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Type 'q()' to quit R. > x <- array(list(519164,0,517009,0,509933,0,509127,0,500857,0,506971,0,569323,0,579714,0,577992,0,565464,0,547344,0,554788,0,562325,0,560854,0,555332,0,543599,0,536662,0,542722,0,593530,0,610763,0,612613,0,611324,0,594167,0,595454,0,590865,0,589379,0,584428,0,573100,0,567456,0,569028,0,620735,0,628884,0,628232,0,612117,0,595404,0,597141,0,593408,0,590072,0,579799,0,574205,0,572775,0,572942,0,619567,0,625809,0,619916,0,587625,0,565742,0,557274,0,560576,1,548854,1,531673,1,525919,1,511038,1,498662,1,555362,1,564591,1,541657,1,527070,1,509846,1,514258,1,516922,1,507561,1,492622,1,490243,1,469357,1,477580,1,528379,1,533590,1,517945,1,506174,1,501866,1),dim=c(2,71),dimnames=list(c('WerklozenTotaal','Kredietcrisis'),1:71)) > y <- array(NA,dim=c(2,71),dimnames=list(c('WerklozenTotaal','Kredietcrisis'),1:71)) > for (i in 1:dim(x)[1]) + { + for (j in 1:dim(x)[2]) + { + y[i,j] <- as.numeric(x[i,j]) + } + } > par3 = 'No Linear Trend' > par2 = 'Do not include Seasonal Dummies' > par1 = '1' > #'GNU S' R Code compiled by R2WASP v. 1.0.44 () > #Author: Prof. Dr. P. Wessa > #To cite this work: AUTHOR(S), (YEAR), YOUR SOFTWARE TITLE (vNUMBER) in Free Statistics Software (v$_version), Office for Research Development and Education, URL http://www.wessa.net/rwasp_YOURPAGE.wasp/ > #Source of accompanying publication: Office for Research, Development, and Education > #Technical description: Write here your technical program description (don't use hard returns!) > library(lattice) > 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 WerklozenTotaal Kredietcrisis 1 519164 0 2 517009 0 3 509933 0 4 509127 0 5 500857 0 6 506971 0 7 569323 0 8 579714 0 9 577992 0 10 565464 0 11 547344 0 12 554788 0 13 562325 0 14 560854 0 15 555332 0 16 543599 0 17 536662 0 18 542722 0 19 593530 0 20 610763 0 21 612613 0 22 611324 0 23 594167 0 24 595454 0 25 590865 0 26 589379 0 27 584428 0 28 573100 0 29 567456 0 30 569028 0 31 620735 0 32 628884 0 33 628232 0 34 612117 0 35 595404 0 36 597141 0 37 593408 0 38 590072 0 39 579799 0 40 574205 0 41 572775 0 42 572942 0 43 619567 0 44 625809 0 45 619916 0 46 587625 0 47 565742 0 48 557274 0 49 560576 1 50 548854 1 51 531673 1 52 525919 1 53 511038 1 54 498662 1 55 555362 1 56 564591 1 57 541657 1 58 527070 1 59 509846 1 60 514258 1 61 516922 1 62 507561 1 63 492622 1 64 490243 1 65 469357 1 66 477580 1 67 528379 1 68 533590 1 69 517945 1 70 506174 1 71 501866 1 > k <- length(x[1,]) > df <- as.data.frame(x) > (mylm <- lm(df)) Call: lm(formula = df) Coefficients: (Intercept) Kredietcrisis 574853 -56081 > (mysum <- summary(mylm)) Call: lm(formula = df) Residuals: Min 1Q Median 3Q Max -73995.8 -17242.2 -826.5 19932.7 54031.2 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 574853 4544 126.513 < 2e-16 *** Kredietcrisis -56081 7983 -7.025 1.2e-09 *** --- Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 Residual standard error: 31480 on 69 degrees of freedom Multiple R-squared: 0.417, Adjusted R-squared: 0.4085 F-statistic: 49.35 on 1 and 69 DF, p-value: 1.200e-09 > postscript(file="/var/www/html/rcomp/tmp/1gg6p1229865135.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) > 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() null device 1 > postscript(file="/var/www/html/rcomp/tmp/24u151229865135.