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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Type 'contributors()' for more information and
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Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.
> x <- array(list(121.6
+ ,0
+ ,97.2
+ ,111.5
+ ,114.0
+ ,118.8
+ ,118.8
+ ,0
+ ,102.5
+ ,97.2
+ ,111.5
+ ,114.0
+ ,114.0
+ ,1
+ ,113.4
+ ,102.5
+ ,97.2
+ ,111.5
+ ,111.5
+ ,1
+ ,109.8
+ ,113.4
+ ,102.5
+ ,97.2
+ ,97.2
+ ,1
+ ,104.9
+ ,109.8
+ ,113.4
+ ,102.5
+ ,102.5
+ ,1
+ ,126.1
+ ,104.9
+ ,109.8
+ ,113.4
+ ,113.4
+ ,1
+ ,80.0
+ ,126.1
+ ,104.9
+ ,109.8
+ ,109.8
+ ,1
+ ,96.8
+ ,80.0
+ ,126.1
+ ,104.9
+ ,104.9
+ ,1
+ ,117.2
+ ,96.8
+ ,80.0
+ ,126.1
+ ,126.1
+ ,1
+ ,112.3
+ ,117.2
+ ,96.8
+ ,80.0
+ ,80.0
+ ,1
+ ,117.3
+ ,112.3
+ ,117.2
+ ,96.8
+ ,96.8
+ ,1
+ ,111.1
+ ,117.3
+ ,112.3
+ ,117.2
+ ,117.2
+ ,1
+ ,102.2
+ ,111.1
+ ,117.3
+ ,112.3
+ ,112.3
+ ,1
+ ,104.3
+ ,102.2
+ ,111.1
+ ,117.3
+ ,117.3
+ ,1
+ ,122.9
+ ,104.3
+ ,102.2
+ ,111.1
+ ,111.1
+ ,0
+ ,107.6
+ ,122.9
+ ,104.3
+ ,102.2
+ ,102.2
+ ,0
+ ,121.3
+ ,107.6
+ ,122.9
+ ,104.3
+ ,104.3
+ ,0
+ ,131.5
+ ,121.3
+ ,107.6
+ ,122.9
+ ,122.9
+ ,0
+ ,89.0
+ ,131.5
+ ,121.3
+ ,107.6
+ ,107.6
+ ,0
+ ,104.4
+ ,89.0
+ ,131.5
+ ,121.3
+ ,121.3
+ ,0
+ ,128.9
+ ,104.4
+ ,89.0
+ ,131.5
+ ,131.5
+ ,0
+ ,135.9
+ ,128.9
+ ,104.4
+ ,89.0
+ ,89.0
+ ,0
+ ,133.3
+ ,135.9
+ ,128.9
+ ,104.4
+ ,104.4
+ ,0
+ ,121.3
+ ,133.3
+ ,135.9
+ ,128.9
+ ,128.9
+ ,0
+ ,120.5
+ ,121.3
+ ,133.3
+ ,135.9
+ ,135.9
+ ,0
+ ,120.4
+ ,120.5
+ ,121.3
+ ,133.3
+ ,133.3
+ ,0
+ ,137.9
+ ,120.4
+ ,120.5
+ ,121.3
+ ,121.3
+ ,0
+ ,126.1
+ ,137.9
+ ,120.4
+ ,120.5
+ ,120.5
+ ,0
+ ,133.2
+ ,126.1
+ ,137.9
+ ,120.4
+ ,120.4
+ ,0
+ ,151.1
+ ,133.2
+ ,126.1
+ ,137.9
+ ,137.9
+ ,0
+ ,105.0
+ ,151.1
+ ,133.2
+ ,126.1
+ ,126.1
+ ,0
+ ,119.0
+ ,105.0
+ ,151.1
+ ,133.2
+ ,133.2
+ ,0
+ ,140.4
+ ,119.0
+ ,105.0
+ ,151.1
+ ,151.1
+ ,0
+ ,156.6
+ ,140.4
+ ,119.0
+ ,105.0
+ ,105.0
+ ,0
+ ,137.1
+ ,156.6
+ ,140.4
+ ,119.0
+ ,119.0
+ ,0
+ ,122.7
+ ,137.1
+ ,156.6
+ ,140.4
+ ,140.4
+ ,0
+ ,125.8
+ ,122.7
+ ,137.1
+ ,156.6
+ ,156.6
+ ,0
+ ,139.3
+ ,125.8
+ ,122.7
+ ,137.1
+ ,137.1
+ ,0
+ ,134.9
+ ,139.3
+ ,125.8
+ ,122.7
+ ,122.7
+ ,0
+ ,149.2
+ ,134.9
+ ,139.3
+ ,125.8
+ ,125.8
+ ,0
+ ,132.3
+ ,149.2
+ ,134.9
+ ,139.3
+ ,139.3
+ ,0
+ ,149.0
+ ,132.3
+ ,149.2
+ ,134.9
+ ,134.9
+ ,0
+ ,117.2
+ ,149.0
+ ,132.3
+ ,149.2
+ ,149.2
+ ,1
+ ,119.6
+ ,117.2
+ ,149.0
+ ,132.3
+ ,132.3
+ ,0
+ ,152.0
+ ,119.6
