WS 7: model met seizoenaliteit en trend

*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: Fri, 20 Nov 2009 10:06:03 -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/t1258736865881l7wctxrwzx3z.htm/, Retrieved Fri, 20 Nov 2009 18:07:57 +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/t1258736865881l7wctxrwzx3z.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:

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423 114 427 116 441 153 449 162 452 161 462 149 455 139 461 135 461 130 463 127 462 122 456 117 455 112 456 113 472 149 472 157 471 157 465 147 459 137 465 132 468 125 467 123 463 117 460 114 462 111 461 112 476 144 476 150 471 149 453 134 443 123 442 116 444 117 438 111 427 105 424 102 416 95 406 93 431 124 434 130 418 124 412 115 404 106 409 105 412 105 406 101 398 95 397 93 385 84 390 87 413 116 413 120 401 117 397 109 397 105 409 107 419 109 424 109 428 108 430 107

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 Y[t] = + 210.097277375847 + 2.01219960132561X[t] + 4.33105354315315M1[t] + 1.87434713285987M2[t] -46.1727465198532M3[t] -57.4977706975701M4[t] -59.5154383836216M5[t] -42.8281894982728M6[t] -31.5653398155752M7[t] -20.1732478205662M8[t] -13.195795347148M9[t] -8.60370335213898M10[t] -3.18965207474387M11[t] + 0.244506808967836t + 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) 210.097277375847 38.65252 5.4355 2e-06 1e-06 X 2.01219960132561 0.289594 6.9484 0 0 M1 4.33105354315315 8.888965 0.4872 0.628403 0.314201 M2 1.87434713285987 8.714392 0.2151 0.830651 0.415325 M3 -46.1727465198532 10.885047 -4.2419 0.000106 5.3e-05 M4 -57.4977706975701 12.353443 -4.6544 2.8e-05 1.4e-05 M5 -59.5154383836216 12.025613 -4.9491 1e-05 5e-06 M6 -42.8281894982728 10.093164 -4.2433 0.000106 5.3e-05 M7 -31.5653398155752 8.942847 -3.5297 0.000957 0.000479 M8 -20.1732478205662 8.700421 -2.3187 0.024911 0.012456 M9 -13.195795347148 8.598451 -1.5347 0.131715 0.065857 M10 -8.60370335213898 8.427509 -1.0209 0.312638 0.156319 M11 -3.18965207474387 8.253434 -0.3865 0.700935 0.350468 t 0.244506808967836 0.222528 1.0988 0.277587 0.138794 Multiple Linear Regression - Regression Statistics Multiple R 0.899625961873798 R-squared 0.809326871277356 Adjusted R-squared 0.75544098707313 F-TEST (value) 15.0192742167882 F-TEST (DF numerator) 13 F-TEST (DF denominator) 46 p-value 2.02726724296554e-12 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 13.0130086667657 Sum Squared Residuals 7789.5661498207 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 423 444.063592279089 -21.0635922790891 2 427 445.875791880414 -18.875791880414 3 441 472.524590285717 -31.5245902857167 4 449 479.553869328898 -30.5538693288981 5 452 475.768508850489 -23.7685088504889 6 462 468.553869328898 -6.55386932889807 7 455 459.939229807307 -4.93922980730737 8 461 463.527030205982 -2.52703020598172 9 461 460.68799148174 0.312008518260225 10 463 459.48799148174 3.51200851826021 11 462 455.085551561475 6.91444843852534 12 456 448.458712438558 7.54128756144169 13 455 442.973274784051 12.0267252159488 14 456 442.773274784051 13.2267252159486 15 472 467.409873588028 4.5901264119718 16 472 472.426953029884 -0.42695302988406 17 471 470.6537921528 0.346207847199586 18 465 467.463551833861 -2.46355183386091 19 459 458.84891231227 0.151087687729826 20 465 460.424513109619 4.57548689038106 21 468 453.561075182726 14.4389248172743 22 467 454.373274784051 12.6267252159486 23 463 447.958635262461 15.0413647375394 24 460 445.356195342196 14.6438046578045 25 462 443.89515689034 18.1048431096604 26 461 443.69515689034 17.3048431096602 27 476 460.282957289014 15.7170427109858 28 476 461.275637528219 14.7243624717812 29 471 457.490277049810 13.5097229501905 30 453 444.239038724242 8.76096127575803 31 443 433.612199601326 9.38780039867439 32 442 431.163401196023 10.8365988039768 33 444 440.397560079735 3.60243992026513 34 438 433.160961275758 4.83903872424196 35 427 426.746321754167 0.253678245832703 36 424 424.143881833902 -0.143881833902165 37 416 414.634044976744 1.36595502325616 38 406 408.397446172767 -2.39744617276718 39 431 422.973046970116 8.02695302988407 40 434 423.965727209321 10.0342727906794 41 418 410.119368724283 7.88063127571678 42 412 408.941328006669 3.05867199333065 43 404 402.338888086404 1.66111191359578 44 409 411.963287289055 -2.96328728905545 45 412 419.185246571442 -7.18524657144154 46 406 415.973046970116 -9.97304697011593 47 398 409.558407448525 -11.5584074485252 48 397 408.968167129586 -11.9681671295857 49 385 