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) > plot(mysum$resid, type='b', pch=19, main='Residuals', ylab='value of Residuals', xlab='time or index') > grid() > dev.off() null device 1 > postscript(file="/var/www/html/rcomp/tmp/3fuk01229865135.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) > hist(mysum$resid, main='Residual Histogram', xlab='values of Residuals') > grid() > dev.off() null device 1 > postscript(file="/var/www/html/rcomp/tmp/4vc1g1229865135.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) > densityplot(~mysum$resid,col='black',main='Residual Density Plot', xlab='values of Residuals') > dev.off() null device 1 > postscript(file="/var/www/html/rcomp/tmp/5vz4l1229865135.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) > qqnorm(mysum$resid, main='Residual Normal Q-Q Plot') > grid() > dev.off() null device 1 > (myerror <- as.ts(mysum$resid)) Time Series: Start = 1 End = 71 Frequency = 1 1 2 3 4 5 6 -55688.7917 -57843.7917 -64919.7917 -65725.7917 -73995.7917 -67881.7917 7 8 9 10 11 12 -5529.7917 4861.2083 3139.2083 -9388.7917 -27508.7917 -20064.7917 13 14 15 16 17 18 -12527.7917 -13998.7917 -19520.7917 -31253.7917 -38190.7917 -32130.7917 19 20 21 22 23 24 18677.2083 35910.2083 37760.2083 36471.2083 19314.2083 20601.2083 25 26 27 28 29 30 16012.2083 14526.2083 9575.2083 -1752.7917 -7396.7917 -5824.7917 31 32 33 34 35 36 45882.2083 54031.2083 53379.2083 37264.2083 20551.2083 22288.2083 37 38 39 40 41 42 18555.2083 15219.2083 4946.2083 -647.7917 -2077.7917 -1910.7917 43 44 45 46 47 48 44714.2083 50956.2083 45063.2083 12772.2083 -9110.7917 -17578.7917 49 50 51 52 53 54 41804.4783 30082.4783 12901.4783 7147.4783 -7733.5217 -20109.5217 55 56 57 58 59 60 36590.4783 45819.4783 22885.4783 8298.4783 -8925.5217 -4513.5217 61 62 63 64 65 66 -1849.5217 -11210.5217 -26149.5217 -28528.5217 -49414.5217 -41191.5217 67 68 69 70 71 9607.4783 14818.4783 -826.5217 -12597.5217 -16905.5217 > postscript(file="/var/www/html/rcomp/tmp/6zkzi1229865135.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) > dum <- cbind(lag(myerror,k=1),myerror) > dum Time Series: Start = 0 End = 71 Frequency = 1 lag(myerror, k = 1) myerror 0 -55688.7917 NA 1 -57843.7917 -55688.7917 2 -64919.7917 -57843.7917 3 -65725.7917 -64919.7917 4 -73995.7917 -65725.7917 5 -67881.7917 -73995.7917 6 -5529.7917 -67881.7917 7 4861.2083 -5529.7917 8 3139.2083 4861.2083 9 -9388.7917 3139.2083 10 -27508.7917 -9388.7917 11 -20064.7917 -27508.7917 12 -12527.7917 -20064.7917 13 -13998.7917 -12527.7917 14 -19520.7917 -13998.7917 15 -31253.7917 -19520.7917 16 -38190.7917 -31253.7917 17 -32130.7917 -38190.7917 18 18677.2083 -32130.7917 19 35910.2083 18677.2083 20 37760.2083 35910.2083 21 36471.2083 37760.2083 22 19314.2083 36471.2083 23 20601.2083 19314.2083 24 16012.2083 20601.2083 25 14526.2083 16012.2083 26 9575.2083 14526.2083 27 -1752.7917 9575.2083 28 -7396.7917 -1752.7917 29 -5824.7917 -7396.7917 30 45882.2083 -5824.7917 31 54031.2083 45882.2083 32 53379.2083 54031.2083 33 37264.2083 53379.2083 34 20551.2083 37264.2083 35 22288.2083 20551.2083 36 18555.2083 22288.2083 37 15219.2083 18555.2083 38 4946.2083 15219.2083 39 -647.7917 4946.2083 40 -2077.7917 -647.7917 41 -1910.7917 -2077.7917 42 44714.2083 -1910.7917 43 50956.2083 44714.2083 44 45063.2083 50956.2083 45 12772.2083 45063.2083 46 -9110.7917 12772.2083 47 -17578.7917 -9110.7917 48 41804.4783 -17578.7917 49 30082.4783 41804.4783 50 12901.4783 30082.4783 