*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, 03 Dec 2010 22:32:37 +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/Dec/03/t1291415460qe6g7xsrj7e3rif.htm/, Retrieved Fri, 03 Dec 2010 23:31:10 +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/Dec/03/t1291415460qe6g7xsrj7e3rif.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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12 1221.53 2617.2 10168.52 6957.61 23448.78 11 1180.55 2506.13 9937.04 6688.49 23007.99 10 1183.26 2679.07 9202.45 6601.37 23096.32 9 1141.2 2589.73 9369.35 6229.02 22358.17 8 1049.33 2457.46 8824.06 5925.22 20536.49 7 1101.6 2517.3 9537.3 6147.97 21029.81 6 1030.71 2386.53 9382.64 5965.52 20128.99 5 1089.41 2453.37 9768.7 5964.33 19765.19 4 1186.69 2529.66 11057.4 6135.7 21108.59 3 1169.43 2475.14 11089.94 6153.55 21239.35 2 1104.49 2525.93 10126.03 5598.46 20608.7 1 1073.87 2480.93 10198.04 5608.79 20121.99 12 1115.1 2229.85 10546.44 5957.43 21872.5 11 1095.63 2169.14 9345.55 5625.95 21821.5 10 1036.19 2030.98 10034.74 5414.96 21752.87 9 1057.08 2071.37 10133.23 5675.16 20955.25 8 1020.62 1953.35 10492.53 5458.04 19724.19 7 987.48 1748.74 10356.83 5332.14 20573.33 6 919.32 1696.58 9958.44 4808.64 18378.73 5 919.14 1900.09 9522.5 4940.82 18171 4 872.81 1908.64 8828.26 4769.45 15520.99 3 797.87 1881.46 8109.53 4084.76 13576.02 2 735.09 2100.18 7568.42 3843.74 12811.57 1 825.88 2672.2 79 etc...

