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Type 'q()' to quit R. > x <- array(list(34,71,152,74,99,765,36,54,99,79,128,1,37,71,92,80,57,2,17,75,138,37,95,232,25,61,106,55,205,230,21,686,95,46,51,828,21,88,145,46,59,2,29,7,181,63,194,906,36,90,190,78,27,2,24,40,150,53,9,1,22,50,186,48,24,1,21,14,174,45,189,1,30,63,151,66,37,820,22,91,112,48,81,107,37,89,143,81,72,1,31,83,120,68,81,870,19,22,169,42,90,1,31,24,135,69,216,731,18,74,161,40,216,2,30,24,98,66,13,521,21,12,142,46,153,2,17,23,190,36,185,2,38,49,169,84,131,100,30,68,130,65,136,34,35,87,160,77,182,325,26,69,176,57,139,2,29,16,111,64,42,2,23,78,165,50,213,477,32,89,117,69,184,1,34,35,122,75,44,2),dim=c(6,30),dimnames=list(c('Y_t','X_1t','X_2t','X_3t','X_4t','X_5t'),1:30)) > y <- array(NA,dim=c(6,30),dimnames=list(c('Y_t','X_1t','X_2t','X_3t','X_4t','X_5t'),1:30)) > 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' > 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 Y_t X_1t X_2t X_3t X_4t X_5t 1 34 71 152 74 99 765 2 36 54 99 79 128 1 3 37 71 92 80 57 2 4 17 75 138 37 95 232 5 25 61 106 55 205 230 6 21 686 95 46 51 828 7 21 88 145 46 59 2 8 29 7 181 63 194 906 9 36 90 190 78 27 2 10 24 40 150 53 9 1 11 22 50 186 48 24 1 12 21 14 174 45 189 1 13 30 63 151 66 37 820 14 22 91 112 48 81 107 15 37 89 143 81 72 1 16 31 83 120 68 81 870 17 19 22 169 42 90 1 18 31 24 135 69 216 731 19 18 74 161 40 216 2 20 30 24 98 66 13 521 21 21 12 142 46 153 2 22 17 23 190 36 185 2 23 38 49 169 84 131 100 24 30 68 130 65 136 34 25 35 87 160 77 182 325 26 26 69 176 57 139 2 27 29 16 111 64 42 2 28 23 78 165 50 213 477 29 32 89 117 69 184 1 30 34 35 122 75 44 2 > k <- length(x[1,]) > df <- as.data.frame(x) > (mylm <- lm(df)) Call: lm(formula = df) Coefficients: (Intercept) X_1t X_2t X_3t X_4t X_5t -0.1873581 0.0003319 0.0014476 0.4562736 0.0003834 -0.0001591 > (mysum <- summary(mylm)) Call: lm(formula = df) Residuals: Min 1Q Median 3Q Max -0.46540 -0.18466 -0.04234 0.21147 0.50720 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) -0.1873581 0.4333189 -0.432 0.669 X_1t 0.0003319 0.0005189 0.640 0.529 X_2t 0.0014476 0.0019371 0.747 0.462 X_3t 0.4562736 0.0038957 117.123 <2e-16 *** X_4t 0.0003834 0.0008135 0.471 0.642 X_5t -0.0001591 0.0001729 -0.920 0.367 --- Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 Residual standard error: 0.2833 on 24 degrees of freedom Multiple R-squared: 0.9985, Adjusted R-squared: 0.9982 F-statistic: 3229 on 5 and 24 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)$p.value + } + if (gqarr[mypoint-kp3+1,2] < 0.01) numsignificant1 <- numsignificant1 + 1 + if (gqarr[mypoint-kp3+1,2] < 0.05) numsignificant5 <- numsignificant5 + 1 + if (gqarr[mypoint-kp3+1,2] < 0.10) numsignificant10 <- numsignificant10 + 1 + } + gqarr + } [,1] [,2] [,3] [1,] 0.31846479 0.6369296 0.6815352 [2,] 0.46315166 0.9263033 0.5368483 [3,] 0.30302749 0.6060550 0.6969725 [4,] 0.42172739 0.8434548 0.5782726 [5,] 0.30824902 0.6164980 0.6917510 [6,] 0.23496094 0.4699219 0.7650391 [7,] 0.18880109 0.3776022 0.8111989 [8,] 0.11153116 0.2230623 0.8884688 [9,] 0.09612356 0.1922471 0.9038764 [10,] 0.20313086 0.4062617 0.7968691 [11,] 0.63983968 0.7203206 0.3601603 [12,] 0.64789687 0.7042063 0.3521031 [13,] 0.89035018 0.2192996 0.1096498 > postscript(file="/var/www/rcomp/tmp/1ck9m1321626013.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) > plot(x[,1], type='l', main='Actuals and Interpolation', ylab='value of Actuals and Interpolation (dots)', xlab='time or index') > points(x[,1]-mysum$resid) > grid() > dev.off() null device 1 > postscript(file="/var/www/rcomp/tmp/2lhel1321626013.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) > plot(mysum$resid, type='b', pch=19, main='Residuals', ylab='value of Residuals', xlab='time or index') > grid() > dev.off() null device 1 > postscript(file="/var/www/rcomp/tmp/3g4b11321626013.