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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: Mon, 15 Dec 2008 11:01:30 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Dec/15/t12293641606az1gbyjanm46tm.htm/, Retrieved Mon, 15 Dec 2008 19:02:51 +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/2008/Dec/15/t12293641606az1gbyjanm46tm.htm/}, year = {2008}, } @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 = {2008}, 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:

» Textbox « » Textfile « » CSV «

467 0 460 0 448 0 443 0 436 0 431 0 484 0 510 0 513 0 503 0 471 0 471 0 476 0 475 0 470 0 461 0 455 0 456 0 517 0 525 0 523 0 519 0 509 0 512 0 519 0 517 0 510 0 509 0 501 0 507 0 569 0 580 0 578 0 565 0 547 0 555 0 562 0 561 0 555 1 544 1 537 1 543 1 594 1 611 1 613 1 611 1 594 1 595 1 591 1 589 1 584 1 573 1 567 1 569 1 621 1 629 1 628 1 612 1 595 1 597 1 593 1 590 1 580 1 574 1 573 1 573 1 620 1 626 1 620 1 588 1 566 1 557 1 561 1 549 1 532 1 526 1 511 1 499 1 555 1 565 1 542 1 527 1 510 1 514 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] = + 498.611111111111 + 64.8055555555555DUM[t] + 6.37251984126993M1[t] + 2.21924603174606M2[t] -16.0491071428571M3[t] -23.2023809523809M4[t] -30.4985119047619M5[t] -30.9375M6[t] + 23.4806547619048M7[t] + 35.6130952380953M8[t] + 31.3169642857143M9[t] + 18.0208333333334M10[t] -1.13244047619046M11[t] + 0.153273809523811t + 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) 498.611111111111 15.017254 33.2025 0 0 DUM 64.8055555555555 14.577629 4.4455 3.2e-05 1.6e-05 M1 6.37251984126993 17.765095 0.3587 0.720892 0.360446 M2 2.21924603174606 17.742193 0.1251 0.900816 0.450408 M3 -16.0491071428571 17.876635 -0.8978 0.372386 0.186193 M4 -23.2023809523809 17.833622 -1.301 0.197509 0.098754 M5 -30.4985119047619 17.795584 -1.7138 0.090986 0.045493 M6 -30.9375 17.762551 -1.7417 0.085949 0.042975 M7 23.4806547619048 17.734553 1.324 0.189808 0.094904 M8 35.6130952380953 17.711612 2.0107 0.048208 0.024104 M9 31.3169642857143 17.693749 1.7699 0.081091 0.040545 M10 18.0208333333334 17.680978 1.0192 0.311608 0.155804 M11 -1.13244047619046 17.673311 -0.0641 0.949092 0.474546 t 0.153273809523811 0.300586 0.5099 0.611713 0.305857 Multiple Linear Regression - Regression Statistics Multiple R 0.810706186028269 R-squared 0.657244520064502 Adjusted R-squared 0.593589930933624 F-TEST (value) 10.3251710369721 F-TEST (DF numerator) 13 F-TEST (DF denominator) 70 p-value 1.00146557713288e-11 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 33.0589549310589 Sum Squared Residuals 76502.6150793651 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 467 505.136904761905 -38.1369047619045 2 460 501.136904761905 -41.1369047619049 3 448 483.021825396825 -35.0218253968254 4 443 476.021825396825 -33.0218253968254 5 436 468.878968253968 -32.8789682539682 6 431 468.593253968254 -37.593253968254 7 484 523.164682539683 -39.1646825396826 8 510 535.450396825397 -25.4503968253967 9 513 531.30753968254 -18.3075396825397 10 503 518.164682539683 -15.1646825396825 11 471 499.164682539683 -28.1646825396826 12 471 500.450396825397 -29.4503968253968 13 476 506.976190476191 -30.9761904761905 14 475 502.976190476190 -27.9761904761905 15 470 484.861111111111 -14.8611111111111 16 461 477.861111111111 -16.8611111111111 17 455 470.718253968254 -15.7182539682540 18 456 470.43253968254 -14.4325396825397 19 517 525.003968253968 -8.00396825396826 20 525 537.289682539683 -12.2896825396826 21 523 533.146825396825 -10.1468253968254 22 519 520.003968253968 -1.00396825396826 23 509 501.003968253968 7.99603174603175 24 512 502.289682539683 9.71031746031748 25 519 508.815476190476 10.1845238095238 26 517 504.815476190476 12.1845238095238 27 510 486.700396825397 23.2996031746032 28 509 479.700396825397 29.2996031746032 29 501 472.55753968254 28.4424603174603 30 507 472.271825396825 34.7281746031746 31 569 526.843253968254 42.156746031746 32 580 539.128968253968 40.8710317460317 33 578 534.986111111111 43.0138888888889 34 565 521.843253968254 43.156746031746 35 547 502.843253968254 44.1567460317460 36 555 504.128968253968 50.8710317460318 37 562 510.654761904762 51.345238095238 38 561 506.654761904762 54.3452380952381 39 555 553.345238095238 1.65476190476194 40 544 546.345238095238 -2.34523809523807 41 537 539.202380952381 -2.20238095238093 42 543 538.916666666667 4.08333333333335 43 594 593.488095238095 0.511904761904775 44 611 605.77380952381 5.22619047619049 45 613 601.630952380952 11.3690476190476 46 611 588.488095238095 22.5119047619048 47 594 569.488095238095 24.5119047619048 48 595 570.77380952381 24.2261904761905 49 591 577.299603174603 13.7003968253968 50 589 573.299603174603 15.7003968253968 51 584 555.184523809524 28.8154761904762 52 573 548.184523809524 24.8154761904762 53 567 541.041666666667 25.9583333333333 