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Type 'q()' to quit R. > x <- array(list(70,168,72,174,78,177,81,180,84,182,88,187,90,188,91,190,93,191,95,192),dim=c(2,10),dimnames=list(c('Y-nanogram','X-weight'),1:10)) > y <- array(NA,dim=c(2,10),dimnames=list(c('Y-nanogram','X-weight'),1:10)) > for (i in 1:dim(x)[1]) + { + for (j in 1:dim(x)[2]) + { + y[i,j] <- as.numeric(x[i,j]) + } + } > par5 = '0' > par4 = '0' > par3 = 'Linear Trend' > par2 = 'Do not include Seasonal Dummies' > par1 = '1' > par5 <- '0' > par4 <- '0' > par3 <- 'Linear Trend' > par2 <- 'Do not include Seasonal Dummies' > par1 <- '1' > #'GNU S' R Code compiled by R2WASP v. 1.2.327 (Wed, 08 Jun 2016 16:18:16 +0100) > #Author: root > #To cite this work: Wessa P., (2015), Multiple Regression (v1.0.38) 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 > mywarning <- '' > par1 <- as.numeric(par1) > if(is.na(par1)) { + par1 <- 1 + mywarning = 'Warning: you did not specify the column number of the endogenous series! The first column was selected by default.' + } > if (par4=='') par4 <- 0 > par4 <- as.numeric(par4) > if (par5=='') par5 <- 0 > par5 <- as.numeric(par5) > x <- na.omit(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'){ + (n <- n -1) + x2 <- array(0, dim=c(n,k), dimnames=list(1:n, paste('(1-B)',colnames(x),sep=''))) + for (i in 1:n) { + for (j in 1:k) { + x2[i,j] <- x[i+1,j] - x[i,j] + } + } + x <- x2 + } > if (par3 == 'Seasonal Differences (s=12)'){ + (n <- n - 12) + x2 <- array(0, dim=c(n,k), dimnames=list(1:n, paste('(1-B12)',colnames(x),sep=''))) + for (i in 1:n) { + for (j in 1:k) { + x2[i,j] <- x[i+12,j] - x[i,j] + } + } + x <- x2 + } > if (par3 == 'First and Seasonal Differences (s=12)'){ + (n <- n -1) + x2 <- array(0, dim=c(n,k), dimnames=list(1:n, paste('(1-B)',colnames(x),sep=''))) + for (i in 1:n) { + for (j in 1:k) { + x2[i,j] <- x[i+1,j] - x[i,j] + } + } + x <- x2 + (n <- n - 12) + x2 <- array(0, dim=c(n,k), dimnames=list(1:n, paste('(1-B12)',colnames(x),sep=''))) + for (i in 1:n) { + for (j in 1:k) { + x2[i,j] <- x[i+12,j] - x[i,j] + } + } + x <- x2 + } > if(par4 > 0) { + x2 <- array(0, dim=c(n-par4,par4), dimnames=list(1:(n-par4), paste(colnames(x)[par1],'(t-',1:par4,')',sep=''))) + for (i in 1:(n-par4)) { + for (j in 1:par4) { + x2[i,j] <- x[i+par4-j,par1] + } + } + x <- cbind(x[(par4+1):n,], x2) + n <- n - par4 + } > if(par5 > 0) { + x2 <- array(0, dim=c(n-par5*12,par5), dimnames=list(1:(n-par5*12), paste(colnames(x)[par1],'(t-',1:par5,'s)',sep=''))) + for (i in 1:(n-par5*12)) { + for (j in 1:par5) { + x2[i,j] <- x[i+par5*12-j*12,par1] + } + } + x <- cbind(x[(par5*12+1):n,], x2) + n <- n - par5*12 + } > 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[n,])) [1] 2 > if (par3 == 'Linear Trend'){ + x <- cbind(x, c(1:n)) + colnames(x)[k+1] <- 't' + } > x Y-nanogram X-weight t 1 70 168 1 2 72 174 2 3 78 177 3 4 81 180 4 5 84 182 5 6 88 187 6 7 90 188 7 8 91 190 8 9 93 191 9 10 95 192 10 > (k <- length(x[n,])) [1] 3 > head(x) Y-nanogram X-weight t 1 70 168 1 2 72 174 2 3 78 177 3 4 81 180 4 5 84 182 5 6 88 187 6 > df <- as.data.frame(x) > (mylm <- lm(df)) Call: lm(formula = df) Coefficients: (Intercept) `X-weight` t -51.4986 0.7123 0.9843 > (mysum <- summary(mylm)) Call: lm(formula = df) Residuals: Min 1Q Median 3Q Max -2.4152 -0.3391 0.3648 0.6339 0.9333 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) -51.4986 35.5330 -1.449 0.1905 `X-weight` 0.7123 0.2107 3.381 0.0117 * t 0.9843 0.5620 1.751 0.1233 --- Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 Residual standard error: 1.139 on 7 degrees of freedom Multiple R-squared: 0.9868, Adjusted R-squared: 0.983 F-statistic: 261.7 on 2 and 7 DF, p-value: 2.641e-07 > 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/1wu931478538616.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$resid) > grid() > dev.off() null device 1 > postscript(file="/var/wessaorg/rcomp/tmp/2x6021478538616.