R version 2.15.2 (2012-10-26) -- "Trick or Treat"
Copyright (C) 2012 The R Foundation for Statistical Computing
ISBN 3-900051-07-0
Platform: i686-pc-linux-gnu (32-bit)
R is free software and comes with ABSOLUTELY NO WARRANTY.
You are welcome to redistribute it under certain conditions.
Type 'license()' or 'licence()' for distribution details.
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Type 'contributors()' for more information and
'citation()' on how to cite R or R packages in publications.
Type 'demo()' for some demos, 'help()' for on-line help, or
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> x <- array(list(73,80,75,152,93,88,93,185,89,91,90,180,96,98,100,196,73,66,70,142,53,46,55,101,69,74,77,149,47,56,60,115,87,79,90,175,79,70,88,164,69,70,73,141,70,65,74,141,93,95,91,184,79,80,73,152,70,73,78,148,93,89,96,192,78,75,68,147,81,90,93,183,88,92,86,177,78,83,77,159,82,86,90,177,86,82,89,175,78,83,85,175,76,83,71,149,96,93,95,192),dim=c(4,25),dimnames=list(c('EXAM1','EXAM2','EXAM3','FINAL'),1:25))
> y <- array(NA,dim=c(4,25),dimnames=list(c('EXAM1','EXAM2','EXAM3','FINAL'),1:25))
> 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 = '4'
> par3 <- 'No Linear Trend'
> par2 <- 'Do not include Seasonal Dummies'
> par1 <- '4'
> #'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
FINAL EXAM1 EXAM2 EXAM3
1 152 73 80 75
2 185 93 88 93
3 180 89 91 90
4 196 96 98 100
5 142 73 66 70
6 101 53 46 55
7 149 69 74 77
8 115 47 56 60
9 175 87 79 90
10 164 79 70 88
11 141 69 70 73
12 141 70 65 74
13 184 93 95 91
14 152 79 80 73
15 148 70 73 78
16 192 93 89 96
17 147 78 75 68
18 183 81 90 93
19 177 88 92 86
20 159 78 83 77
21 177 82 86 90
22 175 86 82 89
23 175 78 83 85
24 149 76 83 71
25 192 96 93 95
> k <- length(x[1,])
> df <- as.data.frame(x)
> (mylm <- lm(df))
Call:
lm(formula = df)
Coefficients:
(Intercept) EXAM1 EXAM2 EXAM3
-4.3361 0.3559 0.5425 1.1674
> (mysum <- summary(mylm))
Call:
lm(formula = df)
Residuals:
Min 1Q Median 3Q Max
-3.7452 -1.6328 -0.2984 0.8046 7.3111
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -4.3361 3.7642 -1.152 0.26230
EXAM1 0.3559 0.1214 2.932 0.00796 **
EXAM2 0.5425 0.1008 5.379 2.46e-05 ***
EXAM3 1.1674 0.1030 11.333 2.08e-10 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 2.614 on 21 degrees of freedom
Multiple R-squared: 0.9897, Adjusted R-squared: 0.9882
F-statistic: 670.1 on 3 and 21 DF, p-value: < 2.2e-16
> 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/1mxux1353431768.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$resid)
> grid()
> dev.off()
null device
1
> postscript(file="/var/fisher/rcomp/tmp/2wgq61353431768.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556)
> plot(mysum$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/3wngx1353431768.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556)
> hist(mysum$resid, main='Residual Histogram', xlab='values of Residuals')
> grid()
> dev.off()
null device
1
> postscript(file="/var/fisher/rcomp/tmp/4wude1353431768.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556)
> densityplot(~mysum$resid,col='black',main='Residual Density Plot', xlab='values of Residuals')
> dev.off()
null device
1
> postscript(file="/var/fisher/rcomp/tmp/5inkf1353431768.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 = 25
Frequency = 1
1 2 3 4 5 6
-0.60720439 -0.08011472 -1.78158547 -3.74522647 2.82527930 -2.69391793
7 8 9 10 11 12
-1.26322740 2.17930272 0.44051606 -0.49442094 -2.42337551 -1.23416416
13 14 15 16 17 18
-2.54285759 -0.40794527 -3.24409108 2.87503387 3.49780782 1.10610639
19 20 21 22 23 24
-0.29838914 0.65065981 0.42257585 0.33634222 7.31110608 -1.63279846
25
0.80458840
> postscript(file="/var/fisher/rcomp/tmp/6q6xe1353431768.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 = 25
Frequency = 1
lag(myerror, k = 1) myerror
0 -0.60720439 NA
1 -0.08011472 -0.60720439
2 -1.78158547 -0.08011472
3 -3.74522647 -1.78158547
4 2.82527930 -3.74522647
5 -2.69391793 2.82527930
6 -1.26322740 -2.69391793
7 2.17930272 -1.26322740
8 0.44051606 2.17930272
9 -0.49442094 0.44051606
10 -2.42337551 -0.49442094
11 -1.23416416 -2.42337551
12 -2.54285759 -1.23416416
13 -0.40794527 -2.54285759
14 -3.24409108 -0.40794527
15 2.87503387 -3.24409108
16 3.49780782 2.87503387
17 1.10610639 3.49780782
18 -0.29838914 1.10610639
19 0.65065981 -0.29838914
20 0.42257585 0.65065981
21 0.33634222 0.42257585
22 7.31110608 0.33634222
23 -1.63279846 7.31110608
24 0.80458840 -1.63279846
25 NA 0.80458840
> dum1 <- dum[2:length(myerror),]
> dum1
lag(myerror, k = 1) myerror
