R version 2.9.0 (2009-04-17)
Copyright (C) 2009 The R Foundation for Statistical Computing
ISBN 3-900051-07-0
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> x <- array(list(13.7
+ ,15
+ ,14.4
+ ,15.3
+ ,14.3
+ ,14.5
+ ,14.2
+ ,15.5
+ ,13.7
+ ,14.4
+ ,15.3
+ ,14.3
+ ,13.5
+ ,15.1
+ ,14.2
+ ,13.7
+ ,14.4
+ ,15.3
+ ,11.9
+ ,11.7
+ ,13.5
+ ,14.2
+ ,13.7
+ ,14.4
+ ,14.6
+ ,16.3
+ ,11.9
+ ,13.5
+ ,14.2
+ ,13.7
+ ,15.6
+ ,16.7
+ ,14.6
+ ,11.9
+ ,13.5
+ ,14.2
+ ,14.1
+ ,15
+ ,15.6
+ ,14.6
+ ,11.9
+ ,13.5
+ ,14.9
+ ,14.9
+ ,14.1
+ ,15.6
+ ,14.6
+ ,11.9
+ ,14.2
+ ,14.6
+ ,14.9
+ ,14.1
+ ,15.6
+ ,14.6
+ ,14.6
+ ,15.3
+ ,14.2
+ ,14.9
+ ,14.1
+ ,15.6
+ ,17.2
+ ,17.9
+ ,14.6
+ ,14.2
+ ,14.9
+ ,14.1
+ ,15.4
+ ,16.4
+ ,17.2
+ ,14.6
+ ,14.2
+ ,14.9
+ ,14.3
+ ,15.4
+ ,15.4
+ ,17.2
+ ,14.6
+ ,14.2
+ ,17.5
+ ,17.9
+ ,14.3
+ ,15.4
+ ,17.2
+ ,14.6
+ ,14.5
+ ,15.9
+ ,17.5
+ ,14.3
+ ,15.4
+ ,17.2
+ ,14.4
+ ,13.9
+ ,14.5
+ ,17.5
+ ,14.3
+ ,15.4
+ ,16.6
+ ,17.8
+ ,14.4
+ ,14.5
+ ,17.5
+ ,14.3
+ ,16.7
+ ,17.9
+ ,16.6
+ ,14.4
+ ,14.5
+ ,17.5
+ ,16.6
+ ,17.4
+ ,16.7
+ ,16.6
+ ,14.4
+ ,14.5
+ ,16.9
+ ,16.7
+ ,16.6
+ ,16.7
+ ,16.6
+ ,14.4
+ ,15.7
+ ,16
+ ,16.9
+ ,16.6
+ ,16.7
+ ,16.6
+ ,16.4
+ ,16.6
+ ,15.7
+ ,16.9
+ ,16.6
+ ,16.7
+ ,18.4
+ ,19.1
+ ,16.4
+ ,15.7
+ ,16.9
+ ,16.6
+ ,16.9
+ ,17.8
+ ,18.4
+ ,16.4
+ ,15.7
+ ,16.9
+ ,16.5
+ ,17.2
+ ,16.9
+ ,18.4
+ ,16.4
+ ,15.7
+ ,18.3
+ ,18.6
+ ,16.5
+ ,16.9
+ ,18.4
+ ,16.4
+ ,15.1
+ ,16.3
+ ,18.3
+ ,16.5
+ ,16.9
+ ,18.4
+ ,15.7
+ ,15.1
+ ,15.1
+ ,18.3
+ ,16.5
+ ,16.9
+ ,18.1
+ ,19.2
+ ,15.7
+ ,15.1
+ ,18.3
+ ,16.5
+ ,16.8
+ ,17.7
+ ,18.1
+ ,15.7
+ ,15.1
+ ,18.3
+ ,18.9
+ ,19.1
+ ,16.8
+ ,18.1
+ ,15.7
+ ,15.1
+ ,19
+ ,18
+ ,18.9
+ ,16.8
+ ,18.1
+ ,15.7
+ ,18.1
+ ,17.5
+ ,19
+ ,18.9
+ ,16.8
+ ,18.1
+ ,17.8
+ ,17.8
+ ,18.1
+ ,19
+ ,18.9
+ ,16.8
+ ,21.5
+ ,21.1
+ ,17.8
+ ,18.1
+ ,19
+ ,18.9
+ ,17.1
+ ,17.2
+ ,21.5
+ ,17.8
+ ,18.1
+ ,19
+ ,18.7
+ ,19.4
+ ,17.1
+ ,21.5
+ ,17.8
+ ,18.1
+ ,19
+ ,19.8
+ ,18.7
+ ,17.1
+ ,21.5
+ ,17.8
+ ,16.4
+ ,17.6
+ ,19
+ ,18.7
+ ,17.1
+ ,21.5
+ ,16.9
+ ,16.2
+ ,16.4
+ ,19
+ ,18.7
+ ,17.1
+ ,18.6
+ ,19.5
+ ,16.9
+ ,16.4
+ ,19
+ ,18.7
+ ,19.3
+ ,19.9
+ ,18.6
+ ,16.9
+ ,16.4
+ ,19
+ ,19.4
+ ,20
+ ,19.3
+ ,18.6
+ ,16.9
+ ,16.4
+ ,17.6
+ ,17.3
+ ,19.4
+ ,19.3
+ ,18.6
+ ,16.9
+ ,18.6
+ ,18.9
+ ,17.6
+ ,19.4
+ ,19.3
+ ,18.6
+ ,18.1
+ ,18.6
+ ,18.6
+ ,17.6
+ ,19.4
+ ,19.3
+ ,20.4
+ ,21.4
+ ,18.1
+ ,18.6
+ ,17.6
+ ,19.4
+ ,18.1
+ ,18.6
+ ,20.4
+ ,18.1
+ ,18.6
+ ,17.6
+ ,19.6
+ ,19.8
+ ,18.1
+ ,20.4
+ ,18.1
+ ,18.6
+ ,19.9
+ ,20.8
+ ,19.6
+ ,18.1
+ ,20.4
+ ,18.1
+ ,19.2
+ ,19.6
+ ,19.9
+ ,19.6
+ ,18.1
+ ,20.4
+ ,17.8
+ ,17.7
+ ,19.2
+ ,19.9
+ ,19.6
+ ,18.1
+ ,19.2
+ ,19.8
+ ,17.8
+ ,19.2
+ ,19.9
+ ,19.6
+ ,22
+ ,22.2
+ ,19.2
+ ,17.8
+ ,19.2
+ ,19.9
+ ,21.1
+ ,20.7
+ ,22
+ ,19.2
+ ,17.8
+ ,19.2
+ ,19.5
+ ,17.9
+ ,21.1
