Workshop 7

*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, 19 Nov 2009 13:00:46 -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/19/t1258660888990q65ewn7ufsjp.htm/, Retrieved Thu, 19 Nov 2009 21:01:40 +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/19/t1258660888990q65ewn7ufsjp.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:

Workshop 7 link 3

Dataseries X:

» Textbox « » Textfile « » CSV «

449 0 452 0 462 0 455 0 461 0 461 0 463 0 462 0 456 0 455 0 456 0 472 0 472 0 471 0 465 0 459 0 465 0 468 0 467 0 463 0 460 0 462 0 461 0 476 0 476 0 471 0 453 0 443 0 442 0 444 0 438 0 427 0 424 0 416 0 406 0 431 0 434 0 418 0 412 0 404 0 409 0 412 1 406 1 398 1 397 1 385 1 390 1 413 1 413 1 401 1 397 1 397 1 409 1 419 1 424 1 428 1 430 1 424 1 433 1 456 1 459 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 5 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Y[t] = + 483.691428571429 -11.4133928571428X[t] -3.96173611111105M1[t] -17.4843650793651M2[t] -21.4641964285714M3[t] -26.8440277777778M4[t] -20.4238591269841M5[t] -13.7210119047619M6[t] -14.1008432539683M7[t] -17.2806746031746M8[t] -18.6605059523810M9[t] -22.8403373015873M10[t] -21.2201686507937M11[t] -0.820168650793652t + 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) 483.691428571429 10.494045 46.092 0 0 X -11.4133928571428 9.098821 -1.2544 0.215906 0.107953 M1 -3.96173611111105 11.574235 -0.3423 0.733659 0.36683 M2 -17.4843650793651 12.142857 -1.4399 0.156527 0.078263 M3 -21.4641964285714 12.126631 -1.77 0.083213 0.041607 M4 -26.8440277777778 12.115197 -2.2157 0.03159 0.015795 M5 -20.4238591269841 12.10857 -1.6867 0.098283 0.049142 M6 -13.7210119047619 12.146916 -1.1296 0.264382 0.132191 M7 -14.1008432539683 12.120481 -1.1634 0.250544 0.125272 M8 -17.2806746031746 12.09881 -1.4283 0.159819 0.079909 M9 -18.6605059523810 12.081927 -1.5445 0.129175 0.064588 M10 -22.8403373015873 12.069854 -1.8923 0.064614 0.032307 M11 -21.2201686507937 12.062604 -1.7592 0.085057 0.042529 t -0.820168650793652 0.241493 -3.3962 0.001398 0.000699 Multiple Linear Regression - Regression Statistics Multiple R 0.76690115829855 R-squared 0.588137386599658 Adjusted R-squared 0.474217940339989 F-TEST (value) 5.16274794084806 F-TEST (DF numerator) 13 F-TEST (DF denominator) 47 p-value 1.37133299228376e-05 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 19.0688290645920 Sum Squared Residuals 17090.1513690476 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 449 478.909523809523 -29.9095238095235 2 452 464.566726190476 -12.5667261904762 3 462 459.766726190476 2.2332738095238 4 455 453.566726190476 1.43327380952374 5 461 459.166726190476 1.83327380952379 6 461 465.049404761905 -4.04940476190479 7 463 463.849404761905 -0.84940476190481 8 462 459.849404761905 2.15059523809525 9 456 457.649404761905 -1.64940476190476 10 455 452.649404761905 2.35059523809522 11 456 453.449404761905 2.55059523809523 12 472 473.849404761905 -1.84940476190477 13 472 469.0675 2.93249999999991 14 471 454.724702380952 16.2752976190476 15 465 449.924702380952 15.0752976190476 16 459 443.724702380952 15.2752976190476 17 465 449.324702380952 15.6752976190476 18 468 455.207380952381 12.7926190476190 19 467 454.007380952381 12.9926190476191 20 463 450.007380952381 12.9926190476190 21 460 447.807380952381 12.1926190476190 22 462 442.807380952381 19.1926190476191 23 461 443.607380952381 17.3926190476190 24 476 464.007380952381 11.9926190476190 25 476 459.225476190476 16.7745238095237 26 471 444.882678571429 26.1173214285714 27 453 440.082678571429 12.9173214285714 28 443 433.882678571429 9.11732142857146 29 442 439.482678571429 2.51732142857144 30 444 445.365357142857 -1.36535714285713 31 438 444.165357142857 -6.16535714285712 32 427 440.165357142857 -13.1653571428571 33 424 437.965357142857 -13.9653571428571 34 416 432.965357142857 -16.9653571428571 35 406 433.765357142857 -27.7653571428571 36 431 454.165357142857 -23.1653571428571 37 434 449.383452380952 -15.3834523809524 38 418 435.040654761905 -17.0406547619047 39 412 430.240654761905 -18.2406547619048 40 404 424.040654761905 -20.0406547619047 41 409 429.640654761905 -20.6406547619048 42 412 424.10994047619 -12.1099404761905 43 406 422.90994047619 -16.9099404761905 44 398 418.90994047619 -20.9099404761905 45 397 416.70994047619 -19.7099404761905 46 385 411.70994047619 -26.7099404761905 47 390 412.50994047619 -22.5099404761905 48 413 432.90994047619 -19.9099404761905 49 