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Type 'q()' to quit R. > x <- array(list(274412,0,272433,0,268361,0,268586,0,264768,0,269974,0,304744,0,309365,0,308347,0,298427,0,289231,0,291975,0,294912,0,293488,0,290555,0,284736,0,281818,0,287854,0,316263,0,325412,0,326011,0,328282,0,317480,0,317539,0,313737,0,312276,0,309391,0,302950,0,300316,0,304035,0,333476,0,337698,0,335932,0,323931,0,313927,0,314485,0,313218,0,309664,0,302963,0,298989,0,298423,0,301631,0,329765,0,335083,0,327616,0,309119,0,295916,0,291413,0,291542,1,284678,1,276475,1,272566,1,264981,1,263290,1,296806,1,303598,1,286994,1,276427,1,266424,1,267153,1,268381,1,262522,1,255542,1,253158,1,243803,1,250741,1,280445,1,285257,1,270976,1,261076,1,255603,1),dim=c(2,71),dimnames=list(c('WerklozenVrouwen','Kredietcrisis'),1:71)) > y <- array(NA,dim=c(2,71),dimnames=list(c('WerklozenVrouwen','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 WerklozenVrouwen Kredietcrisis 1 274412 0 2 272433 0 3 268361 0 4 268586 0 5 264768 0 6 269974 0 7 304744 0 8 309365 0 9 308347 0 10 298427 0 11 289231 0 12 291975 0 13 294912 0 14 293488 0 15 290555 0 16 284736 0 17 281818 0 18 287854 0 19 316263 0 20 325412 0 21 326011 0 22 328282 0 23 317480 0 24 317539 0 25 313737 0 26 312276 0 27 309391 0 28 302950 0 29 300316 0 30 304035 0 31 333476 0 32 337698 0 33 335932 0 34 323931 0 35 313927 0 36 314485 0 37 313218 0 38 309664 0 39 302963 0 40 298989 0 41 298423 0 42 301631 0 43 329765 0 44 335083 0 45 327616 0 46 309119 0 47 295916 0 48 291413 0 49 291542 1 50 284678 1 51 276475 1 52 272566 1 53 264981 1 54 263290 1 55 296806 1 56 303598 1 57 286994 1 58 276427 1 59 266424 1 60 267153 1 61 268381 1 62 262522 1 63 255542 1 64 253158 1 65 243803 1 66 250741 1 67 280445 1 68 285257 1 69 270976 1 70 261076 1 71 255603 1 > k <- length(x[1,]) > df <- as.data.frame(x) > (mylm <- lm(df)) Call: lm(formula = df) Coefficients: (Intercept) Kredietcrisis 304186 -32950 > (mysum <- summary(mylm)) Call: lm(formula = df) Residuals: Min 1Q Median 3Q Max -39418.0 -11454.5 -260.4 12685.5 33512.0 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 304186 2620 116.106 < 2e-16 *** Kredietcrisis -32950 4603 -7.158 6.87e-10 *** --- Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 Residual standard error: 18150 on 69 degrees of freedom Multiple R-squared: 0.4261, Adjusted R-squared: 0.4178 F-statistic: 51.24 on 1 and 69 DF, p-value: 6.871e-10 > postscript(file="/var/www/html/rcomp/tmp/1qxr51229866289.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/2oyto1229866289.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) > plot(mysum$resid, type='b', pch=19, main='Residuals', ylab='value of Residuals', xlab='time or index') > grid() > dev.off() null device 1 > postscript(file="/var/www/html/rcomp/tmp/3m5xg1229866289.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) > hist(mysum$resid, main='Residual Histogram', xlab='values of Residuals') > grid() > dev.off() null device 1 > postscript(file="/var/www/html/rcomp/tmp/4wee11229866289.