+ ,22
+ ,19.2
+ ,17.8
+ ,22.2
+ ,20.9
+ ,19.5
+ ,21.1
+ ,22
+ ,19.2
+ ,20.9
+ ,21.2
+ ,22.2
+ ,19.5
+ ,21.1
+ ,22
+ ,22.2
+ ,21.4
+ ,20.9
+ ,22.2
+ ,19.5
+ ,21.1
+ ,23.5
+ ,23
+ ,22.2
+ ,20.9
+ ,22.2
+ ,19.5
+ ,21.5
+ ,21.3
+ ,23.5
+ ,22.2
+ ,20.9
+ ,22.2
+ ,24.3
+ ,23.9
+ ,21.5
+ ,23.5
+ ,22.2
+ ,20.9
+ ,22.8
+ ,22.4
+ ,24.3
+ ,21.5
+ ,23.5
+ ,22.2
+ ,20.3
+ ,18.3
+ ,22.8
+ ,24.3
+ ,21.5
+ ,23.5
+ ,23.7
+ ,22.8
+ ,20.3
+ ,22.8
+ ,24.3
+ ,21.5
+ ,23.3
+ ,22.3
+ ,23.7
+ ,20.3
+ ,22.8
+ ,24.3
+ ,19.6
+ ,17.8
+ ,23.3
+ ,23.7
+ ,20.3
+ ,22.8
+ ,18
+ ,16.4
+ ,19.6
+ ,23.3
+ ,23.7
+ ,20.3
+ ,17.3
+ ,16
+ ,18
+ ,19.6
+ ,23.3
+ ,23.7
+ ,16.8
+ ,16.4
+ ,17.3
+ ,18
+ ,19.6
+ ,23.3
+ ,18.2
+ ,17.7
+ ,16.8
+ ,17.3
+ ,18
+ ,19.6
+ ,16.5
+ ,16.6
+ ,18.2
+ ,16.8
+ ,17.3
+ ,18
+ ,16
+ ,16.2
+ ,16.5
+ ,18.2
+ ,16.8
+ ,17.3
+ ,18.4
+ ,18.3
+ ,16
+ ,16.5
+ ,18.2
+ ,16.8)
+ ,dim=c(6
+ ,74)
+ ,dimnames=list(c('Y'
+ ,'X'
+ ,'Y1'
+ ,'Y2'
+ ,'Y3'
+ ,'Y4')
+ ,1:74))
> y <- array(NA,dim=c(6,74),dimnames=list(c('Y','X','Y1','Y2','Y3','Y4'),1:74))
> for (i in 1:dim(x)[1])
+ {
+ for (j in 1:dim(x)[2])
+ {
+ y[i,j] <- as.numeric(x[i,j])
+ }
+ }
> par3 = 'Linear Trend'
> par2 = 'Include Monthly 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.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
Y X Y1 Y2 Y3 Y4 M1 M2 M3 M4 M5 M6 M7 M8 M9 M10 M11 t
1 13.7 15.0 14.4 15.3 14.3 14.5 1 0 0 0 0 0 0 0 0 0 0 1
2 14.2 15.5 13.7 14.4 15.3 14.3 0 1 0 0 0 0 0 0 0 0 0 2
3 13.5 15.1 14.2 13.7 14.4 15.3 0 0 1 0 0 0 0 0 0 0 0 3
4 11.9 11.7 13.5 14.2 13.7 14.4 0 0 0 1 0 0 0 0 0 0 0 4
5 14.6 16.3 11.9 13.5 14.2 13.7 0 0 0 0 1 0 0 0 0 0 0 5
6 15.6 16.7 14.6 11.9 13.5 14.2 0 0 0 0 0 1 0 0 0 0 0 6
7 14.1 15.0 15.6 14.6 11.9 13.5 0 0 0 0 0 0 1 0 0 0 0 7
8 14.9 14.9 14.1 15.6 14.6 11.9 0 0 0 0 0 0 0 1 0 0 0 8
9 14.2 14.6 14.9 14.1 15.6 14.6 0 0 0 0 0 0 0 0 1 0 0 9
10 14.6 15.3 14.2 14.9 14.1 15.6 0 0 0 0 0 0 0 0 0 1 0 10
11 17.2 17.9 14.6 14.2 14.9 14.1 0 0 0 0 0 0 0 0 0 0 1 11
12 15.4 16.4 17.2 14.6 14.2 14.9 0 0 0 0 0 0 0 0 0 0 0 12
13 14.3 15.4 15.4 17.2 14.6 14.2 1 0 0 0 0 0 0 0 0 0 0 13
14 17.5 17.9 14.3 15.4 17.2 14.6 0 1 0 0 0 0 0 0 0 0 0 14
15 14.5 15.9 17.5 14.3 15.4 17.2 0 0 1 0 0 0 0 0 0 0 0 15
16 14.4 13.9 14.5 17.5 14.3 15.4 0 0 0 1 0 0 0 0 0 0 0 16
17 16.6 17.8 14.4 14.5 17.5 14.3 0 0 0 0 1 0 0 0 0 0 0 17
18 16.7 17.9 16.6 14.4 14.5 17.5 0 0 0 0 0 1 0 0 0 0 0 18
19 16.6 17.4 16.7 16.6 14.4 14.5 0 0 0 0 0 0 1 0 0 0 0 19
20 16.9 16.7 16.6 16.7 16.6 14.4 0 0 0 0 0 0 0 1 0 0 0 20
21 15.7 16.0 16.9 16.6 16.7 16.6 0 0 0 0 0 0 0 0 1 0 0 21
22 16.4 16.6 15.7 16.9 16.6 16.7 0 0 0 0 0 0 0 0 0 1 0 22
23 18.4 19.1 16.4 15.7 16.9 16.6 0 0 0 0 0 0 0 0 0 0 1 23
24 16.9 17.8 18.4 16.4 15.7 16.9 0 0 0 0 0 0 0 0 0 0 0 24
25 16.5 17.2 16.9 18.4 16.4 15.7 1 0 0 0 0 0 0 0 0 0 0 25
26 18.3 18.6 16.5 16.9 18.4 16.4 0 1 0 0 0 0 0 0 0 0 0 26
