Paper Multiple Regression zonder monthly dummies en lineaire 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: Thu, 17 Dec 2009 09:50:00 -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/Dec/17/t1261068653ro2x1qyb92f7rjh.htm/, Retrieved Thu, 17 Dec 2009 17:51:05 +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/Dec/17/t1261068653ro2x1qyb92f7rjh.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:

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Dataseries X:

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7.6 1.62 8.3 1.49 8.4 1.79 8.4 1.8 8.4 1.58 8.4 1.86 8.6 1.74 8.9 1.59 8.8 1.26 8.3 1.13 7.5 1.92 7.2 2.61 7.4 2.26 8.8 2.41 9.3 2.26 9.3 2.03 8.7 2.86 8.2 2.55 8.3 2.27 8.5 2.26 8.6 2.57 8.5 3.07 8.2 2.76 8.1 2.51 7.9 2.87 8.6 3.14 8.7 3.11 8.7 3.16 8.5 2.47 8.4 2.57 8.5 2.89 8.7 2.63 8.7 2.38 8.6 1.69 8.5 1.96 8.3 2.19 8 1.87 8.2 1.6 8.1 1.63 8.1 1.22 8 1.21 7.9 1.49 7.9 1.64 8 1.66 8 1.77 7.9 1.82 8 1.78 7.7 1.28 7.2 1.29 7.5 1.37 7.3 1.12 7 1.51 7 2.24 7 2.94 7.2 3.09 7.3 3.46 7.1 3.64 6.8 4.39 6.4 4.15 6.1 5.21 6.5 5.8 7.7 5.91 7.9 5.39 7.5 5.46 6.9 4.72 6.6 3.14 6.9 2.63 7.7 2.32 8 1.93 8 0.62 7.7 0.6 7.3 -0.37 7.4 -1.1