413 428.128035714286 -15.1280357142858 50 401 413.785238095238 -12.7852380952381 51 397 408.985238095238 -11.9852380952381 52 397 402.785238095238 -5.78523809523807 53 409 408.385238095238 0.614761904761917 54 419 414.267916666667 4.73208333333334 55 424 413.067916666667 10.9320833333334 56 428 409.067916666667 18.9320833333333 57 430 406.867916666667 23.1320833333333 58 424 401.867916666667 22.1320833333333 59 433 402.667916666667 30.3320833333333 60 456 423.067916666667 32.9320833333333 61 459 418.286011904762 40.7139880952381 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.0567678577580559 0.113535715516112 0.943232142241944 18 0.0171422508672685 0.034284501734537 0.982857749132731 19 0.00547092909035969 0.0109418581807194 0.99452907090964 20 0.00205654063939279 0.00411308127878558 0.997943459360607 21 0.000591869430322539 0.00118373886064508 0.999408130569677 22 0.000174969646268988 0.000349939292537975 0.99982503035373 23 5.69802119387683e-05 0.000113960423877537 0.999943019788061 24 1.84628907941010e-05 3.69257815882019e-05 0.999981537109206 25 7.78241757841023e-06 1.55648351568205e-05 0.999992217582422 26 9.0285995226325e-06 1.8057199045265e-05 0.999990971400477 27 0.000633450145352484 0.00126690029070497 0.999366549854648 28 0.0179369438120853 0.0358738876241706 0.982063056187915 29 0.347441500971369 0.694883001942738 0.652558499028631 30 0.61236363330171 0.775272733396581 0.387636366698290 31 0.838348859805008 0.323302280389984 0.161651140194992 32 0.935796435895031 0.128407128209938 0.0642035641049688 33 0.961609181886978 0.076781636226045 0.0383908181130225 34 0.985894334535324 0.0282113309293518 0.0141056654646759 35 0.989937587496556 0.0201248250068872 0.0100624125034436 36 0.986188714461378 0.027622571077244 0.013811285538622 37 0.974310925087187 0.0513781498256265 0.0256890749128133 38 0.965508506799553 0.0689829864008929 0.0344914932004465 39 0.952838537719198 0.0943229245616049 0.0471614622808024 40 0.923133025481806 0.153733949036388 0.0768669745181939 41 0.86750735071664 0.264985298566721 0.132492649283361 42 0.949694242275446 0.100611515449108 0.0503057577245541 43 0.981933543850821 0.0361329122983578 0.0180664561491789 44 0.975813948459364 0.0483721030812725 0.0241860515406362 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 8 0.285714285714286 NOK 5% type I error level 16 0.571428571428571 NOK 10% type I error level 20 0.714285714285714 NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Nov/19/t1258660888990q65ewn7ufsjp/10rvg41258660840.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/19/t1258660888990q65ewn7ufsjp/10rvg41258660840.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/19/t1258660888990q65ewn7ufsjp/13l6t1258660840.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/19/t1258660888990q65ewn7ufsjp/13l6t1258660840.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/19/t1258660888990q65ewn7ufsjp/2vz2g1258660840.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/19/t1258660888990q65ewn7ufsjp/2vz2g1258660840.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/19/t1258660888990q65ewn7ufsjp/3l0661258660840.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/19/t1258660888990q65ewn7ufsjp/3l0661258660840.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/19/t1258660888990q65ewn7ufsjp/4vv5w1258660840.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/19/t1258660888990q65ewn7ufsjp/4vv5w1258660840.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/19/t1258660888990q65ewn7ufsjp/5orxq1258660840.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/19/t1258660888990q65ewn7ufsjp/5orxq1258660840.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/19/t1258660888990q65ewn7ufsjp/6rhxn1258660840.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/19/t1258660888990q65ewn7ufsjp/6rhxn1258660840.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/19/t1258660888990q65ewn7ufsjp/7h10p1258660840.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/19/t1258660888990q65ewn7ufsjp/7h10p1258660840.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/19/t1258660888990q65ewn7ufsjp/89cca1258660840.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/19/t1258660888990q65ewn7ufsjp/89cca1258660840.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/19/t1258660888990q65ewn7ufsjp/98zkv1258660840.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/19/t1258660888990q65ewn7ufsjp/98zkv1258660840.ps (open in new window)

Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;

R code (references can be found in the software module):

library(lattice) library(lmtest) n25 <- 25 #minimum number of obs. for Goldfeld-Quandt test par1 <- as.numeric(par1) x <- t(y) k <- length(x[1,]) n <- length(x[,1]) x1 <- cbind(x[,par1], x[,1:k!=par1]) mycolnames <- c(colnames(x)[par1], colnames(x)[1:k!=par1]) colnames(x1) <- mycolnames #colnames(x)[par1] x <- x1 if (par3 == 'First Differences'){ x2 <- array(0, dim=c(n-1,k), dimnames=list(1:(n-1), paste('(1-B)',colnames(x),sep=''))) for (i in 1:n-1) { for (j in 1:k) { x2[i,j] <- x[i+1,j] - x[i,j] } } x <- x2 } if (par2 == 'Include Monthly Dummies'){ x2 <- array(0, dim=c(n,11), dimnames=list(1:n, paste('M', seq(1:11), sep =''))) for (i in 1:11){ x2[seq(i,n,12),i] <- 1 } x <- cbind(x, x2) } if (par2 == 'Include Quarterly Dummies'){ x2 <- array(0, dim=c(n,3), dimnames=list(1:n, paste('Q', seq(1:3), sep =''))) for (i in 1:3){ x2[seq(i,n,4),i] <- 1 } x <- cbind(x, x2) } k <- length(x[1,]) if (par3 == 'Linear Trend'){ x <- cbind(x, c(1:n)) colnames(x)[k+1] <- 't' } x k <- length(x[1,]) df <- as.data.frame(x) (mylm <- lm(df)) (mysum <- summary(mylm)) if (n > n25) { kp3 <- k + 3 nmkm3 <- n - k - 3 gqarr <- array(NA, dim=c(nmkm3-kp3+1,3)) numgqtests <- 0 numsignificant1 <- 0 numsignificant5 <- 0 numsignificant10 <- 0 for (mypoint in kp3:nmkm3) { j <- 0 numgqtests <- numgqtests + 1 for (myalt in c('greater', 'two.sided', 'less')) { j <- j + 1 gqarr[mypoint-kp3+1,j] <- gqtest(mylm, point=mypoint, alternative=myalt)$p.value } if (gqarr[mypoint-kp3+1,2] < 0.01) numsignificant1 <- numsignificant1 + 1 if (gqarr[mypoint-kp3+1,2] < 0.05) numsignificant5 <- numsignificant5 + 1 if (gqarr[mypoint-kp3+1,2] < 0.10) numsignificant10 <- numsignificant10 + 1 } gqarr } bitmap(file='test0.png') plot(x[,1], type='l', main='Actuals and Interpolation', ylab='value of Actuals and Interpolation (dots)', xlab='time or index') points(x[,1]-mysum$resid) grid() dev.off() bitmap(file='test1.png') plot(mysum$resid, type='b', pch=19, main='Residuals', ylab='value of Residuals', xlab='time or index') grid() dev.off() bitmap(file='test2.png') hist(mysum$resid, main='Residual Histogram', xlab='values of Residuals') grid() dev.off() bitmap(file='test3.png') densityplot(~mysum$resid,col='black',main='Residual Density Plot', xlab='values of Residuals') dev.off() bitmap(file='test4.png') qqnorm(mysum$resid, main='Residual Normal Q-Q Plot') qqline(mysum$resid) grid() dev.off() (myerror <- as.ts(mysum$resid)) bitmap(file='test5.png') dum <- cbind(lag(myerror,k=1),myerror) dum dum1 <- dum[2:length(myerror),] dum1 z <- as.data.frame(dum1) z plot(z,main=paste('Residual Lag plot, lowess, and regression line'), ylab='values of Residuals', xlab='lagged values of Residuals') lines(lowess(z)) abline(lm(z)) grid() dev.off() bitmap(file='test6.png') acf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Autocorrelation