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) > hist(mysum$resid, main='Residual Histogram', xlab='values of Residuals') > grid() > dev.off() null device 1 > postscript(file="/var/www/rcomp/tmp/4gj1p1321626013.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) > densityplot(~mysum$resid,col='black',main='Residual Density Plot', xlab='values of Residuals') > dev.off() null device 1 > postscript(file="/var/www/rcomp/tmp/5x85r1321626013.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) > qqnorm(mysum$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 = 30 Frequency = 1 1 2 3 4 5 6 0.263288216 -0.068399254 0.507197963 0.081072744 -0.123373163 -0.054217117 7 8 9 10 11 12 -0.062631672 0.247571241 0.283077933 -0.228844173 -0.008658937 0.326221420 13 14 15 16 17 18 -0.049899317 0.079868564 -0.034786008 0.066877913 -0.262419694 -0.465403153 19 20 21 22 23 24 -0.403697147 0.001391109 -0.069104688 0.408227883 -0.434836036 0.272092962 25 26 27 28 29 30 -0.224255660 -0.150881163 -0.195925189 0.103180099 0.435194472 -0.237930148 > postscript(file="/var/www/rcomp/tmp/64jnh1321626013.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 = 30 Frequency = 1 lag(myerror, k = 1) myerror 0 0.263288216 NA 1 -0.068399254 0.263288216 2 0.507197963 -0.068399254 3 0.081072744 0.507197963 4 -0.123373163 0.081072744 5 -0.054217117 -0.123373163 6 -0.062631672 -0.054217117 7 0.247571241 -0.062631672 8 0.283077933 0.247571241 9 -0.228844173 0.283077933 10 -0.008658937 -0.228844173 11 0.326221420 -0.008658937 12 -0.049899317 0.326221420 13 0.079868564 -0.049899317 14 -0.034786008 0.079868564 15 0.066877913 -0.034786008 16 -0.262419694 0.066877913 17 -0.465403153 -0.262419694 18 -0.403697147 -0.465403153 19 0.001391109 -0.403697147 20 -0.069104688 0.001391109 21 0.408227883 -0.069104688 22 -0.434836036 0.408227883 23 0.272092962 -0.434836036 24 -0.224255660 0.272092962 25 -0.150881163 -0.224255660 26 -0.195925189 -0.150881163 27 0.103180099 -0.195925189 28 0.435194472 0.103180099 29 -0.237930148 0.435194472 30 NA -0.237930148 > dum1 <- dum[2:length(myerror),] > dum1 lag(myerror, k = 1) myerror [1,] -0.068399254 0.263288216 [2,] 0.507197963 -0.068399254 [3,] 0.081072744 0.507197963 [4,] -0.123373163 0.081072744 [5,] -0.054217117 -0.123373163 [6,] -0.062631672 -0.054217117 [7,] 0.247571241 -0.062631672 [8,] 0.283077933 0.247571241 [9,] -0.228844173 0.283077933 [10,] -0.008658937 -0.228844173 [11,] 0.326221420 -0.008658937 [12,] -0.049899317 0.326221420 [13,] 0.079868564 -0.049899317 [14,] -0.034786008 0.079868564 [15,] 0.066877913 -0.034786008 [16,] -0.262419694 0.066877913 [17,] -0.465403153 -0.262419694 [18,] -0.403697147 -0.465403153 [19,] 0.001391109 -0.403697147 [20,] -0.069104688 0.001391109 [21,] 0.408227883 -0.069104688 [22,] -0.434836036 0.408227883 [23,] 0.272092962 -0.434836036 [24,] -0.224255660 0.272092962 [25,] -0.150881163 -0.224255660 [26,] -0.195925189 -0.150881163 [27,] 0.103180099 -0.195925189 [28,] 0.435194472 0.103180099 [29,] -0.237930148 0.435194472 > z <- as.data.frame(dum1) > z lag(myerror, k = 1) myerror 1 -0.068399254 0.263288216 2 0.507197963 -0.068399254 3 0.081072744 0.507197963 4 -0.123373163 0.081072744 5 -0.054217117 -0.123373163 6 -0.062631672 -0.054217117 7 0.247571241 -0.062631672 8 0.283077933 0.247571241 9 -0.228844173 0.283077933 10 -0.008658937 -0.228844173 11 0.326221420 -0.008658937 12 -0.049899317 0.326221420 13 0.079868564 -0.049899317 14 -0.034786008 0.079868564 15 0.066877913 -0.034786008 16 -0.262419694 0.066877913 17 -0.465403153 -0.262419694 18 -0.403697147 -0.465403153 19 0.001391109 -0.403697147 20 -0.069104688 0.001391109 21 0.408227883 -0.069104688 22 -0.434836036 0.408227883 23 0.272092962 -0.434836036 24 -0.224255660 0.272092962 25 -0.150881163 -0.224255660 26 -0.195925189 -0.150881163 27 0.103180099 -0.195925189 28 0.435194472 0.103180099 29 -0.237930148 0.435194472 > 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/7kpxl1321626013.