Workshop 7 data 1

*Unverified author*

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

Title produced by software: Multiple Regression

Date of computation: Fri, 20 Nov 2009 10:42:34 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Nov/20/t1258739488n7gtf948m7i48t6.htm/, Retrieved Fri, 20 Nov 2009 18:51:40 +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/2009/Nov/20/t1258739488n7gtf948m7i48t6.htm/}, year = {2009}, } @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 = {2009}, 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 «

543 0 594 0 611 0 613 0 611 0 594 0 595 0 591 0 589 0 584 0 573 0 567 0 569 0 621 0 629 0 628 0 612 0 595 0 597 0 593 0 590 0 580 0 574 0 573 0 573 0 620 0 626 0 620 0 588 0 566 0 557 0 561 0 549 0 532 0 526 0 511 0 499 0 555 0 565 0 542 0 527 0 510 0 514 0 517 0 508 0 493 0 490 0 469 1 478 1 528 1 534 1 518 1 506 1 502 1 516 1 528 1 533 1 536 1 537 1 524 1 536 1

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 3 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Yt[t] = + 569.68085106383 -52.1808510638297X[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) 569.68085106383 5.308843 107.3079 0 0 X -52.1808510638297 11.081557 -4.7088 1.6e-05 8e-06 Multiple Linear Regression - Regression Statistics Multiple R 0.522642943159927 R-squared 0.273155646034871 Adjusted R-squared 0.260836250204954 F-TEST (value) 22.1728118656207 F-TEST (DF numerator) 1 F-TEST (DF denominator) 59 p-value 1.55495900285851e-05 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 36.3955931319028 Sum Squared Residuals 78153.7127659575 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 543 569.680851063832 -26.6808510638318 2 594 569.68085106383 24.3191489361702 3 611 569.68085106383 41.3191489361703 4 613 569.68085106383 43.3191489361703 5 611 569.68085106383 41.3191489361703 6 594 569.68085106383 24.3191489361703 7 595 569.68085106383 25.3191489361703 8 591 569.68085106383 21.3191489361703 9 589 569.68085106383 19.3191489361703 10 584 569.68085106383 14.3191489361703 11 573 569.68085106383 3.31914893617026 12 567 569.68085106383 -2.68085106382974 13 569 569.68085106383 -0.680851063829743 14 621 569.68085106383 51.3191489361703 15 629 569.68085106383 59.3191489361703 16 628 569.68085106383 58.3191489361703 17 612 569.68085106383 42.3191489361703 18 595 569.68085106383 25.3191489361703 19 597 569.68085106383 27.3191489361703 20 593 569.68085106383 23.3191489361703 21 590 569.68085106383 20.3191489361703 22 580 569.68085106383 10.3191489361703 23 574 569.68085106383 4.31914893617026 24 573 569.68085106383 3.31914893617026 25 573 569.68085106383 3.31914893617026 26 620 569.68085106383 50.3191489361703 27 626 569.68085106383 56.3191489361703 28 620 569.68085106383 50.3191489361703 29 588 569.68085106383 18.3191489361703 30 566 569.68085106383 -3.68085106382974 31 557 569.68085106383 -12.6808510638297 32 561 569.68085106383 -8.68085106382974 33 549 569.68085106383 -20.6808510638297 34 532 569.68085106383 -37.6808510638297 35 526 569.68085106383 -43.6808510638297 36 511 569.68085106383 -58.6808510638297 37 499 569.68085106383 -70.6808510638297 38 555 569.68085106383 -14.6808510638297 39 565 569.68085106383 -4.68085106382974 40 542 569.68085106383 -27.6808510638297 41 527 569.68085106383 -42.6808510638297 42 510 569.68085106383 -59.6808510638297 43 514 569.68085106383 -55.6808510638297 44 517 569.68085106383 -52.6808510638297 45 508 569.68085106383 -61.6808510638297 46 493 569.68085106383 -76.6808510638297 47 490 569.68085106383 -79.6808510638297 48 469 517.5 -48.5 49 478 517.5 -39.5 50 528 517.5 10.5 51 534 517.5 16.5 52 518 517.5 0.500000000000005 53 506 517.5 -11.5 54 502 517.5 -15.5 55 516 517.5 -1.49999999999999 56 528 517.5 10.5 57 533 517.5 15.5 58 536 517.5 18.5 59 537 517.5 19.5 60 524 517.5 6.5 61 536 517.5 18.5 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 0.550132965500736 0.899734068998529 0.449867034499264 6 0.381458253837893 0.762916507675786 0.618541746162107 7 0.246813233244325 0.49362646648865 0.753186766755675 8 0.149967196209082 0.299934392418165 0.850032803790918 9 0.0865867027370563 0.173173405474113 0.913413297262944 10 0.0494182516752721 0.0988365033505441 0.950581748324728 11 0.0336218657637210 0.0672437315274419 0.96637813423628 12 0.026009855272522 0.052019710545044 0.973990144727478 13 0.0176698752155813 0.0353397504311626 0.982330124784419 14 0.0249370605876578 0.0498741211753156 0.975062939412342 15 0.0455819908046473 0.0911639816092946 0.954418009195353 16 0.0696055914909289 0.139211182981858 0.930394408509071 17 0.0632861641017665 0.126572328203533 0.936713835898233 