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Type 'q()' to quit R. > x <- array(list(7.8,0,7.6,0,7.5,0,7.6,0,7.5,0,7.3,0,7.6,0,7.5,0,7.6,0,7.9,0,7.9,0,8.1,0,8.2,0,8.0,0,7.5,0,6.8,0,6.5,0,6.6,0,7.6,0,8.0,0,8.0,0,7.7,0,7.5,0,7.6,0,7.7,0,7.9,0,7.8,0,7.5,0,7.5,0,7.1,0,7.5,0,7.5,0,7.6,0,7.7,0,7.7,1,7.9,1,8.1,1,8.2,1,8.2,1,8.1,1,7.9,1,7.3,1,6.9,1,6.6,1,6.7,1,6.9,1,7.0,1,7.1,1,7.2,1,7.1,1,6.9,1,7.0,1,6.8,1,6.4,1,6.7,1,6.7,1,6.4,1,6.3,1,6.2,1,6.5,1,6.8,1,6.8,1,6.5,1,6.3,1,5.9,1,5.9,1,6.4,1,6.4,1),dim=c(2,68),dimnames=list(c('y','x'),1:68)) > y <- array(NA,dim=c(2,68),dimnames=list(c('y','x'),1:68)) > 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 = '0' > #'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) > 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 x 1 7.8 0 2 7.6 0 3 7.5 0 4 7.6 0 5 7.5 0 6 7.3 0 7 7.6 0 8 7.5 0 9 7.6 0 10 7.9 0 11 7.9 0 12 8.1 0 13 8.2 0 14 8.0 0 15 7.5 0 16 6.8 0 17 6.5 0 18 6.6 0 19 7.6 0 20 8.0 0 21 8.0 0 22 7.7 0 23 7.5 0 24 7.6 0 25 7.7 0 26 7.9 0 27 7.8 0 28 7.5 0 29 7.5 0 30 7.1 0 31 7.5 0 32 7.5 0 33 7.6 0 34 7.7 0 35 7.7 1 36 7.9 1 37 8.1 1 38 8.2 1 39 8.2 1 40 8.1 1 41 7.9 1 42 7.3 1 43 6.9 1 44 6.6 1 45 6.7 1 46 6.9 1 47 7.0 1 48 7.1 1 49 7.2 1 50 7.1 1 51 6.9 1 52 7.0 1 53 6.8 1 54 6.4 1 55 6.7 1 56 6.7 1 57 6.4 1 58 6.3 1 59 6.2 1 60 6.5 1 61 6.8 1 62 6.8 1 63 6.5 1 64 6.3 1 65 5.9 1 66 5.9 1 67 6.4 1 68 6.4 1 > k <- length(x[1,]) > df <- as.data.frame(x) > (mylm <- lm(df)) Call: lm(formula = df) Coefficients: (Intercept) x 7.5794 -0.6441 > (mysum <- summary(mylm)) Call: lm(formula = df) Residuals: Min 1Q Median 3Q Max -1.07941 -0.24632 -0.03529 0.23162 1.26471 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 7.57941 0.09132 82.999 < 2e-16 *** x -0.64412 0.12915 -4.988 4.7e-06 *** --- Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 Residual standard error: 0.5325 on 66 degrees of freedom Multiple R-squared: 0.2737, Adjusted R-squared: 0.2627 F-statistic: 24.88 on 1 and 66 DF, p-value: 4.704e-06 > postscript(file="/var/www/html/rcomp/tmp/1bmrp1227554922.ps",horizontal=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/html/rcomp/tmp/2ug5k1227554922.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) > plot(mysum$resid, type='b', pch=19, main='Residuals', ylab='value of Residuals', xlab='time or index') > grid() > dev.off() null device 1 > postscript(file="/var/www/html/rcomp/tmp/3p6fb1227554922.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) > hist(mysum$resid, main='Residual Histogram', xlab='values of Residuals') > grid() > dev.off() null device 1 > postscript(file="/var/www/html/rcomp/tmp/4nw7v1227554922.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) > densityplot(~mysum$resid,col='black',main='Residual Density Plot', xlab='values of Residuals') > dev.off() null device 1 > postscript(file="/var/www/html/rcomp/tmp/5q2gh1227554922.