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/8ulh71321626013.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/96qtr1321626013.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/1088do1321626013.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$coefficients)[i] != 't') myeq <- paste(myeq, '[t]', sep='') + } + } > myeq <- paste(myeq, ' + e[t]') > a<-table.row.start(a) > a<-table.element(a, myeq) > a<-table.row.end(a) > a<-table.end(a) > table.save(a,file="/var/www/rcomp/tmp/11doqu1321626013.tab") > a<-table.start() > a<-table.row.start(a) > a<-table.element(a,hyperlink('http://www.xycoon.com/ols1.htm','Multiple Linear Regression - Ordinary Least Squares',''), 6, TRUE) > a<-table.row.end(a) > a<-table.row.start(a) > a<-table.element(a,'Variable',header=TRUE) > a<-table.element(a,'Parameter',header=TRUE) > a<-table.element(a,'S.D.',header=TRUE) > a<-table.element(a,'T-STAT
H0: parameter = 0',header=TRUE) > a<-table.element(a,'2-tail p-value',header=TRUE) > a<-table.element(a,'1-tail p-value',header=TRUE) > a<-table.row.end(a) > for (i in 1:k){ + a<-table.row.start(a) + a<-table.element(a,rownames(mysum$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$coefficients[i,4]/2,6)) + a<-table.row.end(a) + } > a<-table.end(a) > table.save(a,file="/var/www/rcomp/tmp/127rj51321626013.tab") > a<-table.start() > a<-table.row.start(a) > a<-table.element(a, 'Multiple Linear Regression - Regression Statistics', 2, TRUE) > a<-table.row.end(a) > a<-table.row.start(a) > a<-table.element(a, 'Multiple R',1,TRUE) > a<-table.element(a, sqrt(mysum$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$sigma) > a<-table.row.end(a) > a<-table.row.start(a) > a<-table.element(a, 'Sum Squared Residuals',1,TRUE) > a<-table.element(a, sum(myerror*myerror)) > a<-table.row.end(a) > a<-table.end(a) > table.save(a,file="/var/www/rcomp/tmp/13zow41321626013.tab") > a<-table.start() > a<-table.row.start(a) > a<-table.element(a, 'Multiple Linear Regression - Actuals, Interpolation, and Residuals', 4, TRUE) > a<-table.row.end(a) > a<-table.row.start(a) > a<-table.element(a, 'Time or Index', 1, TRUE) > a<-table.element(a, 'Actuals', 1, TRUE) > a<-table.element(a, 'Interpolation
Forecast', 1, TRUE) > a<-table.element(a, 'Residuals
Prediction Error', 1, TRUE) > a<-table.row.end(a) > for (i in 1:n) { + a<-table.row.start(a) + a<-table.element(a,i, 1, TRUE) + a<-table.element(a,x[i]) + a<-table.element(a,x[i]-mysum$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/148kls1321626013.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/159jd31321626013.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/165vbb1321626013.tab") + } > > try(system("convert tmp/1ck9m1321626013.ps tmp/1ck9m1321626013.png",intern=TRUE)) character(0) > try(system("convert tmp/2lhel1321626013.ps tmp/2lhel1321626013.png",intern=TRUE)) character(0) > try(system("convert tmp/3g4b11321626013.ps tmp/3g4b11321626013.png",intern=TRUE)) character(0) > try(system("convert tmp/4gj1p1321626013.ps tmp/4gj1p1321626013.png",intern=TRUE)) character(0) > try(system("convert tmp/5x85r1321626013.ps tmp/5x85r1321626013.png",intern=TRUE)) character(0) > try(system("convert tmp/64jnh1321626013.ps tmp/64jnh1321626013.png",intern=TRUE)) character(0) > try(system("convert tmp/7kpxl1321626013.ps tmp/7kpxl1321626013.png",intern=TRUE)) character(0) > try(system("convert tmp/8ulh71321626013.ps tmp/8ulh71321626013.png",intern=TRUE)) character(0) > try(system("convert tmp/96qtr1321626013.ps tmp/96qtr1321626013.png",intern=TRUE)) character(0) > try(system("convert tmp/1088do1321626013.ps tmp/1088do1321626013.png",intern=TRUE)) character(0) > > > proc.time() user system elapsed 3.248 0.532 3.812