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Type 'q()' to quit R. > x <- array(list(5.5865,4.6052,.9809,5.5951,4.6328,.9700,5.6032,4.6549,.9528,5.6164,4.6681,.9486,5.6215,4.6691,.9458,5.6366,4.6738,.9563,5.6563,4.6932,.9639,5.6671,4.7050,.9578,5.6788,4.7167,.9613,5.6958,4.7371,.9609,5.7044,4.7510,.9536,5.7197,4.7681,.9547,5.7456,4.7808,.9613,5.7614,4.7999,.9647,5.7770,4.8219,.9574,5.8003,4.8434,.9570,5.8177,4.8691,.9563,5.8424,4.8888,.9547,5.8576,4.9082,.9490,5.8786,4.9409,.9462,5.8880,4.9656,.9219,5.9113,4.9774,.9384,5.9399,5.0013,.9423,5.9512,5.0291,.9270),dim=c(3,24),dimnames=list(c('lnM1b','lnBa','lnm-1'),1:24)) > y <- array(NA,dim=c(3,24),dimnames=list(c('lnM1b','lnBa','lnm-1'),1:24)) > 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' > par3 <- 'No Linear Trend' > par2 <- 'Do not include Seasonal Dummies' > par1 <- '1' > #'GNU S' R Code compiled by R2WASP v. 1.2.327 () > #Author: root > #To cite this work: Wessa P., (2013), Multiple Regression (v1.0.29) in Free Statistics Software (v$_version), Office for Research Development and Education, URL http://www.wessa.net/rwasp_multipleregression.wasp/ > #Source of accompanying publication: Office for Research, Development, and Education > # > library(lattice) > library(lmtest) Loading required package: zoo Attaching package: 'zoo' The following objects 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 lnM1b lnBa lnm-1 1 5.5865 4.6052 0.9809 2 5.5951 4.6328 0.9700 3 5.6032 4.6549 0.9528 4 5.6164 4.6681 0.9486 5 5.6215 4.6691 0.9458 6 5.6366 4.6738 0.9563 7 5.6563 4.6932 0.9639 8 5.6671 4.7050 0.9578 9 5.6788 4.7167 0.9613 10 5.6958 4.7371 0.9609 11 5.7044 4.7510 0.9536 12 5.7197 4.7681 0.9547 13 5.7456 4.7808 0.9613 14 5.7614 4.7999 0.9647 15 5.7770 4.8219 0.9574 16 5.8003 4.8434 0.9570 17 5.8177 4.8691 0.9563 18 5.8424 4.8888 0.9547 19 5.8576 4.9082 0.9490 20 5.8786 4.9409 0.9462 21 5.8880 4.9656 0.9219 22 5.9113 4.9774 0.9384 23 5.9399 5.0013 0.9423 24 5.9512 5.0291 0.9270 > k <- length(x[1,]) > df <- as.data.frame(x) > (mylm <- lm(df)) Call: lm(formula = df) Coefficients: (Intercept) lnBa `lnm-1` 0.2285 0.9782 0.8684 > (mysum <- summary(mylm)) Call: lm(formula = df) Residuals: Min 1Q Median 3Q Max -0.0077452 -0.0020405 0.0001394 0.0024900 0.0055435 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 0.228546 0.118184 1.934 0.0667 . lnBa 0.978240 0.008814 110.983 < 2e-16 *** `lnm-1` 0.868360 0.088107 9.856 2.5e-09 *** --- Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 Residual standard error: 0.003717 on 21 degrees of freedom Multiple R-squared: 0.9991, Adjusted R-squared: 0.999 F-statistic: 1.129e+04 on 2 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/wessaorg/rcomp/tmp/1xas51424030466.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$resid) > grid() > dev.off() null device 1 > postscript(file="/var/wessaorg/rcomp/tmp/2d10v1424030466.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) > plot(mysum$resid, type='b', pch=19, main='Residuals', ylab='value of Residuals', xlab='time or index') > grid() > dev.off() null device 1 > postscript(file="/var/wessaorg/rcomp/tmp/3jhv11424030466.