R version 2.13.0 (2011-04-13)
Copyright (C) 2011 The R Foundation for Statistical Computing
ISBN 3-900051-07-0
Platform: i486-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.
R is a collaborative project with many contributors.
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
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.
> x <- array(list(3,18,407,4,42,596,1,93,71,2,21,437,6,48,622,1,86,75,5,22,421,5,51,640,0,84,106,1,24,365,6,50,549,3,90,92,1,33,366,5,34,568,0,71,85,4,21,355,11,39,523,5,51,57,1,24,342,10,48,530,3,73,59,0,31,358,23,38,493,0,61,77,6,41,305,24,36,454,3,60,64,0,40,321,28,33,441,1,55,68,6,48,303,36,24,455,5,62,89,1,35,230,42,23,330,5,49,70,2,41,206,54,20,284,0,43,70,1,37,241,61,15,267,2,36,53,1,42,224,69,18,243,2,39,58,1,33,213,68,12,239,3,35,60,2,30,196,82,20,216,3,35,48),dim=c(9,17),dimnames=list(c('15km/u','30km/u','50km/u','60Km/u','70km/u','80km/u','90km/u','100km/u','120km/u'),1:17))
> y <- array(NA,dim=c(9,17),dimnames=list(c('15km/u','30km/u','50km/u','60Km/u','70km/u','80km/u','90km/u','100km/u','120km/u'),1:17))
> for (i in 1:dim(x)[1])
+ {
+ for (j in 1:dim(x)[2])
+ {
+ y[i,j] <- as.numeric(x[i,j])
+ }
+ }
> par3 = 'No Linear Trend'
> par2 = 'Do not include Seasonal Dummies'
> par1 = '1'
> #'GNU S' R Code compiled by R2WASP v. 1.0.44 ()
> #Author: Prof. Dr. P. Wessa
> #To cite this work: AUTHOR(S), (YEAR), YOUR SOFTWARE TITLE (vNUMBER) in Free Statistics Software (v$_version), Office for Research Development and Education, URL http://www.wessa.net/rwasp_YOURPAGE.wasp/
> #Source of accompanying publication: Office for Research, Development, and Education
> #Technical description: Write here your technical program description (don't use hard returns!)
> library(lattice)
> library(lmtest)
Loading required package: zoo
> 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
15km/u 30km/u 50km/u 60Km/u 70km/u 80km/u 90km/u 100km/u 120km/u
1 3 18 407 4 42 596 1 93 71
2 2 21 437 6 48 622 1 86 75
3 5 22 421 5 51 640 0 84 106
4 1 24 365 6 50 549 3 90 92
5 1 33 366 5 34 568 0 71 85
6 4 21 355 11 39 523 5 51 57
7 1 24 342 10 48 530 3 73 59
8 0 31 358 23 38 493 0 61 77
9 6 41 305 24 36 454 3 60 64
10 0 40 321 28 33 441 1 55 68
11 6 48 303 36 24 455 5 62 89
12 1 35 230 42 23 330 5 49 70
13 2 41 206 54 20 284 0 43 70
14 1 37 241 61 15 267 2 36 53
15 1 42 224 69 18 243 2 39 58
16 1 33 213 68 12 239 3 35 60
17 2 30 196 82 20 216 3 35 48
> k <- length(x[1,])
> df <- as.data.frame(x)
> (mylm <- lm(df))
Call:
lm(formula = df)
Coefficients:
(Intercept) `30km/u` `50km/u` `60Km/u` `70km/u` `80km/u`
-19.93952 0.05554 -0.04992 0.19382 -0.02461 0.07354
`90km/u` `100km/u` `120km/u`
0.36129 -0.01613 -0.02051
> (mysum <- summary(mylm))
Call:
lm(formula = df)
Residuals:
Min 1Q Median 3Q Max
-1.7484 -0.9448 -0.2219 1.0483 2.9332
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -19.93952 10.18160 -1.958 0.0859 .
