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Type 'q()' to quit R. > x <- array(list(95,2768,252,22,324,8760219,438465.0625,150,4108,333,29,308,8760195,438474.0625,4,4045,62,5,249,8760168,438480.0625,0,4572,85,8,14,8760135,438489.0625,0,4614,115,10,63,8760105,438495.0625,80,4321,176,16,130,8760072,438498.0625,95,3886,72,6,199,8760039,438504.0625,20,4206,57,5,32,8760012,438507.0625,90,4192,266,23,197,8759985,438513.0625,10,4051,69,6,113,8759955,4385190625,10,3746,62,5,149,8759922,438519.0625,50,3789,42,3,218,8759895,438525.0625,45,3771,44,4,53,8759865,438531.0625,60,3796,48,4,101,8759838,438534.0625,55,3885,77,7,332,8759811,438537.0625,3,4295,113,10,18,8759787,438540.0625,33,4467,147,13,50,8759760,438546.0625,0,4764,12,1,276,8759730,438552.0625,35,4313,38,3,350,8759703,438552.0625,45,4387,40,3,46,8759673,438558.0625),dim=c(7,20),dimnames=list(c('Sneeuwhoogte','hoogte(berg)','ruwheid','helling','Orientering','breedtegraad','lengte'),1:20)) > y <- array(NA,dim=c(7,20),dimnames=list(c('Sneeuwhoogte','hoogte(berg)','ruwheid','helling','Orientering','breedtegraad','lengte'),1:20)) > 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' > 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) > library(lmtest) Loading required package: zoo Attaching package: 'zoo' The following object(s) are masked from 'package:base': as.Date, as.Date.numeric > 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 Sneeuwhoogte hoogte(berg) ruwheid helling Orientering breedtegraad 1 95 2768 252 22 324 8760219 2 150 4108 333 29 308 8760195 3 4 4045 62 5 249 8760168 4 0 4572 85 8 14 8760135 5 0 4614 115 10 63 8760105 6 80 4321 176 16 130 8760072 7 95 3886 72 6 199 8760039 8 20 4206 57 5 32 8760012 9 90 4192 266 23 197 8759985 10 10 4051 69 6 113 8759955 11 10 3746 62 5 149 8759922 12 50 3789 42 3 218 8759895 13 45 3771 44 4 53 8759865 14 60 3796 48 4 101 8759838 15 55 3885 77 7 332 8759811 16 3 4295 113 10 18 8759787 17 33 4467 147 13 50 8759760 18 0 4764 12 1 276 8759730 19 35 4313 38 3 350 8759703 20 45 4387 40 3 46 8759673 lengte 1 438465.1 2 438474.1 3 438480.1 4 438489.1 5 438495.1 6 438498.1 7 438504.1 8 438507.1 9 438513.1 10 4385190625.0 11 438519.1 12 438525.1 13 438531.1 14 438534.1 15 438537.1 16 438540.1 17 438546.1 18 438552.1 19 438552.1 20 438558.1 > k <- length(x[1,]) > df <- as.data.frame(x) > (mylm <- lm(df)) Call: lm(formula = df) Coefficients: (Intercept) `hoogte(berg)` ruwheid helling Orientering 3.336e+05 -2.437e-02 9.202e-01 -6.776e+00 6.229e-02 breedtegraad lengte -3.807e-02 -4.678e-09 > (mysum <- summary(mylm)) Call: lm(formula = df) Residuals: Min 1Q Median 3Q Max -35.430 -17.212 -2.643 18.689 55.548 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 3.336e+05 4.384e+05 0.761 0.460 `hoogte(berg)` -2.437e-02 1.802e-02 -1.352 0.199 ruwheid 9.202e-01 2.037e+00 0.452 0.659 helling -6.776e+00 2.304e+01 -0.294 0.773 Orientering 6.229e-02 6.746e-02 0.923 0.373 breedtegraad -3.807e-02 5.005e-02 -0.761 0.460 lengte -4.678e-09 7.017e-09 -0.667 0.517 Residual standard error: 29.58 on 13 degrees of freedom Multiple R-squared: 0.6493, Adjusted R-squared: 0.4874 F-statistic: 4.011 on 6 and 13 DF, p-value: 0.01707 > 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 + } > postscript(file="/var/fisher/rcomp/tmp/1941e1352109808.ps",horizontal=F,onefile=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$resid) > grid() > dev.off() null device 1 > postscript(file="/var/fisher/rcomp/tmp/23lcz1352109808.