R version 3.2.2 (2015-08-14) -- "Fire Safety"
Copyright (C) 2015 The R Foundation for Statistical Computing
Platform: x86_64-pc-linux-gnu (64-bit)
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> x <- array(list(1,11,6,1,8,0,1,5,2,1,14,8,1,19,11,1,6,4,1,10,13,1,6,1,1,11,8,1,3,0,0,16,13,0,13,10,0,11,18,0,9,5,0,21,23,0,16,12,0,12,5,0,12,16,0,7,1,0,12,20),dim=c(3,20),dimnames=list(c('V1','V2','V3'),1:20))
> y <- array(NA,dim=c(3,20),dimnames=list(c('V1','V2','V3'),1:20))
> 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 = '3'
> par3 <- 'No Linear Trend'
> par2 <- 'Do not include Seasonal Dummies'
> par1 <- '3'
> #'GNU S' R Code compiled by R2WASP v. 1.2.327 (Sun, 26 Jul 2015 13:26:06 +0100)
> #Author: root
> #To cite this work: Wessa P., (2015), Multiple Regression (v1.0.32) 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.'
+ }
> 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
V3 V1 V2
1 6 1 11
2 0 1 8
3 2 1 5
4 8 1 14
5 11 1 19
6 4 1 6
7 13 1 10
8 1 1 6
9 8 1 11
10 0 1 3
11 13 0 16
12 10 0 13
13 18 0 11
14 5 0 9
15 23 0 21
16 12 0 16
17 5 0 12
18 16 0 12
19 1 0 7
20 20 0 12
> k <- length(x[1,])
> df <- as.data.frame(x)
> (mylm <- lm(df))
Call:
lm(formula = df)
Coefficients:
(Intercept) V1 V2
0.3198 -3.6567 0.9287
> (mysum <- summary(mylm))
Call:
lm(formula = df)
Residuals:
Min 1Q Median 3Q Max
-6.464 -3.211 -1.057 2.118 8.536
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 0.3198 3.4953 0.092 0.92816
V1 -3.6567 2.2325 -1.638 0.11980
V2 0.9287 0.2466 3.766 0.00154 **
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 4.58 on 17 degrees of freedom
Multiple R-squared: 0.6034, Adjusted R-squared: 0.5567
F-statistic: 12.93 on 2 and 17 DF, p-value: 0.0003857
> 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/124g01446094176.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$resid)
> grid()
> dev.off()
null device
1
> postscript(file="/var/wessaorg/rcomp/tmp/2jnhi1446094176.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556)
> plot(mysum$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/3uzo11446094176.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556)
> hist(mysum$resid, main='Residual Histogram', xlab='values of Residuals')
> grid()
> dev.off()
null device
1
> postscript(file="/var/wessaorg/rcomp/tmp/4prmc1446094176.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556)
> densityplot(~mysum$resid,col='black',main='Residual Density Plot', xlab='values of Residuals')
> dev.off()
null device
1
> postscript(file="/var/wessaorg/rcomp/tmp/5inoe1446094176.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 = 20
Frequency = 1
1 2 3 4 5 6 7
-0.8787826 -4.0926957 0.6933913 -1.6648696 -3.3083478 1.7646957 7.0499130
8 9 10 11 12 13 14
-1.2353043 1.1212174 0.5507826 -2.1789565 -2.3928696 7.4645217 -3.6780870
15 16 17 18 19 20
3.1775652 -3.1789565 -6.4641739 4.5358261 -5.8206957 8.5358261
> postscript(file="/var/wessaorg/rcomp/tmp/6o97m1446094176.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 = 20
Frequency = 1
lag(myerror, k = 1) myerror
0 -0.8787826 NA
1 -4.0926957 -0.8787826
2 0.6933913 -4.0926957
3 -1.6648696 0.6933913
4 -3.3083478 -1.6648696
5 1.7646957 -3.3083478
6 7.0499130 1.7646957
7 -1.2353043 7.0499130
8 1.1212174 -1.2353043
9 0.5507826 1.1212174
10 -2.1789565 0.5507826
11 -2.3928696 -2.1789565
12 7.4645217 -2.3928696
13 -3.6780870 7.4645217
14 3.1775652 -3.6780870
15 -3.1789565 3.1775652
16 -6.4641739 -3.1789565
17 4.5358261 -6.4641739
18 -5.8206957 4.5358261
19 8.5358261 -5.8206957
20 NA 8.5358261
> dum1 <- dum[2:length(myerror),]
> dum1
lag(myerror, k = 1) myerror
[1,] -4.0926957 -0.8787826
[2,] 0.6933913 -4.0926957
[3,] -1.6648696 0.6933913
[4,] -3.3083478 -1.6648696
[5,] 1.7646957 -3.3083478
[6,] 7.0499130 1.7646957
[7,] -1.2353043 7.0499130
[8,] 1.1212174 -1.2353043
[9,] 0.5507826 1.1212174
[10,] -2.1789565 0.5507826
[11,] -2.3928696 -2.1789565
[12,] 7.4645217 -2.3928696
[13,] -3.6780870 7.4645217