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) > qqnorm(mysum$resid, main='Residual Normal Q-Q Plot') > grid() > dev.off() null device 1 > (myerror <- as.ts(mysum$resid)) Time Series: Start = 1 End = 68 Frequency = 1 1 2 3 4 5 6 0.22058824 0.02058824 -0.07941176 0.02058824 -0.07941176 -0.27941176 7 8 9 10 11 12 0.02058824 -0.07941176 0.02058824 0.32058824 0.32058824 0.52058824 13 14 15 16 17 18 0.62058824 0.42058824 -0.07941176 -0.77941176 -1.07941176 -0.97941176 19 20 21 22 23 24 0.02058824 0.42058824 0.42058824 0.12058824 -0.07941176 0.02058824 25 26 27 28 29 30 0.12058824 0.32058824 0.22058824 -0.07941176 -0.07941176 -0.47941176 31 32 33 34 35 36 -0.07941176 -0.07941176 0.02058824 0.12058824 0.76470588 0.96470588 37 38 39 40 41 42 1.16470588 1.26470588 1.26470588 1.16470588 0.96470588 0.36470588 43 44 45 46 47 48 -0.03529412 -0.33529412 -0.23529412 -0.03529412 0.06470588 0.16470588 49 50 51 52 53 54 0.26470588 0.16470588 -0.03529412 0.06470588 -0.13529412 -0.53529412 55 56 57 58 59 60 -0.23529412 -0.23529412 -0.53529412 -0.63529412 -0.73529412 -0.43529412 61 62 63 64 65 66 -0.13529412 -0.13529412 -0.43529412 -0.63529412 -1.03529412 -1.03529412 67 68 -0.53529412 -0.53529412 > postscript(file="/var/www/html/rcomp/tmp/68il11227554922.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) > dum <- cbind(lag(myerror,k=1),myerror) > dum Time Series: Start = 0 End = 68 Frequency = 1 lag(myerror, k = 1) myerror 0 0.22058824 NA 1 0.02058824 0.22058824 2 -0.07941176 0.02058824 3 0.02058824 -0.07941176 4 -0.07941176 0.02058824 5 -0.27941176 -0.07941176 6 0.02058824 -0.27941176 7 -0.07941176 0.02058824 8 0.02058824 -0.07941176 9 0.32058824 0.02058824 10 0.32058824 0.32058824 11 0.52058824 0.32058824 12 0.62058824 0.52058824 13 0.42058824 0.62058824 14 -0.07941176 0.42058824 15 -0.77941176 -0.07941176 16 -1.07941176 -0.77941176 17 -0.97941176 -1.07941176 18 0.02058824 -0.97941176 19 0.42058824 0.02058824 20 0.42058824 0.42058824 21 0.12058824 0.42058824 22 -0.07941176 0.12058824 23 0.02058824 -0.07941176 24 0.12058824 0.02058824 25 0.32058824 0.12058824 26 0.22058824 0.32058824 27 -0.07941176 0.22058824 28 -0.07941176 -0.07941176 29 -0.47941176 -0.07941176 30 -0.07941176 -0.47941176 31 -0.07941176 -0.07941176 32 0.02058824 -0.07941176 33 0.12058824 0.02058824 34 0.76470588 0.12058824 35 0.96470588 0.76470588 36 1.16470588 0.96470588 37 1.26470588 1.16470588 38 1.26470588 1.26470588 39 1.16470588 1.26470588 40 0.96470588 1.16470588 41 0.36470588 0.96470588 42 -0.03529412 0.36470588 43 -0.33529412 -0.03529412 44 -0.23529412 -0.33529412 45 -0.03529412 -0.23529412 46 0.06470588 -0.03529412 47 0.16470588 0.06470588 48 0.26470588 0.16470588 49 0.16470588 0.26470588 50 -0.03529412 0.16470588 51 0.06470588 -0.03529412 52 -0.13529412 0.06470588 53 -0.53529412 -0.13529412 54 -0.23529412 -0.53529412 55 -0.23529412 -0.23529412 56 -0.53529412 -0.23529412 57 -0.63529412 -0.53529412 58 -0.73529412 -0.63529412 59 -0.43529412 -0.73529412 60 -0.13529412 -0.43529412 61 -0.13529412 -0.13529412 62 -0.43529412 -0.13529412 63 -0.63529412 -0.43529412 64 -1.03529412 -0.63529412 65 -1.03529412 -1.03529412 66 -0.53529412 -1.03529412 67 -0.53529412 -0.53529412 68 NA -0.53529412 > dum1 <- dum[2:length(myerror),] > dum1 lag(myerror, k = 1) myerror [1,] 0.02058824 0.22058824 [2,] -0.07941176 0.02058824 [3,] 0.02058824 -0.07941176 [4,] -0.07941176 0.02058824 [5,] -0.27941176 -0.07941176 [6,] 0.02058824 -0.27941176 [7,] -0.07941176 0.02058824 [8,] 0.02058824 -0.07941176 [9,] 0.32058824 0.02058824 [10,] 0.32058824 0.32058824 [11,] 0.52058824 0.32058824 [12,] 0.62058824 0.52058824 [13,] 0.42058824 0.62058824 [14,] -0.07941176 0.42058824 [15,] -0.77941176 -0.07941176 [16,] -1.07941176 -0.77941176 [17,] -0.97941176 -1.07941176 [18,] 0.02058824 -0.97941176 [19,] 0.42058824 0.02058824 [20,] 0.42058824 0.42058824 [21,] 0.12058824 0.42058824 [22,] -0.07941176 0.12058824 [23,] 0.02058824 -0.07941176 [24,] 0.12058824 0.02058824 [25,] 0.32058824 0.12058824 [26,] 0.22058824 0.32058824 [27,] -0.07941176 0.22058824 [28,] -0.07941176 -0.07941176 [29,] -0.47941176 -0.07941176 [30,] -0.07941176 -0.47941176 [31,] -0.07941176 -0.07941176 [32,] 0.02058824 -0.07941176 [33,] 0.12058824 0.02058824 [34,] 0.76470588 0.12058824 [35,] 0.96470588 0.76470588 [36,] 1.16470588 0.96470588 [37,] 1.26470588 1.16470588 [38,] 1.26470588 1.26470588 [39,] 1.16470588 1.26470588 [40,] 0.96470588 1.16470588 [41,] 0.36470588 0.96470588 [42,] -0.03529412 0.36470588 [43,] -0.33529412 -0.03529412 [44,] -0.23529412 -0.33529412 [45,] -0.03529412 -0.23529412 [46,] 0.06470588 -0.03529412 [47,] 0.16470588 0.06470588 [48,] 0.26470588 0.16470588 [49,] 0.16470588 0.26470588 [50,] -0.03529412 0.16470588 [51,] 0.06470588 -0.03529412 [52,] -0.13529412 0.06470588 [53,] -0.53529412 -0.13529412 [54,] -0.23529412 -0.53529412 [55,] -0.23529412 -0.23529412 [56,] -0.53529412 -0.23529412 [57,] -0.63529412 -0.53529412 [58,] -0.73529412 -0.63529412 [59,] -0.43529412 -0.73529412 [60,] -0.13529412 -0.43529412 [61,] -0.13529412 -0.13529412 [62,] -0.43529412 -0.13529412 [63,] -0.63529412 -0.43529412 [64,] -1.03529412 -0.63529412 [65,] -1.03529412 -1.03529412 [66,] -0.53529412 -1.03529412 [67,] -0.53529412 -0.53529412 > z <- as.data.frame(dum1) > z lag(myerror, k = 1) myerror 1 0.02058824 0.22058824 2 -0.07941176 0.02058824 3 0.02058824 -0.07941176 4 -0.07941176 0.02058824 5 -0.27941176 -0.07941176 6 0.02058824 -0.27941176 7 -0.07941176 0.02058824 8 0.02058824 -0.07941176 9 0.32058824 0.02058824 10 0.32058824 0.32058824 11 0.52058824 0.32058824 12 0.62058824 0.52058824 13 0.42058824 0.62058824 14 -0.07941176 0.42058824 15 -0.77941176 -0.07941176 16 -1.07941176 -0.77941176 17 -0.97941176 -1.07941176 18 0.02058824 -0.97941176 19 0.42058824 0.02058824 20 0.42058824 0.42058824 21 0.12058824 0.42058824 22 -0.07941176 0.12058824 23 0.02058824 -0.07941176 24 0.12058824 0.02058824 25 0.32058824 0.12058824 26 0.22058824 0.32058824 27 -0.07941176 0.22058824 28 -0.07941176 -0.07941176 29 -0.47941176 -0.07941176 30 -0.07941176 -0.47941176 31 -0.07941176 -0.07941176 32 0.02058824 -0.07941176 33 0.12058824 0.02058824 34 0.76470588 0.12058824 35 0.96470588 0.76470588 36 1.16470588 0.96470588 37 1.26470588 1.16470588 38 1.26470588 