*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: Wed, 09 Dec 2009 08:00:24 -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/09/t1260371301pv334d0lx9pcbal.htm/, Retrieved Wed, 09 Dec 2009 16:08:33 +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/09/t1260371301pv334d0lx9pcbal.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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24 33 22 34 25 36 24 36 29 38 26 42 26 35 21 25 23 24 22 22 21 27 16 17 19 30 16 30 25 34 27 37 23 36 22 33 23 33 20 33 24 37 23 40 20 35 21 37 22 43 17 42 21 33 19 39 23 40 22 37 15 44 23 42 21 43 18 40 18 30 18 30 18 31 10 18 13 24 10 22 9 26 9 28 6 23 11 17 9 12 10 9 9 19 16 21 10 18 7 18 7 15 14 24 11 18 10 19 6 30 8 33 13 35 12 36 15 47 16 46 16 43

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 S.[t] = + 17.8743967092323 + 0.28362403777993E.S[t] -1.28301434053189M1[t] -5.00054413482562M2[t] -0.949437394542677M3[t] -1.00592757515550M4[t] -0.554820834872551M5[t] -1.56043890214559M6[t] -4.24968100719855M7[t] -1.74770215357581M8[t] -0.153320220848849M9[t] -0.675314250341956M10[t] -1.44818039317485M11[t] -0.25110674028295t + 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) 17.8743967092323 1.836813 9.7312 0 0 E.S 0.28362403777993 0.036843 7.6983 0 0 M1 -1.28301434053189 1.536526 -0.835 0.407937 0.203968 M2 -5.00054413482562 1.614555 -3.0972 0.003292 0.001646 M3 -0.949437394542677 1.612181 -0.5889 0.558738 0.279369 M4 -1.00592757515550 1.606739 -0.6261 0.534299 0.26715 M5 -0.554820834872551 1.60516 -0.3456 0.731149 0.365575 M6 -1.56043890214559 1.603934 -0.9729 0.335592 0.167796 M7 -4.24968100719855 1.604423 -2.6487 0.010967 0.005484 M8 -1.74770215357581 1.601678 -1.0912 0.280761 0.14038 M9 -0.153320220848849 1.600764 -0.0958 0.924103 0.462052 M10 -0.675314250341956 1.60063 -0.4219 0.675018 0.337509 M11 -1.44818039317485 1.600518 -0.9048 0.370176 0.185088 t -0.25110674028295 0.019249 -13.0454 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.932411502373107 R-squared 0.869391209757674 Adjusted R-squared 0.833265374158733 F-TEST (value) 24.0656360010440 F-TEST (DF numerator) 13 F-TEST (DF denominator) 47 p-value 2.22044604925031e-16 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 2.52938346360975 Sum Squared Residuals 300.695693181175 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 24 25.6998688751552 -1.69986887515521 2 22 22.0148563783584 -0.0148563783583963 3 25 26.3821044539183 -1.38210445391827 4 24 26.0745075330225 -2.07450753302250 5 29 26.8417556085823 2.15824439141765 6 26 26.7195269521461 -0.719526952146089 7 26 21.7938098423507 4.20619015764934 8 21 21.2084415778911 -0.208441577891149 9 23 22.2680927325552 0.731907267444769 10 22 20.9277438872193 1.07225611278068 11 21 21.3218911930031 -0.321891193003126 12 16 19.6827244680957 -3.68272446809572 13 19 21.8357158784200 -2.83571587841997 14 16 17.8670793438433 -1.86707934384330 15 25 22.801575494963 2.19842450503699 16 27 23.344850687407 3.65514931259298 17 23 23.2612266496271 -0.261226649627091 18 22 21.1536297287313 0.846370271268685 19 23 18.2132808833954 4.7867191166046 20 20 20.4641529967352 -0.464152996735191 21 24 22.9419243402989 1.05807565970108 22 23 23.0196956838627 -0.0196956838626574 23 20 20.5776026118472 -0.577602611847163 24 21 22.3419243402989 -1.34192434029892 25 22 22.5095474861637 -0.509547486163658 26 17 18.2572869138071 -1.25728691380705 27 21 19.5046705737877 1.49532942621232 28 19 20.8988178795715 -1.89881787957148 29 23 21.3824419173514 1.61755808264859 30 22 19.2748449964556 2.72515500354436 31 15 18.3198644155792 -3.31986441557923 32 23 20.0034884533592 2.99651154664084 33 21 21.6303876835831 -0.630387683583105 34 18 20.0064148004673 -2.00641480046726 35 18 16.1462015395521 1.85379846044789 36 18 17.343275192444 0.656724807555986 37 18 16.0927781494091 1.90722185059090 38 10 8.43702912369333 1.56297087630667 39 13 13.9387733503729 -0.938773350372907 40 10 13.0639283539173 -3.06392835391727 41 9 14.398424505037 -5.39842450503699 42 9 13.7089477730409 -4.70894777304087 43 6 9.3504787388053 -3.3504787388053 44 11 9.89960662546551 1.10039337453449 45 9 9.82476162900988 -0.824761629009875 46 10 8.20078874589403 1.79921125410597 47 9 10.0130562405775 -1.01305624057748 48 16 11.7773779690292 4.22262203097076 49 10 9.3923847748746 0.607615225125391 