REVIEW 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: Tue, 24 Nov 2009 13:27:08 -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/24/t1259094492wgpqtfjoo482kcn.htm/, Retrieved Tue, 24 Nov 2009 21:28:23 +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/24/t1259094492wgpqtfjoo482kcn.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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825 444 696 627 677 387 825 696 656 327 677 825 785 448 656 677 412 225 785 656 352 182 412 785 839 460 352 412 729 411 839 352 696 342 729 839 641 361 696 729 695 377 641 696 638 331 695 641 762 428 638 695 635 340 762 638 721 352 635 762 854 461 721 635 418 221 854 721 367 198 418 854 824 422 367 418 687 329 824 367 601 320 687 824 676 375 601 687 740 364 676 601 691 351 740 676 683 380 691 740 594 319 683 691 729 322 594 683 731 386 729 594 386 221 731 729 331 187 386 731 707 344 331 386 715 342 707 331 657 365 715 707 653 313 657 715 642 356 653 657 643 337 642 653 718 389 643 642 654 326 718 643 632 343 654 718 731 357 632 654 392 220 731 632 344 228 392 731 792 391 344 392 852 425 792 344 649 332 852 792 629 298 649 852 685 360 629 649 617 326 685 629 715 325 617 685 715 393 715 617 629 301 715 715 916 426 629 715 531 265 916 629 357 210 531 916 917 429 357 531 828 440 917 357 708 357 828 917 858 431 708 828

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] = + 104.978382790316 + 1.33316588097806X[t] -0.0404063636190839`Y-1`[t] + 0.149771378690737`Y-2`[t] + 15.9683744756981M1[t] -10.3645147838434M2[t] + 23.2324200251082M3[t] + 50.5247874887435M4[t] -76.4952318017308M5[t] -150.366438656282M6[t] + 89.9676465933025M7[t] + 92.380418573932M8[t] -18.7460270834543M9[t] -2.90954882184988M10[t] + 4.9443989866286M11[t] + 0.819374350182732t + 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) 104.978382790316 95.582205 1.0983 0.278328 0.139164 X 1.33316588097806 0.168793 7.8982 0 0 `Y-1` -0.0404063636190839 0.112674 -0.3586 0.721681 0.36084 `Y-2` 0.149771378690737 0.105295 1.4224 0.162297 0.081149 M1 15.9683744756981 27.845693 0.5735 0.569392 0.284696 M2 -10.3645147838434 25.659976 -0.4039 0.688323 0.344161 M3 23.2324200251082 27.416124 0.8474 0.401575 0.200788 M4 50.5247874887435 28.806008 1.754 0.086731 0.043366 M5 -76.4952318017308 35.512308 -2.154 0.037021 0.01851 M6 -150.366438656282 44.611142 -3.3706 0.001618 0.000809 M7 89.9676465933025 52.117241 1.7263 0.091652 0.045826 M8 92.380418573932 44.592746 2.0716 0.044477 0.022238 M9 -18.7460270834543 30.517866 -0.6143 0.542354 0.271177 M10 -2.90954882184988 28.604565 -0.1017 0.919466 0.459733 M11 4.9443989866286 27.515537 0.1797 0.858256 0.429128 t 0.819374350182732 0.300993 2.7222 0.0094 0.0047 Multiple Linear Regression - Regression Statistics Multiple R 0.975945174039772 R-squared 0.95246898273152 Adjusted R-squared 0.935493619421349 F-TEST (value) 56.1089011957001 F-TEST (DF numerator) 15 F-TEST (DF denominator) 42 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 37.3795930765591 Sum Squared Residuals 58683.827099904 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 825 779.475608130668 45.5243918693321 2 677 683.093442228357 -6.0934422283567 3 656 662.820448195537 -6.82044819553671 4 785 830.927631197472 -45.9276311974719 5 412 399.073374939705 12.9266250602948 6 352 303.087491034303 48.9125089656967 7 839 861.420723111472 -22.4207231114720 8 729 770.663559470421 -41.6635594704212 9 696 645.75140379622 50.2485962037806 10 641 672.595966490038 -31.5959664900384 11 695 699.879837246604 -4.87983724660396 12 638 624.009812621746 13.9901873782538 13 762 780.505469078087 -18.5054690780867 14 635 624.12599896852 10.8740010314800 15 721 698.243557836666 22.7564421633339 16 854 849.174468312128 4.82553168787193 17 418 410.520304143167 7.47969585683312 18 367 344.342424280091 22.6575757199086 19 824 820.885444654357 3.11455534564345 20 687 674.02911556706 12.9708844329398 21 601 625.704743208535 -24.7047432085354 22 676 698.640987664726 -22.6409876647261 23 740 676.738669293794 63.261330706206 24 691 663.929334334817 27.0706656651828 25 683 730.944173762604 -47.9441737626042 26 594 617.09199346669 -23.0919934666902 27 729 657.905795601331 71.0942043986688 28 731 752.555642005693 -21.5556420056934 29 386 426.520950100033 -40.5209501000329 30 331 322.381215848376 8.6187841516245 31 707 723.392943112444 -16.3929431124440 32 715 700.528539132534 14.4714608674659 33 657 676.87507056659 -19.8750705665903 34 653 627.748037486951 25.2519625130490 35 