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Type 'q()' to quit R. > x <- array(list(2148,77.405,82.145,315.4,2118,85.056,78.213,329.3,1603,90.088,88.099,308.2,2066,99.285,106.25,335.8,2095,80.428,80.487,343.7,2210,88.017,80.336,349.2,1609,93.489,90.065,312.4,1964,103.961,108.888,337.6,2114,82.591,82.747,360.2,2054,90.913,82.213,372.1,1424,96.787,93.41,341.8,2025,106.045,109.465,377.4,2003,84.752,84.373,337.2,2017,94.173,98.715,384.6,1528,97.733,99.646,358.6,2130,108.499,115.239,383.4,2017,87.972,89.082,384.4,2260,96.091,89.934,402.7,1805,101.846,99.957,372.1,2394,115.652,122.717,364.9,2586,91.269,95.895,314.9,2429,100.911,97.085,320.7,1910,105.248,109.414,308.6,2515,118.681,126.945,328.7),dim=c(4,24),dimnames=list(c('FallBelg','Brutoloonindex','wgbijdrage','brutoomzetindex '),1:24)) > y <- array(NA,dim=c(4,24),dimnames=list(c('FallBelg','Brutoloonindex','wgbijdrage','brutoomzetindex '),1:24)) > 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' > #'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 Brutoloonindex FallBelg wgbijdrage brutoomzetindex\r 1 77.405 2148 82.145 315.4 2 85.056 2118 78.213 329.3 3 90.088 1603 88.099 308.2 4 99.285 2066 106.250 335.8 5 80.428 2095 80.487 343.7 6 88.017 2210 80.336 349.2 7 93.489 1609 90.065 312.4 8 103.961 1964 108.888 337.6 9 82.591 2114 82.747 360.2 10 90.913 2054 82.213 372.1 11 96.787 1424 93.410 341.8 12 106.045 2025 109.465 377.4 13 84.752 2003 84.373 337.2 14 94.173 2017 98.715 384.6 15 97.733 1528 99.646 358.6 16 108.499 2130 115.239 383.4 17 87.972 2017 89.082 384.4 18 96.091 2260 89.934 402.7 19 101.846 1805 99.957 372.1 20 115.652 2394 122.717 364.9 21 91.269 2586 95.895 314.9 22 100.911 2429 97.085 320.7 23 105.248 1910 109.414 308.6 24 118.681 2515 126.945 328.7 > k <- length(x[1,]) > df <- as.data.frame(x) > (mylm <- lm(df)) Call: lm(formula = df) Coefficients: (Intercept) FallBelg wgbijdrage 19.775609 -0.001543 0.732770 `brutoomzetindex\r` 0.024479 > (mysum <- summary(mylm)) Call: lm(formula = df) Residuals: Min 1Q Median 3Q Max -6.9706 -2.7143 0.3138 2.5139 5.8916 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 19.775609 11.013638 1.796 0.0877 . FallBelg -0.001543 0.002583 -0.597 0.5571 wgbijdrage 0.732770 0.055427 13.220 2.41e-11 *** `brutoomzetindex\r` 0.024479 0.026830 0.912 0.3724 --- Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 Residual standard error: 3.578 on 20 degrees of freedom Multiple R-squared: 0.902, Adjusted R-squared: 0.8873 F-statistic: 61.34 on 3 and 20 DF, p-value: 2.894e-10 > 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/www/rcomp/tmp/1p9zs1291977235.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$resid) > grid() > dev.off() null device 1 > postscript(file="/var/www/rcomp/tmp/2i0gd1291977235.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) > plot(mysum$resid, type='b', pch=19, main='Residuals', ylab='value of Residuals', xlab='time or index') > grid() > dev.off() null device 1 > postscript(file="/var/www/rcomp/tmp/3i0gd1291977235.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) > hist(mysum$resid, main='Residual Histogram', xlab='values of Residuals') > grid() > dev.off() null device 1 > postscript(file="/var/www/rcomp/tmp/4i0gd1291977235.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) > densityplot(~mysum$resid,col='black',main='Residual Density Plot', xlab='values of Residuals') > dev.off() null device 1 > postscript(file="/var/www/rcomp/tmp/5i0gd1291977235.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 = 24 Frequency = 1 1 2 3 4 5 6 -6.97056517 3.17514879 0.68493895 -3.37985197 -3.50714560 4.23529348 7 8 9 10 11 12 2.55176056 -0.83832637 -3.37478825 4.95464717 2.39355613 -0.05727048 13 14 15 16 17 18 -2.01351631 -4.24058448 -1.48078364 -1.81915922 -3.37791829 4.04370655 19 20 21 22 23 24 2.50122227 0.71434422 -2.49415888 5.89164844 0.68980380 1.71799829 > postscript(file="/var/www/rcomp/tmp/6argg1291977235.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 = 24 Frequency = 1 lag(myerror, k = 1) myerror 0 -6.97056517 NA 1 3.17514879 -6.97056517 2 0.68493895 3.17514879 3 -3.37985197 0.68493895 4 -3.50714560 -3.37985197 5 4.23529348 -3.50714560 6 2.55176056 4.23529348 7 -0.83832637 2.55176056 8 -3.37478825 -0.83832637 9 4.95464717 -3.37478825 10 2.39355613 4.95464717 11 -0.05727048 2.39355613 12 -2.01351631 -0.05727048 13 -4.24058448 -2.01351631 14 -1.48078364 -4.24058448 15 -1.81915922 -1.48078364 16 -3.37791829 -1.81915922 17 4.04370655 -3.37791829 18 2.50122227 4.04370655 19 0.71434422 2.50122227 20 -2.49415888 0.71434422 21 5.89164844 -2.49415888 22 0.68980380 5.89164844 23 1.71799829 