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) > hist(mysum$resid, main='Residual Histogram', xlab='values of Residuals') > grid() > dev.off() null device 1 > postscript(file="/var/wessaorg/rcomp/tmp/4u7rl1424030466.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) > densityplot(~mysum$resid,col='black',main='Residual Density Plot', xlab='values of Residuals') > dev.off() null device 1 > postscript(file="/var/wessaorg/rcomp/tmp/5apic1424030466.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 = 24 Frequency = 1 1 2 3 4 5 0.0011890500 -0.0077452447 -0.0063285488 -0.0023942027 0.0041589665 6 7 8 9 10 0.0055434543 -0.0003339402 0.0042198267 0.0014351576 -0.0011735936 11 12 13 14 15 0.0001679019 -0.0022151981 0.0055299756 -0.0003068332 0.0001109185 16 17 18 19 20 0.0027261034 -0.0044068115 0.0024112377 0.0035830367 -0.0049740011 21 22 23 24 0.0013646297 -0.0012065487 0.0006269104 -0.0019822464 > postscript(file="/var/wessaorg/rcomp/tmp/6680e1424030466.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 = 24 Frequency = 1 lag(myerror, k = 1) myerror 0 0.0011890500 NA 1 -0.0077452447 0.0011890500 2 -0.0063285488 -0.0077452447 3 -0.0023942027 -0.0063285488 4 0.0041589665 -0.0023942027 5 0.0055434543 0.0041589665 6 -0.0003339402 0.0055434543 7 0.0042198267 -0.0003339402 8 0.0014351576 0.0042198267 9 -0.0011735936 0.0014351576 10 0.0001679019 -0.0011735936 11 -0.0022151981 0.0001679019 12 0.0055299756 -0.0022151981 13 -0.0003068332 0.0055299756 14 0.0001109185 -0.0003068332 15 0.0027261034 0.0001109185 16 -0.0044068115 0.0027261034 17 0.0024112377 -0.0044068115 18 0.0035830367 0.0024112377 19 -0.0049740011 0.0035830367 20 0.0013646297 -0.0049740011 21 -0.0012065487 0.0013646297 22 0.0006269104 -0.0012065487 23 -0.0019822464 0.0006269104 24 NA -0.0019822464 > dum1 <- dum[2:length(myerror),] > dum1 lag(myerror, k = 1) myerror [1,] -0.0077452447 0.0011890500 [2,] -0.0063285488 -0.0077452447 [3,] -0.0023942027 -0.0063285488 [4,] 0.0041589665 -0.0023942027 [5,] 0.0055434543 0.0041589665 [6,] -0.0003339402 0.0055434543 [7,] 0.0042198267 -0.0003339402 [8,] 0.0014351576 0.0042198267 [9,] -0.0011735936 0.0014351576 [10,] 0.0001679019 -0.0011735936 [11,] -0.0022151981 0.0001679019 [12,] 0.0055299756 -0.0022151981 [13,] -0.0003068332 0.0055299756 [14,] 0.0001109185 -0.0003068332 [15,] 0.0027261034 0.0001109185 [16,] -0.0044068115 0.0027261034 [17,] 0.0024112377 -0.0044068115 [18,] 0.0035830367 0.0024112377 [19,] -0.0049740011 0.0035830367 [20,] 0.0013646297 -0.0049740011 [21,] -0.0012065487 0.0013646297 [22,] 0.0006269104 -0.0012065487 [23,] -0.0019822464 0.0006269104 > z <- as.data.frame(dum1) > z lag(myerror, k = 1) myerror 1 -0.0077452447 0.0011890500 2 -0.0063285488 -0.0077452447 3 -0.0023942027 -0.0063285488 4 0.0041589665 -0.0023942027 5 0.0055434543 0.0041589665 6 -0.0003339402 0.0055434543 7 0.0042198267 -0.0003339402 8 0.0014351576 0.0042198267 9 -0.0011735936 0.0014351576 10 0.0001679019 -0.0011735936 11 -0.0022151981 0.0001679019 12 0.0055299756 -0.0022151981 13 -0.0003068332 0.0055299756 14 0.0001109185 -0.0003068332 15 0.0027261034 0.0001109185 16 -0.0044068115 0.0027261034 17 0.0024112377 -0.0044068115 18 0.0035830367 0.0024112377 19 -0.0049740011 0.0035830367 20 0.0013646297 -0.0049740011 21 -0.0012065487 0.0013646297 22 0.0006269104 -0.0012065487 23 -0.0019822464 0.0006269104 > 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/wessaorg/rcomp/tmp/7s3x21424030466.