R version 2.12.1 (2010-12-16) Copyright (C) 2010 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(408,187,5,2,2,1,250,133,16,10,159,55,336,70,138,46,97,105,1272,321,88,17,201,104,102,35,127,76,209,103,247,178,145,31,3517,1347,27,14,101,91,2,1,5,2,100,65,34,9,1418,418,206,82,130,117,865,137,229,162,1,1,229,87,17,3,92,16),dim=c(2,33),dimnames=list(c('omzet','Personeel'),1:33)) > y <- array(NA,dim=c(2,33),dimnames=list(c('omzet','Personeel'),1:33)) > for (i in 1:dim(x)[1]) + { + for (j in 1:dim(x)[2]) + { + y[i,j] <- as.numeric(x[i,j]) + } + } > par3 = '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 omzet Personeel t 1 408 187 1 2 5 2 2 3 2 1 3 4 250 133 4 5 16 10 5 6 159 55 6 7 336 70 7 8 138 46 8 9 97 105 9 10 1272 321 10 11 88 17 11 12 201 104 12 13 102 35 13 14 127 76 14 15 209 103 15 16 247 178 16 17 145 31 17 18 3517 1347 18 19 27 14 19 20 101 91 20 21 2 1 21 22 5 2 22 23 100 65 23 24 34 9 24 25 1418 418 25 26 206 82 26 27 130 117 27 28 865 137 28 29 229 162 29 30 1 1 30 31 229 87 31 32 17 3 32 33 92 16 33 > k <- length(x[1,]) > df <- as.data.frame(x) > (mylm <- lm(df)) Call: lm(formula = df) Coefficients: (Intercept) Personeel t -24.481 2.696 1.303 > (mysum <- summary(mylm)) Call: lm(formula = df) Residuals: Min 1Q Median 3Q Max -229.16 -72.88 -8.29 27.41 483.72 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) -24.4813 58.4896 -0.419 0.679 Personeel 2.6955 0.1183 22.779 <2e-16 *** t 1.3026 2.9203 0.446 0.659 --- Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 Residual standard error: 159.7 on 30 degrees of freedom Multiple R-squared: 0.9454, Adjusted R-squared: 0.9418 F-statistic: 259.8 on 2 and 30 DF, p-value: < 2.2e-16 > 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 + } [,1] [,2] [,3] [1,] 0.007054435 0.01410887 0.9929456 [2,] 0.036363037 0.07272607 0.9636370 [3,] 0.016754766 0.03350953 0.9832452 [4,] 0.053981379 0.10796276 0.9460186 [5,] 0.483387017 0.96677403 0.5166130 [6,] 0.375770741 0.75154148 0.6242293 [7,] 0.364854122 0.72970824 0.6351459 [8,] 0.269257631 0.53851526 0.7307424 [9,] 0.213632832 0.42726566 0.7863672 [10,] 0.157877784 0.31575557 0.8421222 [11,] 0.247310670 0.49462134 0.7526893 [12,] 0.207318619 0.41463724 0.7926814 [13,] 0.252874188 0.50574838 0.7471258 [14,] 0.176131455 0.35226291 0.8238685 [15,] 0.144920343 0.28984069 0.8550797 [16,] 0.092656378 0.18531276 0.9073436 [17,] 0.055900074 0.11180015 0.9440999 [18,] 0.031292228 0.06258446 0.9687078 [19,] 0.016261739 0.03252348 0.9837383 [20,] 0.024819868 0.04963974 0.9751801 [21,] 0.010754873 0.02150975 0.9892451 [22,] 0.022650312 0.04530062 0.9773497 > postscript(file="/var/www/rcomp/tmp/1u4b11322059986.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$resid) > grid() > dev.off() null device 1 > postscript(file="/var/www/rcomp/tmp/2p3pe1322059986.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) > plot(mysum$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/3sg0h1322059986.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) > hist(mysum$resid, main='Residual Histogram', xlab='values of Residuals') > grid() > dev.off() null device 1 > postscript(file="/var/www/rcomp/tmp/4p7zs1322059986.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) > densityplot(~mysum$resid,col='black',main='Residual Density Plot', xlab='values of Residuals') > dev.off() null device 1 > postscript(file="/var/www/rcomp/tmp/5qhdr1322059986.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 = 33 Frequency = 1 1 2 3 4 5 6 -72.882684 21.485127 19.878081 -89.232529 7.013319 27.412560 7 8 9 10 11 12 162.677266 28.067077 -173.270899 418.195186 52.329345 -70.483067 13 14 15 16 17 18 15.204943 -71.613754 -63.695235 -229.161460 63.776761 -112.824230 19 20 21 22 23 24 -11.004597 -145.861853 -3.568017 -4.566094 -80.686133 2.960176 25 26 27 28 29 30 283.191765 -24.417580 -196.063184 483.723944 -220.966505 -16.291066 31 32 33 -21.407962 -8.287219 30.368518 > postscript(file="/var/www/rcomp/tmp/69t201322059986.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 = 33 Frequency = 1 lag(myerror, k = 1) myerror 0 -72.882684 NA 1 21.485127 -72.882684 2 19.878081 21.485127 3 -89.232529 19.878081 4 7.013319 -89.232529 5 27.412560 7.013319 6 162.677266 27.412560 7 28.067077 162.677266 8 -173.270899 28.067077 9 418.195186 -173.270899 10 52.329345 418.195186 11 -70.483067 52.329345 12 15.204943 -70.483067 13 -71.613754 15.204943 14 -63.695235 -71.613754 15 -229.161460 -63.695235 16 63.776761 -229.161460 17 -112.824230 63.776761 18 -11.004597 -112.824230 19 -145.861853 -11.004597 20 -3.568017 -145.861853 21 -4.566094 -3.568017 22 -80.686133 -4.566094 23 2.960176 -80.686133 24 283.191765 2.960176 25 -24.417580 283.191765 26 -196.063184 -24.417580 27 483.723944 -196.063184 28 -220.966505 