+ ,117.2
+ ,149.0
+ ,149.0
+ ,1
+ ,149.4
+ ,152.0
+ ,119.6
+ ,117.2
+ ,117.2
+ ,1
+ ,127.3
+ ,149.4
+ ,152.0
+ ,119.6
+ ,119.6
+ ,1
+ ,114.1
+ ,127.3
+ ,149.4
+ ,152.0
+ ,152.0
+ ,1
+ ,102.1
+ ,114.1
+ ,127.3
+ ,149.4
+ ,149.4
+ ,1
+ ,107.7
+ ,102.1
+ ,114.1
+ ,127.3
+ ,127.3
+ ,1
+ ,104.4
+ ,107.7
+ ,102.1
+ ,114.1
+ ,114.1
+ ,1
+ ,102.1
+ ,104.4
+ ,107.7
+ ,102.1
+ ,102.1
+ ,1
+ ,96.0
+ ,102.1
+ ,104.4
+ ,107.7
+ ,107.7
+ ,1
+ ,109.3
+ ,96.0
+ ,102.1
+ ,104.4
+ ,104.4
+ ,1
+ ,90.0
+ ,109.3
+ ,96.0
+ ,102.1
+ ,102.1
+ ,1
+ ,83.9
+ ,90.0
+ ,109.3
+ ,96.0)
+ ,dim=c(6
+ ,56)
+ ,dimnames=list(c('X'
+ ,'Y'
+ ,'y(t)'
+ ,'y(t-1)'
+ ,'y(t-2)'
+ ,'y(t-3)')
+ ,1:56))
> y <- array(NA,dim=c(6,56),dimnames=list(c('X','Y','y(t)','y(t-1)','y(t-2)','y(t-3)'),1:56))
> 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
X Y y(t) y(t-1) y(t-2) y(t-3) M1 M2 M3 M4 M5 M6 M7 M8 M9 M10 M11 t
1 121.6 0 97.2 111.5 114.0 118.8 1 0 0 0 0 0 0 0 0 0 0 1
2 118.8 0 102.5 97.2 111.5 114.0 0 1 0 0 0 0 0 0 0 0 0 2
3 114.0 1 113.4 102.5 97.2 111.5 0 0 1 0 0 0 0 0 0 0 0 3
4 111.5 1 109.8 113.4 102.5 97.2 0 0 0 1 0 0 0 0 0 0 0 4
5 97.2 1 104.9 109.8 113.4 102.5 0 0 0 0 1 0 0 0 0 0 0 5
6 102.5 1 126.1 104.9 109.8 113.4 0 0 0 0 0 1 0 0 0 0 0 6
7 113.4 1 80.0 126.1 104.9 109.8 0 0 0 0 0 0 1 0 0 0 0 7
8 109.8 1 96.8 80.0 126.1 104.9 0 0 0 0 0 0 0 1 0 0 0 8
9 104.9 1 117.2 96.8 80.0 126.1 0 0 0 0 0 0 0 0 1 0 0 9
10 126.1 1 112.3 117.2 96.8 80.0 0 0 0 0 0 0 0 0 0 1 0 10
11 80.0 1 117.3 112.3 117.2 96.8 0 0 0 0 0 0 0 0 0 0 1 11
12 96.8 1 111.1 117.3 112.3 117.2 0 0 0 0 0 0 0 0 0 0 0 12
13 117.2 1 102.2 111.1 117.3 112.3 1 0 0 0 0 0 0 0 0 0 0 13
14 112.3 1 104.3 102.2 111.1 117.3 0 1 0 0 0 0 0 0 0 0 0 14
15 117.3 1 122.9 104.3 102.2 111.1 0 0 1 0 0 0 0 0 0 0 0 15
16 111.1 0 107.6 122.9 104.3 102.2 0 0 0 1 0 0 0 0 0 0 0 16
17 102.2 0 121.3 107.6 122.9 104.3 0 0 0 0 1 0 0 0 0 0 0 17
18 104.3 0 131.5 121.3 107.6 122.9 0 0 0 0 0 1 0 0 0 0 0 18
19 122.9 0 89.0 131.5 121.3 107.6 0 0 0 0 0 0 1 0 0 0 0 19
20 107.6 0 104.4 89.0 131.5 121.3 0 0 0 0 0 0 0 1 0 0 0 20
21 121.3 0 128.9 104.4 89.0 131.5 0 0 0 0 0 0 0 0 1 0 0 21
22 131.5 0 135.9 128.9 104.4 89.0 0 0 0 0 0 0 0 0 0 1 0 22
23 89.0 0 133.3 135.9 128.9 104.4 0 0 0 0 0 0 0 0 0 0 1 23
24 104.4 0 121.3 133.3 135.9 128.9 0 0 0 0 0 0 0 0 0 0 0 24
25 128.9 0 120.5 121.3 133.3 135.9 1 0 0 0 0 0 0 0 0 0 0 25
26 135.9 0 120.4 120.5 121.3 133.3 0 1 0 0 0 0 0 0 0 0 0 26
27 133.3 0 137.9 120.4 120.5 121.3 0 0 1 0 0 0 0 0 0 0 0 27