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) > plot(mysum$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/3apy01478538616.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) > hist(mysum$resid, main='Residual Histogram', xlab='values of Residuals') > grid() > dev.off() null device 1 > postscript(file="/var/wessaorg/rcomp/tmp/4osb51478538616.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) > densityplot(~mysum$resid,col='black',main='Residual Density Plot', xlab='values of Residuals') > dev.off() null device 1 > postscript(file="/var/wessaorg/rcomp/tmp/5eql11478538616.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$resid)) Time Series: Start = 1 End = 10 Frequency = 1 1 2 3 4 5 6 7 0.8430884 -2.4151930 0.4635118 0.3422167 0.9332503 0.3872976 0.6906600 8 9 10 -0.7183064 -0.4149440 -0.1115816 > postscript(file="/var/wessaorg/rcomp/tmp/66sr61478538616.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) > dum <- cbind(lag(myerror,k=1),myerror) > dum Time Series: Start = 0 End = 10 Frequency = 1 lag(myerror, k = 1) myerror 0 0.8430884 NA 1 -2.4151930 0.8430884 2 0.4635118 -2.4151930 3 0.3422167 0.4635118 4 0.9332503 0.3422167 5 0.3872976 0.9332503 6 0.6906600 0.3872976 7 -0.7183064 0.6906600 8 -0.4149440 -0.7183064 9 -0.1115816 -0.4149440 10 NA -0.1115816 > dum1 <- dum[2:length(myerror),] > dum1 lag(myerror, k = 1) myerror [1,] -2.4151930 0.8430884 [2,] 0.4635118 -2.4151930 [3,] 0.3422167 0.4635118 [4,] 0.9332503 0.3422167 [5,] 0.3872976 0.9332503 [6,] 0.6906600 0.3872976 [7,] -0.7183064 0.6906600 [8,] -0.4149440 -0.7183064 [9,] -0.1115816 -0.4149440 > z <- as.data.frame(dum1) > z lag(myerror, k = 1) myerror 1 -2.4151930 0.8430884 2 0.4635118 -2.4151930 3 0.3422167 0.4635118 4 0.9332503 0.3422167 5 0.3872976 0.9332503 6 0.6906600 0.3872976 7 -0.7183064 0.6906600 8 -0.4149440 -0.7183064 9 -0.1115816 -0.4149440 > plot(z,main=paste('Residual Lag plot, lowess, and regression line'), ylab='values of Residuals', xlab='lagged values of Residuals') > lines(lowess(z)) > abline(lm(z)) > grid() > dev.off() null device 1 > postscript(file="/var/wessaorg/rcomp/tmp/7n4wz1478538616.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) > acf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Autocorrelation Function') > grid() > dev.off() null device 1 > postscript(file="/var/wessaorg/rcomp/tmp/84n271478538616.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) > pacf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Partial Autocorrelation Function') > grid() > dev.off() null device 1 > postscript(file="/var/wessaorg/rcomp/tmp/9x3vn1478538616.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) > opar <- par(mfrow = c(2,2), oma = c(0, 0, 1.1, 0)) > plot(mylm, las = 1, sub='Residual Diagnostics') > par(opar) > dev.off() null device 1 > if (n > n25) { + postscript(file="/var/wessaorg/rcomp/tmp/10ttu51478538616.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) + plot(kp3:nmkm3,gqarr[,2], main='Goldfeld-Quandt test',ylab='2-sided p-value',xlab='breakpoint') + grid() + dev.off() + } > > #Note: the /var/wessaorg/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab > load(file="/var/wessaorg/rcomp/createtable") > > a<-table.start() > a<-table.row.start(a) > a<-table.element(a, 'Multiple Linear Regression - Estimated Regression Equation', 1, TRUE) > a<-table.row.end(a) > myeq <- colnames(x)[1] > myeq <- paste(myeq, '[t] = ', sep='') > for (i in 1:k){ + if (mysum$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.row.start(a) > a<-table.element(a, mywarning) > a<-table.row.end(a) > a<-table.end(a) > table.save(a,file="/var/wessaorg/rcomp/tmp/119d2t1478538616.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$coefficients)[i],header=TRUE) + a<-table.element(a,formatC(signif(mysum$coefficients[i,1],5),format='g',flag='+')) + a<-table.element(a,formatC(signif(mysum$coefficients[i,2],5),format='g',flag=' ')) + a<-table.element(a,formatC(signif(mysum$coefficients[i,3],4),format='e',flag='+')) + a<-table.element(a,formatC(signif(mysum$coefficients[i,4],4),format='g',flag=' ')) + a<-table.element(a,formatC(signif(mysum$coefficients[i,4]/2,4),format='g',flag=' ')) + a<-table.row.end(a) + } > a<-table.end(a) > table.save(a,file="/var/wessaorg/rcomp/tmp/12atiw1478538616.