Model 5

*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: Sat, 21 Nov 2009 06:34:09 -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/21/t1258810494b8aete8y6ux8099.htm/, Retrieved Sat, 21 Nov 2009 14:35:06 +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/21/t1258810494b8aete8y6ux8099.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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8.5 99.2 8.6 116.5 8.5 98.4 8.2 90.6 8.1 130.5 7.9 107.4 8.6 106 8.7 196.5 8.7 107.8 8.5 90.5 8.4 123.8 8.5 114.7 8.7 115.3 8.7 197 8.6 88.4 8.5 93.8 8.3 111.3 8 105.9 8.2 123.6 8.1 171 8.1 97 8 99.2 7.9 126.6 7.9 103.4 8 121.3 8 129.6 7.9 110.8 8 98.9 7.7 122.8 7.2 120.9 7.5 133.1 7.3 203.1 7 110.2 7 119.5 7 135.1 7.2 113.9 7.3 137.4 7.1 157.1 6.8 126.4 6.4 112.2 6.1 128.8 6.5 136.8 7.7 156.5 7.9 215.2 7.5 146.7 6.9 130.8 6.6 133.1 6.9 153.4 7.7 159.9 8 174.6 8 145 7.7 112.9 7.3 137.8 7.4 150.6 8.1 162.1 8.3 226.4