28 121.3 0 126.1 137.9 120.4 120.5 0 0 0 1 0 0 0 0 0 0 0 28
29 120.5 0 133.2 126.1 137.9 120.4 0 0 0 0 1 0 0 0 0 0 0 29
30 120.4 0 151.1 133.2 126.1 137.9 0 0 0 0 0 1 0 0 0 0 0 30
31 137.9 0 105.0 151.1 133.2 126.1 0 0 0 0 0 0 1 0 0 0 0 31
32 126.1 0 119.0 105.0 151.1 133.2 0 0 0 0 0 0 0 1 0 0 0 32
33 133.2 0 140.4 119.0 105.0 151.1 0 0 0 0 0 0 0 0 1 0 0 33
34 151.1 0 156.6 140.4 119.0 105.0 0 0 0 0 0 0 0 0 0 1 0 34
35 105.0 0 137.1 156.6 140.4 119.0 0 0 0 0 0 0 0 0 0 0 1 35
36 119.0 0 122.7 137.1 156.6 140.4 0 0 0 0 0 0 0 0 0 0 0 36
37 140.4 0 125.8 122.7 137.1 156.6 1 0 0 0 0 0 0 0 0 0 0 37
38 156.6 0 139.3 125.8 122.7 137.1 0 1 0 0 0 0 0 0 0 0 0 38
39 137.1 0 134.9 139.3 125.8 122.7 0 0 1 0 0 0 0 0 0 0 0 39
40 122.7 0 149.2 134.9 139.3 125.8 0 0 0 1 0 0 0 0 0 0 0 40
41 125.8 0 132.3 149.2 134.9 139.3 0 0 0 0 1 0 0 0 0 0 0 41
42 139.3 0 149.0 132.3 149.2 134.9 0 0 0 0 0 1 0 0 0 0 0 42
43 134.9 0 117.2 149.0 132.3 149.2 0 0 0 0 0 0 1 0 0 0 0 43
44 149.2 1 119.6 117.2 149.0 132.3 0 0 0 0 0 0 0 1 0 0 0 44
45 132.3 0 152.0 119.6 117.2 149.0 0 0 0 0 0 0 0 0 1 0 0 45
46 149.0 1 149.4 152.0 119.6 117.2 0 0 0 0 0 0 0 0 0 1 0 46
47 117.2 1 127.3 149.4 152.0 119.6 0 0 0 0 0 0 0 0 0 0 1 47
48 119.6 1 114.1 127.3 149.4 152.0 0 0 0 0 0 0 0 0 0 0 0 48
49 152.0 1 102.1 114.1 127.3 149.4 1 0 0 0 0 0 0 0 0 0 0 49
50 149.4 1 107.7 102.1 114.1 127.3 0 1 0 0 0 0 0 0 0 0 0 50
51 127.3 1 104.4 107.7 102.1 114.1 0 0 1 0 0 0 0 0 0 0 0 51
52 114.1 1 102.1 104.4 107.7 102.1 0 0 0 1 0 0 0 0 0 0 0 52
53 102.1 1 96.0 102.1 104.4 107.7 0 0 0 0 1 0 0 0 0 0 0 53
54 107.7 1 109.3 96.0 102.1 104.4 0 0 0 0 0 1 0 0 0 0 0 54
55 104.4 1 90.0 109.3 96.0 102.1 0 0 0 0 0 0 1 0 0 0 0 55
56 102.1 1 83.9 90.0 109.3 96.0 0 0 0 0 0 0 0 1 0 0 0 56
> k <- length(x[1,])
> df <- as.data.frame(x)
> (mylm <- lm(df))
Call:
lm(formula = df)
Coefficients:
(Intercept) Y `y(t)` `y(t-1)` `y(t-2)` `y(t-3)`
-14.58669 3.81450 -0.06149 0.29835 0.44321 0.18274
M1 M2 M3 M4 M5 M6
32.29672 42.87337 36.71937 23.92885 13.74819 20.46761
M7 M8 M9 M10 M11 t
22.44288 22.59901 38.32861 48.79545 -7.94034 0.18070
> (mysum <- summary(mylm))
Call:
lm(formula = df)
Residuals:
Min 1Q Median 3Q Max
-17.0854 -3.1291 -0.7408 3.5476 13.0437
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -14.58669 14.15494 -1.031 0.309289
Y 3.81450 2.59774 1.468 0.150228
`y(t)` -0.06149 0.14179 -0.434 0.666990
`y(t-1)` 0.29835 0.13699 2.178 0.035682 *
`y(t-2)` 0.44321 0.14282 3.103 0.003604 **
`y(t-3)` 0.18274 0.15041 1.215 0.231876