27 15.1 16.3 18.3 16.5 16.9 18.4 0 0 1 0 0 0 0 0 0 0 0 27
28 15.7 15.1 15.1 18.3 16.5 16.9 0 0 0 1 0 0 0 0 0 0 0 28
29 18.1 19.2 15.7 15.1 18.3 16.5 0 0 0 0 1 0 0 0 0 0 0 29
30 16.8 17.7 18.1 15.7 15.1 18.3 0 0 0 0 0 1 0 0 0 0 0 30
31 18.9 19.1 16.8 18.1 15.7 15.1 0 0 0 0 0 0 1 0 0 0 0 31
32 19.0 18.0 18.9 16.8 18.1 15.7 0 0 0 0 0 0 0 1 0 0 0 32
33 18.1 17.5 19.0 18.9 16.8 18.1 0 0 0 0 0 0 0 0 1 0 0 33
34 17.8 17.8 18.1 19.0 18.9 16.8 0 0 0 0 0 0 0 0 0 1 0 34
35 21.5 21.1 17.8 18.1 19.0 18.9 0 0 0 0 0 0 0 0 0 0 1 35
36 17.1 17.2 21.5 17.8 18.1 19.0 0 0 0 0 0 0 0 0 0 0 0 36
37 18.7 19.4 17.1 21.5 17.8 18.1 1 0 0 0 0 0 0 0 0 0 0 37
38 19.0 19.8 18.7 17.1 21.5 17.8 0 1 0 0 0 0 0 0 0 0 0 38
39 16.4 17.6 19.0 18.7 17.1 21.5 0 0 1 0 0 0 0 0 0 0 0 39
40 16.9 16.2 16.4 19.0 18.7 17.1 0 0 0 1 0 0 0 0 0 0 0 40
41 18.6 19.5 16.9 16.4 19.0 18.7 0 0 0 0 1 0 0 0 0 0 0 41
42 19.3 19.9 18.6 16.9 16.4 19.0 0 0 0 0 0 1 0 0 0 0 0 42
43 19.4 20.0 19.3 18.6 16.9 16.4 0 0 0 0 0 0 1 0 0 0 0 43
44 17.6 17.3 19.4 19.3 18.6 16.9 0 0 0 0 0 0 0 1 0 0 0 44
45 18.6 18.9 17.6 19.4 19.3 18.6 0 0 0 0 0 0 0 0 1 0 0 45
46 18.1 18.6 18.6 17.6 19.4 19.3 0 0 0 0 0 0 0 0 0 1 0 46
47 20.4 21.4 18.1 18.6 17.6 19.4 0 0 0 0 0 0 0 0 0 0 1 47
48 18.1 18.6 20.4 18.1 18.6 17.6 0 0 0 0 0 0 0 0 0 0 0 48
49 19.6 19.8 18.1 20.4 18.1 18.6 1 0 0 0 0 0 0 0 0 0 0 49
50 19.9 20.8 19.6 18.1 20.4 18.1 0 1 0 0 0 0 0 0 0 0 0 50
51 19.2 19.6 19.9 19.6 18.1 20.4 0 0 1 0 0 0 0 0 0 0 0 51
52 17.8 17.7 19.2 19.9 19.6 18.1 0 0 0 1 0 0 0 0 0 0 0 52
53 19.2 19.8 17.8 19.2 19.9 19.6 0 0 0 0 1 0 0 0 0 0 0 53
54 22.0 22.2 19.2 17.8 19.2 19.9 0 0 0 0 0 1 0 0 0 0 0 54
55 21.1 20.7 22.0 19.2 17.8 19.2 0 0 0 0 0 0 1 0 0 0 0 55
56 19.5 17.9 21.1 22.0 19.2 17.8 0 0 0 0 0 0 0 1 0 0 0 56
57 22.2 20.9 19.5 21.1 22.0 19.2 0 0 0 0 0 0 0 0 1 0 0 57
58 20.9 21.2 22.2 19.5 21.1 22.0 0 0 0 0 0 0 0 0 0 1 0 58
59 22.2 21.4 20.9 22.2 19.5 21.1 0 0 0 0 0 0 0 0 0 0 1 59
60 23.5 23.0 22.2 20.9 22.2 19.5 0 0 0 0 0 0 0 0 0 0 0 60
61 21.5 21.3 23.5 22.2 20.9 22.2 1 0 0 0 0 0 0 0 0 0 0 61
62 24.3 23.9 21.5 23.5 22.2 20.9 0 1 0 0 0 0 0 0 0 0 0 62
63 22.8 22.4 24.3 21.5 23.5 22.2 0 0 1 0 0 0 0 0 0 0 0 63
64 20.3 18.3 22.8 24.3 21.5 23.5 0 0 0 1 0 0 0 0 0 0 0 64
65 23.7 22.8 20.3 22.8 24.3 21.5 0 0 0 0 1 0 0 0 0 0 0 65
66 23.3 22.3 23.7 20.3 22.8 24.3 0 0 0 0 0 1 0 0 0 0 0 66
67 19.6 17.8 23.3 23.7 20.3 22.8 0 0 0 0 0 0 1 0 0 0 0 67
68 18.0 16.4 19.6 23.3 23.7 20.3 0 0 0 0 0 0 0 1 0 0 0 68
69 17.3 16.0 18.0 19.6 23.3 23.7 0 0 0 0 0 0 0 0 1 0 0 69
70 16.8 16.4 17.3 18.0 19.6 23.3 0 0 0 0 0 0 0 0 0 1 0 70
71 18.2 17.7 16.8 17.3 18.0 19.6 0 0 0 0 0 0 0 0 0 0 1 71
72 16.5 16.6 18.2 16.8 17.3 18.0 0 0 0 0 0 0 0 0 0 0 0 72
73 16.0 16.2 16.5 18.2 16.8 17.3 1 0 0 0 0 0 0 0 0 0 0 73
74 18.4 18.3 16.0 16.5 18.2 16.8 0 1 0 0 0 0 0 0 0 0 0 74
