Multiple Regression Analysis Paper

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R Software Module: /rwasp_multipleregression.wasp (opens new window with default values)

Title produced by software: Multiple Regression

Date of computation: Sun, 20 Dec 2009 02:33:59 -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/20/t1261303787k3072jbke6m43nx.htm/, Retrieved Sun, 20 Dec 2009 11:10:01 +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/20/t1261303787k3072jbke6m43nx.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}, }

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Dataseries X:

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-1,2 23,6 -2,4 25,7 0,8 32,5 -0,1 33,5 -1,5 34,5 -4,4 27,9 -4,2 45,3 3,5 40,8 10 58,5 8,6 32,5 9,5 35,5 9,9 46,7 10,4 53,2 16 36,1 12,7 54 10,2 58,1 8,9 41,8 12,6 43,1 13,6 76 14,8 42,8 9,5 41 13,7 61,4 17 34,2 14,7 53,8 17,4 80,7 9 79,5 9,1 96,5 12,2 108,3 15,9 100,1 12,9 108,5 10,9 127,4 10,6 86,5 13,2 71,4 9,6 88,2 6,4 135,6 5,8 70,5 -1 87,5 -0,2 73,3 2,7 92,2 3,6 61,1 -0,9 45,7 0,3 30,5 -1,1 34,8 -2,5 29,2 -3,4 56,7 -3,5 67,1 -3,9 41,8 -4,6 46,8 -0,1 50,1 4,3 81,9 10,2 115,8 8,7 102,5 13,3 106,6 15 101,4 20,7 136,1 20,7 143,4 26,4 127,5 31,2 113,8 31,4 75,3 26,6 98,5 26,6 113,7 19,2 103,7 6,5 73,9 3,1 52,5 -0,2 63,9 -4 44,9 -12,6 31,3 -13 24,9 -17,6 22,8 -21,7 24,8 -23,2 22,8 -16,8 20,9 -19,8 21,5

