x <- array(list(-15 ,-7 ,55 ,23 ,39 ,24 ,-8 ,-2 ,19 ,4 ,-22 ,11 ,-8 ,-7 ,-1 ,54 ,20 ,19 ,23 ,-12 ,-3 ,18 ,6 ,-15 ,9 ,-1 ,-6 ,0 ,52 ,20 ,14 ,19 ,-10 ,0 ,20 ,5 ,-16 ,13 ,1 ,-6 ,-3 ,55 ,22 ,15 ,25 ,-11 ,-4 ,21 ,4 ,-22 ,12 ,-1 ,2 ,4 ,56 ,25 ,7 ,21 ,-13 ,-3 ,18 ,5 ,-21 ,5 ,2 ,-4 ,2 ,54 ,22 ,12 ,19 ,-10 ,-3 ,19 ,5 ,-11 ,13 ,2 ,-4 ,3 ,53 ,26 ,12 ,20 ,-10 ,-3 ,19 ,4 ,-10 ,11 ,1 ,-8 ,0 ,59 ,27 ,14 ,20 ,-11 ,-4 ,19 ,3 ,-6 ,8 ,-1 ,-10 ,-10 ,62 ,41 ,9 ,17 ,-11 ,-5 ,21 ,2 ,-8 ,8 ,-2 ,-16 ,-10 ,63 ,29 ,8 ,25 ,-11 ,-5 ,19 ,3 ,-15 ,8 ,-2 ,-14 ,-9 ,64 ,33 ,4 ,19 ,-10 ,-6 ,19 ,2 ,-16 ,8 ,-1 ,-30 ,-22 ,75 ,39 ,7 ,13 ,-13 ,-10 ,17 ,-1 ,-24 ,0 ,-8 ,-33 ,-16 ,77 ,27 ,3 ,15 ,-12 ,-11 ,16 ,0 ,-27 ,3 ,-4 ,-40 ,-18 ,79 ,27 ,5 ,15 ,-13 ,-13 ,16 ,-2 ,-33 ,0 ,-6 ,-38 ,-14 ,77 ,25 ,0 ,13 ,-15 ,-12 ,17 ,1 ,-29 ,-1 ,-3 ,-39 ,-12 ,82 ,19 ,-2 ,11 ,-16 ,-13 ,16 ,-2 ,-34 ,-1 ,-3 ,-46 ,-17 ,83 ,15 ,6 ,9 ,-18 ,-12 ,15 ,-2 ,-37 ,-4 ,-7 ,-50 ,-23 ,81 ,19 ,11 ,2 ,-17 ,-15 ,16 ,-2 ,-31 ,1 ,-9 ,-55 ,-28 ,78 ,23 ,9 ,-2 ,-18 ,-14 ,16 ,-6 ,-33 ,-1 ,-11 ,-66 ,-31 ,79 ,23 ,17 ,-4 ,-20 ,-16 ,16 ,-4 ,-25 ,0 ,-13 ,-63 ,-21 ,79 ,7 ,21 ,-2 ,-22 ,-16 ,18 ,-2 ,-27 ,-1 ,-11 ,-56 ,-19 ,73 ,1 ,21 ,1 ,-17 ,-12 ,19 ,0 ,-21 ,6 ,-9 ,-66 ,-22 ,72 ,7 ,41 ,-13 ,-19 ,-16 ,16 ,-5 ,-32 ,0 ,-17 ,-63 ,-22 ,67 ,4 ,57 ,-11 ,-18 ,-15 ,16 ,-4 ,-31 ,-3 ,-22 ,-69 ,-25 ,67 ,-8 ,65 ,-14 ,-26 ,-17 ,16 ,-5 ,-32 ,-3 ,-25 ,-69 ,-16 ,50 ,-14 ,68 ,-4 ,-19 ,-15 ,18 ,-1 ,-30 ,4 ,-20 ,-72 ,-22 ,45 ,-10 ,73 ,-9 ,-23 ,-14 ,16 ,-2 ,-34 ,1 ,-24 ,-69 ,-21 ,39 ,-11 ,71 ,-5 ,-21 ,-15 ,15 ,-4 ,-35 ,0 ,-24 ,-67 ,-10 ,39 ,-10 ,71 ,-4 ,-27 ,-14 ,15 ,-1 ,-37 ,-4 ,-22 ,-64 ,-7 ,37 ,-8 ,70 ,-8 ,-27 ,-16 ,16 ,1 ,-32 ,-2 ,-19 ,-61 ,-5 ,30 ,-8 ,69 ,-1 ,-21 ,-11 ,18 ,1 ,-28 ,3 ,-18 ,-58 ,-4 ,24 ,-7 ,65 ,-2 ,-22 ,-14 ,16 ,-2 ,-26 ,2 ,-17 ,-47 ,7 ,27 ,-8 ,57 ,-1 ,-24 ,-12 ,19 ,1 ,-24 ,5 ,-11 ,-44 ,6 ,19 ,-4 ,57 ,8 ,-21 ,-11 ,19 ,1 ,-27 ,6 ,-11 ,-42 ,3 ,19 ,3 ,57 ,8 ,-21 ,-13 ,18 ,3 ,-26 ,6 ,-12 ,-34 ,10 ,25 ,-5 ,55 ,6 ,-22 ,-12 ,17 ,3 ,-27 ,3 ,-10 ,-38 ,0 ,16 ,-4 ,65 ,7 ,-25 ,-12 ,19 ,1 ,-27 ,4 ,-15 ,-41 ,-2 ,20 ,5 ,65 ,2 ,-21 ,-10 ,22 ,1 ,-24 ,7 ,-15 ,-38 ,-1 ,25 ,3 ,64 ,3 ,-26 ,-12 ,19 ,0 ,-28 ,5 ,-15 ,-37 ,2 ,34 ,6 ,60 ,0 ,-27 ,-11 ,19 ,2 ,-23 ,6 ,-13 ,-22 ,8 ,39 ,10 ,43 ,5 ,-22 ,-10 ,16 ,2 ,-23 ,1 ,-8 ,-37 ,-6 ,40 ,16 ,47 ,-1 ,-22 ,-12 ,18 ,-1 ,-29 ,3 ,-13 ,-36 ,-4 ,38 ,11 ,40 ,3 ,-20 ,-12 ,20 ,1 ,-25 ,6 ,-9 ,-25 ,4 ,42 ,10 ,31 ,4 ,-21 ,-11 ,17 ,0 ,-24 ,0 ,-7 ,-15 ,7 ,46 ,21 ,27 ,8 ,-16 ,-12 ,17 ,1 ,-20 ,3 ,-4 ,-17 ,3 ,48 ,18 ,24 ,10 ,-17 ,-9 ,17 ,1 ,-22 ,4 ,-4 ,-19 ,3 ,51 ,20 ,23 ,14 ,-19 ,-6 ,20 ,3 ,-24 ,7 ,-2 ,-12 ,8 ,55 ,18 ,17 ,15 ,-20 ,-7 ,21 ,2 ,-27 ,6 ,0 ,-17 ,3 ,52 ,23 ,16 ,9 ,-20 ,-7 ,19 ,0 ,-25 ,6 ,-2 ,-21 ,-3 ,55 ,28 ,15 ,8 ,-20 ,-10 ,18 ,0 ,-26 ,6 ,-3 ,-10 ,4 ,58 ,31 ,8 ,10 ,-19 ,-8 ,20 ,3 ,-24 ,6 ,1 ,-19 ,-5 ,72 ,38 ,5 ,5 ,-20 ,-11 ,17 ,-2 ,-26 ,2 ,-2 ,-14 ,-1 ,70 ,27 ,6 ,4 ,-25 ,-12 ,15 ,0 ,-22 ,2 ,-1 ,-8 ,5 ,70 ,21 ,5 ,8 ,-25 ,-11 ,17 ,1 ,-20 ,2 ,1 ,-16 ,0 ,63 ,31 ,12 ,8 ,-22 ,-11 ,18 ,-1 ,-26 ,3 ,-3 ,-14 ,-6 ,66 ,31 ,8 ,10 ,-19 ,-9 ,20 ,-2 ,-22 ,-1 ,-4 ,-30 ,-13 ,65 ,29 ,17 ,8 ,-20 ,-9 ,19 ,-1 ,-29 ,-4 ,-9 ,-33 ,-15 ,55 ,24 ,22 ,10 ,-18 ,-12 ,20 ,-1 ,-30 ,4 ,-9 ,-37 ,-8 ,57 ,27 ,24 ,-8 ,-17 ,-10 ,22 ,1 ,-26 ,5 ,-7 ,-47 ,-20 ,60 ,36 ,36 ,-6 ,-17 ,-10 ,20 ,-2 ,-30 ,3 ,-14) ,dim=c(13 ,60) ,dimnames=list(c('X_1t' ,'X_2t' ,'X_3t' ,'X_4t' ,'X_5t' ,'X_6t' ,'X_7t' ,'X_8t' ,'X_9t' ,'X_10t' ,'X_11t' ,'X_12t' ,'Y_t') ,1:60)) y <- array(NA,dim=c(13,60),dimnames=list(c('X_1t','X_2t','X_3t','X_4t','X_5t','X_6t','X_7t','X_8t','X_9t','X_10t','X_11t','X_12t','Y_t'),1:60)) 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 = '13' library(lattice) library(lmtest) 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 k <- length(x[1,]) df <- as.data.frame(x) (mylm <- lm(df)) (mysum <- summary(mylm)) 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)$p.value } if (gqarr[mypoint-kp3+1,2] < 0.01) numsignificant1 <- numsignificant1 + 1 if (gqarr[mypoint-kp3+1,2] < 0.05) numsignificant5 <- numsignificant5 + 1 if (gqarr[mypoint-kp3+1,2] < 0.10) numsignificant10 <- numsignificant10 + 1 } gqarr } postscript(file="/var/fisher/rcomp/tmp/1iriw1352129298.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) plot(x[,1], type='l', main='Actuals and Interpolation', ylab='value of Actuals and Interpolation (dots)', xlab='time or index') points(x[,1]-mysum$resid) grid() dev.off() postscript(file="/var/fisher/rcomp/tmp/2kknd1352129298.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) plot(mysum$resid, type='b', pch=19, main='Residuals', ylab='value of Residuals', xlab='time or index') grid() dev.off() postscript(file="/var/fisher/rcomp/tmp/3v1b31352129298.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) hist(mysum$resid, main='Residual Histogram', xlab='values of Residuals') grid() dev.off() postscript(file="/var/fisher/rcomp/tmp/4bjf31352129298.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) densityplot(~mysum$resid,col='black',main='Residual Density Plot', xlab='values of Residuals') dev.off() postscript(file="/var/fisher/rcomp/tmp/5el4j1352129298.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) qqnorm(mysum$resid, main='Residual Normal Q-Q Plot') qqline(mysum$resid) grid() dev.off() (myerror <- as.ts(mysum$resid)) postscript(file="/var/fisher/rcomp/tmp/6wyho1352129298.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) dum <- cbind(lag(myerror,k=1),myerror) dum dum1 <- dum[2:length(myerror),] dum1 z <- as.data.frame(dum1) z 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() postscript(file="/var/fisher/rcomp/tmp/7a5dw1352129298.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() postscript(file="/var/fisher/rcomp/tmp/82nvh1352129298.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() postscript(file="/var/fisher/rcomp/tmp/98j5c1352129298.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() if (n > n25) { postscript(file="/var/fisher/rcomp/tmp/10vvfi1352129298.