51 7147.4783 12901.4783 52 -7733.5217 7147.4783 53 -20109.5217 -7733.5217 54 36590.4783 -20109.5217 55 45819.4783 36590.4783 56 22885.4783 45819.4783 57 8298.4783 22885.4783 58 -8925.5217 8298.4783 59 -4513.5217 -8925.5217 60 -1849.5217 -4513.5217 61 -11210.5217 -1849.5217 62 -26149.5217 -11210.5217 63 -28528.5217 -26149.5217 64 -49414.5217 -28528.5217 65 -41191.5217 -49414.5217 66 9607.4783 -41191.5217 67 14818.4783 9607.4783 68 -826.5217 14818.4783 69 -12597.5217 -826.5217 70 -16905.5217 -12597.5217 71 NA -16905.5217 > dum1 <- dum[2:length(myerror),] > dum1 lag(myerror, k = 1) myerror [1,] -57843.7917 -55688.7917 [2,] -64919.7917 -57843.7917 [3,] -65725.7917 -64919.7917 [4,] -73995.7917 -65725.7917 [5,] -67881.7917 -73995.7917 [6,] -5529.7917 -67881.7917 [7,] 4861.2083 -5529.7917 [8,] 3139.2083 4861.2083 [9,] -9388.7917 3139.2083 [10,] -27508.7917 -9388.7917 [11,] -20064.7917 -27508.7917 [12,] -12527.7917 -20064.7917 [13,] -13998.7917 -12527.7917 [14,] -19520.7917 -13998.7917 [15,] -31253.7917 -19520.7917 [16,] -38190.7917 -31253.7917 [17,] -32130.7917 -38190.7917 [18,] 18677.2083 -32130.7917 [19,] 35910.2083 18677.2083 [20,] 37760.2083 35910.2083 [21,] 36471.2083 37760.2083 [22,] 19314.2083 36471.2083 [23,] 20601.2083 19314.2083 [24,] 16012.2083 20601.2083 [25,] 14526.2083 16012.2083 [26,] 9575.2083 14526.2083 [27,] -1752.7917 9575.2083 [28,] -7396.7917 -1752.7917 [29,] -5824.7917 -7396.7917 [30,] 45882.2083 -5824.7917 [31,] 54031.2083 45882.2083 [32,] 53379.2083 54031.2083 [33,] 37264.2083 53379.2083 [34,] 20551.2083 37264.2083 [35,] 22288.2083 20551.2083 [36,] 18555.2083 22288.2083 [37,] 15219.2083 18555.2083 [38,] 4946.2083 15219.2083 [39,] -647.7917 4946.2083 [40,] -2077.7917 -647.7917 [41,] -1910.7917 -2077.7917 [42,] 44714.2083 -1910.7917 [43,] 50956.2083 44714.2083 [44,] 45063.2083 50956.2083 [45,] 12772.2083 45063.2083 [46,] -9110.7917 12772.2083 [47,] -17578.7917 -9110.7917 [48,] 41804.4783 -17578.7917 [49,] 30082.4783 41804.4783 [50,] 12901.4783 30082.4783 [51,] 7147.4783 12901.4783 [52,] -7733.5217 7147.4783 [53,] -20109.5217 -7733.5217 [54,] 36590.4783 -20109.5217 [55,] 45819.4783 36590.4783 [56,] 22885.4783 45819.4783 [57,] 8298.4783 22885.4783 [58,] -8925.5217 8298.4783 [59,] -4513.5217 -8925.5217 [60,] -1849.5217 -4513.5217 [61,] -11210.5217 -1849.5217 [62,] -26149.5217 -11210.5217 [63,] -28528.5217 -26149.5217 [64,] -49414.5217 -28528.5217 [65,] -41191.5217 -49414.5217 [66,] 9607.4783 -41191.5217 [67,] 14818.4783 9607.4783 [68,] -826.5217 14818.4783 [69,] -12597.5217 -826.5217 [70,] -16905.5217 -12597.5217 > z <- as.data.frame(dum1) > z lag(myerror, k = 1) myerror 1 -57843.7917 -55688.7917 2 -64919.7917 -57843.7917 3 -65725.7917 -64919.7917 4 -73995.7917 -65725.7917 5 -67881.7917 -73995.7917 6 -5529.7917 -67881.7917 7 4861.2083 -5529.7917 8 3139.2083 4861.2083 9 -9388.7917 3139.2083 10 -27508.7917 -9388.7917 11 -20064.7917 -27508.7917 12 -12527.7917 -20064.7917 13 -13998.7917 -12527.7917 14 -19520.7917 -13998.7917 15 -31253.7917 -19520.7917 16 -38190.7917 -31253.7917 17 -32130.7917 -38190.7917 18 18677.2083 -32130.7917 19 35910.2083 18677.2083 20 37760.2083 35910.2083 21 36471.2083 37760.2083 22 19314.2083 36471.2083 23 20601.2083 19314.2083 24 16012.2083 20601.2083 25 14526.2083 16012.2083 26 9575.2083 14526.2083 27 -1752.7917 9575.2083 28 -7396.7917 -1752.7917 29 -5824.7917 -7396.7917 30 45882.2083 -5824.7917 31 