382512277 0.980048765024554 0.509975617487723 138 0.448030038720837 0.896060077441675 0.551969961279163 139 0.452139455560086 0.904278911120171 0.547860544439914 140 0.4996347288623 0.9992694577246 0.5003652711377 141 0.608770395001238 0.782459209997525 0.391229604998762 142 0.554940671241365 0.89011865751727 0.445059328758635 143 0.515761486521094 0.968477026957811 0.484238513478906 144 0.851610237853437 0.296779524293125 0.148389762146562 145 0.781267291470078 0.437465417059845 0.218732708529922 146 0.699738864973273 0.600522270053454 0.300261135026727 147 0.866363200846664 0.267273598306673 0.133636799153336 148 0.736388356069854 0.527223287860291 0.263611643930146 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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