395.433931069776 -10.4339310697761 50 390 399.258330272428 -9.25833027242754 51 413 409.809531867125 3.19046813287494 52 413 406.777812903678 6.22218709632153 53 401 398.968053222618 2.03194677738203 54 397 399.80221210633 -2.8022121063297 55 397 403.260770192693 -6.26077019269264 56 409 418.921768199321 -9.92176819932071 57 419 430.168126684358 -11.1681266843580 58 424 435.004725488335 -11.0047254883349 59 428 438.651083973372 -10.6510839733722 60 430 440.073043255758 -10.0730432557583 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.203860561261707 0.407721122523413 0.796139438738293 18 0.947924487538912 0.104151024922176 0.0520755124610878 19 0.993215065415365 0.0135698691692694 0.0067849345846347 20 0.999178363433336 0.00164327313332895 0.000821636566664476 21 0.999557350251942 0.000885299496116107 0.000442649748058053 22 0.999531968932488 0.000936062135024819 0.000468031067512409 23 0.999720503396542 0.000558993206915858 0.000279496603457929 24 0.999765079180705 0.000469841638589092 0.000234920819294546 25 0.99986907963005 0.000261840739900887 0.000130920369950443 26 0.999982131685213 3.57366295740064e-05 1.78683147870032e-05 27 0.999948457969302 0.00010308406139658 5.154203069829e-05 28 0.99994792676719 0.000104146465621301 5.20732328106504e-05 29 0.99996808247702 6.38350459611116e-05 3.19175229805558e-05 30 0.99999596473287 8.07053426188669e-06 4.03526713094334e-06 31 0.999995986271414 8.02745717195955e-06 4.01372858597977e-06 32 0.999996207025988 7.58594802362209e-06 3.79297401181105e-06 33 0.999997162797819 5.67440436255619e-06 2.83720218127809e-06 34 0.99999897631518 2.04736963938165e-06 1.02368481969082e-06 35 0.999998695651274 2.60869745158581e-06 1.30434872579290e-06 36 0.99999851642368 2.96715264074869e-06 1.48357632037435e-06 37 0.99999808242185 3.8351562993739e-06 1.91757814968695e-06 38 0.99998954801883 2.09039623387719e-05 1.04519811693860e-05 39 0.999961555546264 7.68889074714701e-05 3.84444537357351e-05 40 0.999967087104287 6.58257914263479e-05 3.29128957131740e-05 41 0.99989938329164 0.000201233416721552 0.000100616708360776 42 0.999980649510907 3.87009781866758e-05 1.93504890933379e-05 43 0.999623458638953 0.000753082722094944 0.000376541361047472 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 24 0.888888888888889 NOK 5% type I error level 25 0.925925925925926 NOK 10% type I error level 25 0.925925925925926 NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Nov/20/t1258736865881l7wctxrwzx3z/10bw2h1258736758.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/20/t1258736865881l7wctxrwzx3z/10bw2h1258736758.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/20/t1258736865881l7wctxrwzx3z/1q6du1258736758.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/20/t1258736865881l7wctxrwzx3z/1q6du1258736758.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/20/t1258736865881l7wctxrwzx3z/2s4ap1258736758.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/20/t1258736865881l7wctxrwzx3z/2s4ap1258736758.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/20/t1258736865881l7wctxrwzx3z/3w7sa1258736758.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/20/t1258736865881l7wctxrwzx3z/3w7sa1258736758.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/20/t1258736865881l7wctxrwzx3z/48fzg1258736758.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/20/t1258736865881l7wctxrwzx3z/48fzg1258736758.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/20/t1258736865881l7wctxrwzx3z/565ab1258736758.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/20/t1258736865881l7wctxrwzx3z/565ab1258736758.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/20/t1258736865881l7wctxrwzx3z/6r62b1258736758.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/20/t1258736865881l7wctxrwzx3z/6r62b1258736758.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/20/t1258736865881l7wctxrwzx3z/7fetx1258736758.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/20/t1258736865881l7wctxrwzx3z/7fetx1258736758.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/20/t1258736865881l7wctxrwzx3z/8bhdn1258736758.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/20/t1258736865881l7wctxrwzx3z/8bhdn1258736758.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/20/t1258736865881l7wctxrwzx3z/9xdka1258736758.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/20/t1258736865881l7wctxrwzx3z/9xdka1258736758.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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