54031.2083 45882.2083 32 53379.2083 54031.2083 33 37264.2083 53379.2083 34 20551.2083 37264.2083 35 22288.2083 20551.2083 36 18555.2083 22288.2083 37 15219.2083 18555.2083 38 4946.2083 15219.2083 39 -647.7917 4946.2083 40 -2077.7917 -647.7917 41 -1910.7917 -2077.7917 42 44714.2083 -1910.7917 43 50956.2083 44714.2083 44 45063.2083 50956.2083 45 12772.2083 45063.2083 46 -9110.7917 12772.2083 47 -17578.7917 -9110.7917 48 41804.4783 -17578.7917 49 30082.4783 41804.4783 50 12901.4783 30082.4783 51 7147.4783 12901.4783 52 -7733.5217 7147.4783 53 -20109.5217 -7733.5217 54 36590.4783 -20109.5217 55 45819.4783 36590.4783 56 22885.4783 45819.4783 57 8298.4783 22885.4783 58 -8925.5217 8298.4783 59 -4513.5217 -8925.5217 60 -1849.5217 -4513.5217 61 -11210.5217 -1849.5217 62 -26149.5217 -11210.5217 63 -28528.5217 -26149.5217 64 -49414.5217 -28528.5217 65 -41191.5217 -49414.5217 66 9607.4783 -41191.5217 67 14818.4783 9607.4783 68 -826.5217 14818.4783 69 -12597.5217 -826.5217 70 -16905.5217 -12597.5217 > 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() null device 1 > postscript(file="/var/www/html/rcomp/tmp/7oz9s1229865135.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) > acf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Autocorrelation Function') > grid() > dev.off() null device 1 > postscript(file="/var/www/html/rcomp/tmp/8ew531229865135.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) > pacf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Partial Autocorrelation Function') > grid() > dev.off() null device 1 > postscript(file="/var/www/html/rcomp/tmp/97oqo1229865135.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) > opar <- par(mfrow = c(2,2), oma = c(0, 0, 1.1, 0)) > plot(mylm, las = 1, sub='Residual Diagnostics') > par(opar) > dev.off() null device 1 > > #Note: the /var/www/html/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab > load(file="/var/www/html/rcomp/createtable") > > a<-table.start() > a<-table.row.start(a) > a<-table.element(a, 'Multiple Linear Regression - Estimated Regression Equation', 1, TRUE) > a<-table.row.end(a) > myeq <- colnames(x)[1] > myeq <- paste(myeq, '[t] = ', sep='') > for (i in 1:k){ + if (mysum$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="/var/www/html/rcomp/tmp/10m45o1229865135.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
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="/var/www/html/rcomp/tmp/11orha1229865135.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="/var/www/html/rcomp/tmp/12m4m01229865135.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
Forecast', 1, TRUE) > a<-table.element(a, 'Residuals
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="/var/www/html/rcomp/tmp/13rcb31229865135.tab") > > system("convert tmp/1gg6p1229865135.ps tmp/1gg6p1229865135.png") > system("convert tmp/24u151229865135.ps tmp/24u151229865135.png") > system("convert tmp/3fuk01229865135.ps tmp/3fuk01229865135.png") > system("convert tmp/4vc1g1229865135.ps tmp/4vc1g1229865135.png") > system("convert tmp/5vz4l1229865135.ps tmp/5vz4l1229865135.png") > system("convert tmp/6zkzi1229865135.ps tmp/6zkzi1229865135.png") > system("convert tmp/7oz9s1229865135.ps tmp/7oz9s1229865135.png") > system("convert tmp/8ew531229865135.ps tmp/8ew531229865135.png") > system("convert tmp/97oqo1229865135.ps tmp/97oqo1229865135.png") > > > proc.time() user system elapsed 1.962 1.437 2.906