54 569 540.755952380952 28.2440476190476 55 621 595.327380952381 25.6726190476191 56 629 607.613095238095 21.3869047619048 57 628 603.470238095238 24.5297619047619 58 612 590.327380952381 21.6726190476191 59 595 571.327380952381 23.6726190476191 60 597 572.613095238095 24.3869047619048 61 593 579.138888888889 13.8611111111111 62 590 575.138888888889 14.8611111111111 63 580 557.02380952381 22.9761904761905 64 574 550.02380952381 23.9761904761905 65 573 542.880952380952 30.1190476190476 66 573 542.595238095238 30.4047619047619 67 620 597.166666666667 22.8333333333333 68 626 609.452380952381 16.5476190476190 69 620 605.309523809524 14.6904761904762 70 588 592.166666666667 -4.16666666666668 71 566 573.166666666667 -7.16666666666667 72 557 574.452380952381 -17.4523809523809 73 561 580.978174603175 -19.9781746031746 74 549 576.978174603175 -27.9781746031746 75 532 558.863095238095 -26.8630952380952 76 526 551.863095238095 -25.8630952380952 77 511 544.720238095238 -33.7202380952381 78 499 544.434523809524 -45.4345238095238 79 555 599.005952380952 -44.0059523809524 80 565 611.291666666667 -46.2916666666667 81 542 607.14880952381 -65.1488095238095 82 527 594.005952380952 -67.0059523809524 83 510 575.005952380952 -65.0059523809524 84 514 576.291666666667 -62.2916666666666 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.00443682196697483 0.00887364393394965 0.995563178033025 18 0.00151582934339904 0.00303165868679808 0.998484170656601 19 0.00171440124034058 0.00342880248068115 0.99828559875966 20 0.000496463002353067 0.000992926004706133 0.999503536997647 21 0.000237337141038655 0.000474674282077309 0.999762662858961 22 6.30835634383049e-05 0.000126167126876610 0.999936916436562 23 0.000174954798676825 0.00034990959735365 0.999825045201323 24 0.000350441701963382 0.000700883403926764 0.999649558298037 25 0.000337496142353299 0.000674992284706598 0.999662503857647 26 0.000311830589173177 0.000623661178346354 0.999688169410827 27 0.000223904655270814 0.000447809310541629 0.999776095344729 28 0.000231786756582422 0.000463573513164845 0.999768213243418 29 0.000171641434506976 0.000343282869013953 0.999828358565493 30 0.00022527795358093 0.00045055590716186 0.99977472204642 31 0.000344032020069031 0.000688064040138062 0.99965596797993 32 0.000244855840982108 0.000489711681964215 0.999755144159018 33 0.000136722170074406 0.000273444340148812 0.999863277829926 34 5.83270146681578e-05 0.000116654029336316 0.999941672985332 35 2.63150825791699e-05 5.26301651583399e-05 0.99997368491742 36 1.55321118429844e-05 3.10642236859689e-05 0.999984467888157 37 6.53495045239512e-06 1.30699009047902e-05 0.999993465049548 38 2.86431758605355e-06 5.7286351721071e-06 0.999997135682414 39 2.1420666166537e-06 4.2841332333074e-06 0.999997857933383 40 2.39787931630456e-06 4.79575863260911e-06 0.999997602120684 41 3.57186969861603e-06 7.14373939723206e-06 0.999996428130301 42 4.87742954737019e-06 9.75485909474038e-06 0.999995122570453 43 1.14033511071758e-05 2.28067022143517e-05 0.999988596648893 44 2.38424138113253e-05 4.76848276226507e-05 0.999976157586189 45 3.51289396470053e-05 7.02578792940106e-05 0.999964871060353 46 2.82291416623263e-05 5.64582833246525e-05 0.999971770858338 47 2.65792677272753e-05 5.31585354545506e-05 0.999973420732273 48 2.23854678120492e-05 4.47709356240983e-05 0.999977614532188 49 4.44039336057256e-05 8.88078672114513e-05 0.999955596066394 50 7.23785169558272e-05 0.000144757033911654 0.999927621483044 51 7.21508093960795e-05 0.000144301618792159 0.999927849190604 52 0.000154156078957436 0.000308312157914871 0.999845843921043 53 0.000396652618074659 0.000793305236149318 0.999603347381925 54 0.000732679280305701 0.00146535856061140 0.999267320719694 55 0.00235951127566180 0.00471902255132361 0.997640488724338 56 0.0190596485282554 0.0381192970565108 0.980940351471745 57 0.0518258179001295 0.103651635800259 0.94817418209987 58 0.125988844121487 0.251977688242973 0.874011155878513 59 0.234674234423846 0.469348468847692 0.765325765576154 60 0.381340147595673 0.762680295191346 0.618659852404327 61 0.664202728856171 0.671594542287658 0.335797271143829 62 0.779438833835543 0.441122332328914 0.220561166164457 63 0.803468316973206 0.393063366053589 0.196531683026794 64 0.82271008465884 0.354579830682321 0.177289915341160 65 0.730402203794189 0.539195592411623 0.269597796205811 66 0.697012098332214 0.605975803335572 0.302987901667786 67 0.572625929271561 0.854748141456879 0.427374070728439 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 39 0.764705882352941 NOK 5% type I error level 40 0.784313725490196 NOK 10% type I error level 40 0.784313725490196 NOK

Charts produced by software:

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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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