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/fisher/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab load(file="/var/fisher/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$coefficients)[i] != 't') myeq <- paste(myeq, '[t]', sep='') } } myeq <- paste(myeq, ' + e[t]') a<-table.row.start(a) a<-table.element(a, myeq) a<-table.row.end(a) a<-table.end(a) table.save(a,file="/var/fisher/rcomp/tmp/11b68x1352129298.tab") a<-table.start() a<-table.row.start(a) a<-table.element(a,hyperlink('http://www.xycoon.com/ols1.htm','Multiple Linear Regression - Ordinary Least Squares',''), 6, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Variable',header=TRUE) a<-table.element(a,'Parameter',header=TRUE) a<-table.element(a,'S.D.',header=TRUE) a<-table.element(a,'T-STAT
H0: parameter = 0',header=TRUE) a<-table.element(a,'2-tail p-value',header=TRUE) a<-table.element(a,'1-tail p-value',header=TRUE) a<-table.row.end(a) for (i in 1:k){ a<-table.row.start(a) a<-table.element(a,rownames(mysum$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$coefficients[i,4]/2,6)) a<-table.row.end(a) } a<-table.end(a) table.save(a,file="/var/fisher/rcomp/tmp/12d3m71352129298.tab") a<-table.start() a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Regression Statistics', 2, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Multiple R',1,TRUE) a<-table.element(a, sqrt(mysum$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$sigma) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Sum Squared Residuals',1,TRUE) a<-table.element(a, sum(myerror*myerror)) a<-table.row.end(a) a<-table.end(a) table.save(a,file="/var/fisher/rcomp/tmp/13kdkn1352129298.tab") a<-table.start() a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Actuals, Interpolation, and Residuals', 4, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Time or Index', 1, TRUE) a<-table.element(a, 'Actuals', 1, TRUE) a<-table.element(a, 'Interpolation
Forecast', 1, TRUE) a<-table.element(a, 'Residuals
Prediction Error', 1, TRUE) a<-table.row.end(a) for (i in 1:n) { a<-table.row.start(a) a<-table.element(a,i, 1, TRUE) a<-table.element(a,x[i]) a<-table.element(a,x[i]-mysum$resid[i]) a<-table.element(a,mysum$resid[i]) a<-table.row.end(a) } a<-table.end(a) table.save(a,file="/var/fisher/rcomp/tmp/14dlbl1352129298.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/fisher/rcomp/tmp/15o8kt1352129298.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/fisher/rcomp/tmp/16elyu1352129298.tab") } try(system("convert tmp/1iriw1352129298.ps tmp/1iriw1352129298.png",intern=TRUE)) try(system("convert tmp/2kknd1352129298.ps tmp/2kknd1352129298.png",intern=TRUE)) try(system("convert tmp/3v1b31352129298.ps tmp/3v1b31352129298.png",intern=TRUE)) try(system("convert tmp/4bjf31352129298.ps tmp/4bjf31352129298.png",intern=TRUE)) try(system("convert tmp/5el4j1352129298.ps tmp/5el4j1352129298.png",intern=TRUE)) try(system("convert tmp/6wyho1352129298.ps tmp/6wyho1352129298.png",intern=TRUE)) try(system("convert tmp/7a5dw1352129298.ps tmp/7a5dw1352129298.png",intern=TRUE)) try(system("convert tmp/82nvh1352129298.ps tmp/82nvh1352129298.png",intern=TRUE)) try(system("convert tmp/98j5c1352129298.ps tmp/98j5c1352129298.png",intern=TRUE)) try(system("convert tmp/10vvfi1352129298.ps tmp/10vvfi1352129298.png",intern=TRUE))