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) > plot(mysum$resid, type='b', pch=19, main='Residuals', ylab='value of Residuals', xlab='time or index') > grid() > dev.off() null device 1 > postscript(file="/var/fisher/rcomp/tmp/3se5l1352109808.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) > hist(mysum$resid, main='Residual Histogram', xlab='values of Residuals') > grid() > dev.off() null device 1 > postscript(file="/var/fisher/rcomp/tmp/4lqoo1352109808.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) > densityplot(~mysum$resid,col='black',main='Residual Density Plot', xlab='values of Residuals') > dev.off() null device 1 > postscript(file="/var/fisher/rcomp/tmp/5af9b1352109808.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) > qqnorm(mysum$resid, main='Residual Normal Q-Q Plot') > qqline(mysum$resid) > grid() > dev.off() null device 1 > (myerror <- as.ts(mysum$resid)) Time Series: Start = 1 End = 20 Frequency = 1 1 2 3 4 5 -2.984654e+01 3.078608e+01 -2.735458e+01 -5.968316e+00 -2.319273e+01 6 7 8 9 10 2.876236e+01 5.554799e+01 4.746320e+00 -7.251667e+00 -7.798778e-08 11 12 13 14 15 -3.177778e+01 8.796240e+00 1.742815e+01 2.533896e+01 7.344221e-01 16 17 18 19 20 -3.542975e+01 -1.521798e+01 -1.328551e+01 -5.285513e+00 2.246984e+01 > postscript(file="/var/fisher/rcomp/tmp/673ez1352109808.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) > dum <- cbind(lag(myerror,k=1),myerror) > dum Time Series: Start = 0 End = 20 Frequency = 1 lag(myerror, k = 1) myerror 0 -2.984654e+01 NA 1 3.078608e+01 -2.984654e+01 2 -2.735458e+01 3.078608e+01 3 -5.968316e+00 -2.735458e+01 4 -2.319273e+01 -5.968316e+00 5 2.876236e+01 -2.319273e+01 6 5.554799e+01 2.876236e+01 7 4.746320e+00 5.554799e+01 8 -7.251667e+00 4.746320e+00 9 -7.798778e-08 -7.251667e+00 10 -3.177778e+01 -7.798778e-08 11 8.796240e+00 -3.177778e+01 12 1.742815e+01 8.796240e+00 13 2.533896e+01 1.742815e+01 14 7.344221e-01 2.533896e+01 15 -3.542975e+01 7.344221e-01 16 -1.521798e+01 -3.542975e+01 17 -1.328551e+01 -1.521798e+01 18 -5.285513e+00 -1.328551e+01 19 2.246984e+01 -5.285513e+00 20 NA 2.246984e+01 > dum1 <- dum[2:length(myerror),] > dum1 lag(myerror, k = 1) myerror [1,] 3.078608e+01 -2.984654e+01 [2,] -2.735458e+01 3.078608e+01 [3,] -5.968316e+00 -2.735458e+01 [4,] -2.319273e+01 -5.968316e+00 [5,] 2.876236e+01 -2.319273e+01 [6,] 5.554799e+01 2.876236e+01 [7,] 4.746320e+00 5.554799e+01 [8,] -7.251667e+00 4.746320e+00 [9,] -7.798778e-08 -7.251667e+00 [10,] -3.177778e+01 -7.798778e-08 [11,] 8.796240e+00 -3.177778e+01 [12,] 1.742815e+01 8.796240e+00 [13,] 2.533896e+01 1.742815e+01 [14,] 7.344221e-01 2.533896e+01 [15,] -3.542975e+01 7.344221e-01 [16,] -1.521798e+01 -3.542975e+01 [17,] -1.328551e+01 -1.521798e+01 [18,] -5.285513e+00 -1.328551e+01 [19,] 2.246984e+01 -5.285513e+00 > z <- as.data.frame(dum1) > z lag(myerror, k = 1) myerror 1 3.078608e+01 -2.984654e+01 2 -2.735458e+01 3.078608e+01 3 -5.968316e+00 -2.735458e+01 4 -2.319273e+01 -5.968316e+00 5 2.876236e+01 -2.319273e+01 6 5.554799e+01 2.876236e+01 7 4.746320e+00 5.554799e+01 8 -7.251667e+00 4.746320e+00 9 -7.798778e-08 -7.251667e+00 10 -3.177778e+01 -7.798778e-08 11 8.796240e+00 -3.177778e+01 12 1.742815e+01 8.796240e+00 13 2.533896e+01 1.742815e+01 14 7.344221e-01 2.533896e+01 15 -3.542975e+01 7.344221e-01 16 -1.521798e+01 -3.542975e+01 17 -1.328551e+01 -1.521798e+01 18 -5.285513e+00 -1.328551e+01 19 2.246984e+01 -5.285513e+00 > 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/fisher/rcomp/tmp/7c8zf1352109808.