R version 2.10.1 (2009-12-14)
Copyright (C) 2009 The R Foundation for Statistical Computing
ISBN 3-900051-07-0
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> x <- array(list(52.3,36.4,78.44,46.8,88.76,57.2,54.08,67.6,111.44,74.3,105.2,86.5,45.73,91.3,122.35,102.8,142.24,114.5,86.22,120.9,174.5,135,185.2,144,111.8,156,214.6,173.7,144.6,182,174.36,199.2,215.4,208,286.24,217.8,188.56,223.2,237.2,234,181.8,251,373,260,191.6,289.5,247.12,296.4,269.6,312),dim=c(2,25),dimnames=list(c('CONS','INCOME'),1:25))
> y <- array(NA,dim=c(2,25),dimnames=list(c('CONS','INCOME'),1:25))
> 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
CONS INCOME
1 52.30 36.4
2 78.44 46.8
3 88.76 57.2
4 54.08 67.6
5 111.44 74.3
6 105.20 86.5
7 45.73 91.3
8 122.35 102.8
9 142.24 114.5
10 86.22 120.9
11 174.50 135.0
12 185.20 144.0
13 111.80 156.0
14 214.60 173.7
15 144.60 182.0
16 174.36 199.2
17 215.40 208.0
18 286.24 217.8
19 188.56 223.2
20 237.20 234.0
21 181.80 251.0
22 373.00 260.0
23 191.60 289.5
24 247.12 296.4
25 269.60 312.0
> k <- length(x[1,])
> df <- as.data.frame(x)
> (mylm <- lm(df))
Call:
lm(formula = df)
Coefficients:
(Intercept) INCOME
30.7063 0.8124
> (mysum <- summary(mylm))
Call:
lm(formula = df)
Residuals:
Min 1Q Median 3Q Max
-74.297 -31.545 4.221 18.514 131.069
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 30.7063 20.6438 1.487 0.150
INCOME 0.8124 0.1132 7.180 2.60e-07 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 46.14 on 23 degrees of freedom
Multiple R-squared: 0.6915, Adjusted R-squared: 0.6781
F-statistic: 51.55 on 1 and 23 DF, p-value: 2.605e-07
> 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/yougetitorg/rcomp/tmp/1vhe81293642397.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$resid)
> grid()
> dev.off()
null device
1
> postscript(file="/var/yougetitorg/rcomp/tmp/2vhe81293642397.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556)
> plot(mysum$resid, type='b', pch=19, main='Residuals', ylab='value of Residuals', xlab='time or index')
> grid()
> dev.off()
null device
1
> postscript(file="/var/yougetitorg/rcomp/tmp/3vhe81293642397.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556)
> hist(mysum$resid, main='Residual Histogram', xlab='values of Residuals')
> grid()
> dev.off()
null device
1
> postscript(file="/var/yougetitorg/rcomp/tmp/4nqvs1293642397.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556)
> densityplot(~mysum$resid,col='black',main='Residual Density Plot', xlab='values of Residuals')
> dev.off()
null device
1
> postscript(file="/var/yougetitorg/rcomp/tmp/5nqvs1293642397.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 = 25
Frequency = 1
1 2 3 4 5 6 7
-7.977764 9.713254 11.584272 -31.544709 20.372196 4.220891 -59.148639
8 9 10 11 12 13 14
8.128737 18.513632 -42.705741 34.119389 37.507770 -45.641055 42.779428
15 16 17 18 19 20 21
-33.963510 -18.176826 15.714035 78.592495 -23.474476 16.391581 -52.819255
22 23 24 25
131.069126 -74.296736 -24.382310 -14.575783
> postscript(file="/var/yougetitorg/rcomp/tmp/6nqvs1293642397.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 = 25
Frequency = 1
lag(myerror, k = 1) myerror
0 -7.977764 NA
1 9.713254 -7.977764
2 11.584272 9.713254
3 -31.544709 11.584272
4 20.372196 -31.544709
5 4.220891 20.372196
6 -59.148639 4.220891
7 8.128737 -59.148639
8 18.513632 8.128737
9 -42.705741 18.513632
10 34.119389 -42.705741
11 37.507770 34.119389
12 -45.641055 37.507770
13 42.779428 -45.641055
14 -33.963510 42.779428
15 -18.176826 -33.963510
16 15.714035 -18.176826
17 78.592495 15.714035
18 -23.474476 78.592495
19 16.391581 -23.474476
20 -52.819255 16.391581
21 131.069126 -52.819255
22 -74.296736 131.069126
23 -24.382310 -74.296736
24 -14.575783 -24.382310
25 NA -14.575783
> dum1 <- dum[2:length(myerror),]
> dum1
lag(myerror, k = 1) myerror
[1,] 9.713254 -7.977764
[2,] 11.584272 9.713254
[3,] -31.544709 11.584272
[4,] 20.372196 -31.544709
[5,] 4.220891 20.372196
[6,] -59.148639 4.220891
[7,] 8.128737 -59.148639
[8,] 18.513632 8.128737
[9,] -42.705741 18.513632
[10,] 34.119389 -42.705741
[11,] 37.507770 34.119389
[12,] -45.641055 37.507770
[13,] 42.779428 -45.641055