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 Yt-2[t] = + 54.4478692187951 + 4.89094083246159X[t] + 8.17504404347599M1[t] + 35.332449512388M2[t] -6.22759448550611M3[t] -18.3563632168033M4[t] + 6.48832450184722M5[t] + 4.07046168730386M6[t] + 11.9911214733882M7[t] + 76.9885269423002M8[t] -3.9423174731238M9[t] -9.25381268360943M10[t] + 10.0205980226587M11[t] + 0.986956897789507t + 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) 54.4478692187951 35.369472 1.5394 0.131207 0.065603 X 4.89094083246159 4.104381 1.1916 0.240093 0.120047 M1 8.17504404347599 9.210087 0.8876 0.379801 0.1899 M2 35.332449512388 9.242163 3.823 0.00043 0.000215 M3 -6.22759448550611 9.185475 -0.678 0.501501 0.25075 M4 -18.3563632168033 9.127969 -2.011 0.050773 0.025386 M5 6.48832450184722 9.140753 0.7098 0.481736 0.240868 M6 4.07046168730386 9.165552 0.4441 0.659247 0.329623 M7 11.9911214733882 9.282158 1.2918 0.203474 0.101737 M8 76.9885269423002 9.338817 8.2439 0 0 M9 -3.9423174731238 9.630967 -0.4093 0.684372 0.342186 M10 -9.25381268360943 9.620139 -0.9619 0.341595 0.170797 M11 10.0205980226587 9.640061 1.0395 0.304531 0.152266 t 0.986956897789507 0.156688 6.2989 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.928748055628976 R-squared 0.862572950834603 Adjusted R-squared 0.820036007045314 F-TEST (value) 20.2782069889044 F-TEST (DF numerator) 13 F-TEST (DF denominator) 42 p-value 5.19584375524573e-14 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 13.5936681097854 Sum Squared Residuals 7761.08813251787 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 99.2 105.182867235984 -5.98286723598409 2 116.5 133.816323685932 -17.3163236859318 3 98.4 92.754142502581 5.64585749741893 4 90.6 80.1450484193349 10.4549515806651 5 130.5 105.487598952529 25.0124010474712 6 107.4 103.078504869283 4.32149513071737 7 106 115.409780135880 -9.40978013587954 8 196.5 181.883236585827 14.6167634141728 9 107.8 101.939349068193 5.86065093180723 10 90.5 96.6366225890043 -6.13662258900427 11 123.8 116.408896109816 7.39110389018417 12 114.7 107.864349068193 6.83565093180724 13 115.3 118.004538175951 -2.70453817595057 14 197 146.148900542652 50.8510994573479 15 88.4 105.086719359301 -16.6867193593013 16 93.8 93.4558134425475 0.344186557452507 17 111.3 118.309269892495 -7.0092698924952 18 105.9 115.411081726003 -9.51108172600286 19 123.6 125.296886576369 -1.696886576369 20 171 190.792154859824 -19.7921548598244 21 97 110.84826734219 -13.8482673421899 22 99.2 106.034634946248 -6.8346349462476 23 126.6 125.806908467059 0.793091532940871 24 103.4 116.77326734219 -13.3732673421899 25 121.3 126.424362366702 -5.12436236670156 26 129.6 154.568724733403 -24.9687247334031 27 110.8 113.506543550052 -2.70654355005232 28 98.9 102.853825799791 -3.95382579979078 29 122.8 127.218188166492 -4.41818816649232 30 120.9 123.341811833508 -2.44181183350767 31 133.1 133.71671076712 -0.616710767119976 32 203.1 198.722884967329 4.37711503267079 33 110.2 117.311715199956 -7.11171519995622 34 119.5 112.987176887260 6.5128231127399 35 135.1 133.248544491318 1.85145550868221 36 113.9 125.193091532941 -11.2930915329409 37 137.4 134.844186557453 2.55581344254747 38 157.1 162.010360757662 -4.91036075766174 39 126.4 119.969991407819 6.43000859218135 40 112.2 106.871803241326 5.32819675867367 41 128.8 131.236165608028 -2.43616560802787 42 136.8 131.761636024259 5.03836397574135 43 156.5 146.538381707086 9.96161829291363 44 215.2 213.500932240280 1.69906775971974 45 146.7 131.600668389661 15.0993316103389 46 130.8 124.341565577488 6.45843442251198 47 133.1 143.135650931807 -10.0356509318072 48 153.4 135.569292056676 17.8307079433235 49 159.9 148.644045663911 11.2559543360887 50 174.6 178.255690280351 -3.65569028035125 51 145 137.682603180247 7.31739681975335 52 112.9 125.073509097000 -12.1735090970005 53 137.8 148.948777380456 -11.1487773804558 54 150.6 148.006965546948 2.59303445305181 55 162.1 160.338240813545 1.76175918645488 56 226.4 227.300791346739 -0.900791346738928 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.999981449015207 3.71019695860039e-05 1.85509847930020e-05 18 0.999968134442427 6.37311151467366e-05 3.18655575733683e-05 19 0.999933285300983 0.000133429398033199 6.67146990165996e-05 20 0.99995918619029 8.16276194210365e-05 4.08138097105183e-05 21 0.999898567541707 0.000202864916585699 0.000101432458292849 22 0.99974621372632 0.000507572547359565 0.000253786273679782 23 0.999662128160101 0.000675743679798275 0.000337871839899138 24 0.999253175171666 0.00149364965666900 0.000746824828334502 25 0.998492250864936 0.00301549827012846 0.00150774913506423 26 0.999048212423894 0.00190357515221102 0.00095178757610551 27 0.99838936297129 0.00322127405742173 0.00161063702871087 28 0.996438991643483 0.0071220167130337 0.00356100835651685 29 0.995176291079508 0.00964741784098373 0.00482370892049187 30 0.990778457030604 0.0184430859387918 0.00922154296939588 31 0.983615137330343 0.0327697253393138 0.0163848626696569 32 0.972194534729024 0.0556109305419526 0.0278054652709763 33 0.980436544249 0.0391269115020001 0.0195634557510000 34 0.96478885664628 0.0704222867074411 0.0352111433537206 35 0.992179250499202 0.0156414990015954 0.00782074950079772 36 0.993635218746245 0.0127295625075106 0.00636478125375532 37 0.990805230397972 0.018389539204057 0.0091947696020285 38 0.979566308208543 0.040867383582914 0.020433691791457 39 0.977170741751491 0.0456585164970175 0.0228292582485088 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 13 0.565217391304348 NOK 5% type I error level 21 0.91304347826087 NOK 10% type I error level 23 1 NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Nov/21/t1258810494b8aete8y6ux8099/10ndal1258810444.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/21/t1258810494b8aete8y6ux8099/10ndal1258810444.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/21/t1258810494b8aete8y6ux8099/1v32f1258810444.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/21/t1258810494b8aete8y6ux8099/1v32f1258810444.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/21/t1258810494b8aete8y6ux8099/2dou41258810444.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/21/t1258810494b8aete8y6ux8099/2dou41258810444.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/21/t1258810494b8aete8y6ux8099/3559v1258810444.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/21/t1258810494b8aete8y6ux8099/3559v1258810444.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/21/t1258810494b8aete8y6ux8099/4difz1258810444.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/21/t1258810494b8aete8y6ux8099/4difz1258810444.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/21/t1258810494b8aete8y6ux8099/5xsnv1258810444.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/21/t1258810494b8aete8y6ux8099/5xsnv1258810444.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/21/t1258810494b8aete8y6ux8099/6ukbo1258810444.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/21/t1258810494b8aete8y6ux8099/6ukbo1258810444.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/21/t1258810494b8aete8y6ux8099/7wwn61258810444.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/21/t1258810494b8aete8y6ux8099/7wwn61258810444.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/21/t1258810494b8aete8y6ux8099/8koii1258810444.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/21/t1258810494b8aete8y6ux8099/8koii1258810444.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/21/t1258810494b8aete8y6ux8099/92t001258810444.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/21/t1258810494b8aete8y6ux8099/92t001258810444.ps (open in new window)

Parameters (Session):

par1 = 2 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 2 ; 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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