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) > acf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Autocorrelation Function') > grid() > dev.off() null device 1 > postscript(file="/var/wessaorg/rcomp/tmp/8vf801424030466.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) > pacf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Partial Autocorrelation Function') > grid() > dev.off() null device 1 > postscript(file="/var/wessaorg/rcomp/tmp/9t8b91424030466.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) > opar <- par(mfrow = c(2,2), oma = c(0, 0, 1.1, 0)) > plot(mylm, las = 1, sub='Residual Diagnostics') > par(opar) > dev.off() null device 1 > if (n > n25) { + postscript(file="/var/wessaorg/rcomp/tmp/106y2b1424030466.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) + plot(kp3:nmkm3,gqarr[,2], main='Goldfeld-Quandt test',ylab='2-sided p-value',xlab='breakpoint') + grid() + dev.off() + } > > #Note: the /var/wessaorg/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab > load(file="/var/wessaorg/rcomp/createtable") > > a<-table.start() > a<-table.row.start(a) > a<-table.element(a, 'Multiple Linear Regression - Estimated Regression Equation', 1, TRUE) > a<-table.row.end(a) > myeq <- colnames(x)[1] > myeq <- paste(myeq, '[t] = ', sep='') > for (i in 1:k){ + if (mysum$coefficients[i,1] > 0) myeq <- paste(myeq, '+', '') + myeq <- paste(myeq, signif(mysum$coefficients[i,1],6), sep=' ') + if (rownames(mysum$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/wessaorg/rcomp/tmp/117rqp1424030466.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$coefficients)[i],header=TRUE) + a<-table.element(a,signif(mysum$coefficients[i,1],6)) + a<-table.element(a, signif(mysum$coefficients[i,2],6)) + a<-table.element(a, signif(mysum$coefficients[i,3],4)) + a<-table.element(a, signif(mysum$coefficients[i,4],6)) + a<-table.element(a, signif(mysum$coefficients[i,4]/2,6)) + a<-table.row.end(a) + } > a<-table.end(a) > table.save(a,file="/var/wessaorg/rcomp/tmp/12tfq41424030466.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, signif(sqrt(mysum$r.squared),6)) > a<-table.row.end(a) > a<-table.row.start(a) > a<-table.element(a, 'R-squared',1,TRUE) > a<-table.element(a, signif(mysum$r.squared,6)) > a<-table.row.end(a) > a<-table.row.start(a) > a<-table.element(a, 'Adjusted R-squared',1,TRUE) > a<-table.element(a, signif(mysum$adj.r.squared,6)) > a<-table.row.end(a) > a<-table.row.start(a) > a<-table.element(a, 'F-TEST (value)',1,TRUE) > a<-table.element(a, signif(mysum$fstatistic[1],6)) > a<-table.row.end(a) > a<-table.row.start(a) > a<-table.element(a, 'F-TEST (DF numerator)',1,TRUE) > a<-table.element(a, signif(mysum$fstatistic[2],6)) > a<-table.row.end(a) > a<-table.row.start(a) > a<-table.element(a, 'F-TEST (DF denominator)',1,TRUE) > a<-table.element(a, signif(mysum$fstatistic[3],6)) > a<-table.row.end(a) > a<-table.row.start(a) > a<-table.element(a, 