M1 32.29672 4.90681 6.582 9.09e-08 ***
M2 42.87337 5.30026 8.089 8.71e-10 ***
M3 36.71937 6.06347 6.056 4.77e-07 ***
M4 23.92885 5.85319 4.088 0.000217 ***
M5 13.74819 5.13766 2.676 0.010934 *
M6 20.46761 6.18625 3.309 0.002059 **
M7 22.44288 5.62810 3.988 0.000293 ***
M8 22.59901 5.64127 4.006 0.000277 ***
M9 38.32861 8.76751 4.372 9.24e-05 ***
M10 48.79545 9.17732 5.317 4.91e-06 ***
M11 -7.94034 6.75937 -1.175 0.247417
t 0.18070 0.06585 2.744 0.009215 **
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 6.556 on 38 degrees of freedom
Multiple R-squared: 0.8944, Adjusted R-squared: 0.8472
F-statistic: 18.94 on 17 and 38 DF, p-value: 1.548e-13
> 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,] 0.20262049 0.40524098 0.7973795
[2,] 0.15980078 0.31960156 0.8401992
[3,] 0.07832361 0.15664722 0.9216764
[4,] 0.03459187 0.06918373 0.9654081
[5,] 0.03648995 0.07297989 0.9635101
[6,] 0.36632033 0.73264066 0.6336797
[7,] 0.26977225 0.53954450 0.7302277
[8,] 0.17632954 0.35265907 0.8236705
[9,] 0.15207570 0.30415139 0.8479243
[10,] 0.12144586 0.24289171 0.8785541
[11,] 0.08215135 0.16430270 0.9178487
[12,] 0.12234733 0.24469465 0.8776527
[13,] 0.15640554 0.31281107 0.8435945
[14,] 0.41917318 0.83834636 0.5808268
[15,] 0.27002990 0.54005980 0.7299701
> postscript(file="/var/www/html/rcomp/tmp/1dxph1258623266.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$resid)
> grid()
> dev.off()
null device
1
> postscript(file="/var/www/html/rcomp/tmp/222ei1258623266.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556)
> plot(mysum$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/3ylix1258623266.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556)
> hist(mysum$resid, main='Residual Histogram', xlab='values of Residuals')
> grid()
> dev.off()
null device
1
> postscript(file="/var/www/html/rcomp/tmp/4z2jh1258623266.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556)
> densityplot(~mysum$resid,col='black',main='Residual Density Plot', xlab='values of Residuals')
> dev.off()
null device
1
> postscript(file="/var/www/html/rcomp/tmp/52i941258623266.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 = 56
Frequency = 1
1 2 3 4 5 6
4.1841261 -2.7956867 0.4467929 7.3474168 -1.9793407 -1.2103027
7 8 9 10 11 12
1.2035481 3.5533143 -4.4572471 0.6860578 0.7990311 6.0487422
13 14 15 16 17 18
-6.0467361 -17.0854407 -0.5174281 3.9123955 1.7921660 -3.0861603
19 20 21 22 23 24
4.4253858 -4.6087478 7.0651200 0.6795144 -1.1865527 -1.4494016
25 26 27 28 29 30