> k <- length(x[1,])
> df <- as.data.frame(x)
> (mylm <- lm(df))
Call:
lm(formula = df)
Coefficients:
(Intercept) X Y1 Y2 Y3 Y4
-2.899990 0.873628 0.024549 0.145315 0.110702 -0.022539
M1 M2 M3 M4 M5 M6
-0.361337 -0.055659 -0.472649 0.625633 -0.223771 0.365365
M7 M8 M9 M10 M11 t
0.360499 0.676363 0.420586 0.048551 0.465681 0.006736
> (mysum <- summary(mylm))
Call:
lm(formula = df)
Residuals:
Min 1Q Median 3Q Max
-0.86404 -0.22635 0.04134 0.24195 0.72766
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -2.899990 0.614110 -4.722 1.60e-05 ***
X 0.873628 0.048506 18.011 < 2e-16 ***
Y1 0.024549 0.052890 0.464 0.64434
Y2 0.145315 0.048801 2.978 0.00429 **
Y3 0.110702 0.050477 2.193 0.03247 *
Y4 -0.022539 0.057631 -0.391 0.69721
M1 -0.361337 0.260616 -1.386 0.17110
M2 -0.055659 0.271460 -0.205 0.83829
M3 -0.472649 0.256836 -1.840 0.07103 .
M4 0.625633 0.289713 2.159 0.03511 *
M5 -0.223771 0.316335 -0.707 0.48226
M6 0.365365 0.296280 1.233 0.22266
M7 0.360499 0.243658 1.480 0.14460
M8 0.676363 0.284027 2.381 0.02067 *
M9 0.420586 0.268535 1.566 0.12293
M10 0.048551 0.266358 0.182 0.85602
M11 0.465681 0.292402 1.593 0.11688
t 0.006736 0.004765 1.414 0.16299
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 0.3854 on 56 degrees of freedom
Multiple R-squared: 0.9843, Adjusted R-squared: 0.9796
F-statistic: 207.1 on 17 and 56 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
+ }
[,1] [,2] [,3]
[1,] 6.419712e-02 1.283942e-01 0.9358029
[2,] 4.085154e-02 8.170307e-02 0.9591485
[3,] 1.572857e-02 3.145713e-02 0.9842714
[4,] 5.019520e-03 1.003904e-02 0.9949805
[5,] 1.447173e-03 2.894346e-03 0.9985528
[6,] 5.760603e-04 1.152121e-03 0.9994239
[7,] 1.694150e-04 3.388300e-04 0.9998306
[8,] 1.027830e-04 2.055660e-04 0.9998972
[9,] 3.327369e-05 6.654738e-05 0.9999667
[10,] 1.107922e-05 2.215843e-05 0.9999889
[11,] 3.286950e-06 6.573899e-06 0.9999967
[12,] 2.224590e-05 4.449180e-05 0.9999778
[13,] 1.529912e-04 3.059823e-04 0.9998470
[14,] 7.367471e-05 1.473494e-04 0.9999263
[15,] 1.094427e-02 2.188853e-02 0.9890557
[16,] 2.981430e-02 5.962860e-02 0.9701857
[17,] 2.060381e-02 4.120763e-02 0.9793962
[18,] 8.129365e-02 1.625873e-01 0.9187063
[19,] 5.757230e-02 1.151446e-01 0.9424277
[20,] 1.081168e-01 2.162336e-01 0.8918832
[21,] 1.132634e-01 2.265267e-01 0.8867366
[22,] 7.624663e-02 1.524933e-01 0.9237534
[23,] 8.159909e-02 1.631982e-01 0.9184009
[24,] 6.506434e-02 1.301287e-01 0.9349357
[25,] 1.145111e-01 2.290222e-01 0.8854889
[26,] 1.103438e-01 2.206876e-01 0.8896562
[27,] 2.515580e-01 5.031160e-01 0.7484420
[28,] 2.253759e-01 4.507517e-01 0.7746241
[29,] 4.555393e-01 9.110785e-01 0.5444607
[30,] 5.390079e-01 9.219842e-01 0.4609921
[31,] 4.575037e-01 9.150074e-01 0.5424963
[32,] 4.138323e-01 8.276647e-01 0.5861677
[33,] 2.677728e-01 5.355455e-01 0.7322272
