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(1,16,68,4.1,2,17,71,4.6,3,15,62,3.8,4,17,75,4.4,5,17,58,3.2,6,16,60,3.1,7,16,67,3.8,8,16,68,4.1,9,17,71,4.3,10,17,69,3.7,11,16,68,3.5,12,16,67,3.2,13,15,63,3.7,14,16,62,3.3,15,15,60,3.4,16,15,63,4.0,17,16,65,4.1,18,17,67,3.8,19,15,63,3.4,20,16,61,3.6),dim=c(4,20),dimnames=list(c('Student','Age','Height','Self-Esteem'),1:20))
> y <- array(NA,dim=c(4,20),dimnames=list(c('Student','Age','Height','Self-Esteem'),1:20))
> 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 = '2'
> 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
Age Student Height Self-Esteem
1 16 1 68 4.1
2 17 2 71 4.6
3 15 3 62 3.8
4 17 4 75 4.4
5 17 5 58 3.2
6 16 6 60 3.1
7 16 7 67 3.8
8 16 8 68 4.1
9 17 9 71 4.3
10 17 10 69 3.7
11 16 11 68 3.5
12 16 12 67 3.2
13 15 13 63 3.7
14 16 14 62 3.3
15 15 15 60 3.4
16 15 16 63 4.0
17 16 17 65 4.1
18 17 18 67 3.8
19 15 19 63 3.4
20 16 20 61 3.6
> k <- length(x[1,])
> df <- as.data.frame(x)
> (mylm <- lm(df))
Call:
lm(formula = df)
Coefficients:
(Intercept) Student Height `Self-Esteem`
10.55839 -0.02348 0.10858 -0.36294
> (mysum <- summary(mylm))
Call:
lm(formula = df)
Residuals:
Min 1Q Median 3Q Max
-0.8406 -0.4443 -0.1383 0.4629 1.4229
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 10.55839 2.58024 4.092 0.000851 ***
Student -0.02348 0.02797 -0.840 0.413523
Height 0.10858 0.05198 2.089 0.053062 .
`Self-Esteem` -0.36294 0.53372 -0.680 0.506205
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 0.6722 on 16 degrees of freedom
Multiple R-squared: 0.3397, Adjusted R-squared: 0.2159
F-statistic: 2.744 on 3 and 16 DF, p-value: 0.07729
> 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)$p.value
+ }
+ if (gqarr[mypoint-kp3+1,2] < 0.01) numsignificant1 <- numsignificant1 + 1
+ if (gqarr[mypoint-kp3+1,2] < 0.05) numsignificant5 <- numsignificant5 + 1
+ if (gqarr[mypoint-kp3+1,2] < 0.10) numsignificant10 <- numsignificant10 + 1
+ }
+ gqarr
+ }
> postscript(file="/var/wessaorg/rcomp/tmp/1b6sa1323615062.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556)
> plot(x[,1], type='l', main='Actuals and Interpolation', ylab='value of Actuals and Interpolation (dots)', xlab='time or index')
> points(x[,1]-mysum$resid)
> grid()
> dev.off()
null device
1
> postscript(file="/var/wessaorg/rcomp/tmp/2fcq61323615062.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556)
> plot(mysum$resid, type='b', pch=19, main='Residuals', ylab='value of Residuals', xlab='time or index')
> grid()
> dev.off()
null device
1
> postscript(file="/var/wessaorg/rcomp/tmp/3v7u81323615062.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556)
> hist(mysum$resid, main='Residual Histogram', xlab='values of Residuals')
> grid()
> dev.off()
null device
1
> postscript(file="/var/wessaorg/rcomp/tmp/43fiv1323615062.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556)
> densityplot(~mysum$resid,col='black',main='Residual Density Plot', xlab='values of Residuals')
> dev.off()
null device
1
> postscript(file="/var/wessaorg/rcomp/tmp/56uug1323615062.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556)