-6.0226295 -3.7538300 3.2728544 -1.8735826 3.5456808 -2.4402483
31 32 33 34 35 36
3.7381772 -3.0145589 2.4748118 6.5581711 -1.0621421 -1.3413875
37 38 39 40 41 42
-2.2497921 13.0437370 -3.5237361 -9.6716610 -2.3942504 4.7408912
43 44 45 46 47 48
-3.8759790 11.5947241 -5.0826847 -7.9237432 1.4496637 -3.2579531
49 50 51 52 53 54
10.1350316 10.5912204 0.3215169 0.2854313 -0.9642558 1.9958201
55 56
-5.4911320 -7.5247318
> postscript(file="/var/www/html/rcomp/tmp/6bpkp1258623266.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 = 56
Frequency = 1
lag(myerror, k = 1) myerror
0 4.1841261 NA
1 -2.7956867 4.1841261
2 0.4467929 -2.7956867
3 7.3474168 0.4467929
4 -1.9793407 7.3474168
5 -1.2103027 -1.9793407
6 1.2035481 -1.2103027
7 3.5533143 1.2035481
8 -4.4572471 3.5533143
9 0.6860578 -4.4572471
10 0.7990311 0.6860578
11 6.0487422 0.7990311
12 -6.0467361 6.0487422
13 -17.0854407 -6.0467361
14 -0.5174281 -17.0854407
15 3.9123955 -0.5174281
16 1.7921660 3.9123955
17 -3.0861603 1.7921660
18 4.4253858 -3.0861603
19 -4.6087478 4.4253858
20 7.0651200 -4.6087478
21 0.6795144 7.0651200
22 -1.1865527 0.6795144
23 -1.4494016 -1.1865527
24 -6.0226295 -1.4494016
25 -3.7538300 -6.0226295
26 3.2728544 -3.7538300
27 -1.8735826 3.2728544
28 3.5456808 -1.8735826
29 -2.4402483 3.5456808
30 3.7381772 -2.4402483
31 -3.0145589 3.7381772
32 2.4748118 -3.0145589
33 6.5581711 2.4748118
34 -1.0621421 6.5581711
35 -1.3413875 -1.0621421
36 -2.2497921 -1.3413875
37 13.0437370 -2.2497921
38 -3.5237361 13.0437370
39 -9.6716610 -3.5237361
40 -2.3942504 -9.6716610
41 4.7408912 -2.3942504
42 -3.8759790 4.7408912
43 11.5947241 -3.8759790
44 -5.0826847 11.5947241
45 -7.9237432 -5.0826847
46 1.4496637 -7.9237432
47 -3.2579531 1.4496637
48 10.1350316 -3.2579531
49 10.5912204 10.1350316
50 0.3215169 10.5912204
51 0.2854313 0.3215169
52 -0.9642558 0.2854313
53 1.9958201 -0.9642558
54 -5.4911320 1.9958201
55 -7.5247318 -5.4911320
56 NA -7.5247318
> dum1 <- dum[2:length(myerror),]
> dum1
lag(myerror, k = 1) myerror
[1,] -2.7956867 4.1841261
[2,] 0.4467929 -2.7956867
[3,] 7.3474168 0.4467929
[4,] -1.9793407 7.3474168
[5,] -1.2103027 -1.9793407
[6,] 1.2035481 -1.2103027
[7,] 3.5533143 1.2035481
[8,] -4.4572471 3.5533143
[9,] 0.6860578 -4.4572471
[10,] 0.7990311 0.6860578
[11,] 6.0487422 0.7990311
[12,] -6.0467361 6.0487422
[13,] -17.0854407 -6.0467361
[14,] -0.5174281 -17.0854407
[15,] 3.9123955 -0.5174281
[16,] 1.7921660 3.9123955
[17,] -3.0861603 1.7921660
[18,] 4.4253858 -3.0861603
