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.
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Type 'demo()' for some demos, 'help()' for on-line help, or
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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 = '3'
> 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
50km/u 15km/u 30km/u 60Km/u 70km/u 80km/u 90km/u 100km/u 120km/u
1 407 3 18 4 42 596 1 93 71
2 437 2 21 6 48 622 1 86 75
3 421 5 22 5 51 640 0 84 106
4 365 1 24 6 50 549 3 90 92
5 366 1 33 5 34 568 0 71 85
6 355 4 21 11 39 523 5 51 57
7 342 1 24 10 48 530 3 73 59
8 358 0 31 23 38 493 0 61 77
9 305 6 41 24 36 454 3 60 64
10 321 0 40 28 33 441 1 55 68
11 303 6 48 36 24 455 5 62 89
12 230 1 35 42 23 330 5 49 70
13 206 2 41 54 20 284 0 43 70
14 241 1 37 61 15 267 2 36 53
15 224 1 42 69 18 243 2 39 58
16 213 1 33 68 12 239 3 35 60
17 196 2 30 82 20 216 3 35 48
> k <- length(x[1,])
> df <- as.data.frame(x)
> (mylm <- lm(df))
Call:
lm(formula = df)
Coefficients:
(Intercept) `15km/u` `30km/u` `60Km/u` `70km/u` `80km/u`
-72.24546 -3.33197 -0.21623 1.68881 -0.37376 0.90083
`90km/u` `100km/u` `120km/u`
-1.47565 -0.01798 -0.47892
> (mysum <- summary(mylm))
Call:
lm(formula = df)
Residuals:
Min 1Q Median 3Q Max
-19.627 -4.973 3.851 6.205 15.626
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -72.24546 97.89454 -0.738 0.481603
`15km/u` -3.33197 2.63723 -1.263 0.242008
`30km/u` -0.21623 0.68709 -0.315 0.761032
`60Km/u` 1.68881 0.75451 2.238 0.055572 .
`70km/u` -0.37376 0.87811 -0.426 0.681590
`80km/u` 0.90083 0.17247 5.223 0.000799 ***
`90km/u` -1.47565 2.62791 -0.562 0.589816
`100km/u` -0.01798 0.55215 -0.033 0.974825
`120km/u` -0.47892 0.40200 -1.191 0.267660
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 14.89 on 8 degrees of freedom
Multiple R-squared: 0.9825, Adjusted R-squared: 0.965
F-statistic: 56.14 on 8 and 8 DF, p-value: 3.148e-06
> 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)$p.value
+ }
+ if (gqarr[mypoint-kp3+1,2] < 0.01) numsignificant1 <- numsignificant1 + 1
+ if (gqarr[mypoint-kp3+1,2] < 0.05) numsignificant5 <- numsignificant5 + 1
+ if (gqarr[mypoint-kp3+1,2] < 0.10) numsignificant10 <- numsignificant10 + 1
+ }
+ gqarr
+ }
> postscript(file="/var/wessaorg/rcomp/tmp/1w9r61322044642.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556)
> plot(x[,1], type='l', main='Actuals and Interpolation', ylab='value of Actuals and Interpolation (dots)', xlab='time or index')
> points(x[,1]-mysum$resid)
> grid()
> dev.off()
null device
1
> postscript(file="/var/wessaorg/rcomp/tmp/2nr4h1322044642.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556)
> plot(mysum$resid, type='b', pch=19, main='Residuals', ylab='value of Residuals', xlab='time or index')
> grid()
> dev.off()
null device
1
> postscript(file="/var/wessaorg/rcomp/tmp/3pgxr1322044642.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556)
> hist(mysum$resid, main='Residual Histogram', xlab='values of Residuals')
> grid()
> dev.off()
null device
1
> postscript(file="/var/wessaorg/rcomp/tmp/40scj1322044642.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556)
> densityplot(~mysum$resid,col='black',main='Residual Density Plot', xlab='values of Residuals')
> dev.off()
null device
1
> postscript(file="/var/wessaorg/rcomp/tmp/5ux5t1322044642.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556)
> qqnorm(mysum$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 7
2.330576 6.880426 1.022650 9.870403 -16.711608 5.571775 -19.626588
8 9 10 11 12 13 14
6.171693 6.204998 4.705765 -4.972726 -4.679328 -11.484778 15.625777
15 16 17
11.386261 3.851334 -16.146630
> postscript(file="/var/wessaorg/rcomp/tmp/6yyri1322044642.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 2.330576 NA
1 6.880426 2.330576
2 1.022650 6.880426
3 9.870403 1.022650
4 -16.711608 9.870403
5 5.571775 -16.711608
6 -19.626588 5.571775
7 6.171693 -19.626588
8 6.204998 6.171693
9 4.705765 6.204998
10 -4.972726 4.705765
11 -4.679328 -4.972726
12 -11.484778 -4.679328
13 15.625777 -11.484778
14 11.386261 15.625777
15 3.851334 11.386261
16 -16.146630 3.851334
17 NA -16.146630
> dum1 <- dum[2:length(myerror),]
> dum1
lag(myerror, k = 1) myerror
[1,] 6.880426 2.330576
[2,] 1.022650 6.880426
[3,] 9.870403 1.022650
[4,] -16.711608 9.870403
[5,] 5.571775 -16.711608
[6,] -19.626588 5.571775
[7,] 6.171693 -19.626588
[8,] 6.204998 6.171693
[9,] 4.705765 6.204998
[10,] -4.972726 4.705765
[11,] -4.679328 -4.972726
[12,] -11.484778 -4.679328
[13,] 15.625777 -11.484778