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 Energiedragers[t] = -8.85490132222897 + 0.228988934930444Invoer[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) -8.85490132222897 2.289304 -3.8679 0.000241 0.00012 Invoer 0.228988934930444 0.031468 7.2769 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.653609633980933 R-squared 0.42720555363269 Adjusted R-squared 0.419138026219066 F-TEST (value) 52.9537157706144 F-TEST (DF numerator) 1 F-TEST (DF denominator) 71 p-value 3.63723495766521e-10 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 8.91644228646388 Sum Squared Residuals 5644.70895639673 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 -1.2 -3.45076245787053 2.25076245787053 2 -2.4 -2.96988569451657 0.569885694516568 3 0.8 -1.41276093698955 2.21276093698955 4 -0.1 -1.18377200205911 1.08377200205911 5 -1.5 -0.954783067128662 -0.545216932871338 6 -4.4 -2.46611003766959 -1.93388996233041 7 -4.2 1.51829743012013 -5.71829743012013 8 3.5 0.487847222933135 3.01215277706687 9 10 4.54095137120199 5.45904862879801 10 8.6 -1.41276093698955 10.0127609369895 11 9.5 -0.725794132198217 10.2257941321982 12 9.9 1.83888193902276 8.06111806097725 13 10.4 3.32731001607064 7.07268998392936 14 16 -0.588400771239954 16.5884007712400 15 12.7 3.51050116401500 9.189498835985 16 10.2 4.44935579722982 5.75064420277018 17 8.9 0.716836157863579 8.18316384213642 18 12.6 1.01452177327316 11.5854782267268 19 13.6 8.54825773248476 5.05174226751524 20 14.8 0.945825092794022 13.8541749072060 21 9.5 0.533645009919226 8.96635499008077 22 13.7 5.20501928250028 8.49498071749972 23 17 -1.02347974760779 18.0234797476078 24 14.7 3.46470337702891 11.2352966229711 25 17.4 9.62450572665785 7.77549427334215 26 9 9.34971900474132 -0.349719004741315 27 9.1 13.2425308985589 -4.14253089855886 28 12.2 15.9446003307381 -3.7446003307381 29 15.9 14.0668910643085 1.83310893569154 30 12.9 15.9903981177242 -3.09039811772419 31 10.9 20.3182889879096 -9.41828898790958 32 10.6 10.9526415492544 -0.352641549254424 33 13.2 7.49490863180472 5.70509136819528 34 9.6 11.3419227386362 -1.74192273863618 35 6.4 22.1959982543392 -15.7959982543392 36 5.8 7.28881859036732 -1.48881859036732 37 -1 11.1816304841849 -12.1816304841849 38 -0.2 7.92998760817256 -8.12998760817256 39 2.7 12.2578784783580 -9.55787847835795 40 3.6 5.13632260202115 -1.53632260202115 41 -0.9 1.60989300409231 -2.50989300409231 42 0.3 -1.87073880685044 2.17073880685044 43 -1.1 -0.88608638664953 -0.213913613350471 44 -2.5 -2.16842442226001 -0.331575577739986 45 -3.4 4.12877128832719 -7.52877128832719 46 -3.5 6.51025621160381 -10.0102562116038 47 -3.9 0.716836157863578 -4.61683615786358 48 -4.6 1.8617808325158 -6.4617808325158 49 -0.1 2.61744431778626 -2.71744431778626 50 4.3 9.89929244857438 -5.59929244857438 51 10.2 17.6620173427164 -7.46201734271643 52 8.7 14.6164645081415 -5.91646450814153 53 13.3 15.5553191413563 -2.25531914135634 54 15 14.3645766797180 0.635423320281963 55 20.7 22.3104927218044 -1.61049272180444 56 20.7 23.9821119467967 -3.28211194679668 57 26.4 20.3411878814026 6.05881211859738 58 31.2 17.2040394728555 13.9959605271445 59 31.4 8.38796547803345 23.0120345219666 60 26.6 13.7005087684198 12.8994912315803 61 26.6 17.1811405793625 9.4188594206375 62 19.2 14.8912512300581 4.30874876994194 63 6.5 8.06738096913083 -1.56738096913083 64 3.1 3.16701776161933 -0.0670177616193288 65 -0.2 5.77749161982639 -5.97749161982639 66 -4 1.42670185614795 -5.42670185614795 67 -12.6 -1.68754765890608 -10.9124523410939 68 -13 -3.15307684246092 -9.84692315753908 69 -17.6 -3.63395360581486 -13.9660463941851 70 -21.7 -3.17597573595397 -18.5240242640460 71 -23.2 -3.63395360581486 -19.5660463941851 72 -16.8 -4.0690325821827 -12.7309674178173 73 -19.8 -3.93163922122443 -15.8683607787756 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 0.00328799365613576 0.00657598731227153 0.996712006343864 6 0.00279195886066903 0.00558391772133806 0.99720804113933 7 0.00161074944497052 0.00322149888994104 0.99838925055503 8 0.00267381653504353 0.00534763307008707 0.997326183464956 9 0.00386202391260903 0.00772404782521807 0.996137976087391 10 0.0146029270351029 0.0292058540702057 0.985397072964897 11 0.0231272264302581 0.0462544528605162 0.976872773569742 12 0.0167694077817766 0.0335388155635532 0.983230592218223 13 0.00926954488317182 0.0185390897663436 0.990730455116828 14 0.0491062177905269 0.0982124355810537 0.950893782209473 15 0.0343496369779317 0.0686992739558633 0.965650363022068 16 0.0208653783658002 0.0417307567316003 0.9791346216342 17 0.0146061875689685 0.029212375137937 0.985393812431032 18 0.0155217696384160 0.0310435392768321 0.984478230361584 19 0.0106267597191646 0.0212535194383293 0.989373240280835 20 0.0181957606700019 0.0363915213400038 0.981804239329998 21 0.0150840285959316 0.0301680571918631 0.984915971404069 22 0.0109797095648642 0.0219594191297284 0.989020290435136 23 0.0591300779788116 0.118260155957623 0.940869922021188 24 0.0673827225635583 0.134765445127117 0.932617277436442 25 0.0568228349784259 0.113645669956852 0.943177165021574 26 0.0598203828873574 0.119640765774715 0.940179617112643 27 0.0690104439887441 0.138020887977488 0.930989556011256 28 0.0579482908117367 0.115896581623473 0.942051709188263 29 0.0405161486477352 0.0810322972954705 0.959483851352265 30 0.0296887528103806 0.0593775056207611 0.97031124718962 31 0.0338750647326505 0.067750129465301 0.96612493526735 32 0.0229452403533273 0.0458904807066545 0.977054759646673 33 0.0196790277713521 0.0393580555427042 0.980320972228648 34 0.0132778084802949 0.0265556169605897 0.986722191519705 35 0.0428449981494032 0.0856899962988063 0.957155001850597 36 0.0320717709423274 0.0641435418846548 0.967928229057673 37 0.0622039824638089 0.124407964927618 0.937796017536191 38 0.0705958782568804 0.141191756513761 0.92940412174312 39 0.081270719057496 0.162541438114992 0.918729280942504 40 0.064114724136907 0.128229448273814 0.935885275863093 41 0.0600783310316573 0.120156662063315 0.939921668968343 42 0.0669291908094713 0.133858381618943 0.933070809190529 43 0.0697296020839478 0.139459204167896 0.930270397916052 44 0.0808419954631103 0.161683990926221 0.91915800453689 45 0.0828118923684586 0.165623784736917 0.917188107631541 46 0.095912422745131 0.191824845490262 0.904087577254869 47 0.090694117681911 0.181388235363822 0.909305882318089 48 0.0853106647517075 0.170621329503415 0.914689335248293 49 0.0700034456109666 0.140006891221933 0.929996554389033 50 0.0534201118277348 0.106840223655470 0.946579888172265 51 0.0610474687795586 0.122094937559117 0.938952531220441 52 0.0563850853067975 0.112770170613595 0.943614914693202 53 0.0462063766635572 0.0924127533271143 0.953793623336443 54 0.0340755119185451 0.0681510238370902 0.965924488081455 55 0.0545199441408237 0.109039888281647 0.945480055859176 56 0.251726542634028 0.503453085268057 0.748273457365972 57 0.3829714457195 0.765942891439 0.6170285542805 58 0.412904118437818 0.825808236875636 0.587095881562182 59 0.990600376907403 0.0187992461851931 0.00939962309259656 60 0.995700622829132 0.00859875434173533 0.00429937717086767 61 0.991691161629112 0.016617676741776 0.008308838370888 62 0.986104197584627 0.0277916048307463 0.0138958024153732 63 0.97499385448077 0.050012291038461 0.0250061455192305 64 0.978951939175075 0.0420961216498512 0.0210480608249256 65 0.974316891089307 0.0513662178213862 0.0256831089106931 66 0.941603171301847 0.116793657396306 0.0583968286981532 67 0.888579469563637 0.222841060872726 0.111420530436363 68 0.957738068389496 0.0845238632210085 0.0422619316105042 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 6 0.09375 NOK 5% type I error level 24 0.375 NOK 10% type I error level 36 0.5625 NOK

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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