> qqnorm(mysum$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 = 20
Frequency = 1
1 2 3 4 5 6
-0.43013321 0.44908438 -0.84059252 -0.01085864 1.42290907 0.19293756
7 8 9 10 11 12
-0.28956715 -0.26578289 0.50455124 0.52741857 -0.41311396 -0.38994099
13 14 15 16 17 18
-0.75067866 0.23619983 -0.48687143 -0.57135935 0.27125812 0.96869763
19 20
-0.71869042 0.59453281
> postscript(file="/var/wessaorg/rcomp/tmp/6asoi1323615063.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 = 20
Frequency = 1
lag(myerror, k = 1) myerror
0 -0.43013321 NA
1 0.44908438 -0.43013321
2 -0.84059252 0.44908438
3 -0.01085864 -0.84059252
4 1.42290907 -0.01085864
5 0.19293756 1.42290907
6 -0.28956715 0.19293756
7 -0.26578289 -0.28956715
8 0.50455124 -0.26578289
9 0.52741857 0.50455124
10 -0.41311396 0.52741857
11 -0.38994099 -0.41311396
12 -0.75067866 -0.38994099
13 0.23619983 -0.75067866
14 -0.48687143 0.23619983
15 -0.57135935 -0.48687143
16 0.27125812 -0.57135935
17 0.96869763 0.27125812
18 -0.71869042 0.96869763
19 0.59453281 -0.71869042
20 NA 0.59453281
> dum1 <- dum[2:length(myerror),]
> dum1
lag(myerror, k = 1) myerror
[1,] 0.44908438 -0.43013321
[2,] -0.84059252 0.44908438
[3,] -0.01085864 -0.84059252
[4,] 1.42290907 -0.01085864
[5,] 0.19293756 1.42290907
[6,] -0.28956715 0.19293756
[7,] -0.26578289 -0.28956715
[8,] 0.50455124 -0.26578289
[9,] 0.52741857 0.50455124
[10,] -0.41311396 0.52741857
[11,] -0.38994099 -0.41311396
[12,] -0.75067866 -0.38994099
[13,] 0.23619983 -0.75067866
[14,] -0.48687143 0.23619983
[15,] -0.57135935 -0.48687143
[16,] 0.27125812 -0.57135935
[17,] 0.96869763 0.27125812
[18,] -0.71869042 0.96869763
[19,] 0.59453281 -0.71869042
> z <- as.data.frame(dum1)
> z
lag(myerror, k = 1) myerror
1 0.44908438 -0.43013321
2 -0.84059252 0.44908438
3 -0.01085864 -0.84059252
4 1.42290907 -0.01085864
5 0.19293756 1.42290907
6 -0.28956715 0.19293756
7 -0.26578289 -0.28956715
8 0.50455124 -0.26578289
9 0.52741857 0.50455124
10 -0.41311396 0.52741857
11 -0.38994099 -0.41311396
12 -0.75067866 -0.38994099
13 0.23619983 -0.75067866
14 -0.48687143 0.23619983
15 -0.57135935 -0.48687143
16 0.27125812 -0.57135935
17 0.96869763 0.27125812
18 -0.71869042 0.96869763
19 0.59453281 -0.71869042
> 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/7ipw41323615063.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/84zpf1323615063.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/96iql1323615063.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/10vhrq1323615063.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$coefficients)[i] != 't') myeq <- paste(myeq, '[t]', sep='')
+ }
+ }
> myeq <- paste(myeq, ' + e[t]')
> a<-table.row.start(a)
> a<-table.element(a, myeq)
> a<-table.row.end(a)
> a<-table.end(a)
> table.save(a,file="/var/wessaorg/rcomp/tmp/11omzr1323615063.tab")
> a<-table.start()
> a<-table.row.start(a)
> a<-table.element(a,hyperlink('http://www.xycoon.com/ols1.htm','Multiple Linear Regression - Ordinary Least Squares',''), 6, TRUE)
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a,'Variable',header=TRUE)
> a<-table.element(a,'Parameter',header=TRUE)
> a<-table.element(a,'S.D.',header=TRUE)