> postscript(file="/var/www/html/rcomp/tmp/16oab1258796927.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$resid)
> grid()
> dev.off()
null device
1
> postscript(file="/var/www/html/rcomp/tmp/2n4v21258796927.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556)
> plot(mysum$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/3bblo1258796927.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556)
> hist(mysum$resid, main='Residual Histogram', xlab='values of Residuals')
> grid()
> dev.off()
null device
1
> postscript(file="/var/www/html/rcomp/tmp/49c9s1258796927.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556)
> densityplot(~mysum$resid,col='black',main='Residual Density Plot', xlab='values of Residuals')
> dev.off()
null device
1
> postscript(file="/var/www/html/rcomp/tmp/5vzdu1258796927.ps",horizontal=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 = 74
Frequency = 1
1 2 3 4 5 6
0.017123958 -0.199345048 0.071976661 0.339026537 -0.067122901 0.242536175
7 8 9 10 11 12
-0.029720245 0.091594041 0.051210230 0.294494334 0.168726496 0.111681828
13 14 15 16 17 18
-0.153777924 0.559501126 0.056165010 0.288243425 -0.016875700 -0.235356678
19 20 21 22 23 24
-0.279107458 0.051957952 -0.241779288 0.298532149 -0.187674407 -0.104228405
25 26 27 28 29 30
0.016204879 0.302878512 -0.252454920 0.118342687 0.021136363 -0.315584730
31 32 33 34 35 36
0.104078124 0.727664738 0.403908652 -0.047091847 0.520480339 0.041222279
37 38 39 40 41 42
-0.342882405 -0.520997340 -0.458148503 -0.096149077 -0.068056288 -0.133184372
43 44 45 46 47 48
-0.500589276 -0.545492453 -0.703774383 -0.334661052 -0.836208834 -0.366183425
49 50 51 52 53 54
0.240192484 -0.614331560 0.225392364 -0.864035327 -0.319298141 0.041448054
55 56 57 58 59 60
0.317046806 0.269279958 0.489088775 -0.378737445 0.119071685 0.302250136
61 62 63 64 65 66
0.125963161 0.029092421 0.357069389 0.214571755 0.450216668 0.400141552
67 68 69 70 71 72
0.388292048 -0.595004234 0.001346013 0.167463862 0.215604721 0.015257586
73 74
0.097175847 0.443201889
> postscript(file="/var/www/html/rcomp/tmp/6sysq1258796927.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 = 74
Frequency = 1
lag(myerror, k = 1) myerror
0 0.017123958 NA
1 -0.199345048 0.017123958
2 0.071976661 -0.199345048
3 0.339026537 0.071976661
4 -0.067122901 0.339026537
5 0.242536175 -0.067122901
6 -0.029720245 0.242536175
7 0.091594041 -0.029720245
8 0.051210230 0.091594041
9 0.294494334 0.051210230
10 0.168726496 0.294494334
11 0.111681828 0.168726496
12 -0.153777924 0.111681828
13 0.559501126 -0.153777924
14 0.056165010 0.559501126
15 0.288243425 0.056165010
16 -0.016875700 0.288243425
17 -0.235356678 -0.016875700
18 -0.279107458 -0.235356678
19 0.051957952 -0.279107458
20 -0.241779288 0.051957952
21 0.298532149 -0.241779288
22 -0.187674407 0.298532149