Function') grid() dev.off() bitmap(file='test7.png') pacf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Partial Autocorrelation Function') grid() dev.off() bitmap(file='test8.png') opar <- par(mfrow = c(2,2), oma = c(0, 0, 1.1, 0)) plot(mylm, las = 1, sub='Residual Diagnostics') par(opar) dev.off() if (n > n25) { bitmap(file='test9.png') plot(kp3:nmkm3,gqarr[,2], main='Goldfeld-Quandt test',ylab='2-sided p-value',xlab='breakpoint') grid() dev.off() } load(file='createtable') a<-table.start() a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Estimated Regression Equation', 1, TRUE) a<-table.row.end(a) myeq <- colnames(x)[1] myeq <- paste(myeq, '[t] = ', sep='') for (i in 1:k){ if (mysum$coefficients[i,1] > 0) myeq <- paste(myeq, '+', '') myeq <- paste(myeq, mysum$coefficients[i,1], sep=' ') if (rownames(mysum$coefficients)[i] != '(Intercept)') { myeq <- paste(myeq, rownames(mysum$coefficients)[i], sep='') if (rownames(mysum$coefficients)[i] != 't') myeq <- paste(myeq, '[t]', sep='') } } myeq <- paste(myeq, ' + e[t]') a<-table.row.start(a) a<-table.element(a, myeq) a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable1.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a,hyperlink('http://www.xycoon.com/ols1.htm','Multiple Linear Regression - Ordinary Least Squares',''), 6, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Variable',header=TRUE) a<-table.element(a,'Parameter',header=TRUE) a<-table.element(a,'S.D.',header=TRUE) a<-table.element(a,'T-STAT<br />H0: parameter = 0',header=TRUE) a<-table.element(a,'2-tail p-value',header=TRUE) a<-table.element(a,'1-tail p-value',header=TRUE) a<-table.row.end(a) for (i in 1:k){ a<-table.row.start(a) a<-table.element(a,rownames(mysum$coefficients)[i],header=TRUE) a<-table.element(a,mysum$coefficients[i,1]) a<-table.element(a, round(mysum$coefficients[i,2],6)) a<-table.element(a, round(mysum$coefficients[i,3],4)) a<-table.element(a, round(mysum$coefficients[i,4],6)) a<-table.element(a, round(mysum$coefficients[i,4]/2,6)) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable2.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Regression Statistics', 2, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Multiple R',1,TRUE) a<-table.element(a, sqrt(mysum$r.squared)) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'R-squared',1,TRUE) a<-table.element(a, mysum$r.squared) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Adjusted R-squared',1,TRUE) a<-table.element(a, mysum$adj.r.squared) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'F-TEST (value)',1,TRUE) a<-table.element(a, mysum$fstatistic[1]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'F-TEST (DF numerator)',1,TRUE) a<-table.element(a, mysum$fstatistic[2]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'F-TEST (DF denominator)',1,TRUE) a<-table.element(a, mysum$fstatistic[3]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'p-value',1,TRUE) a<-table.element(a, 1-pf(mysum$fstatistic[1],mysum$fstatistic[2],mysum$fstatistic[3])) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Residual Statistics', 2, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Residual Standard Deviation',1,TRUE) a<-table.element(a, mysum$sigma) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Sum Squared Residuals',1,TRUE) a<-table.element(a, sum(myerror*myerror)) a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable3.