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) > acf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Autocorrelation Function') > grid() > dev.off() null device 1 > postscript(file="/var/fisher/rcomp/tmp/8otrb1352109808.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) > pacf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Partial Autocorrelation Function') > grid() > dev.off() null device 1 > postscript(file="/var/fisher/rcomp/tmp/9cbjh1352109808.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) > opar <- par(mfrow = c(2,2), oma = c(0, 0, 1.1, 0)) > plot(mylm, las = 1, sub='Residual Diagnostics') Warning messages: 1: Not plotting observations with leverage one: 10 2: Not plotting observations with leverage one: 10 > par(opar) > dev.off() null device 1 > if (n > n25) { + postscript(file="/var/fisher/rcomp/tmp/10sfcf1352109808.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) + plot(kp3:nmkm3,gqarr[,2], main='Goldfeld-Quandt test',ylab='2-sided p-value',xlab='breakpoint') + grid() + dev.off() + } > > #Note: the /var/fisher/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab > load(file="/var/fisher/rcomp/createtable") > > a<-table.start() > a<-table.row.start(a) > a<-table.element(a, 'Multiple Linear Regression - Estimated Regression Equation', 1, TRUE) > a<-table.row.end(a) > myeq <- colnames(x)[1] > myeq <- paste(myeq, '[t] = ', sep='') > for (i in 1:k){ + if (mysum$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/fisher/rcomp/tmp/1160ws1352109809.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/fisher/rcomp/tmp/128eau1352109809.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/fisher/rcomp/tmp/132ot21352109809.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/fisher/rcomp/tmp/14rgzm1352109809.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="/var/fisher/rcomp/tmp/15luyg1352109809.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="/var/fisher/rcomp/tmp/16n17n1352109809.tab") + } > > try(system("convert tmp/1941e1352109808.ps tmp/1941e1352109808.png",intern=TRUE)) character(0) > try(system("convert tmp/23lcz1352109808.ps tmp/23lcz1352109808.png",intern=TRUE)) character(0) > try(system("convert tmp/3se5l1352109808.ps tmp/3se5l1352109808.png",intern=TRUE)) character(0) > try(system("convert tmp/4lqoo1352109808.ps tmp/4lqoo1352109808.png",intern=TRUE)) character(0) > try(system("convert tmp/5af9b1352109808.ps tmp/5af9b1352109808.png",intern=TRUE)) character(0) > try(system("convert tmp/673ez1352109808.ps tmp/673ez1352109808.png",intern=TRUE)) character(0) > try(system("convert tmp/7c8zf1352109808.ps tmp/7c8zf1352109808.png",intern=TRUE)) character(0) > try(system("convert tmp/8otrb1352109808.ps tmp/8otrb1352109808.png",intern=TRUE)) character(0) > try(system("convert tmp/9cbjh1352109808.ps tmp/9cbjh1352109808.png",intern=TRUE)) character(0) > try(system("convert tmp/10sfcf1352109808.ps tmp/10sfcf1352109808.png",intern=TRUE)) convert: unable to open image `tmp/10sfcf1352109808.ps': @ error/blob.c/OpenBlob/2587. convert: missing an image filename `tmp/10sfcf1352109808.png' @ error/convert.c/ConvertImageCommand/3011. character(0) attr(,"status") [1] 1 Warning message: running command 'convert tmp/10sfcf1352109808.ps tmp/10sfcf1352109808.png' had status 1 > > > proc.time() user system elapsed 4.925 0.969 5.898