> a<-table.element(a,'T-STAT
H0: parameter = 0',header=TRUE)
> a<-table.element(a,'2-tail p-value',header=TRUE)
> a<-table.element(a,'1-tail p-value',header=TRUE)
> a<-table.row.end(a)
> for (i in 1:k){
+ a<-table.row.start(a)
+ a<-table.element(a,rownames(mysum$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$coefficients[i,4]/2,6))
+ a<-table.row.end(a)
+ }
> a<-table.end(a)
> table.save(a,file="/var/wessaorg/rcomp/tmp/122hn81323615063.tab")
> a<-table.start()
> a<-table.row.start(a)
> a<-table.element(a, 'Multiple Linear Regression - Regression Statistics', 2, TRUE)
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a, 'Multiple R',1,TRUE)
> a<-table.element(a, sqrt(mysum$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$sigma)
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a, 'Sum Squared Residuals',1,TRUE)
> a<-table.element(a, sum(myerror*myerror))
> a<-table.row.end(a)
> a<-table.end(a)
> table.save(a,file="/var/wessaorg/rcomp/tmp/13chpn1323615063.tab")
> a<-table.start()
> a<-table.row.start(a)
> a<-table.element(a, 'Multiple Linear Regression - Actuals, Interpolation, and Residuals', 4, TRUE)
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a, 'Time or Index', 1, TRUE)
> a<-table.element(a, 'Actuals', 1, TRUE)
> a<-table.element(a, 'Interpolation
Forecast', 1, TRUE)
> a<-table.element(a, 'Residuals
Prediction Error', 1, TRUE)
> a<-table.row.end(a)
> for (i in 1:n) {
+ a<-table.row.start(a)
+ a<-table.element(a,i, 1, TRUE)
+ a<-table.element(a,x[i])
+ a<-table.element(a,x[i]-mysum$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/14ad5s1323615063.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/1531w71323615063.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/161mn71323615063.tab")
+ }
>
> try(system("convert tmp/1b6sa1323615062.ps tmp/1b6sa1323615062.png",intern=TRUE))
character(0)
> try(system("convert tmp/2fcq61323615062.ps tmp/2fcq61323615062.png",intern=TRUE))
character(0)
> try(system("convert tmp/3v7u81323615062.ps tmp/3v7u81323615062.png",intern=TRUE))
character(0)
> try(system("convert tmp/43fiv1323615062.ps tmp/43fiv1323615062.png",intern=TRUE))
character(0)
> try(system("convert tmp/56uug1323615062.ps tmp/56uug1323615062.png",intern=TRUE))
character(0)
> try(system("convert tmp/6asoi1323615063.ps tmp/6asoi1323615063.png",intern=TRUE))
character(0)
> try(system("convert tmp/7ipw41323615063.ps tmp/7ipw41323615063.png",intern=TRUE))
character(0)
> try(system("convert tmp/84zpf1323615063.ps tmp/84zpf1323615063.png",intern=TRUE))
character(0)
> try(system("convert tmp/96iql1323615063.ps tmp/96iql1323615063.png",intern=TRUE))
character(0)
> try(system("convert tmp/10vhrq1323615063.ps tmp/10vhrq1323615063.png",intern=TRUE))
convert: unable to open image `tmp/10vhrq1323615063.ps': No such file or directory @ blob.c/OpenBlob/2480.
convert: missing an image filename `tmp/10vhrq1323615063.png' @ convert.c/ConvertImageCommand/2838.
character(0)
Warning message:
running command 'convert tmp/10vhrq1323615063.ps tmp/10vhrq1323615063.png' had status 1
>
>
> proc.time()
user system elapsed
2.630 0.472 3.151