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 4 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation TWG[t] = + 8.31234571227639 -0.164256724306461Infl[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) 8.31234571227639 0.164944 50.395 0 0 Infl -0.164256724306461 0.061712 -2.6617 0.00961 0.004805 Multiple Linear Regression - Regression Statistics Multiple R 0.301210274670713 R-squared 0.0907276295672066 Adjusted R-squared 0.0779209764625194 F-TEST (value) 7.0844137672473 F-TEST (DF numerator) 1 F-TEST (DF denominator) 71 p-value 0.00960975317040769 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.669507188914518 Sum Squared Residuals 31.8250311965836 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 7.6 8.04624981889995 -0.446249818899948 2 8.3 8.06760319305976 0.232396806940240 3 8.4 8.01832617576782 0.381673824232178 4 8.4 8.01668360852476 0.383316391475243 5 8.4 8.05282008787218 0.347179912127822 6 8.4 8.00682820506637 0.393171794933631 7 8.6 8.02653901198314 0.573460988016855 8 8.9 8.05117752062911 0.848822479370886 9 8.8 8.10538223965025 0.694617760349754 10 8.3 8.12673561381009 0.173264386189914 11 7.5 7.99697280160798 -0.496972801607982 12 7.2 7.88363566183652 -0.683635661836524 13 7.4 7.94112551534378 -0.541125515343785 14 8.8 7.91648700669782 0.883512993302185 15 9.3 7.94112551534378 1.35887448465622 16 9.3 7.97890456193427 1.32109543806573 17 8.7 7.8425714807599 0.85742851924009 18 8.2 7.89349106529491 0.306508934705088 19 8.3 7.93948294810072 0.36051705189928 20 8.5 7.94112551534378 0.558874484656215 21 8.6 7.89020593080878 0.709794069191217 22 8.5 7.80807756865555 0.691922431344448 23 8.2 7.85899715319055 0.341002846809445 24 8.1 7.90006133426717 0.199938665732830 25 7.9 7.84092891351684 0.0590710864831564 26 8.6 7.7965795979541 0.8034204020459 27 8.7 7.80150729968329 0.898492700316706 28 8.7 7.79329446346797 0.906705536532029 29 8.5 7.90663160323943 0.593368396760572 30 8.4 7.89020593080878 0.509794069191218 31 8.5 7.83764377903071 0.662356220969285 32 8.7 7.8803505273504 0.819649472649605 33 8.7 7.92141470842701 0.778585291572989 34 8.6 8.03475184819847 0.565248151801532 35 8.5 7.99040253263572 0.509597467364276 36 8.3 7.95262348604524 0.347376513954763 37 8 8.0051856378233 -0.00518563782330506 38 8.2 8.04953495338605 0.150465046613950 39 8.1 8.04460725165686 0.0553927483431439 40 8.1 8.1119525086225 -0.0119525086225051 41 8 8.11359507586557 -0.113595075865569 42 7.9 8.06760319305976 -0.16760319305976 43 7.9 8.04296468441379 -0.142964684413791 44 8 8.03967954992766 -0.0396795499276619 45 8 8.02161131025395 -0.0216113102539512 46 7.9 8.01339847403863 -0.113398474038628 47 8 8.01996874301089 -0.0199687430108866 48 7.7 8.10209710516412 -0.402097105164117 49 7.2 8.10045453792105 -0.900454537921052 50 7.5 8.08731399997654 -0.587313999976536 51 7.3 8.12837818105315 -0.828378181053151 52 7 8.06431805857363 -1.06431805857363 53 7 7.94441064982991 -0.944410649829914 54 7 7.8294309428154 -0.829430942815392 55 7.2 7.80479243416942 -0.604792434169422 56 7.3 7.74401744617603 -0.444017446176032 57 7.1 7.71445123580087 -0.614451235800869 58 6.8 7.59125869257102 -0.791258692571023 59 6.4 7.63068030640457 -1.23068030640457 60 6.1 7.45656817863973 -1.35656817863973 61 6.5 7.35965671129891 -0.859656711298913 62 7.7 7.3415884716252 0.358411528374798 63 7.9 7.42700196826456 0.472998031735438 64 7.5 7.41550399756311 0.0844960024368902 65 6.9 7.53705397354989 -0.63705397354989 66 6.6 7.7965795979541 -1.1965795979541 67 6.9 7.8803505273504 -0.980350527350394 68 7.7 7.9312701118854 -0.231270111885397 69 8 7.99533023436492 0.00466976563508258 70 8 8.21050654320638 -0.210506543206381 71 7.7 8.21379167769251 -0.513791677692511 72 7.3 8.37312070026978 -1.07312070026978 73 7.4 8.4930281090135 -1.09302810901349 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 0.192638798544805 0.385277597089609 0.807361201455195 6 0.0865950751287496 0.173190150257499 0.91340492487125 7 0.0509082103972539 0.101816420794508 0.949091789602746 8 0.0789818423212792 0.157963684642558 0.921018157678721 9 0.0555060862848742 0.111012172569748 0.944493913715126 10 0.0323974128299748 0.0647948256599496 0.967602587170025 11 0.0614451424688348 0.122890284937670 0.938554857531165 12 0.0446935710515724 0.0893871421031448 0.955306428948428 13 0.029689823887186 0.059379647774372 0.970310176112814 14 0.123050236729187 0.246100473458374 0.876949763270813 15 0.352002407848666 0.704004815697333 0.647997592151334 16 0.521199701946872 0.957600596106255 0.478800298053128 17 0.518409190662043 0.963181618675914 0.481590809337957 18 0.444009511720745 0.88801902344149 0.555990488279255 19 0.374609272113806 0.749218544227612 0.625390727886194 20 0.324917108262227 0.649834216524455 0.675082891737773 21 0.296779107591493 0.593558215182986 0.703220892408507 22 0.264575012507504 0.529150025015008 0.735424987492496 23 0.217499155046452 0.434998310092905 0.782500844953548 24 0.176489461468782 0.352978922937564 0.823510538531218 25 0.146331763583434 0.292663527166868 0.853668236416566 26 0.145498386726515 0.290996773453030 0.854501613273485 27 0.159421096932160 0.318842193864319 0.84057890306784 28 0.17921252969181 0.35842505938362 0.82078747030819 29 0.168436432746825 0.33687286549365 0.831563567253175 30 0.154091274451661 0.308182548903322 0.845908725548339 31 0.157820153793297 0.315640307586594 0.842179846206703 32 0.197625792978046 0.395251585956093 0.802374207021954 33 0.252551938387244 0.505103876774488 0.747448061612756 34 0.284553226928896 0.569106453857792 0.715446773071104 35 0.316842593057213 0.633685186114425 0.683157406942787 36 0.330794450891482 0.661588901782964 0.669205549108518 37 0.318068633008445 0.63613726601689 0.681931366991555 38 0.313428984438097 0.626857968876194 0.686571015561903 39 0.304786703502833 0.609573407005666 0.695213296497167 40 0.289928054943088 0.579856109886176 0.710071945056912 41 0.271031466419639 0.542062932839278 0.728968533580361 42 0.256561657120794 0.513123314241587 0.743438342879206 43 0.246475468942596 0.492950937885191 0.753524531057404 44 0.245883933546859 0.491767867093718 0.754116066453141 45 0.254220620632751 0.508441241265502 0.745779379367249 46 0.259932126508711 0.519864253017422 0.740067873491289 47 0.284668393314229 0.569336786628458 0.715331606685771 48 0.270901844197062 0.541803688394125 0.729098155802938 49 0.304346980027453 0.608693960054906 0.695653019972547 50 0.282132930604282 0.564265861208563 0.717867069395718 51 0.265215234613155 0.53043046922631 0.734784765386845 52 0.318643428983295 0.63728685796659 0.681356571016705 53 0.393764415714989 0.787528831429979 0.60623558428501 54 0.47428140352803 0.94856280705606 0.52571859647197 55 0.481237767964089 0.962475535928178 0.518762232035911 56 0.463304012459805 0.92660802491961 0.536695987540195 57 0.446641561041263 0.893283122082526 0.553358438958737 58 0.450751176167866 0.901502352335733 0.549248823832134 59 0.561898778211104 0.876202443577792 0.438101221788896 60 0.769108753770567 0.461782492458866 0.230891246229433 61 0.835211469237232 0.329577061525536 0.164788530762768 62 0.793510040878864 0.412979918242273 0.206489959121136 63 0.818808738358994 0.362382523282013 0.181191261641006 64 0.79393712813469 0.412125743730621 0.206062871865310 65 0.698829155230234 0.602341689539532 0.301170844769766 66 0.811708132245826 0.376583735508348 0.188291867754174 67 0.97051321246718 0.0589735750656389 0.0294867875328195 68 0.96443832380221 0.071123352395581 0.0355616761977905 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 5 0.078125 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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