`30km/u` 0.05554 0.08231 0.675 0.5188
`50km/u` -0.04992 0.03951 -1.263 0.2420
`60Km/u` 0.19382 0.09579 2.023 0.0776 .
`70km/u` -0.02461 0.10835 -0.227 0.8260
`80km/u` 0.07354 0.03591 2.048 0.0748 .
`90km/u` 0.36129 0.30205 1.196 0.2659
`100km/u` -0.01613 0.06735 -0.239 0.8168
`120km/u` -0.02051 0.05290 -0.388 0.7084
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 1.822 on 8 degrees of freedom
Multiple R-squared: 0.5606, Adjusted R-squared: 0.1212
F-statistic: 1.276 on 8 and 8 DF, p-value: 0.3694
> 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/wessaorg/rcomp/tmp/170nl1322044972.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$resid)
> grid()
> dev.off()
null device
1
> postscript(file="/var/wessaorg/rcomp/tmp/2rkg31322044972.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556)
> plot(mysum$resid, type='b', pch=19, main='Residuals', ylab='value of Residuals', xlab='time or index')
> grid()
> dev.off()
null device
1
> postscript(file="/var/wessaorg/rcomp/tmp/327yc1322044972.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556)
> hist(mysum$resid, main='Residual Histogram', xlab='values of Residuals')
> grid()
> dev.off()
null device
1
> postscript(file="/var/wessaorg/rcomp/tmp/407t71322044972.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556)
> densityplot(~mysum$resid,col='black',main='Residual Density Plot', xlab='values of Residuals')
> dev.off()
null device
1
> postscript(file="/var/wessaorg/rcomp/tmp/5qobf1322044972.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 = 17
Frequency = 1
1 2 3 4 5 6
1.282894562 -0.568862299 1.485604534 -0.221905086 -1.635099409 1.048322024
7 8 9 10 11 12
-1.748371607 -1.123799689 2.933176909 -1.381664109 -0.427812935 -0.944803406
13 14 15 16 17
1.216504242 0.772190716 0.084855310 -0.008884716 -0.762345042
> postscript(file="/var/wessaorg/rcomp/tmp/6g2da1322044972.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 = 17
Frequency = 1
lag(myerror, k = 1) myerror
0 1.282894562 NA
1 -0.568862299 1.282894562
2 1.485604534 -0.568862299
3 -0.221905086 1.485604534
4 -1.635099409 -0.221905086
5 1.048322024 -1.635099409
6 -1.748371607 1.048322024
7 -1.123799689 -1.748371607
8 2.933176909 -1.123799689
9 -1.381664109 2.933176909
10 -0.427812935 -1.381664109
11 -0.944803406 -0.427812935
12 1.216504242 -0.944803406
13 0.772190716 1.216504242
14 0.084855310 0.772190716
15 -0.008884716 0.084855310
16 -0.762345042 -0.008884716
17 NA -0.762345042
> dum1 <- dum[2:length(myerror),]
> dum1
lag(myerror, k = 1) myerror
[1,] -0.568862299 1.282894562
[2,] 1.485604534 -0.568862299
[3,] -0.221905086 1.485604534
[4,] -1.635099409 -0.221905086
[5,] 1.048322024 -1.635099409
[6,] -1.748371607 1.048322024
[7,] -1.123799689 -1.748371607
[8,] 2.933176909 -1.123799689
[9,] -1.381664109 2.933176909
[10,] -0.427812935 -1.381664109
[11,] -0.944803406 -0.427812935
[12,] 1.216504242 -0.944803406
[13,] 0.772190716 1.216504242
[14,] 0.084855310 0.772190716
[15,] -0.008884716 0.084855310
[16,] -0.762345042 -0.008884716
> z <- as.data.frame(dum1)
> z
lag(myerror, k = 1) myerror
1 -0.568862299 1.282894562
2 1.485604534 -0.568862299
3 -0.221905086 1.485604534
4 -1.635099409 -0.221905086
5 1.048322024 -1.635099409
6 -1.748371607 1.048322024
7 -1.123799689 -1.748371607
8 2.933176909 -1.123799689
9 -1.381664109 2.933176909
10 -0.427812935 -1.381664109
11 -0.944803406 -0.427812935
12 1.216504242 -0.944803406
