*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 08:09:12 -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/t1258729828bpmpma195zxr10h.htm/, Retrieved Fri, 20 Nov 2009 16:10:40 +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/20/t1258729828bpmpma195zxr10h.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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20366 0 22782 0 19169 0 13807 0 29743 0 25591 0 29096 0 26482 0 22405 0 27044 0 17970 0 18730 0 19684 0 19785 0 18479 0 10698 0 31956 0 29506 0 34506 0 27165 0 26736 0 23691 0 18157 0 17328 0 18205 0 20995 0 17382 0 9367 0 31124 0 26551 0 30651 0 25859 0 25100 0 25778 0 20418 0 18688 0 20424 0 24776 0 19814 0 12738 0 31566 0 30111 0 30019 0 31934 1 25826 1 26835 1 20205 1 17789 1 20520 1 22518 1 15572 1 11509 1 25447 1 24090 1 27786 1 26195 1 20516 1 22759 1 19028 1 16971 1 20036 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 3 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Y[t] = + 18131.4750853242 -1137.48634812287X[t] + 1926.67861205915M1[t] + 4104.92480091012M2[t] + 10.6825938566490M3[t] -6454.95961319682M4[t] + 11882.1981797497M5[t] + 9078.55597269624M6[t] + 12314.1137656428M7[t] + 9650.76882821388M8[t] + 6234.12662116041M9[t] + 7332.68441410694M10[t] + 1260.64220705347M11[t] + 6.2422070534699t + 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) 18131.4750853242 1075.08701 16.8651 0 0 X -1137.48634812287 924.549304 -1.2303 0.224702 0.112351 M1 1926.67861205915 1202.869203 1.6017 0.115915 0.057957 M2 4104.92480091012 1262.093215 3.2525 0.002121 0.00106 M3 10.6825938566490 1260.584786 0.0085 0.993274 0.496637 M4 -6454.95961319682 1259.523129 -5.1249 6e-06 3e-06 M5 11882.1981797497 1258.909374 9.4385 0 0 M6 9078.55597269624 1258.744176 7.2124 0 0 M7 12314.1137656428 1259.027711 9.7807 0 0 M8 9650.76882821388 1257.184821 7.6765 0 0 M9 6234.12662116041 1255.61117 4.965 9e-06 5e-06 M10 7332.68441410694 1254.485925 5.8452 0 0 M11 1260.64220705347 1253.810293 1.0054 0.319829 0.159915 t 6.2422070534699 23.767516 0.2626 0.793979 0.396989 Multiple Linear Regression - Regression Statistics Multiple R 0.951798518642867 R-squared 0.905920420090756 Adjusted R-squared 0.879898408626498 F-TEST (value) 34.8136200514336 F-TEST (DF numerator) 13 F-TEST (DF denominator) 47 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 1982.09192304184 Sum Squared Residuals 184648354.395222 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 20366 20064.3959044369 301.604095563121 2 22782 22248.8843003413 533.115699658699 3 19169 18160.8843003413 1008.1156996587 4 13807 11701.4843003413 2105.51569965871 5 29743 30044.8843003413 -301.884300341295 6 25591 27247.4843003413 -1656.48430034130 7 29096 30489.2843003413 -1393.28430034130 8 26482 27832.1815699659 -1350.18156996586 9 22405 24421.7815699659 -2016.78156996586 10 27044 25526.5815699659 1517.41843003412 11 17970 19460.7815699659 -1490.78156996587 12 18730 18206.3815699659 523.61843003413 13 19684 20139.3023890785 -455.302389078494 14 19785 22323.7907849829 -2538.79078498293 15 18479 18235.7907849829 243.209215017066 16 10698 11776.3907849829 -1078.39078498294 17 31956 30119.7907849829 1836.20921501707 18 29506 27322.3907849829 2183.60921501707 19 34506 30564.1907849829 3941.80921501707 20 27165 27907.0880546075 -742.088054607511 21 26736 24496.6880546075 2239.31194539249 22 23691 25601.4880546075 -1910.48805460751 23 18157 19535.6880546075 -1378.68805460751 24 17328 18281.2880546075 -953.288054607507 25 18205 20214.2088737201 -2009.20887372013 26 20995 22398.6972696246 -1403.69726962457 27 17382 18310.6972696246 -928.697269624572 28 9367 11851.2972696246 -2484.29726962457 29 31124 30194.6972696246 929.302730375427 30 26551 27397.2972696246 -846.297269624574 31 30651 30639.0972696246 11.9027303754272 32 25859 27981.9945392491 -2122.99453924915 33 25100 24571.5945392491 528.405460750851 34 25778 25676.3945392491 101.605460750853 35 20418 19610.5945392491 807.405460750851 36 18688 18356.1945392491 331.805460750854 37 20424 20289.1153583618 134.884641638228 38 24776 22473.6037542662 2302.39624573379 39 19814 18385.6037542662 1428.39624573379 40 12738 11926.2037542662 811.796245733788 41 31566 30269.6037542662 1296.39624573379 42 30111 27472.2037542662 2638.79624573379 43 30019 30714.0037542662 -695.003754266211 44 31934 26919.4146757679 5014.58532423208 45 25826 23509.0146757679 2316.98532423208 46 26835 24613.8146757679 2221.18532423208 47 20205 