ws7 Crime

*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: Tue, 23 Nov 2010 15:19:28 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Nov/23/t1290526055pj18hzb2jub05qi.htm/, Retrieved Tue, 23 Nov 2010 16:27:51 +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/2010/Nov/23/t1290526055pj18hzb2jub05qi.htm/}, year = {2010}, } @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 = {2010}, 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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184 74 11 31 20 213 72 11 43 18 347 70 18 16 16 565 71 11 25 19 327 72 9 29 24 260 68 8 32 15 325 68 12 24 14 102 62 13 28 11 38 69 7 25 12 226 66 9 58 15 137 60 13 21 9 369 81 4 77 36 109 66 9 37 12 809 67 11 37 16 29 65 12 35 11 245 64 10 42 14 118 64 12 21 10 148 62 7 81 27 387 59 15 31 16 98 56 15 50 15 608 46 22 24 8 218 54 14 27 13 254 54 20 22 11 697 45 26 18 8 827 57 12 23 11 693 57 9 60 18 448 61 19 14 12 942 52 17 31 10 1017 44 21 24 9 216 43 18 23 8 673 48 19 22 10 989 57 14 25 12 630 47 19 25 9 404 50 19 21 9 692 48 16 32 11 1517 49 13 31 14 879 72 13 13 22 631 59 14 21 13 1375 49 9 46 13 1139 54 13 27 12 3545 62 22 18 15 706 47 17 39 11 451 45 34 15 10 433 48 26 23 12 601 69 23 7 12 1024 42 23 23 11 457 49 18 30 12 1441 57 15 35 13 1022 72 22 15 16 1244 67 26 18 16