642 685.222378018083 -43.2223780180825 36 643 655.6125861281 -12.6125861281004 37 718 740.037069235623 -22.0370692356233 38 654 627.653397931906 26.3466020680939 39 632 698.552387741094 -66.5523877410941 40 731 736.632023652018 -5.63202365201774 41 392 420.492452688246 -28.4924526882461 42 344 386.631070988954 -42.6310709889543 43 792 796.257577265702 -4.25757726570202 44 852 819.526286471263 32.4737135287366 45 649 649.907984069405 -0.907984069405233 46 629 638.424971264057 -9.42497126405656 47 685 700.15911544152 -15.1591154415196 48 617 645.448266915336 -28.4482669153362 49 715 672.037679793018 42.962320206982 50 715 723.035167404527 -8.03516740452706 51 629 649.477810625372 -20.4778106253720 52 916 847.710234832689 68.289765167311 53 531 482.392918128849 48.6070818711511 54 357 394.557797848276 -37.5577978482756 55 917 877.043311856026 39.9566881439745 56 828 846.252499358721 -18.2524993587212 57 708 712.76079835925 -4.76079835924968 58 858 819.590037094228 38.4099629057722 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 19 0.00867581611445193 0.0173516322289039 0.991324183885548 20 0.0222401935198385 0.044480387039677 0.977759806480161 21 0.150627306227219 0.301254612454438 0.849372693772781 22 0.121000386617516 0.242000773235032 0.878999613382484 23 0.100446555046871 0.200893110093742 0.899553444953129 24 0.0798209523085242 0.159641904617048 0.920179047691476 25 0.082934159197278 0.165868318394556 0.917065840802722 26 0.0517558966261964 0.103511793252393 0.948244103373804 27 0.140035209341851 0.280070418683702 0.85996479065815 28 0.187995760267349 0.375991520534699 0.81200423973265 29 0.133533359237555 0.267066718475110 0.866466640762445 30 0.296489936139878 0.592979872279755 0.703510063860122 31 0.212496244886223 0.424992489772446 0.787503755113777 32 0.214404426738184 0.428808853476367 0.785595573261817 33 0.246005972874933 0.492011945749866 0.753994027125067 34 0.283063115393004 0.566126230786008 0.716936884606996 35 0.247846952011914 0.495693904023829 0.752153047988086 36 0.192281523697100 0.384563047394199 0.8077184763029 37 0.169909481974896 0.339818963949791 0.830090518025104 38 0.230885896387156 0.461771792774312 0.769114103612844 39 0.357062269276144 0.714124538552288 0.642937730723856 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 2 0.0952380952380952 NOK 10% type I error level 2 0.0952380952380952 OK

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Nov/24/t1259094492wgpqtfjoo482kcn/10avos1259094423.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/24/t1259094492wgpqtfjoo482kcn/10avos1259094423.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/24/t1259094492wgpqtfjoo482kcn/1lly71259094423.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/24/t1259094492wgpqtfjoo482kcn/1lly71259094423.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/24/t1259094492wgpqtfjoo482kcn/2368d1259094423.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/24/t1259094492wgpqtfjoo482kcn/2368d1259094423.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/24/t1259094492wgpqtfjoo482kcn/335281259094423.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/24/t1259094492wgpqtfjoo482kcn/335281259094423.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/24/t1259094492wgpqtfjoo482kcn/4wsu71259094423.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/24/t1259094492wgpqtfjoo482kcn/4wsu71259094423.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/24/t1259094492wgpqtfjoo482kcn/5kqvy1259094423.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/24/t1259094492wgpqtfjoo482kcn/5kqvy1259094423.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/24/t1259094492wgpqtfjoo482kcn/6v34j1259094423.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/24/t1259094492wgpqtfjoo482kcn/6v34j1259094423.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/24/t1259094492wgpqtfjoo482kcn/7rnde1259094423.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/24/t1259094492wgpqtfjoo482kcn/7rnde1259094423.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/24/t1259094492wgpqtfjoo482kcn/85wma1259094423.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/24/t1259094492wgpqtfjoo482kcn/85wma1259094423.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/24/t1259094492wgpqtfjoo482kcn/9j1ub1259094423.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/24/t1259094492wgpqtfjoo482kcn/9j1ub1259094423.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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