[14,] 3.1775652 -3.6780870
[15,] -3.1789565 3.1775652
[16,] -6.4641739 -3.1789565
[17,] 4.5358261 -6.4641739
[18,] -5.8206957 4.5358261
[19,] 8.5358261 -5.8206957
> z <- as.data.frame(dum1)
> z
lag(myerror, k = 1) myerror
1 -4.0926957 -0.8787826
2 0.6933913 -4.0926957
3 -1.6648696 0.6933913
4 -3.3083478 -1.6648696
5 1.7646957 -3.3083478
6 7.0499130 1.7646957
7 -1.2353043 7.0499130
8 1.1212174 -1.2353043
9 0.5507826 1.1212174
10 -2.1789565 0.5507826
11 -2.3928696 -2.1789565
12 7.4645217 -2.3928696
13 -3.6780870 7.4645217
14 3.1775652 -3.6780870
15 -3.1789565 3.1775652
16 -6.4641739 -3.1789565
17 4.5358261 -6.4641739
18 -5.8206957 4.5358261
19 8.5358261 -5.8206957
> 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/7mq021446094176.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556)
> acf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Autocorrelation Function')
> grid()
> dev.off()
null device
1
> postscript(file="/var/wessaorg/rcomp/tmp/8brez1446094176.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556)
> pacf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Partial Autocorrelation Function')
> grid()
> dev.off()
null device
1
> postscript(file="/var/wessaorg/rcomp/tmp/9mp211446094176.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556)
> opar <- par(mfrow = c(2,2), oma = c(0, 0, 1.1, 0))
> plot(mylm, las = 1, sub='Residual Diagnostics')
> par(opar)
> dev.off()
null device
1
> if (n > n25) {
+ postscript(file="/var/wessaorg/rcomp/tmp/10r3711446094176.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556)
+ plot(kp3:nmkm3,gqarr[,2], main='Goldfeld-Quandt test',ylab='2-sided p-value',xlab='breakpoint')
+ grid()
+ dev.off()
+ }
>
> #Note: the /var/wessaorg/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab
> load(file="/var/wessaorg/rcomp/createtable")
>
> a<-table.start()
> a<-table.row.start(a)
> a<-table.element(a, 'Multiple Linear Regression - Estimated Regression Equation', 1, TRUE)
> a<-table.row.end(a)
> myeq <- colnames(x)[1]
> myeq <- paste(myeq, '[t] = ', sep='')
> for (i in 1:k){
+ if (mysum$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/11o7hz1446094176.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/129wx11446094176.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/1360fl1446094176.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,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/142y9m1446094176.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/15w2qd1446094176.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/16yvvj1446094176.tab")
+ }
>
> try(system("convert tmp/124g01446094176.ps tmp/124g01446094176.png",intern=TRUE))
character(0)
> try(system("convert tmp/2jnhi1446094176.ps tmp/2jnhi1446094176.png",intern=TRUE))
character(0)
> try(system("convert tmp/3uzo11446094176.ps tmp/3uzo11446094176.png",intern=TRUE))
character(0)
> try(system("convert tmp/4prmc1446094176.ps tmp/4prmc1446094176.png",intern=TRUE))
character(0)
> try(system("convert tmp/5inoe1446094176.ps tmp/5inoe1446094176.png",intern=TRUE))
character(0)
> try(system("convert tmp/6o97m1446094176.ps tmp/6o97m1446094176.png",intern=TRUE))
character(0)
> try(system("convert tmp/7mq021446094176.ps tmp/7mq021446094176.png",intern=TRUE))
character(0)
> try(system("convert tmp/8brez1446094176.ps tmp/8brez1446094176.png",intern=TRUE))
character(0)
> try(system("convert tmp/9mp211446094176.ps tmp/9mp211446094176.png",intern=TRUE))
character(0)
> try(system("convert tmp/10r3711446094176.ps tmp/10r3711446094176.png",intern=TRUE))
convert.im6: unable to open image `tmp/10r3711446094176.ps': No such file or directory @ error/blob.c/OpenBlob/2638.
convert.im6: no images defined `tmp/10r3711446094176.png' @ error/convert.c/ConvertImageCommand/3044.
character(0)
attr(,"status")
[1] 1
Warning message:
running command 'convert tmp/10r3711446094176.ps tmp/10r3711446094176.png' had status 1
>
>
> proc.time()
user system elapsed
3.362 0.618 4.028