23 -0.104228405 -0.187674407
24 0.016204879 -0.104228405
25 0.302878512 0.016204879
26 -0.252454920 0.302878512
27 0.118342687 -0.252454920
28 0.021136363 0.118342687
29 -0.315584730 0.021136363
30 0.104078124 -0.315584730
31 0.727664738 0.104078124
32 0.403908652 0.727664738
33 -0.047091847 0.403908652
34 0.520480339 -0.047091847
35 0.041222279 0.520480339
36 -0.342882405 0.041222279
37 -0.520997340 -0.342882405
38 -0.458148503 -0.520997340
39 -0.096149077 -0.458148503
40 -0.068056288 -0.096149077
41 -0.133184372 -0.068056288
42 -0.500589276 -0.133184372
43 -0.545492453 -0.500589276
44 -0.703774383 -0.545492453
45 -0.334661052 -0.703774383
46 -0.836208834 -0.334661052
47 -0.366183425 -0.836208834
48 0.240192484 -0.366183425
49 -0.614331560 0.240192484
50 0.225392364 -0.614331560
51 -0.864035327 0.225392364
52 -0.319298141 -0.864035327
53 0.041448054 -0.319298141
54 0.317046806 0.041448054
55 0.269279958 0.317046806
56 0.489088775 0.269279958
57 -0.378737445 0.489088775
58 0.119071685 -0.378737445
59 0.302250136 0.119071685
60 0.125963161 0.302250136
61 0.029092421 0.125963161
62 0.357069389 0.029092421
63 0.214571755 0.357069389
64 0.450216668 0.214571755
65 0.400141552 0.450216668
66 0.388292048 0.400141552
67 -0.595004234 0.388292048
68 0.001346013 -0.595004234
69 0.167463862 0.001346013
70 0.215604721 0.167463862
71 0.015257586 0.215604721
72 0.097175847 0.015257586
73 0.443201889 0.097175847
74 NA 0.443201889
> dum1 <- dum[2:length(myerror),]
> dum1
lag(myerror, k = 1) myerror
[1,] -0.199345048 0.017123958
[2,] 0.071976661 -0.199345048
[3,] 0.339026537 0.071976661
[4,] -0.067122901 0.339026537
[5,] 0.242536175 -0.067122901
[6,] -0.029720245 0.242536175
[7,] 0.091594041 -0.029720245
[8,] 0.051210230 0.091594041
[9,] 0.294494334 0.051210230
[10,] 0.168726496 0.294494334
[11,] 0.111681828 0.168726496
[12,] -0.153777924 0.111681828
[13,] 0.559501126 -0.153777924
[14,] 0.056165010 0.559501126
[15,] 0.288243425 0.056165010
[16,] -0.016875700 0.288243425
[17,] -0.235356678 -0.016875700
[18,] -0.279107458 -0.235356678
[19,] 0.051957952 -0.279107458
[20,] -0.241779288 0.051957952
[21,] 0.298532149 -0.241779288
[22,] -0.187674407 0.298532149
[23,] -0.104228405 -0.187674407
[24,] 0.016204879 -0.104228405
[25,] 0.302878512 0.016204879
[26,] -0.252454920 0.302878512
[27,] 0.118342687 -0.252454920
[28,] 0.021136363 0.118342687
[29,] -0.315584730 0.021136363
[30,] 0.104078124 -0.315584730
[31,] 0.727664738 0.104078124
[32,] 0.403908652 0.727664738
[33,] -0.047091847 0.403908652
[34,] 0.520480339 -0.047091847
[35,] 0.041222279 0.520480339
[36,] -0.342882405 0.041222279
[37,] -0.520997340 -0.342882405
[38,] -0.458148503 -0.520997340
[39,] -0.096149077 -0.458148503
[40,] -0.068056288 -0.096149077
[41,] -0.133184372 -0.068056288
[42,] -0.500589276 -0.133184372
[43,] -0.545492453 -0.500589276