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 6 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Crimerate[t] = + 1395.25905402689 -22.0239243392042`25+HSgraduate`[t] + 11.3564365152109`Dropouts16-19`[t] -13.0018979457832`CollegeStudents18-24`[t] + 52.8071869293045`25+CollegeGrads`[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) 1395.25905402689 1026.946018 1.3586 0.18103 0.090515 `25+HSgraduate` -22.0239243392042 14.248002 -1.5458 0.129168 0.064584 `Dropouts16-19` 11.3564365152109 21.102839 0.5381 0.593127 0.296564 `CollegeStudents18-24` -13.0018979457832 9.404988 -1.3824 0.173658 0.086829 `25+CollegeGrads` 52.8071869293045 28.752215 1.8366 0.072875 0.036438 Multiple Linear Regression - Regression Statistics Multiple R 0.387809301531643 R-squared 0.150396054354461 Adjusted R-squared 0.0748757036304126 F-TEST (value) 1.99146392876285 F-TEST (DF numerator) 4 F-TEST (DF denominator) 45 p-value 0.112003982595635 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 551.841741660512 Sum Squared Residuals 13703818.8527508 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 184 543.494356859904 -359.494356859904 2 213 325.905056330308 -112.905056330308 3 347 694.884831292732 -347.884831292732 4 565 634.770330622917 -69.7703306229168 5 327 802.06187611668 -475.061876116680 6 260 364.530760757196 -104.530760757196 7 325 461.164503455000 -136.164503455000 8 102 394.23533343439 -292.23533343439 9 38 263.742124735350 -225.742124735350 10 226 81.885699360451 144.114300639549 11 137 423.682093874672 -286.682093874672 12 369 556.659516241847 -187.659516241847 13 109 196.503995433985 -87.5039954339852 14 809 408.421691842421 400.578308157579 15 29 225.793838281084 -196.793838281084 16 245 292.513164757297 -47.5131647572974 17 118 377.037146931949 -259.037146931949 18 148 481.911114085486 -333.911114085486 19 387 708.050220291597 -321.050220291597 20 98 474.278745410024 -376.278745410024 21 608 742.412082493774 -134.412082493774 22 218 700.399436467627 -482.399436467627 23 254 727.933171429199 -473.933171429199 24 697 887.873140568521 -190.873140568521 25 827 558.008008344116 268.991991655884 26 693 412.518783309636 280.481216690364 27 448 719.231635035129 -271.231635035129 28 942 568.087442120621 373.912557879379 29 1017 827.910681586276 189.089318413724 30 216 776.060007396327 -560.060007396327 31 673 795.913094019909 -122.913094019909 32 989 607.524272412276 381.475727587724 33 630 726.124137592459 -96.1241375924588 34 404 712.059956357979 -308.059956357979 35 692 684.631991945748 7.36800805425159 36 1517 799.962216794608 717.037783205392 37 879 949.903615451446 -70.9036154514464 38 631 668.291202446305 -37.2912024463051 39 1375 506.700814617712 868.299185382288 40 1139 636.235813023111 502.764186976889 41 3545 837.690989246338 2707.30901075366 42 706 626.999067179681 79.0009328203192 43 451 1123.34470038617 -672.344700386167 44 433 968.02062553921 -535.020625539211 45 601 679.479272002822 -78.4792720028218 46 1024 1013.28767509950 10.7123249005013 47 457 764.131923457837 -307.131923457837 48 1441 541.668916398959 899.331083601041 49 1022 709.26462662095 312.735373379049 50 1244 825.804300540465 418.195699459535 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 8 0.0235992788881026 0.0471985577762051 0.976400721111897 9 0.010835361680389 0.021670723360778 0.98916463831961 10 0.00308401705664872 0.00616803411329744 0.996915982943351 11 0.000730553498523277 0.00146110699704655 0.999269446501477 12 0.000185246680527109 0.000370493361054218 0.999814753319473 13 3.70348016458373e-05 7.40696032916746e-05 0.999962965198354 14 0.00106866312637741 0.00213732625275482 0.998931336873623 15 0.000457327567321123 0.000914655134642246 0.999542672432679 16 0.000142106641282960 0.000284213282565921 0.999857893358717 17 5.29282624427728e-05 0.000105856524885546 0.999947071737557 18 3.12630951783484e-05 6.25261903566969e-05 0.999968736904822 19 1.15185336732675e-05 2.30370673465350e-05 0.999988481466327 20 6.65435070634497e-06 1.33087014126899e-05 0.999993345649294 21 4.24253734655200e-06 8.48507469310399e-06 0.999995757462653 22 1.97423567481337e-06 3.94847134962674e-06 0.999998025764325 23 9.317249313127e-07 1.8634498626254e-06 0.999999068275069 24 4.01861598763344e-07 8.03723197526689e-07 0.9999995981384 25 2.28966121671521e-06 4.57932243343042e-06 0.999997710338783 26 6.91088999824635e-06 1.38217799964927e-05 0.999993089110002 27 2.51679391435658e-06 5.03358782871317e-06 0.999997483206086 28 5.5137934224229e-06 1.10275868448458e-05 0.999994486206578 29 4.68568667059819e-06 9.37137334119638e-06 0.99999531431333 30 5.43244389242611e-06 1.08648877848522e-05 0.999994567556107 31 1.87138506344722e-06 3.74277012689444e-06 0.999998128614937 32 2.9610561616965e-06 5.922112323393e-06 0.999997038943838 33 9.49798478653584e-07 1.89959695730717e-06 0.999999050201521 34 3.34355683850764e-07 6.68711367701528e-07 0.999999665644316 35 1.09660379377435e-07 2.19320758754870e-07 0.99999989033962 36 6.65310942433421e-07 1.33062188486684e-06 0.999999334689058 37 5.25495056954094e-06 1.05099011390819e-05 0.99999474504943 38 5.56385739546331e-06 1.11277147909266e-05 0.999994436142605 39 5.66393268194933e-06 1.13278653638987e-05 0.999994336067318 40 3.03525818234719e-06 6.07051636469439e-06 0.999996964741818 41 0.755658869435375 0.48868226112925 0.244341130564625 42 0.613546663461366 0.772906673077269 0.386453336538634 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 31 0.885714285714286 NOK 5% type I error level 33 0.942857142857143 NOK 10% type I error level 33 0.942857142857143 NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/23/t1290526055pj18hzb2jub05qi/10btgl1290525561.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290526055pj18hzb2jub05qi/10btgl1290525561.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290526055pj18hzb2jub05qi/14sk91290525561.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290526055pj18hzb2jub05qi/14sk91290525561.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290526055pj18hzb2jub05qi/2xjjc1290525561.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290526055pj18hzb2jub05qi/2xjjc1290525561.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290526055pj18hzb2jub05qi/3xjjc1290525561.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290526055pj18hzb2jub05qi/3xjjc1290525561.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290526055pj18hzb2jub05qi/4xjjc1290525561.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290526055pj18hzb2jub05qi/4xjjc1290525561.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290526055pj18hzb2jub05qi/58bif1290525561.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290526055pj18hzb2jub05qi/58bif1290525561.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290526055pj18hzb2jub05qi/68bif1290525561.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290526055pj18hzb2jub05qi/68bif1290525561.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290526055pj18hzb2jub05qi/7i2hi1290525561.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290526055pj18hzb2jub05qi/7i2hi1290525561.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290526055pj18hzb2jub05qi/8i2hi1290525561.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290526055pj18hzb2jub05qi/8i2hi1290525561.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290526055pj18hzb2jub05qi/9btgl1290525561.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290526055pj18hzb2jub05qi/9btgl1290525561.ps (open in new window)

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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Software written by Ed van Stee & Patrick Wessa

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