[19,] -4.6087478 4.4253858
[20,] 7.0651200 -4.6087478
[21,] 0.6795144 7.0651200
[22,] -1.1865527 0.6795144
[23,] -1.4494016 -1.1865527
[24,] -6.0226295 -1.4494016
[25,] -3.7538300 -6.0226295
[26,] 3.2728544 -3.7538300
[27,] -1.8735826 3.2728544
[28,] 3.5456808 -1.8735826
[29,] -2.4402483 3.5456808
[30,] 3.7381772 -2.4402483
[31,] -3.0145589 3.7381772
[32,] 2.4748118 -3.0145589
[33,] 6.5581711 2.4748118
[34,] -1.0621421 6.5581711
[35,] -1.3413875 -1.0621421
[36,] -2.2497921 -1.3413875
[37,] 13.0437370 -2.2497921
[38,] -3.5237361 13.0437370
[39,] -9.6716610 -3.5237361
[40,] -2.3942504 -9.6716610
[41,] 4.7408912 -2.3942504
[42,] -3.8759790 4.7408912
[43,] 11.5947241 -3.8759790
[44,] -5.0826847 11.5947241
[45,] -7.9237432 -5.0826847
[46,] 1.4496637 -7.9237432
[47,] -3.2579531 1.4496637
[48,] 10.1350316 -3.2579531
[49,] 10.5912204 10.1350316
[50,] 0.3215169 10.5912204
[51,] 0.2854313 0.3215169
[52,] -0.9642558 0.2854313
[53,] 1.9958201 -0.9642558
[54,] -5.4911320 1.9958201
[55,] -7.5247318 -5.4911320
> z <- as.data.frame(dum1)
> z
lag(myerror, k = 1) myerror
1 -2.7956867 4.1841261
2 0.4467929 -2.7956867
3 7.3474168 0.4467929
4 -1.9793407 7.3474168
5 -1.2103027 -1.9793407
6 1.2035481 -1.2103027
7 3.5533143 1.2035481
8 -4.4572471 3.5533143
9 0.6860578 -4.4572471
10 0.7990311 0.6860578
11 6.0487422 0.7990311
12 -6.0467361 6.0487422
13 -17.0854407 -6.0467361
14 -0.5174281 -17.0854407
15 3.9123955 -0.5174281
16 1.7921660 3.9123955
17 -3.0861603 1.7921660
18 4.4253858 -3.0861603
19 -4.6087478 4.4253858
20 7.0651200 -4.6087478
21 0.6795144 7.0651200
22 -1.1865527 0.6795144
23 -1.4494016 -1.1865527
24 -6.0226295 -1.4494016
25 -3.7538300 -6.0226295
26 3.2728544 -3.7538300
27 -1.8735826 3.2728544
28 3.5456808 -1.8735826
29 -2.4402483 3.5456808
30 3.7381772 -2.4402483
31 -3.0145589 3.7381772
32 2.4748118 -3.0145589
33 6.5581711 2.4748118
34 -1.0621421 6.5581711
35 -1.3413875 -1.0621421
36 -2.2497921 -1.3413875
37 13.0437370 -2.2497921
38 -3.5237361 13.0437370
39 -9.6716610 -3.5237361
40 -2.3942504 -9.6716610
41 4.7408912 -2.3942504
42 -3.8759790 4.7408912
43 11.5947241 -3.8759790
44 -5.0826847 11.5947241
45 -7.9237432 -5.0826847
46 1.4496637 -7.9237432
47 -3.2579531 1.4496637
48 10.1350316 -3.2579531
49 10.5912204 10.1350316
50 0.3215169 10.5912204
51 0.2854313 0.3215169
52 -0.9642558 0.2854313
53 1.9958201 -0.9642558
54 -5.4911320 1.9958201
55 -7.5247318 -5.4911320
> 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/7h6lz1258623266.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556)