[44,] -0.703774383 -0.545492453
[45,] -0.334661052 -0.703774383
[46,] -0.836208834 -0.334661052
[47,] -0.366183425 -0.836208834
[48,] 0.240192484 -0.366183425
[49,] -0.614331560 0.240192484
[50,] 0.225392364 -0.614331560
[51,] -0.864035327 0.225392364
[52,] -0.319298141 -0.864035327
[53,] 0.041448054 -0.319298141
[54,] 0.317046806 0.041448054
[55,] 0.269279958 0.317046806
[56,] 0.489088775 0.269279958
[57,] -0.378737445 0.489088775
[58,] 0.119071685 -0.378737445
[59,] 0.302250136 0.119071685
[60,] 0.125963161 0.302250136
[61,] 0.029092421 0.125963161
[62,] 0.357069389 0.029092421
[63,] 0.214571755 0.357069389
[64,] 0.450216668 0.214571755
[65,] 0.400141552 0.450216668
[66,] 0.388292048 0.400141552
[67,] -0.595004234 0.388292048
[68,] 0.001346013 -0.595004234
[69,] 0.167463862 0.001346013
[70,] 0.215604721 0.167463862
[71,] 0.015257586 0.215604721
[72,] 0.097175847 0.015257586
[73,] 0.443201889 0.097175847
> z <- as.data.frame(dum1)
> z
lag(myerror, k = 1) myerror
1 -0.199345048 0.017123958
2 0.071976661 -0.199345048
3 0.339026537 0.071976661
4 -0.067122901 0.339026537
5 0.242536175 -0.067122901
6 -0.029720245 0.242536175
7 0.091594041 -0.029720245
8 0.051210230 0.091594041
9 0.294494334 0.051210230
10 0.168726496 0.294494334
11 0.111681828 0.168726496
12 -0.153777924 0.111681828
13 0.559501126 -0.153777924
14 0.056165010 0.559501126
15 0.288243425 0.056165010
16 -0.016875700 0.288243425
17 -0.235356678 -0.016875700
18 -0.279107458 -0.235356678
19 0.051957952 -0.279107458
20 -0.241779288 0.051957952
21 0.298532149 -0.241779288
22 -0.187674407 0.298532149
23 -0.104228405 -0.187674407
24 0.016204879 -0.104228405
25 0.302878512 0.016204879
26 -0.252454920 0.302878512
27 0.118342687 -0.252454920
28 0.021136363 0.118342687
29 -0.315584730 0.021136363
30 0.104078124 -0.315584730
31 0.727664738 0.104078124
32 0.403908652 0.727664738
33 -0.047091847 0.403908652
34 0.520480339 -0.047091847
35 0.041222279 0.520480339
36 -0.342882405 0.041222279
37 -0.520997340 -0.342882405
38 -0.458148503 -0.520997340
39 -0.096149077 -0.458148503
40 -0.068056288 -0.096149077
41 -0.133184372 -0.068056288
42 -0.500589276 -0.133184372
43 -0.545492453 -0.500589276
44 -0.703774383 -0.545492453
45 -0.334661052 -0.703774383
46 -0.836208834 -0.334661052
47 -0.366183425 -0.836208834
48 0.240192484 -0.366183425
49 -0.614331560 0.240192484
50 0.225392364 -0.614331560
51 -0.864035327 0.225392364
52 -0.319298141 -0.864035327
53 0.041448054 -0.319298141
54 0.317046806 0.041448054
55 0.269279958 0.317046806
56 0.489088775 0.269279958
57 -0.378737445 0.489088775
58 0.119071685 -0.378737445
59 0.302250136 0.119071685
60 0.125963161 0.302250136
61 0.029092421 0.125963161
62 0.357069389 0.029092421
63 0.214571755 0.357069389
64 0.450216668 0.214571755
65 0.400141552 0.450216668
66 0.388292048 0.400141552