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) > densityplot(~mysum$resid,col='black',main='Residual Density Plot', xlab='values of Residuals') > dev.off() null device 1 > postscript(file="/var/www/html/rcomp/tmp/5v0701229866289.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) > qqnorm(mysum$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 -29773.9792 -31752.9792 -35824.9792 -35599.9792 -39417.9792 -34211.9792 7 8 9 10 11 12 558.0208 5179.0208 4161.0208 -5758.9792 -14954.9792 -12210.9792 13 14 15 16 17 18 -9273.9792 -10697.9792 -13630.9792 -19449.9792 -22367.9792 -16331.9792 19 20 21 22 23 24 12077.0208 21226.0208 21825.0208 24096.0208 13294.0208 13353.0208 25 26 27 28 29 30 9551.0208 8090.0208 5205.0208 -1235.9792 -3869.9792 -150.9792 31 32 33 34 35 36 29290.0208 33512.0208 31746.0208 19745.0208 9741.0208 10299.0208 37 38 39 40 41 42 9032.0208 5478.0208 -1222.9792 -5196.9792 -5762.9792 -2554.9792 43 44 45 46 47 48 25579.0208 30897.0208 23430.0208 4933.0208 -8269.9792 -12772.9792 49 50 51 52 53 54 20305.5652 13441.5652 5238.5652 1329.5652 -6255.4348 -7946.4348 55 56 57 58 59 60 25569.5652 32361.5652 15757.5652 5190.5652 -4812.4348 -4083.4348 61 62 63 64 65 66 -2855.4348 -8714.4348 -15694.4348 -18078.4348 -27433.4348 -20495.4348 67 68 69 70 71 9208.5652 14020.5652 -260.4348 -10160.4348 -15633.4348 > postscript(file="/var/www/html/rcomp/tmp/67vgo1229866289.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 -29773.9792 NA 1 -31752.9792 -29773.9792 2 -35824.9792 -31752.9792 3 -35599.9792 -35824.9792 4 -39417.9792 -35599.9792 5 -34211.9792 -39417.9792 6 558.0208 -34211.9792 7 5179.0208 558.0208 8 4161.0208 5179.0208 9 -5758.9792 4161.0208 10 -14954.9792 -5758.9792 11 -12210.9792 -14954.9792 12 -9273.9792 -12210.9792 13 -10697.9792 -9273.9792 14 -13630.9792 -10697.9792 15 -19449.9792 -13630.9792 16 -22367.9792 -19449.9792 17 -16331.9792 -22367.9792 18 12077.0208 -16331.9792 19 21226.0208 12077.0208 20 21825.0208 21226.0208 21 24096.0208 21825.0208 22 13294.0208 24096.0208 23 13353.0208 13294.0208 24 9551.0208 13353.0208 25 8090.0208 9551.0208 26 5205.0208 8090.0208 27 -1235.9792 5205.0208 28 -3869.9792 -1235.9792 29 -150.9792 -3869.9792 30 29290.0208 -150.9792 31 33512.0208 29290.0208 32 31746.0208 33512.0208 33 19745.0208 31746.0208 34 9741.0208 19745.0208 35 10299.0208 9741.0208 36 9032.0208 10299.0208 37 5478.0208 9032.0208 38 -1222.9792 5478.0208 39 -5196.9792 -1222.9792 40 -5762.9792 -5196.9792 41 -2554.9792 -5762.9792 42 25579.0208 -2554.9792 43 30897.0208 25579.0208 44 23430.0208 30897.0208 45 4933.0208 23430.0208 46 -8269.9792 4933.0208 47 -12772.9792 -8269.9792 48 20305.5652 -12772.9792 49 13441.5652 20305.5652 50 5238.5652 13441.5652 51 1329.5652 5238.5652 52 -6255.4348 1329.5652 53 -7946.4348 -6255.4348 54 25569.5652 -7946.4348 55 32361.5652 25569.5652 56 15757.5652 32361.5652 57 5190.5652 15757.5652 58 -4812.4348 5190.5652 59 -4083.4348 -4812.4348 60 -2855.4348 -4083.4348 61 -8714.4348 -2855.4348 62 -15694.4348 -8714.4348 63 -18078.4348 -15694.4348 64 -27433.4348 -18078.4348 