483.723944 29 -16.291066 -220.966505 30 -21.407962 -16.291066 31 -8.287219 -21.407962 32 30.368518 -8.287219 33 NA 30.368518 > dum1 <- dum[2:length(myerror),] > dum1 lag(myerror, k = 1) myerror [1,] 21.485127 -72.882684 [2,] 19.878081 21.485127 [3,] -89.232529 19.878081 [4,] 7.013319 -89.232529 [5,] 27.412560 7.013319 [6,] 162.677266 27.412560 [7,] 28.067077 162.677266 [8,] -173.270899 28.067077 [9,] 418.195186 -173.270899 [10,] 52.329345 418.195186 [11,] -70.483067 52.329345 [12,] 15.204943 -70.483067 [13,] -71.613754 15.204943 [14,] -63.695235 -71.613754 [15,] -229.161460 -63.695235 [16,] 63.776761 -229.161460 [17,] -112.824230 63.776761 [18,] -11.004597 -112.824230 [19,] -145.861853 -11.004597 [20,] -3.568017 -145.861853 [21,] -4.566094 -3.568017 [22,] -80.686133 -4.566094 [23,] 2.960176 -80.686133 [24,] 283.191765 2.960176 [25,] -24.417580 283.191765 [26,] -196.063184 -24.417580 [27,] 483.723944 -196.063184 [28,] -220.966505 483.723944 [29,] -16.291066 -220.966505 [30,] -21.407962 -16.291066 [31,] -8.287219 -21.407962 [32,] 30.368518 -8.287219 > z <- as.data.frame(dum1) > z lag(myerror, k = 1) myerror 1 21.485127 -72.882684 2 19.878081 21.485127 3 -89.232529 19.878081 4 7.013319 -89.232529 5 27.412560 7.013319 6 162.677266 27.412560 7 28.067077 162.677266 8 -173.270899 28.067077 9 418.195186 -173.270899 10 52.329345 418.195186 11 -70.483067 52.329345 12 15.204943 -70.483067 13 -71.613754 15.204943 14 -63.695235 -71.613754 15 -229.161460 -63.695235 16 63.776761 -229.161460 17 -112.824230 63.776761 18 -11.004597 -112.824230 19 -145.861853 -11.004597 20 -3.568017 -145.861853 21 -4.566094 -3.568017 22 -80.686133 -4.566094 23 2.960176 -80.686133 24 283.191765 2.960176 25 -24.417580 283.191765 26 -196.063184 -24.417580 27 483.723944 -196.063184 28 -220.966505 483.723944 29 -16.291066 -220.966505 30 -21.407962 -16.291066 31 -8.287219 -21.407962 32 30.368518 -8.287219 > 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/75rel1322059987.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) > acf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Autocorrelation Function') > grid() > dev.off() null device 1 > postscript(file="/var/www/rcomp/tmp/8sgnm1322059987.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) > pacf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Partial Autocorrelation Function') > grid() > dev.off() null device 1 > postscript(file="/var/www/rcomp/tmp/9lyoa1322059987.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) > opar <- par(mfrow = c(2,2), oma = c(0, 0, 1.1, 0)) > plot(mylm, las = 1, sub='Residual Diagnostics') > par(opar) > dev.off() null device 1 > if (n > n25) { + postscript(file="/var/www/rcomp/tmp/102dpu1322059987.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) + plot(kp3:nmkm3,gqarr[,2], main='Goldfeld-Quandt test',ylab='2-sided p-value',xlab='breakpoint') + grid() + dev.off() + } null device 1 > > #Note: the /var/www/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab > load(file="/var/www/rcomp/createtable") > > a<-table.start() > a<-table.row.start(a) > a<-table.element(a, 'Multiple Linear Regression - Estimated Regression Equation', 1, TRUE) > a<-table.row.end(a) > myeq <- colnames(x)[1] > myeq <- paste(myeq, '[t] = ', sep='') > for (i in 1:k){ + if (mysum$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/11tqcj1322059987.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/12xbbo1322059987.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/13spg21322059987.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/14ii3o1322059987.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/15aia21322059987.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/16zxpk1322059987.tab") + } > > try(system("convert tmp/1u4b11322059986.ps tmp/1u4b11322059986.png",intern=TRUE)) character(0) > try(system("convert tmp/2p3pe1322059986.ps tmp/2p3pe1322059986.png",intern=TRUE)) character(0) > try(system("convert tmp/3sg0h1322059986.ps tmp/3sg0h1322059986.png",intern=TRUE)) character(0) > try(system("convert tmp/4p7zs1322059986.ps tmp/4p7zs1322059986.png",intern=TRUE)) character(0) > try(system("convert tmp/5qhdr1322059986.ps tmp/5qhdr1322059986.png",intern=TRUE)) character(0) > try(system("convert tmp/69t201322059986.ps tmp/69t201322059986.png",intern=TRUE)) character(0) > try(system("convert tmp/75rel1322059987.ps tmp/75rel1322059987.png",intern=TRUE)) character(0) > try(system("convert tmp/8sgnm1322059987.ps tmp/8sgnm1322059987.png",intern=TRUE)) character(0) > try(system("convert tmp/9lyoa1322059987.ps tmp/9lyoa1322059987.png",intern=TRUE)) character(0) > try(system("convert tmp/102dpu1322059987.ps tmp/102dpu1322059987.png",intern=TRUE)) character(0) > > > proc.time() user system elapsed 3.876 0.656 4.508