67 -0.595004234 0.388292048
68 0.001346013 -0.595004234
69 0.167463862 0.001346013
70 0.215604721 0.167463862
71 0.015257586 0.215604721
72 0.097175847 0.015257586
73 0.443201889 0.097175847
> 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/7lmxo1258796927.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556)
> acf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Autocorrelation Function')
> grid()
> dev.off()
null device
1
> postscript(file="/var/www/html/rcomp/tmp/8nu3f1258796927.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556)
> pacf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Partial Autocorrelation Function')
> grid()
> dev.off()
null device
1
> postscript(file="/var/www/html/rcomp/tmp/9grks1258796927.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556)
> opar <- par(mfrow = c(2,2), oma = c(0, 0, 1.1, 0))
> plot(mylm, las = 1, sub='Residual Diagnostics')
> par(opar)
> dev.off()
null device
1
> if (n > n25) {
+ postscript(file="/var/www/html/rcomp/tmp/10bm851258796927.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556)
+ plot(kp3:nmkm3,gqarr[,2], main='Goldfeld-Quandt test',ylab='2-sided p-value',xlab='breakpoint')
+ grid()
+ dev.off()
+ }
null device
1
>
> #Note: the /var/www/html/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab
> load(file="/var/www/html/rcomp/createtable")
>
> a<-table.start()
> a<-table.row.start(a)
> a<-table.element(a, 'Multiple Linear Regression - Estimated Regression Equation', 1, TRUE)
> a<-table.row.end(a)
> myeq <- colnames(x)[1]
> myeq <- paste(myeq, '[t] = ', sep='')
> for (i in 1:k){
+ if (mysum$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/11i0wh1258796927.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/1279t01258796927.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/13oslr1258796927.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/14yzf11258796927.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/www/html/rcomp/tmp/15otox1258796927.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/www/html/rcomp/tmp/160hy81258796927.tab")
+ }
>
> system("convert tmp/16oab1258796927.ps tmp/16oab1258796927.png")
> system("convert tmp/2n4v21258796927.ps tmp/2n4v21258796927.png")
> system("convert tmp/3bblo1258796927.ps tmp/3bblo1258796927.png")
> system("convert tmp/49c9s1258796927.ps tmp/49c9s1258796927.png")
> system("convert tmp/5vzdu1258796927.ps tmp/5vzdu1258796927.png")
> system("convert tmp/6sysq1258796927.ps tmp/6sysq1258796927.png")
> system("convert tmp/7lmxo1258796927.ps tmp/7lmxo1258796927.png")
> system("convert tmp/8nu3f1258796927.ps tmp/8nu3f1258796927.png")
> system("convert tmp/9grks1258796927.ps tmp/9grks1258796927.png")
> system("convert tmp/10bm851258796927.ps tmp/10bm851258796927.png")
>
>
> proc.time()
user system elapsed
2.615 1.569 3.095