13 0.772190716 1.216504242
14 0.084855310 0.772190716
15 -0.008884716 0.084855310
16 -0.762345042 -0.008884716
> 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/wessaorg/rcomp/tmp/73bqn1322044972.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556)
> acf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Autocorrelation Function')
> grid()
> dev.off()
null device
1
> postscript(file="/var/wessaorg/rcomp/tmp/8pa6w1322044972.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556)
> pacf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Partial Autocorrelation Function')
> grid()
> dev.off()
null device
1
> postscript(file="/var/wessaorg/rcomp/tmp/9bth31322044972.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556)
> opar <- par(mfrow = c(2,2), oma = c(0, 0, 1.1, 0))
> plot(mylm, las = 1, sub='Residual Diagnostics')
> par(opar)
> dev.off()
null device
1
> if (n > n25) {
+ postscript(file="/var/wessaorg/rcomp/tmp/10ex6g1322044972.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556)
+ plot(kp3:nmkm3,gqarr[,2], main='Goldfeld-Quandt test',ylab='2-sided p-value',xlab='breakpoint')
+ grid()
+ dev.off()
+ }
>
> #Note: the /var/wessaorg/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab
> load(file="/var/wessaorg/rcomp/createtable")
>
> a<-table.start()
> a<-table.row.start(a)
> a<-table.element(a, 'Multiple Linear Regression - Estimated Regression Equation', 1, TRUE)
> a<-table.row.end(a)
> myeq <- colnames(x)[1]
> myeq <- paste(myeq, '[t] = ', sep='')
> for (i in 1:k){
+ if (mysum$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/wessaorg/rcomp/tmp/1145t51322044972.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/wessaorg/rcomp/tmp/12cnc31322044972.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/wessaorg/rcomp/tmp/13boir1322044972.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/wessaorg/rcomp/tmp/14rw2v1322044972.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/wessaorg/rcomp/tmp/158tix1322044972.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/wessaorg/rcomp/tmp/163ptf1322044972.tab")
+ }
>
> try(system("convert tmp/170nl1322044972.ps tmp/170nl1322044972.png",intern=TRUE))
character(0)
> try(system("convert tmp/2rkg31322044972.ps tmp/2rkg31322044972.png",intern=TRUE))
character(0)
> try(system("convert tmp/327yc1322044972.ps tmp/327yc1322044972.png",intern=TRUE))
character(0)
> try(system("convert tmp/407t71322044972.ps tmp/407t71322044972.png",intern=TRUE))
character(0)
> try(system("convert tmp/5qobf1322044972.ps tmp/5qobf1322044972.png",intern=TRUE))
character(0)
> try(system("convert tmp/6g2da1322044972.ps tmp/6g2da1322044972.png",intern=TRUE))
character(0)
> try(system("convert tmp/73bqn1322044972.ps tmp/73bqn1322044972.png",intern=TRUE))
character(0)
> try(system("convert tmp/8pa6w1322044972.ps tmp/8pa6w1322044972.png",intern=TRUE))
character(0)
> try(system("convert tmp/9bth31322044972.ps tmp/9bth31322044972.png",intern=TRUE))
character(0)
> try(system("convert tmp/10ex6g1322044972.ps tmp/10ex6g1322044972.png",intern=TRUE))
convert: unable to open image `tmp/10ex6g1322044972.ps': No such file or directory @ blob.c/OpenBlob/2480.
convert: missing an image filename `tmp/10ex6g1322044972.png' @ convert.c/ConvertImageCommand/2838.
character(0)
Warning message:
running command 'convert tmp/10ex6g1322044972.ps tmp/10ex6g1322044972.png' had status 1
>
>
> proc.time()
user system elapsed
2.539 0.428 3.052