[14,] -33.963510 42.779428
[15,] -18.176826 -33.963510
[16,] 15.714035 -18.176826
[17,] 78.592495 15.714035
[18,] -23.474476 78.592495
[19,] 16.391581 -23.474476
[20,] -52.819255 16.391581
[21,] 131.069126 -52.819255
[22,] -74.296736 131.069126
[23,] -24.382310 -74.296736
[24,] -14.575783 -24.382310
> z <- as.data.frame(dum1)
> z
lag(myerror, k = 1) myerror
1 9.713254 -7.977764
2 11.584272 9.713254
3 -31.544709 11.584272
4 20.372196 -31.544709
5 4.220891 20.372196
6 -59.148639 4.220891
7 8.128737 -59.148639
8 18.513632 8.128737
9 -42.705741 18.513632
10 34.119389 -42.705741
11 37.507770 34.119389
12 -45.641055 37.507770
13 42.779428 -45.641055
14 -33.963510 42.779428
15 -18.176826 -33.963510
16 15.714035 -18.176826
17 78.592495 15.714035
18 -23.474476 78.592495
19 16.391581 -23.474476
20 -52.819255 16.391581
21 131.069126 -52.819255
22 -74.296736 131.069126
23 -24.382310 -74.296736
24 -14.575783 -24.382310
> 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/yougetitorg/rcomp/tmp/7yzuv1293642397.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556)
> acf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Autocorrelation Function')
> grid()
> dev.off()
null device
1
> postscript(file="/var/yougetitorg/rcomp/tmp/89qbg1293642397.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556)
> pacf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Partial Autocorrelation Function')
> grid()
> dev.off()
null device
1
> postscript(file="/var/yougetitorg/rcomp/tmp/99qbg1293642397.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556)
> opar <- par(mfrow = c(2,2), oma = c(0, 0, 1.1, 0))
> plot(mylm, las = 1, sub='Residual Diagnostics')
> par(opar)
> dev.off()
null device
1
> if (n > n25) {
+ postscript(file="/var/yougetitorg/rcomp/tmp/109qbg1293642397.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556)
+ plot(kp3:nmkm3,gqarr[,2], main='Goldfeld-Quandt test',ylab='2-sided p-value',xlab='breakpoint')
+ grid()
+ dev.off()
+ }
>
> #Note: the /var/yougetitorg/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab
> load(file="/var/yougetitorg/rcomp/createtable")
>
> a<-table.start()
> a<-table.row.start(a)
> a<-table.element(a, 'Multiple Linear Regression - Estimated Regression Equation', 1, TRUE)
> a<-table.row.end(a)
> myeq <- colnames(x)[1]
> myeq <- paste(myeq, '[t] = ', sep='')
> for (i in 1:k){
+ if (mysum$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/yougetitorg/rcomp/tmp/11c9a41293642397.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/yougetitorg/rcomp/tmp/12x9qa1293642397.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/yougetitorg/rcomp/tmp/13man31293642397.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/yougetitorg/rcomp/tmp/14xkn71293642397.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/yougetitorg/rcomp/tmp/150k3u1293642397.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/yougetitorg/rcomp/tmp/16wuj31293642397.tab")
+ }
>
> try(system("convert tmp/1vhe81293642397.ps tmp/1vhe81293642397.png",intern=TRUE))
character(0)
> try(system("convert tmp/2vhe81293642397.ps tmp/2vhe81293642397.png",intern=TRUE))
character(0)
> try(system("convert tmp/3vhe81293642397.ps tmp/3vhe81293642397.png",intern=TRUE))
character(0)
> try(system("convert tmp/4nqvs1293642397.ps tmp/4nqvs1293642397.png",intern=TRUE))
character(0)
> try(system("convert tmp/5nqvs1293642397.ps tmp/5nqvs1293642397.png",intern=TRUE))
character(0)
> try(system("convert tmp/6nqvs1293642397.ps tmp/6nqvs1293642397.png",intern=TRUE))
character(0)
> try(system("convert tmp/7yzuv1293642397.ps tmp/7yzuv1293642397.png",intern=TRUE))
character(0)
> try(system("convert tmp/89qbg1293642397.ps tmp/89qbg1293642397.png",intern=TRUE))
character(0)
> try(system("convert tmp/99qbg1293642397.ps tmp/99qbg1293642397.png",intern=TRUE))
character(0)
> try(system("convert tmp/109qbg1293642397.ps tmp/109qbg1293642397.png",intern=TRUE))
convert: unable to open image `tmp/109qbg1293642397.ps': No such file or directory @ blob.c/OpenBlob/2480.
convert: missing an image filename `tmp/109qbg1293642397.png' @ convert.c/ConvertImageCommand/2838.
character(0)
>
>
> proc.time()
user system elapsed
2.400 1.790 3.099