50 7 5.42374824029793 1.57625175970207 51 7 8.37287612695814 -1.37287612695814 52 14 10.6178955460817 3.38210445391827 53 11 9.11615131940215 1.88384868059785 54 10 8.1430505496261 1.85694945037390 55 6 8.32256611986941 -2.32256611986941 56 8 11.4243103465490 -3.42431034654899 57 13 13.3348336145529 -0.334833614552865 58 12 12.8453568825567 -0.845356882556735 59 15 14.9412484150201 0.0587515849798848 60 16 15.8546980301321 0.145301969867906 61 16 13.4697048359775 2.53029516402254 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.286903576026991 0.573807152053982 0.713096423973009 18 0.503946114457648 0.992107771084704 0.496053885542352 19 0.481022028168762 0.962044056337524 0.518977971831238 20 0.407119981781704 0.814239963563409 0.592880018218296 21 0.29738267450978 0.59476534901956 0.70261732549022 22 0.211446468865883 0.422892937731767 0.788553531134117 23 0.135191231941780 0.270382463883561 0.86480876805822 24 0.113535555728901 0.227071111457801 0.8864644442711 25 0.0748331285526746 0.149666257105349 0.925166871447325 26 0.0535676066650276 0.107135213330055 0.946432393334972 27 0.0338629269635512 0.0677258539271023 0.96613707303645 28 0.0447431544289080 0.0894863088578161 0.955256845571092 29 0.0329532666490065 0.065906533298013 0.967046733350994 30 0.0426618963298799 0.0853237926597598 0.95733810367012 31 0.265821046595439 0.531642093190877 0.734178953404561 32 0.418951292056361 0.837902584112722 0.581048707943639 33 0.389341857138154 0.778683714276309 0.610658142861846 34 0.330675589541358 0.661351179082716 0.669324410458642 35 0.374631726757619 0.749263453515238 0.625368273242381 36 0.319671087180859 0.639342174361718 0.680328912819141 37 0.357930355464067 0.715860710928133 0.642069644535933 38 0.310593790623056 0.621187581246111 0.689406209376944 39 0.536143295009435 0.92771340998113 0.463856704990565 40 0.54729007875488 0.90541984249024 0.45270992124512 41 0.594615516954635 0.81076896609073 0.405384483045365 42 0.651191348414926 0.697617303170148 0.348808651585074 43 0.701200338895713 0.597599322208574 0.298799661104287 44 0.57559147041526 0.848817059169479 0.424408529584739 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 4 0.142857142857143 NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/09/t1260371301pv334d0lx9pcbal/10glhh1260370819.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/09/t1260371301pv334d0lx9pcbal/10glhh1260370819.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/09/t1260371301pv334d0lx9pcbal/1keoq1260370819.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/09/t1260371301pv334d0lx9pcbal/1keoq1260370819.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/09/t1260371301pv334d0lx9pcbal/2wsam1260370819.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/09/t1260371301pv334d0lx9pcbal/2wsam1260370819.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/09/t1260371301pv334d0lx9pcbal/3pqvk1260370819.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/09/t1260371301pv334d0lx9pcbal/3pqvk1260370819.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/09/t1260371301pv334d0lx9pcbal/4xtap1260370819.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/09/t1260371301pv334d0lx9pcbal/4xtap1260370819.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/09/t1260371301pv334d0lx9pcbal/5v9431260370819.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/09/t1260371301pv334d0lx9pcbal/5v9431260370819.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/09/t1260371301pv334d0lx9pcbal/6tjeh1260370819.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/09/t1260371301pv334d0lx9pcbal/6tjeh1260370819.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/09/t1260371301pv334d0lx9pcbal/7kl8x1260370819.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/09/t1260371301pv334d0lx9pcbal/7kl8x1260370819.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/09/t1260371301pv334d0lx9pcbal/8n2o71260370819.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/09/t1260371301pv334d0lx9pcbal/8n2o71260370819.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/09/t1260371301pv334d0lx9pcbal/99tjm1260370819.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/09/t1260371301pv334d0lx9pcbal/99tjm1260370819.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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