1.26470588 39 1.16470588 1.26470588 40 0.96470588 1.16470588 41 0.36470588 0.96470588 42 -0.03529412 0.36470588 43 -0.33529412 -0.03529412 44 -0.23529412 -0.33529412 45 -0.03529412 -0.23529412 46 0.06470588 -0.03529412 47 0.16470588 0.06470588 48 0.26470588 0.16470588 49 0.16470588 0.26470588 50 -0.03529412 0.16470588 51 0.06470588 -0.03529412 52 -0.13529412 0.06470588 53 -0.53529412 -0.13529412 54 -0.23529412 -0.53529412 55 -0.23529412 -0.23529412 56 -0.53529412 -0.23529412 57 -0.63529412 -0.53529412 58 -0.73529412 -0.63529412 59 -0.43529412 -0.73529412 60 -0.13529412 -0.43529412 61 -0.13529412 -0.13529412 62 -0.43529412 -0.13529412 63 -0.63529412 -0.43529412 64 -1.03529412 -0.63529412 65 -1.03529412 -1.03529412 66 -0.53529412 -1.03529412 67 -0.53529412 -0.53529412 > 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/html/rcomp/tmp/765vw1227554922.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) > acf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Autocorrelation Function') > grid() > dev.off() null device 1 > postscript(file="/var/www/html/rcomp/tmp/8zkht1227554922.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) > pacf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Partial Autocorrelation Function') > grid() > dev.off() null device 1 > postscript(file="/var/www/html/rcomp/tmp/9xd3q1227554922.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) > opar <- par(mfrow = c(2,2), oma = c(0, 0, 1.1, 0)) > plot(mylm, las = 1, sub='Residual Diagnostics') hat values (leverages) are all = 0.02941176 and there are no factor predictors; no plot no. 5 > par(opar) > dev.off() null device 1 > > #Note: the /var/www/html/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab > load(file="/var/www/html/rcomp/createtable") > > a<-table.start() > a<-table.row.start(a) > a<-table.element(a, 'Multiple Linear Regression - Estimated Regression Equation', 1, TRUE) > a<-table.row.end(a) > myeq <- colnames(x)[1] > myeq <- paste(myeq, '[t] = ', sep='') > for (i in 1:k){ + if (mysum$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/html/rcomp/tmp/10us5p1227554922.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/html/rcomp/tmp/11xda81227554922.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/html/rcomp/tmp/12kuny1227554922.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/html/rcomp/tmp/13edrc1227554922.tab") > > system("convert tmp/1bmrp1227554922.ps tmp/1bmrp1227554922.png") > system("convert tmp/2ug5k1227554922.ps tmp/2ug5k1227554922.png") > system("convert tmp/3p6fb1227554922.ps tmp/3p6fb1227554922.png") > system("convert tmp/4nw7v1227554922.ps tmp/4nw7v1227554922.png") > system("convert tmp/5q2gh1227554922.ps tmp/5q2gh1227554922.png") > system("convert tmp/68il11227554922.ps tmp/68il11227554922.png") > system("convert tmp/765vw1227554922.ps tmp/765vw1227554922.png") > system("convert tmp/8zkht1227554922.ps tmp/8zkht1227554922.png") > system("convert tmp/9xd3q1227554922.ps tmp/9xd3q1227554922.png") > > > proc.time() user system elapsed 1.898 1.382 2.267