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 7 seconds R Server 'George Udny Yule' @ 72.249.76.132 R Framework error message Warning: there are blank lines in the 'Data X' field. Please, use NA for missing data - blank lines are simply deleted and are NOT treated as missing values. Multiple Linear Regression - Estimated Regression Equation S&P[t] = + 3228.51499047869 -0.0358664385477845month[t] -0.143337992426391Bel20[t] -0.134850414826532Nikkei225[t] + 0.00307994776017903DAX[t] -0.047311126005587HangSeng[t] + 37.6855360142645t + 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) 3228.51499047869 1240.665784 2.6022 0.011459 0.005729 month -0.0358664385477845 0.156162 -0.2297 0.819066 0.409533 Bel20 -0.143337992426391 0.132368 -1.0829 0.282866 0.141433 Nikkei225 -0.134850414826532 0.11438 -1.179 0.242707 0.121353 DAX 0.00307994776017903 0.121581 0.0253 0.979867 0.489934 HangSeng -0.047311126005587 0.073961 -0.6397 0.524632 0.262316 t 37.6855360142645 22.632631 1.6651 0.100707 0.050353 Multiple Linear Regression - Regression Statistics Multiple R 0.489007957167126 R-squared 0.239128782172766 Adjusted R-squared 0.168894515911791 F-TEST (value) 3.40473097966475 F-TEST (DF numerator) 6 F-TEST (DF denominator) 65 p-value 0.0055410281396141 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 1776.52131573894 Sum Squared Residuals 205141819.042863 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 1221.53 431.437685358542 790.092314641458 2 1180.55 536.320208344990 644.22979165501 3 1183.26 643.865187806063 539.394812193937 4 1141.2 705.661761380223 435.538238619777 5 1049.33 921.12510668435 128.204893315649 6 1101.6 831.434987481996 270.165012518003 7 1030.71 950.813536420986 79.8964635790141 8 1089.41 944.101998815085 145.308001184915 9 1186.69 734.076460210492 452.613539789508 10 1169.43 769.093191742964 400.336808257036 11 1104.49 957.64523432911 146.844765670891 12 1073.87 1015.16488206799 58.7051179320082 13 1115.1 959.718499674154 155.381500325846 14 1095.63 1169.47439265095 -73.8443926509476 15 1036.19 1136.65893914294 -100.468939142935 16 1057.08 1193.84720545716 -136.767205457156 17 1020.62 1257.60772025170 -236.987720251705 18 987.48 1302.39517566745 -314.915175667451 19 919.32 1503.53278904737 -584.212789047373 20 919.14 1581.10521420105 -661.96521420105 21 872.81 1836.06677518619 -963.256775186193 22 797.87 2064.51505423660 -1266.64505423660 23 735.09 2179.27914021851 -1444.18914021851 24 825.88 2057.05807130337 -1231.17807130337 25 903.25 1860.12699367616 -956.876993676163 26 896.24 1988.16619628181 -1091.92619628181 27 968.75 1989.41937368322 -1020.66937368322 28 1166.36 1392.86288640964 -226.502886409641 29 1282.83 1009.41979689359 273.410203106413 30 1267.38 966.33586865462 301.04413134538 31 1280 1014.14079497181 265.859205028189 32 1400.38 828.345979021076 572.034020978925 33 1385.59 815.581446178638 570.008553821362 34 1322.7 1163.10294313434 159.597056865660 35 1330.63 946.007749270379 384.622250729622 36 1378.55 1043.61537864604 334.934621353959 37 1468.36 643.54884054745 824.81115945255 38 1481.14 586.244194765567 894.895805234433 39 1549.38 317.186515570651 1232.19348442935 40 1526.75 538.746774195778 988.003225804222 41 1473.99 766.324436735117 707.665563264883 42 1455.27 770.532269611176 684.737730388824 43 1503.35 780.279199837335 723.070800162665 44 1530.62 888.487258159224 642.132741840776 45 1482.37 1010.23016828862 472.139831711376 46 1420.86 1121.73278069811 299.127219301894 47 1406.82 1122.64159514045 284.178404859553 48 1438.24 1179.37875580835 258.861244191652 49 1418.3 1267.65069027816 150.649309721841 50 1400.63 1496.08930721538 -95.4593072153769 51 1377.94 1560.18997859837 -182.249978598374 52 1335.85 1674.65899322706 -338.80899322706 53 1303.82 1683.56908945558 -379.749089455585 54 1276.66 1832.71423432557 -556.054234325567 55 1270.2 1907.67880852277 -637.47880852277 56 1270.09 1983.48114117953 -713.39114117953 57 1310.61 1818.13786279297 -507.527862792975 58 1294.87 1897.79033413742 -602.920334137421 59 1280.66 2063.41873666159 -782.758736661586 60 1280.08 2039.40993597971 -759.329935979712 61 1248.29 2204.98695434495 -956.696954344946 62 1249.48 2405.71411073895 -1156.23411073895 63 1207.01 2655.86203696329 -1448.85203696329 64 1228.81 2657.7412324134 -1428.9312324134 65 1220.33 2877.87432236572 -1657.54432236572 66 1234.18 2973.83028815660 -1739.65028815660 67 1191.33 3088.09430769680 -1896.76430769680 68 1191.5 3615.59113603547 -2424.09113603547 69 11008.9 3256.00214508583 7752.89785491417 70 4348.77 2958.47270862990 1390.29729137010 71 14195.35 5422.48481556862 8772.86518443138 72 12 4623.84941576698 -4611.84941576698 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 10 4.87468363857662e-07 9.74936727715325e-07 0.999999512531636 11 3.12091892860340e-09 6.24183785720681e-09 0.999999996879081 12 2.99971876783194e-11 5.99943753566387e-11 0.999999999970003 13 1.62094173540876e-13 3.24188347081751e-13 0.999999999999838 14 5.75651669508389e-14 1.15130333901678e-13 0.999999999999942 15 6.95481730455344e-16 1.39096346091069e-15 1 16 6.27756798343442e-18 1.25551359668688e-17 1 17 5.40960239270589e-20 1.08192047854118e-19 1 18 4.28573071765793e-22 8.57146143531587e-22 1 19 8.1715484372114e-24 1.63430968744228e-23 1 20 7.23659460762464e-26 1.44731892152493e-25 1 21 8.71493621517294e-28 1.74298724303459e-27 1 22 1.24851151672813e-29 2.49702303345627e-29 1 23 1.11317502942603e-30 2.22635005885206e-30 1 24 1.04128761791383e-31 2.08257523582766e-31 1 25 2.51048493904311e-33 5.02096987808621e-33 1 26 4.02852875411891e-35 8.05705750823781e-35 1 27 2.46562233873463e-36 4.93124467746927e-36 1 28 6.47323413989503e-38 1.29464682797901e-37 1 29 3.43385083210430e-39 6.86770166420861e-39 1 30 3.57357031749248e-40 7.14714063498496e-40 1 31 8.10852722717705e-42 1.62170544543541e-41 1 32 1.35567544327289e-43 2.71135088654577e-43 1 33 2.50852148748147e-45 5.01704297496294e-45 1 34 2.29544544152612e-46 4.59089088305224e-46 1 35 1.34532349848433e-46 2.69064699696866e-46 1 36 1.4274517182839e-45 2.8549034365678e-45 1 37 1.72360626794935e-45 3.44721253589870e-45 1 38 1.22997231242873e-46 2.45994462485747e-46 1 39 1.02329088226278e-46 2.04658176452555e-46 1 40 4.66330295234030e-48 9.32660590468059e-48 1 41 9.51267085054787e-50 1.90253417010957e-49 1 42 2.09668822335721e-51 4.19337644671442e-51 1 43 6.36821614616219e-53 1.27364322923244e-52 1 44 5.32825222291956e-54 1.06565044458391e-53 1 45 2.23656191293479e-55 4.47312382586958e-55 1 46 6.63685763042185e-57 1.32737152608437e-56 1 47 1.25593080939809e-58 2.51186161879618e-58 1 48 1.21723645619164e-59 2.43447291238329e-59 1 49 5.08365303499555e-60 1.01673060699911e-59 1 50 1.48883566250658e-59 2.97767132501317e-59 1 51 2.70242693629776e-60 5.40485387259551e-60 1 52 3.1506289605069e-61 6.3012579210138e-61 1 53 9.07602962651386e-63 1.81520592530277e-62 1 54 2.74776642812588e-63 5.49553285625175e-63 1 55 3.28756691686456e-62 6.57513383372912e-62 1 56 1.99551809903069e-52 3.99103619806137e-52 1 57 5.62934474285537e-53 1.12586894857107e-52 1 58 2.34938268061243e-54 4.69876536122485e-54 1 59 2.16774599118958e-54 4.33549198237915e-54 1 60 2.09672681768252e-52 4.19345363536504e-52 1 61 4.53481723576286e-49 9.06963447152572e-49 1 62 7.50166439480947e-46 1.50033287896189e-45 1 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 53 1 NOK 5% type I error level 53 1 NOK 10% type I error level 53 1 NOK

Charts produced by software:

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Parameters (Session):

Parameters (R input):

par1 = 2 ; par2 = Do not include Seasonal 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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