65 -20495.4348 -27433.4348 66 9208.5652 -20495.4348 67 14020.5652 9208.5652 68 -260.4348 14020.5652 69 -10160.4348 -260.4348 70 -15633.4348 -10160.4348 71 NA -15633.4348 > dum1 <- dum[2:length(myerror),] > dum1 lag(myerror, k = 1) myerror [1,] -31752.9792 -29773.9792 [2,] -35824.9792 -31752.9792 [3,] -35599.9792 -35824.9792 [4,] -39417.9792 -35599.9792 [5,] -34211.9792 -39417.9792 [6,] 558.0208 -34211.9792 [7,] 5179.0208 558.0208 [8,] 4161.0208 5179.0208 [9,] -5758.9792 4161.0208 [10,] -14954.9792 -5758.9792 [11,] -12210.9792 -14954.9792 [12,] -9273.9792 -12210.9792 [13,] -10697.9792 -9273.9792 [14,] -13630.9792 -10697.9792 [15,] -19449.9792 -13630.9792 [16,] -22367.9792 -19449.9792 [17,] -16331.9792 -22367.9792 [18,] 12077.0208 -16331.9792 [19,] 21226.0208 12077.0208 [20,] 21825.0208 21226.0208 [21,] 24096.0208 21825.0208 [22,] 13294.0208 24096.0208 [23,] 13353.0208 13294.0208 [24,] 9551.0208 13353.0208 [25,] 8090.0208 9551.0208 [26,] 5205.0208 8090.0208 [27,] -1235.9792 5205.0208 [28,] -3869.9792 -1235.9792 [29,] -150.9792 -3869.9792 [30,] 29290.0208 -150.9792 [31,] 33512.0208 29290.0208 [32,] 31746.0208 33512.0208 [33,] 19745.0208 31746.0208 [34,] 9741.0208 19745.0208 [35,] 10299.0208 9741.0208 [36,] 9032.0208 10299.0208 [37,] 5478.0208 9032.0208 [38,] -1222.9792 5478.0208 [39,] -5196.9792 -1222.9792 [40,] -5762.9792 -5196.9792 [41,] -2554.9792 -5762.9792 [42,] 25579.0208 -2554.9792 [43,] 30897.0208 25579.0208 [44,] 23430.0208 30897.0208 [45,] 4933.0208 23430.0208 [46,] -8269.9792 4933.0208 [47,] -12772.9792 -8269.9792 [48,] 20305.5652 -12772.9792 [49,] 13441.5652 20305.5652 [50,] 5238.5652 13441.5652 [51,] 1329.5652 5238.5652 [52,] -6255.4348 1329.5652 [53,] -7946.4348 -6255.4348 [54,] 25569.5652 -7946.4348 [55,] 32361.5652 25569.5652 [56,] 15757.5652 32361.5652 [57,] 5190.5652 15757.5652 [58,] -4812.4348 5190.5652 [59,] -4083.4348 -4812.4348 [60,] -2855.4348 -4083.4348 [61,] -8714.4348 -2855.4348 [62,] -15694.4348 -8714.4348 [63,] -18078.4348 -15694.4348 [64,] -27433.4348 -18078.4348 [65,] -20495.4348 -27433.4348 [66,] 9208.5652 -20495.4348 [67,] 14020.5652 9208.5652 [68,] -260.4348 14020.5652 [69,] -10160.4348 -260.4348 [70,] -15633.4348 -10160.4348 > z <- as.data.frame(dum1) > z lag(myerror, k = 1) myerror 1 -31752.9792 -29773.9792 2 -35824.9792 -31752.9792 3 -35599.9792 -35824.9792 4 -39417.9792 -35599.9792 5 -34211.9792 -39417.9792 6 558.0208 -34211.9792 7 5179.0208 558.0208 8 4161.0208 5179.0208 9 -5758.9792 4161.0208 10 -14954.9792 -5758.9792 11 -12210.9792 -14954.9792 12 -9273.9792 -12210.9792 13 -10697.9792 -9273.9792 14 -13630.9792 -10697.9792 15 -19449.9792 -13630.9792 16 -22367.9792 -19449.9792 17 -16331.9792 -22367.9792 18 12077.0208 -16331.9792 19 21226.0208 12077.0208 20 21825.0208 21226.0208 21 24096.0208 21825.0208 22 13294.0208 24096.0208 23 13353.0208 13294.0208 24 9551.0208 13353.0208 25 8090.0208 9551.0208 26 5205.0208 8090.0208 27 -1235.9792 5205.0208 28 -3869.9792 -1235.9792 29 -150.9792 -3869.9792 30 29290.0208 -150.9792 31 33512.0208 29290.0208 32 31746.0208 