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Actuals, Interpolation, and Residuals', 4, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Time or Index', 1, TRUE) a<-table.element(a, 'Actuals', 1, TRUE) a<-table.element(a, 'Interpolation<br />Forecast', 1, TRUE) a<-table.element(a, 'Residuals<br />Prediction Error', 1, TRUE) a<-table.row.end(a) for (i in 1:n) { a<-table.row.start(a) a<-table.element(a,i, 1, TRUE) a<-table.element(a,x[i]) a<-table.element(a,x[i]-mysum$resid[i]) a<-table.element(a,mysum$resid[i]) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable4.tab') if (n > n25) { a<-table.start() a<-table.row.start(a) a<-table.element(a,'Goldfeld-Quandt test for Heteroskedasticity',4,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'p-values',header=TRUE) a<-table.element(a,'Alternative Hypothesis',3,header=TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'breakpoint index',header=TRUE) a<-table.element(a,'greater',header=TRUE) a<-table.element(a,'2-sided',header=TRUE) a<-table.element(a,'less',header=TRUE) a<-table.row.end(a) for (mypoint in kp3:nmkm3) { a<-table.row.start(a) a<-table.element(a,mypoint,header=TRUE) a<-table.element(a,gqarr[mypoint-kp3+1,1]) a<-table.element(a,gqarr[mypoint-kp3+1,2]) a<-table.element(a,gqarr[mypoint-kp3+1,3]) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable5.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a,'Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity',4,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Description',header=TRUE) a<-table.element(a,'# significant tests',header=TRUE) a<-table.element(a,'% significant tests',header=TRUE) a<-table.element(a,'OK/NOK',header=TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'1% type I error level',header=TRUE) a<-table.element(a,numsignificant1) a<-table.element(a,numsignificant1/numgqtests) if (numsignificant1/numgqtests < 0.01) dum <- 'OK' else dum <- 'NOK' a<-table.element(a,dum) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'5% type I error level',header=TRUE) a<-table.element(a,numsignificant5) a<-table.element(a,numsignificant5/numgqtests) if (numsignificant5/numgqtests < 0.05) dum <- 'OK' else dum <- 'NOK' a<-table.element(a,dum) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'10% type I error level',header=TRUE) a<-table.element(a,numsignificant10) a<-table.element(a,numsignificant10/numgqtests) if (numsignificant10/numgqtests < 0.1) dum <- 'OK' else dum <- 'NOK' a<-table.element(a,dum) a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable6.tab') }

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