'p-value',1,TRUE) > a<-table.element(a, signif(1-pf(mysum$fstatistic[1],mysum$fstatistic[2],mysum$fstatistic[3]),6)) > a<-table.row.end(a) > a<-table.row.start(a) > a<-table.element(a, 'Multiple Linear Regression - Residual Statistics', 2, TRUE) > a<-table.row.end(a) > a<-table.row.start(a) > a<-table.element(a, 'Residual Standard Deviation',1,TRUE) > a<-table.element(a, signif(mysum$sigma,6)) > a<-table.row.end(a) > a<-table.row.start(a) > a<-table.element(a, 'Sum Squared Residuals',1,TRUE) > a<-table.element(a, signif(sum(myerror*myerror),6)) > a<-table.row.end(a) > a<-table.end(a) > table.save(a,file="/var/wessaorg/rcomp/tmp/13w84s1424030466.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,signif(x[i],6)) + a<-table.element(a,signif(x[i]-mysum$resid[i],6)) + a<-table.element(a,signif(mysum$resid[i],6)) + a<-table.row.end(a) + } > a<-table.end(a) > table.save(a,file="/var/wessaorg/rcomp/tmp/14b2yw1424030466.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,signif(gqarr[mypoint-kp3+1,1],6)) + a<-table.element(a,signif(gqarr[mypoint-kp3+1,2],6)) + a<-table.element(a,signif(gqarr[mypoint-kp3+1,3],6)) + a<-table.row.end(a) + } + a<-table.end(a) + table.save(a,file="/var/wessaorg/rcomp/tmp/15wznk1424030466.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,signif(numsignificant1,6)) + a<-table.element(a,signif(numsignificant1/numgqtests,6)) + 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,signif(numsignificant5,6)) + a<-table.element(a,signif(numsignificant5/numgqtests,6)) + 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,signif(numsignificant10,6)) + a<-table.element(a,signif(numsignificant10/numgqtests,6)) + 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/wessaorg/rcomp/tmp/16htku1424030466.tab") + } > > try(system("convert tmp/1xas51424030466.ps tmp/1xas51424030466.png",intern=TRUE)) character(0) > try(system("convert tmp/2d10v1424030466.ps tmp/2d10v1424030466.png",intern=TRUE)) character(0) > try(system("convert tmp/3jhv11424030466.ps tmp/3jhv11424030466.png",intern=TRUE)) character(0) > try(system("convert tmp/4u7rl1424030466.ps tmp/4u7rl1424030466.png",intern=TRUE)) character(0) > try(system("convert tmp/5apic1424030466.ps tmp/5apic1424030466.png",intern=TRUE)) character(0) > try(system("convert tmp/6680e1424030466.ps tmp/6680e1424030466.png",intern=TRUE)) character(0) > try(system("convert tmp/7s3x21424030466.ps tmp/7s3x21424030466.png",intern=TRUE)) character(0) > try(system("convert tmp/8vf801424030466.ps tmp/8vf801424030466.png",intern=TRUE)) character(0) > try(system("convert tmp/9t8b91424030466.ps tmp/9t8b91424030466.png",intern=TRUE)) character(0) > try(system("convert tmp/106y2b1424030466.ps tmp/106y2b1424030466.png",intern=TRUE)) convert.im6: unable to open image `tmp/106y2b1424030466.ps': No such file or directory @ error/blob.c/OpenBlob/2638. convert.im6: no images defined `tmp/106y2b1424030466.png' @ error/convert.c/ConvertImageCommand/3044. character(0) attr(,"status") [1] 1 Warning message: running command 'convert tmp/106y2b1424030466.ps tmp/106y2b1424030466.png' had status 1 > > > proc.time() user system elapsed 3.786 0.612 4.443