0.68980380 24 NA 1.71799829 > dum1 <- dum[2:length(myerror),] > dum1 lag(myerror, k = 1) myerror [1,] 3.17514879 -6.97056517 [2,] 0.68493895 3.17514879 [3,] -3.37985197 0.68493895 [4,] -3.50714560 -3.37985197 [5,] 4.23529348 -3.50714560 [6,] 2.55176056 4.23529348 [7,] -0.83832637 2.55176056 [8,] -3.37478825 -0.83832637 [9,] 4.95464717 -3.37478825 [10,] 2.39355613 4.95464717 [11,] -0.05727048 2.39355613 [12,] -2.01351631 -0.05727048 [13,] -4.24058448 -2.01351631 [14,] -1.48078364 -4.24058448 [15,] -1.81915922 -1.48078364 [16,] -3.37791829 -1.81915922 [17,] 4.04370655 -3.37791829 [18,] 2.50122227 4.04370655 [19,] 0.71434422 2.50122227 [20,] -2.49415888 0.71434422 [21,] 5.89164844 -2.49415888 [22,] 0.68980380 5.89164844 [23,] 1.71799829 0.68980380 > z <- as.data.frame(dum1) > z lag(myerror, k = 1) myerror 1 3.17514879 -6.97056517 2 0.68493895 3.17514879 3 -3.37985197 0.68493895 4 -3.50714560 -3.37985197 5 4.23529348 -3.50714560 6 2.55176056 4.23529348 7 -0.83832637 2.55176056 8 -3.37478825 -0.83832637 9 4.95464717 -3.37478825 10 2.39355613 4.95464717 11 -0.05727048 2.39355613 12 -2.01351631 -0.05727048 13 -4.24058448 -2.01351631 14 -1.48078364 -4.24058448 15 -1.81915922 -1.48078364 16 -3.37791829 -1.81915922 17 4.04370655 -3.37791829 18 2.50122227 4.04370655 19 0.71434422 2.50122227 20 -2.49415888 0.71434422 21 5.89164844 -2.49415888 22 0.68980380 5.89164844 23 1.71799829 0.68980380 > 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/rcomp/tmp/730xj1291977235.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) > acf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Autocorrelation Function') > grid() > dev.off() null device 1 > postscript(file="/var/www/rcomp/tmp/830xj1291977235.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) > pacf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Partial Autocorrelation Function') > grid() > dev.off() null device 1 > postscript(file="/var/www/rcomp/tmp/9wsw41291977235.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) > opar <- par(mfrow = c(2,2), oma = c(0, 0, 1.1, 0)) > plot(mylm, las = 1, sub='Residual Diagnostics') > par(opar) > dev.off() null device 1 > if (n > n25) { + postscript(file="/var/www/rcomp/tmp/10wsw41291977235.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) + plot(kp3:nmkm3,gqarr[,2], main='Goldfeld-Quandt test',ylab='2-sided p-value',xlab='breakpoint') + grid() + dev.off() + } > > #Note: the /var/www/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab > load(file="/var/www/rcomp/createtable") > > a<-table.start() > a<-table.row.start(a) > a<-table.element(a, 'Multiple Linear Regression - Estimated Regression Equation', 1, TRUE) > a<-table.row.end(a) > myeq <- colnames(x)[1] > myeq <- paste(myeq, '[t] = ', sep='') > for (i in 1:k){ + if (mysum$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/rcomp/tmp/11hsds1291977235.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/rcomp/tmp/123tby1291977235.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/rcomp/tmp/13h3961291977235.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/rcomp/tmp/14kl8u1291977235.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/rcomp/tmp/15n46i1291977235.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/rcomp/tmp/169mn61291977235.tab") + } > > try(system("convert tmp/1p9zs1291977235.ps tmp/1p9zs1291977235.png",intern=TRUE)) character(0) > try(system("convert tmp/2i0gd1291977235.ps tmp/2i0gd1291977235.png",intern=TRUE)) character(0) > try(system("convert tmp/3i0gd1291977235.ps tmp/3i0gd1291977235.png",intern=TRUE)) character(0) > try(system("convert tmp/4i0gd1291977235.ps tmp/4i0gd1291977235.png",intern=TRUE)) character(0) > try(system("convert tmp/5i0gd1291977235.ps tmp/5i0gd1291977235.png",intern=TRUE)) character(0) > try(system("convert tmp/6argg1291977235.ps tmp/6argg1291977235.png",intern=TRUE)) character(0) > try(system("convert tmp/730xj1291977235.ps tmp/730xj1291977235.png",intern=TRUE)) character(0) > try(system("convert tmp/830xj1291977235.ps tmp/830xj1291977235.png",intern=TRUE)) character(0) > try(system("convert tmp/9wsw41291977235.ps tmp/9wsw41291977235.png",intern=TRUE)) character(0) > try(system("convert tmp/10wsw41291977235.ps tmp/10wsw41291977235.png",intern=TRUE)) convert: unable to open image `tmp/10wsw41291977235.ps': No such file or directory @ magick/blob.c/OpenBlob/2418. convert: missing an image filename `tmp/10wsw41291977235.png' @ wand/convert.c/ConvertImageCommand/2710. character(0) Warning message: running command 'convert tmp/10wsw41291977235.ps tmp/10wsw41291977235.png' had status 1 > > > proc.time() user system elapsed 2.510 1.570 4.057