18548.0146757679 1656.98532423208 48 17789 17293.6146757679 495.385324232083 49 20520 19226.5354948805 1293.46450511946 50 22518 21411.023890785 1106.97610921502 51 15572 17323.0238907850 -1751.02389078498 52 11509 10863.6238907850 645.376109215016 53 25447 29207.023890785 -3760.02389078498 54 24090 26409.623890785 -2319.62389078498 55 27786 29651.423890785 -1865.42389078498 56 26195 26994.3211604096 -799.32116040956 57 20516 23583.9211604096 -3067.92116040956 58 22759 24688.7211604096 -1929.72116040955 59 19028 18622.9211604096 405.078839590442 60 16971 17368.5211604096 -397.521160409556 61 20036 19301.4419795222 734.558020477818 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.417682273976703 0.835364547953405 0.582317726023297 18 0.586268186713937 0.827463626572125 0.413731813286063 19 0.783750275523135 0.432499448953731 0.216249724476865 20 0.678623481798762 0.642753036402477 0.321376518201239 21 0.690251459150382 0.619497081699237 0.309748540849618 22 0.717030870115589 0.565938259768822 0.282969129884411 23 0.637621198668274 0.724757602663452 0.362378801331726 24 0.562536729308479 0.874926541383041 0.437463270691521 25 0.553351434898301 0.893297130203399 0.446648565101699 26 0.525990661324787 0.948018677350427 0.474009338675213 27 0.456883079199242 0.913766158398483 0.543116920800758 28 0.541436530869456 0.917126938261088 0.458563469130544 29 0.448126990423736 0.896253980847472 0.551873009576264 30 0.40072564011397 0.80145128022794 0.59927435988603 31 0.312336515897004 0.624673031794008 0.687663484102996 32 0.487782188972392 0.975564377944783 0.512217811027608 33 0.405641874652116 0.811283749304231 0.594358125347884 34 0.357292831435238 0.714585662870477 0.642707168564762 35 0.388289904624343 0.776579809248685 0.611710095375657 36 0.369289072582691 0.738578145165382 0.63071092741731 37 0.579942384771227 0.840115230457545 0.420057615228773 38 0.59213836044914 0.815723279101721 0.407861639550860 39 0.485775669037473 0.971551338074946 0.514224330962527 40 0.516240367972191 0.967519264055618 0.483759632027809 41 0.431970604070929 0.863941208141858 0.568029395929071 42 0.455729698709730 0.911459397419461 0.54427030129027 43 0.329125011010474 0.658250022020948 0.670874988989526 44 0.360080372421016 0.720160744842033 0.639919627578984 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 0 0 OK

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Nov/20/t1258729828bpmpma195zxr10h/10maxh1258729748.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/20/t1258729828bpmpma195zxr10h/10maxh1258729748.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/20/t1258729828bpmpma195zxr10h/17jkg1258729748.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/20/t1258729828bpmpma195zxr10h/17jkg1258729748.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/20/t1258729828bpmpma195zxr10h/2imrr1258729748.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/20/t1258729828bpmpma195zxr10h/2imrr1258729748.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/20/t1258729828bpmpma195zxr10h/3nvwz1258729748.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/20/t1258729828bpmpma195zxr10h/3nvwz1258729748.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/20/t1258729828bpmpma195zxr10h/476081258729748.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/20/t1258729828bpmpma195zxr10h/476081258729748.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/20/t1258729828bpmpma195zxr10h/5lllz1258729748.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/20/t1258729828bpmpma195zxr10h/5lllz1258729748.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/20/t1258729828bpmpma195zxr10h/6zv1u1258729748.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/20/t1258729828bpmpma195zxr10h/6zv1u1258729748.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/20/t1258729828bpmpma195zxr10h/7u6451258729748.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/20/t1258729828bpmpma195zxr10h/7u6451258729748.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/20/t1258729828bpmpma195zxr10h/87ev31258729748.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/20/t1258729828bpmpma195zxr10h/87ev31258729748.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/20/t1258729828bpmpma195zxr10h/9ruf91258729748.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/20/t1258729828bpmpma195zxr10h/9ruf91258729748.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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