18 0.0455554183754321 0.0911108367508643 0.954444581624568 19 0.0336006850517908 0.0672013701035816 0.96639931494821 20 0.0243648604488628 0.0487297208977256 0.975635139551137 21 0.0176786915741185 0.0353573831482369 0.982321308425882 22 0.0133883297601658 0.0267766595203315 0.986611670239834 23 0.0109438997866438 0.0218877995732875 0.989056100213356 24 0.00897516827345616 0.0179503365469123 0.991024831726544 25 0.00728029601630014 0.0145605920326003 0.9927197039837 26 0.0175403999280261 0.0350807998560522 0.982459600071974 27 0.0689996629398558 0.137999325879712 0.931000337060144 28 0.224410108785943 0.448820217571887 0.775589891214057 29 0.316731087610318 0.633462175220637 0.683268912389682 30 0.392848377236862 0.785696754473724 0.607151622763138 31 0.480995131820644 0.961990263641288 0.519004868179356 32 0.576310544693019 0.847378910613962 0.423689455306981 33 0.667362866823171 0.665274266353657 0.332637133176829 34 0.763392215504913 0.473215568990174 0.236607784495087 35 0.831715935835388 0.336568128329223 0.168284064164612 36 0.901591587703332 0.196816824593336 0.0984084122966678 37 0.955693973591153 0.0886120528176943 0.0443060264088472 38 0.963915076190692 0.0721698476186156 0.0360849238093078 39 0.98609585842938 0.0278082831412398 0.0139041415706199 40 0.990592183933436 0.0188156321331274 0.00940781606656369 41 0.991606576924803 0.0167868461503948 0.0083934230751974 42 0.9914334121037 0.0171331757926007 0.00856658789630036 43 0.990462023284222 0.0190759534315563 0.00953797671577814 44 0.989777981312145 0.0204440373757092 0.0102220186878546 45 0.98835430754682 0.0232913849063585 0.0116456924531792 46 0.98602561392603 0.0279487721479376 0.0139743860739688 47 0.982139072442474 0.0357218551150519 0.0178609275575259 48 0.996160277351776 0.00767944529644774 0.00383972264822387 49 0.999737208116572 0.000525583766855598 0.000262791883427799 50 0.99925449736343 0.00149100527314026 0.000745502636570132 51 0.998269480739515 0.00346103852097008 0.00173051926048504 52 0.995142470686393 0.00971505862721429 0.00485752931360714 53 0.993770813446771 0.0124583731064580 0.00622918655322901 54 0.998354632604871 0.00329073479025708 0.00164536739512854 55 0.998841455704154 0.00231708859169218 0.00115854429584609 56 0.99389267488076 0.0122146502384779 0.00610732511923893 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 7 0.134615384615385 NOK 5% type I error level 27 0.519230769230769 NOK 10% type I error level 35 0.673076923076923 NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Nov/20/t1258739488n7gtf948m7i48t6/109vo11258738950.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/20/t1258739488n7gtf948m7i48t6/109vo11258738950.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/20/t1258739488n7gtf948m7i48t6/15h461258738950.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/20/t1258739488n7gtf948m7i48t6/15h461258738950.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/20/t1258739488n7gtf948m7i48t6/2ncnu1258738950.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/20/t1258739488n7gtf948m7i48t6/2ncnu1258738950.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/20/t1258739488n7gtf948m7i48t6/3km1s1258738950.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/20/t1258739488n7gtf948m7i48t6/3km1s1258738950.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/20/t1258739488n7gtf948m7i48t6/4r1b31258738950.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/20/t1258739488n7gtf948m7i48t6/4r1b31258738950.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/20/t1258739488n7gtf948m7i48t6/5m8xo1258738950.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/20/t1258739488n7gtf948m7i48t6/5m8xo1258738950.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/20/t1258739488n7gtf948m7i48t6/6dk9n1258738950.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/20/t1258739488n7gtf948m7i48t6/6dk9n1258738950.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/20/t1258739488n7gtf948m7i48t6/7aqhk1258738950.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/20/t1258739488n7gtf948m7i48t6/7aqhk1258738950.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/20/t1258739488n7gtf948m7i48t6/8q9911258738950.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/20/t1258739488n7gtf948m7i48t6/8q9911258738950.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/20/t1258739488n7gtf948m7i48t6/9te351258738950.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/20/t1258739488n7gtf948m7i48t6/9te351258738950.ps (open in new window)

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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