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Type 'q()' to quit R. > x <- array(list(73,80,75,152,93,88,93,185,89,91,90,180,96,98,100,196,73,66,70,142,53,46,55,101,69,74,77,149,47,56,60,115,87,79,90,175,79,70,88,164,69,70,73,141,70,65,74,141,93,95,91,184,79,80,73,152,70,73,78,148,93,89,96,192,78,75,68,147,81,90,93,183,88,92,86,177,78,83,77,159,82,86,90,177,86,82,89,175,78,83,85,175,76,83,71,149,96,93,95,192),dim=c(4,25),dimnames=list(c('EXAM1','EXAM2','EXAM3','FINAL'),1:25)) > y <- array(NA,dim=c(4,25),dimnames=list(c('EXAM1','EXAM2','EXAM3','FINAL'),1:25)) > 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 = '4' > par3 <- 'No Linear Trend' > par2 <- 'Do not include Seasonal Dummies' > par1 <- '4' > #'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 Attaching package: 'zoo' The following object(s) are masked from 'package:base': as.Date, as.Date.numeric > 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 FINAL EXAM1 EXAM2 EXAM3 1 152 73 80 75 2 185 93 88 93 3 180 89 91 90 4 196 96 98 100 5 142 73 66 70 6 101 53 46 55 7 149 69 74 77 8 115 47 56 60 9 175 87 79 90 10 164 79 70 88 11 141 69 70 73 12 141 70 65 74 13 184 93 95 91 14 152 79 80 73 15 148 70 73 78 16 192 93 89 96 17 147 78 75 68 18 183 81 90 93 19 177 88 92 86 20 159 78 83 77 21 177 82 86 90 22 175 86 82 89 23 175 78 83 85 24 149 76 83 71 25 192 96 93 95 > k <- length(x[1,]) > df <- as.data.frame(x) > (mylm <- lm(df)) Call: lm(formula = df) Coefficients: (Intercept) EXAM1 EXAM2 EXAM3 -4.3361 0.3559 0.5425 1.1674 > (mysum <- summary(mylm)) Call: lm(formula = df) Residuals: Min 1Q Median 3Q Max -3.7452 -1.6328 -0.2984 0.8046 7.3111 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) -4.3361 3.7642 -1.152 0.26230 EXAM1 0.3559 0.1214 2.932 0.00796 ** EXAM2 0.5425 0.1008 5.379 2.46e-05 *** EXAM3 1.1674 0.1030 11.333 2.08e-10 *** --- Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 Residual standard error: 2.614 on 21 degrees of freedom Multiple R-squared: 0.9897, Adjusted R-squared: 0.9882 F-statistic: 670.1 on 3 and 21 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 + } > postscript(file="/var/fisher/rcomp/tmp/1mxux1353431768.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$resid) > grid() > dev.off() null device 1 > postscript(file="/var/fisher/rcomp/tmp/2wgq61353431768.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) > plot(mysum$resid, type='b', pch=19, main='Residuals', ylab='value of Residuals', xlab='time or index') > grid() > dev.off() null device 1 > postscript(file="/var/fisher/rcomp/tmp/3wngx1353431768.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) > hist(mysum$resid, main='Residual Histogram', xlab='values of Residuals') > grid() > dev.off() null device 1 > postscript(file="/var/fisher/rcomp/tmp/4wude1353431768.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) > densityplot(~mysum$resid,col='black',main='Residual Density Plot', xlab='values of Residuals') > dev.off() null device 1 > postscript(file="/var/fisher/rcomp/tmp/5inkf1353431768.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 = 25 Frequency = 1 1 2 3 4 5 6 -0.60720439 -0.08011472 -1.78158547 -3.74522647 2.82527930 -2.69391793 7 8 9 10 11 12 -1.26322740 2.17930272 0.44051606 -0.49442094 -2.42337551 -1.23416416 13 14 15 16 17 18 -2.54285759 -0.40794527 -3.24409108 2.87503387 3.49780782 1.10610639 19 20 21 22 23 24 -0.29838914 0.65065981 0.42257585 0.33634222 7.31110608 -1.63279846 25 0.80458840 > postscript(file="/var/fisher/rcomp/tmp/6q6xe1353431768.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 = 25 Frequency = 1 lag(myerror, k = 1) myerror 0 -0.60720439 NA 1 -0.08011472 -0.60720439 2 -1.78158547 -0.08011472 3 -3.74522647 -1.78158547 4 2.82527930 -3.74522647 5 -2.69391793 2.82527930 6 -1.26322740 -2.69391793 7 2.17930272 -1.26322740 8 0.44051606 2.17930272 9 -0.49442094 0.44051606 10 -2.42337551 -0.49442094 11 -1.23416416 -2.42337551 12 -2.54285759 -1.23416416 13 -0.40794527 -2.54285759 14 -3.24409108 -0.40794527 15 2.87503387 -3.24409108 16 3.49780782 2.87503387 17 1.10610639 3.49780782 18 -0.29838914 1.10610639 19 0.65065981 -0.29838914 20 0.42257585 0.65065981 21 0.33634222 0.42257585 22 7.31110608 0.33634222 23 -1.63279846 7.31110608 24 0.80458840 -1.63279846 25 NA 0.80458840 > dum1 <- dum[2:length(myerror),] > dum1 lag(myerror, k = 1) myerror [1,] -0.08011472 -0.60720439 [2,] -1.78158547 -0.08011472 [3,] -3.74522647 -1.78158547 [4,] 2.82527930 -3.74522647 [5,] -2.69391793 2.82527930 [6,] -1.26322740 -2.69391793 [7,] 2.17930272 -1.26322740 [8,] 0.44051606 2.17930272 [9,] -0.49442094 0.44051606 [10,] -2.42337551 -0.49442094 [11,] -1.23416416 -2.42337551 [12,] -2.54285759 -1.23416416 [13,] -0.40794527 -2.54285759 [14,] -3.24409108 -0.40794527 [15,] 2.87503387 -3.24409108 [16,] 3.49780782 2.87503387 [17,] 1.10610639 3.49780782 [18,] -0.29838914 1.10610639 [19,] 0.65065981 -0.29838914 [20,] 0.42257585 0.65065981 [21,] 0.33634222 0.42257585 [22,] 7.31110608 0.33634222 [23,] -1.63279846 7.31110608 [24,] 0.80458840 -1.63279846 > z <- as.data.frame(dum1) > z lag(myerror, k = 1) myerror 1 -0.08011472 -0.60720439 2 -1.78158547 -0.08011472 3 -3.74522647 -1.78158547 4 2.82527930 -3.74522647 5 -2.69391793 2.82527930 6 -1.26322740 -2.69391793 7 2.17930272 -1.26322740 8 0.44051606 2.17930272 9 -0.49442094 0.44051606 10 -2.42337551 -0.49442094 11 -1.23416416 -2.42337551 12 -2.54285759 -1.23416416 13 -0.40794527 -2.54285759 14 -3.24409108 -0.40794527 15 2.87503387 -3.24409108 16 3.49780782 2.87503387 17 1.10610639 3.49780782 18 -0.29838914 1.10610639 19 0.65065981 -0.29838914 20 0.42257585 0.65065981 21 0.33634222 0.42257585 22 7.31110608 0.33634222 23 -1.63279846 7.31110608 24 0.80458840 -1.63279846 > 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/fisher/rcomp/tmp/7ezc91353431768.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) > acf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Autocorrelation Function') > grid() > dev.off() null device 1 > postscript(file="/var/fisher/rcomp/tmp/8i37f1353431768.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) > pacf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Partial Autocorrelation Function') > grid() > dev.off() null device 1 > postscript(file="/var/fisher/rcomp/tmp/956291353431768.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) > opar <- par(mfrow = c(2,2), oma = c(0, 0, 1.1, 0)) > plot(mylm, las = 1, sub='Residual Diagnostics') > par(opar) > dev.off() null device 1 > if (n > n25) { + postscript(file="/var/fisher/rcomp/tmp/1089d71353431768.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) + plot(kp3:nmkm3,gqarr[,2], main='Goldfeld-Quandt test',ylab='2-sided p-value',xlab='breakpoint') + grid() + dev.off() + } > > #Note: the /var/fisher/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab > load(file="/var/fisher/rcomp/createtable") > > a<-table.start() > a<-table.row.start(a) > a<-table.element(a, 'Multiple Linear Regression - Estimated Regression Equation', 1, TRUE) > a<-table.row.end(a) > myeq <- colnames(x)[1] > myeq <- paste(myeq, '[t] = ', sep='') > for (i in 1:k){ + if (mysum$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/11k6rb1353431768.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/12gpg01353431769.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/13cks01353431769.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/143ugx1353431769.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/15z03d1353431769.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/160vfi1353431769.tab") + } > > try(system("convert tmp/1mxux1353431768.ps tmp/1mxux1353431768.png",intern=TRUE)) character(0) > try(system("convert tmp/2wgq61353431768.ps tmp/2wgq61353431768.png",intern=TRUE)) character(0) > try(system("convert tmp/3wngx1353431768.ps tmp/3wngx1353431768.png",intern=TRUE)) character(0) > try(system("convert tmp/4wude1353431768.ps tmp/4wude1353431768.png",intern=TRUE)) character(0) > try(system("convert tmp/5inkf1353431768.ps tmp/5inkf1353431768.png",intern=TRUE)) character(0) > try(system("convert tmp/6q6xe1353431768.ps tmp/6q6xe1353431768.png",intern=TRUE)) character(0) > try(system("convert tmp/7ezc91353431768.ps tmp/7ezc91353431768.png",intern=TRUE)) character(0) > try(system("convert tmp/8i37f1353431768.ps tmp/8i37f1353431768.png",intern=TRUE)) character(0) > try(system("convert tmp/956291353431768.ps tmp/956291353431768.png",intern=TRUE)) character(0) > try(system("convert tmp/1089d71353431768.ps tmp/1089d71353431768.png",intern=TRUE)) convert: unable to open image `tmp/1089d71353431768.ps': @ error/blob.c/OpenBlob/2587. convert: missing an image filename `tmp/1089d71353431768.png' @ error/convert.c/ConvertImageCommand/3011. character(0) attr(,"status") [1] 1 Warning message: running command 'convert tmp/1089d71353431768.ps tmp/1089d71353431768.png' had status 1 > > > proc.time() user system elapsed 5.038 1.186 6.234