[14,] 11.386261 15.625777
[15,] 3.851334 11.386261
[16,] -16.146630 3.851334
> z <- as.data.frame(dum1)
> z
lag(myerror, k = 1) myerror
1 6.880426 2.330576
2 1.022650 6.880426
3 9.870403 1.022650
4 -16.711608 9.870403
5 5.571775 -16.711608
6 -19.626588 5.571775
7 6.171693 -19.626588
8 6.204998 6.171693
9 4.705765 6.204998
10 -4.972726 4.705765
11 -4.679328 -4.972726
12 -11.484778 -4.679328
13 15.625777 -11.484778
14 11.386261 15.625777
15 3.851334 11.386261
16 -16.146630 3.851334
> 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/73zog1322044642.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/8r7bo1322044642.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/9h2v41322044642.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/10u0mk1322044642.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$coefficients)[i] != 't') myeq <- paste(myeq, '[t]', sep='')
+ }
+ }
> myeq <- paste(myeq, ' + e[t]')
> a<-table.row.start(a)
> a<-table.element(a, myeq)
> a<-table.row.end(a)
> a<-table.end(a)
> table.save(a,file="/var/wessaorg/rcomp/tmp/11gkbg1322044642.tab")
> a<-table.start()
> a<-table.row.start(a)
> a<-table.element(a,hyperlink('http://www.xycoon.com/ols1.htm','Multiple Linear Regression - Ordinary Least Squares',''), 6, TRUE)
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a,'Variable',header=TRUE)
> a<-table.element(a,'Parameter',header=TRUE)
> a<-table.element(a,'S.D.',header=TRUE)
> a<-table.element(a,'T-STAT
H0: parameter = 0',header=TRUE)
> a<-table.element(a,'2-tail p-value',header=TRUE)
> a<-table.element(a,'1-tail p-value',header=TRUE)
> a<-table.row.end(a)
> for (i in 1:k){
+ a<-table.row.start(a)
+ a<-table.element(a,rownames(mysum$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$coefficients[i,4]/2,6))
+ a<-table.row.end(a)
+ }
> a<-table.end(a)
> table.save(a,file="/var/wessaorg/rcomp/tmp/12cnz71322044642.tab")
> a<-table.start()
> a<-table.row.start(a)
> a<-table.element(a, 'Multiple Linear Regression - Regression Statistics', 2, TRUE)
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a, 'Multiple R',1,TRUE)
> a<-table.element(a, sqrt(mysum$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$sigma)
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a, 'Sum Squared Residuals',1,TRUE)
> a<-table.element(a, sum(myerror*myerror))
> a<-table.row.end(a)
> a<-table.end(a)
> table.save(a,file="/var/wessaorg/rcomp/tmp/13l51j1322044642.tab")
> a<-table.start()
> a<-table.row.start(a)
> a<-table.element(a, 'Multiple Linear Regression - Actuals, Interpolation, and Residuals', 4, TRUE)
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a, 'Time or Index', 1, TRUE)
> a<-table.element(a, 'Actuals', 1, TRUE)
> a<-table.element(a, 'Interpolation
Forecast', 1, TRUE)
> a<-table.element(a, 'Residuals
Prediction Error', 1, TRUE)
> a<-table.row.end(a)
> for (i in 1:n) {
+ a<-table.row.start(a)
+ a<-table.element(a,i, 1, TRUE)
+ a<-table.element(a,x[i])
+ a<-table.element(a,x[i]-mysum$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/143s261322044642.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/15sqnk1322044642.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/16yy9f1322044642.tab")
+ }
>
> try(system("convert tmp/1w9r61322044642.ps tmp/1w9r61322044642.png",intern=TRUE))
character(0)
> try(system("convert tmp/2nr4h1322044642.ps tmp/2nr4h1322044642.png",intern=TRUE))
character(0)
> try(system("convert tmp/3pgxr1322044642.ps tmp/3pgxr1322044642.png",intern=TRUE))
character(0)
> try(system("convert tmp/40scj1322044642.ps tmp/40scj1322044642.png",intern=TRUE))
character(0)
> try(system("convert tmp/5ux5t1322044642.ps tmp/5ux5t1322044642.png",intern=TRUE))
character(0)
> try(system("convert tmp/6yyri1322044642.ps tmp/6yyri1322044642.png",intern=TRUE))
character(0)
> try(system("convert tmp/73zog1322044642.ps tmp/73zog1322044642.png",intern=TRUE))
character(0)
> try(system("convert tmp/8r7bo1322044642.ps tmp/8r7bo1322044642.png",intern=TRUE))
character(0)
> try(system("convert tmp/9h2v41322044642.ps tmp/9h2v41322044642.png",intern=TRUE))
character(0)
> try(system("convert tmp/10u0mk1322044642.ps tmp/10u0mk1322044642.png",intern=TRUE))
convert: unable to open image `tmp/10u0mk1322044642.ps': No such file or directory @ blob.c/OpenBlob/2480.
convert: missing an image filename `tmp/10u0mk1322044642.png' @ convert.c/ConvertImageCommand/2838.
character(0)
Warning message:
running command 'convert tmp/10u0mk1322044642.ps tmp/10u0mk1322044642.png' had status 1
>
>
> proc.time()
user system elapsed
2.585 0.407 3.063