> acf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Autocorrelation Function')
> grid()
> dev.off()
null device
1
> postscript(file="/var/www/html/rcomp/tmp/8x0w41258623266.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556)
> pacf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Partial Autocorrelation Function')
> grid()
> dev.off()
null device
1
> postscript(file="/var/www/html/rcomp/tmp/9lyid1258623266.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556)
> opar <- par(mfrow = c(2,2), oma = c(0, 0, 1.1, 0))
> plot(mylm, las = 1, sub='Residual Diagnostics')
> par(opar)
> dev.off()
null device
1
> if (n > n25) {
+ postscript(file="/var/www/html/rcomp/tmp/101izy1258623266.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556)
+ plot(kp3:nmkm3,gqarr[,2], main='Goldfeld-Quandt test',ylab='2-sided p-value',xlab='breakpoint')
+ grid()
+ dev.off()
+ }
null device
1
>
> #Note: the /var/www/html/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab
> load(file="/var/www/html/rcomp/createtable")
>
> a<-table.start()
> a<-table.row.start(a)
> a<-table.element(a, 'Multiple Linear Regression - Estimated Regression Equation', 1, TRUE)
> a<-table.row.end(a)
> myeq <- colnames(x)[1]
> myeq <- paste(myeq, '[t] = ', sep='')
> for (i in 1:k){
+ if (mysum$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/11v7cs1258623266.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/12mad61258623266.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/138uz81258623267.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/143e691258623267.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/15ez5i1258623267.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/163w291258623267.tab")
+ }
>
> system("convert tmp/1dxph1258623266.ps tmp/1dxph1258623266.png")
> system("convert tmp/222ei1258623266.ps tmp/222ei1258623266.png")
> system("convert tmp/3ylix1258623266.ps tmp/3ylix1258623266.png")
> system("convert tmp/4z2jh1258623266.ps tmp/4z2jh1258623266.png")
> system("convert tmp/52i941258623266.ps tmp/52i941258623266.png")
> system("convert tmp/6bpkp1258623266.ps tmp/6bpkp1258623266.png")
> system("convert tmp/7h6lz1258623266.ps tmp/7h6lz1258623266.png")
> system("convert tmp/8x0w41258623266.ps tmp/8x0w41258623266.png")
> system("convert tmp/9lyid1258623266.ps tmp/9lyid1258623266.png")
> system("convert tmp/101izy1258623266.ps tmp/101izy1258623266.png")
>
>
> proc.time()
user system elapsed
2.310 1.547 2.827