[1,] -0.08011472 -0.60720439
[2,] -1.78158547 -0.08011472
[3,] -3.74522647 -1.78158547
[4,] 2.82527930 -3.74522647
[5,] -2.69391793 2.82527930
[6,] -1.26322740 -2.69391793
[7,] 2.17930272 -1.26322740
[8,] 0.44051606 2.17930272
[9,] -0.49442094 0.44051606
[10,] -2.42337551 -0.49442094
[11,] -1.23416416 -2.42337551
[12,] -2.54285759 -1.23416416
[13,] -0.40794527 -2.54285759
[14,] -3.24409108 -0.40794527
[15,] 2.87503387 -3.24409108
[16,] 3.49780782 2.87503387
[17,] 1.10610639 3.49780782
[18,] -0.29838914 1.10610639
[19,] 0.65065981 -0.29838914
[20,] 0.42257585 0.65065981
[21,] 0.33634222 0.42257585
[22,] 7.31110608 0.33634222
[23,] -1.63279846 7.31110608
[24,] 0.80458840 -1.63279846
> z <- as.data.frame(dum1)
> z
lag(myerror, k = 1) myerror
1 -0.08011472 -0.60720439
2 -1.78158547 -0.08011472
3 -3.74522647 -1.78158547
4 2.82527930 -3.74522647
5 -2.69391793 2.82527930
6 -1.26322740 -2.69391793
7 2.17930272 -1.26322740
8 0.44051606 2.17930272
9 -0.49442094 0.44051606
10 -2.42337551 -0.49442094
11 -1.23416416 -2.42337551
12 -2.54285759 -1.23416416
13 -0.40794527 -2.54285759
14 -3.24409108 -0.40794527
15 2.87503387 -3.24409108
16 3.49780782 2.87503387
17 1.10610639 3.49780782
18 -0.29838914 1.10610639
19 0.65065981 -0.29838914
20 0.42257585 0.65065981
21 0.33634222 0.42257585
22 7.31110608 0.33634222
23 -1.63279846 7.31110608
24 0.80458840 -1.63279846
> 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/7ezc91353431768.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556)
> acf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Autocorrelation Function')
> grid()
> dev.off()
null device
1
> postscript(file="/var/fisher/rcomp/tmp/8i37f1353431768.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556)
> pacf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Partial Autocorrelation Function')
> grid()
> dev.off()
null device
1
> postscript(file="/var/fisher/rcomp/tmp/956291353431768.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556)
> opar <- par(mfrow = c(2,2), oma = c(0, 0, 1.1, 0))
> plot(mylm, las = 1, sub='Residual Diagnostics')
> par(opar)
> dev.off()
null device
1
> if (n > n25) {
+ postscript(file="/var/fisher/rcomp/tmp/1089d71353431768.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556)
+ plot(kp3:nmkm3,gqarr[,2], main='Goldfeld-Quandt test',ylab='2-sided p-value',xlab='breakpoint')
+ grid()
+ dev.off()
+ }
>
> #Note: the /var/fisher/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab
> load(file="/var/fisher/rcomp/createtable")
>
> a<-table.start()
> a<-table.row.start(a)
> a<-table.element(a, 'Multiple Linear Regression - Estimated Regression Equation', 1, TRUE)
> a<-table.row.end(a)
> myeq <- colnames(x)[1]
> myeq <- paste(myeq, '[t] = ', sep='')
> for (i in 1:k){
+ if (mysum$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/11k6rb1353431768.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/12gpg01353431769.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/13cks01353431769.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/143ugx1353431769.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/15z03d1353431769.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/160vfi1353431769.tab")
+ }
>
> try(system("convert tmp/1mxux1353431768.ps tmp/1mxux1353431768.png",intern=TRUE))
character(0)
> try(system("convert tmp/2wgq61353431768.ps tmp/2wgq61353431768.png",intern=TRUE))
character(0)
> try(system("convert tmp/3wngx1353431768.ps tmp/3wngx1353431768.png",intern=TRUE))
character(0)
> try(system("convert tmp/4wude1353431768.ps tmp/4wude1353431768.png",intern=TRUE))
character(0)
> try(system("convert tmp/5inkf1353431768.ps tmp/5inkf1353431768.png",intern=TRUE))
character(0)
> try(system("convert tmp/6q6xe1353431768.ps tmp/6q6xe1353431768.png",intern=TRUE))
character(0)
> try(system("convert tmp/7ezc91353431768.ps tmp/7ezc91353431768.png",intern=TRUE))
character(0)
> try(system("convert tmp/8i37f1353431768.ps tmp/8i37f1353431768.png",intern=TRUE))
character(0)
> try(system("convert tmp/956291353431768.ps tmp/956291353431768.png",intern=TRUE))
character(0)
> try(system("convert tmp/1089d71353431768.ps tmp/1089d71353431768.png",intern=TRUE))
convert: unable to open image `tmp/1089d71353431768.ps': @ error/blob.c/OpenBlob/2587.
convert: missing an image filename `tmp/1089d71353431768.png' @ error/convert.c/ConvertImageCommand/3011.
character(0)
attr(,"status")
[1] 1
Warning message:
running command 'convert tmp/1089d71353431768.ps tmp/1089d71353431768.png' had status 1
>
>
> proc.time()
user system elapsed
5.038 1.186 6.234