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,formatC(signif(sqrt(mysum$r.squared),6),format='g',flag=' ')) > a<-table.row.end(a) > a<-table.row.start(a) > a<-table.element(a, 'R-squared',1,TRUE) > a<-table.element(a,formatC(signif(mysum$r.squared,6),format='g',flag=' ')) > a<-table.row.end(a) > a<-table.row.start(a) > a<-table.element(a, 'Adjusted R-squared',1,TRUE) > a<-table.element(a,formatC(signif(mysum$adj.r.squared,6),format='g',flag=' ')) > a<-table.row.end(a) > a<-table.row.start(a) > a<-table.element(a, 'F-TEST (value)',1,TRUE) > a<-table.element(a,formatC(signif(mysum$fstatistic[1],6),format='g',flag=' ')) > 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,formatC(signif(1-pf(mysum$fstatistic[1],mysum$fstatistic[2],mysum$fstatistic[3]),6),format='g',flag=' ')) > a<-table.row.end(a) > a<-table.row.start(a) > a<-table.element(a, 'Multiple Linear Regression - Residual Statistics', 2, TRUE) > a<-table.row.end(a) > a<-table.row.start(a) > a<-table.element(a, 'Residual Standard Deviation',1,TRUE) > a<-table.element(a,formatC(signif(mysum$sigma,6),format='g',flag=' ')) > a<-table.row.end(a) > a<-table.row.start(a) > a<-table.element(a, 'Sum Squared Residuals',1,TRUE) > a<-table.element(a,formatC(signif(sum(myerror*myerror),6),format='g',flag=' ')) > a<-table.row.end(a) > a<-table.end(a) > table.save(a,file="/var/wessaorg/rcomp/tmp/13ekfl1478538616.tab") > if(n < 200) { + 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,formatC(signif(x[i],6),format='g',flag=' ')) + a<-table.element(a,formatC(signif(x[i]-mysum$resid[i],6),format='g',flag=' ')) + a<-table.element(a,formatC(signif(mysum$resid[i],6),format='g',flag=' ')) + a<-table.row.end(a) + } + a<-table.end(a) + table.save(a,file="/var/wessaorg/rcomp/tmp/14wg061478538616.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,formatC(signif(gqarr[mypoint-kp3+1,1],6),format='g',flag=' ')) + a<-table.element(a,formatC(signif(gqarr[mypoint-kp3+1,2],6),format='g',flag=' ')) + a<-table.element(a,formatC(signif(gqarr[mypoint-kp3+1,3],6),format='g',flag=' ')) + a<-table.row.end(a) + } + a<-table.end(a) + table.save(a,file="/var/wessaorg/rcomp/tmp/1568xx1478538616.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,formatC(signif(numsignificant1/numgqtests,6),format='g',flag=' ')) + 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/1623fi1478538616.tab") + } + } > > try(system("convert tmp/1wu931478538616.ps tmp/1wu931478538616.png",intern=TRUE)) character(0) > try(system("convert tmp/2x6021478538616.ps tmp/2x6021478538616.png",intern=TRUE)) character(0) > try(system("convert tmp/3apy01478538616.ps tmp/3apy01478538616.png",intern=TRUE)) character(0) > try(system("convert tmp/4osb51478538616.ps tmp/4osb51478538616.png",intern=TRUE)) character(0) > try(system("convert tmp/5eql11478538616.ps tmp/5eql11478538616.png",intern=TRUE)) character(0) > try(system("convert tmp/66sr61478538616.ps tmp/66sr61478538616.png",intern=TRUE)) character(0) > try(system("convert tmp/7n4wz1478538616.ps tmp/7n4wz1478538616.png",intern=TRUE)) character(0) > try(system("convert tmp/84n271478538616.ps tmp/84n271478538616.png",intern=TRUE)) character(0) > try(system("convert tmp/9x3vn1478538616.ps tmp/9x3vn1478538616.png",intern=TRUE)) character(0) > try(system("convert tmp/10ttu51478538616.ps tmp/10ttu51478538616.png",intern=TRUE)) convert.im6: unable to open image `tmp/10ttu51478538616.ps': No such file or directory @ error/blob.c/OpenBlob/2641. convert.im6: no images defined `tmp/10ttu51478538616.png' @ error/convert.c/ConvertImageCommand/3044. character(0) attr(,"status") [1] 1 Warning message: running command 'convert tmp/10ttu51478538616.ps tmp/10ttu51478538616.png' had status 1 > > > proc.time() user system elapsed 3.555 0.269 3.882