33512.0208 33 19745.0208 31746.0208 34 9741.0208 19745.0208 35 10299.0208 9741.0208 36 9032.0208 10299.0208 37 5478.0208 9032.0208 38 -1222.9792 5478.0208 39 -5196.9792 -1222.9792 40 -5762.9792 -5196.9792 41 -2554.9792 -5762.9792 42 25579.0208 -2554.9792 43 30897.0208 25579.0208 44 23430.0208 30897.0208 45 4933.0208 23430.0208 46 -8269.9792 4933.0208 47 -12772.9792 -8269.9792 48 20305.5652 -12772.9792 49 13441.5652 20305.5652 50 5238.5652 13441.5652 51 1329.5652 5238.5652 52 -6255.4348 1329.5652 53 -7946.4348 -6255.4348 54 25569.5652 -7946.4348 55 32361.5652 25569.5652 56 15757.5652 32361.5652 57 5190.5652 15757.5652 58 -4812.4348 5190.5652 59 -4083.4348 -4812.4348 60 -2855.4348 -4083.4348 61 -8714.4348 -2855.4348 62 -15694.4348 -8714.4348 63 -18078.4348 -15694.4348 64 -27433.4348 -18078.4348 65 -20495.4348 -27433.4348 66 9208.5652 -20495.4348 67 14020.5652 9208.5652 68 -260.4348 14020.5652 69 -10160.4348 -260.4348 70 -15633.4348 -10160.4348 > 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/7fdx11229866289.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) > acf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Autocorrelation Function') > grid() > dev.off() null device 1 > postscript(file="/var/www/html/rcomp/tmp/8xfg71229866289.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) > pacf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Partial Autocorrelation Function') > grid() > dev.off() null device 1 > postscript(file="/var/www/html/rcomp/tmp/9ia2f1229866289.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) > opar <- par(mfrow = c(2,2), oma = c(0, 0, 1.1, 0)) > plot(mylm, las = 1, sub='Residual Diagnostics') > par(opar) > dev.off() null device 1 > > #Note: the /var/www/html/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab > load(file="/var/www/html/rcomp/createtable") > > a<-table.start() > a<-table.row.start(a) > a<-table.element(a, 'Multiple Linear Regression - Estimated Regression Equation', 1, TRUE) > a<-table.row.end(a) > myeq <- colnames(x)[1] > myeq <- paste(myeq, '[t] = ', sep='') > for (i in 1:k){ + if (mysum$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/10iule1229866289.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/11bz0u1229866289.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/12nu2j1229866289.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/13mtn41229866289.tab") > > system("convert tmp/1qxr51229866289.ps tmp/1qxr51229866289.png") > system("convert tmp/2oyto1229866289.ps tmp/2oyto1229866289.png") > system("convert tmp/3m5xg1229866289.ps tmp/3m5xg1229866289.png") > system("convert tmp/4wee11229866289.ps tmp/4wee11229866289.png") > system("convert tmp/5v0701229866289.ps tmp/5v0701229866289.png") > system("convert tmp/67vgo1229866289.ps tmp/67vgo1229866289.png") > system("convert tmp/7fdx11229866289.ps tmp/7fdx11229866289.png") > system("convert tmp/8xfg71229866289.ps tmp/8xfg71229866289.png") > system("convert tmp/9ia2f1229866289.ps tmp/9ia2f1229866289.png") > > > proc.time() user system elapsed 1.935 1.430 2.357