R version 3.0.2 (2013-09-25) -- "Frisbee Sailing"
Copyright (C) 2013 The R Foundation for Statistical Computing
Platform: i686-pc-linux-gnu (32-bit)
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> x <- array(list(913,730,2,2,0,0,1,773,730,1,1,0,0,2,992,904,1,1,3,0,2,977,904,2,2,0,0,1,691,550,1,1,2,1,2,686,460,1,1,2,1,1,632,590,1,1,2,0,1,683,670,1,1,2,1,1,731,670,1,3,2,1,1,776,715,1,1,3,1,1,820,715,1,3,3,1,1,736,612,1,1,3,1,1,827,612,1,3,3,1,1,841,746,1,1,3,1,1,556,441,1,1,2,0,1),dim=c(7,15),dimnames=list(c('FOB','Weight','Brass','Finish','Aerator','Drain','Box'),1:15))
> y <- array(NA,dim=c(7,15),dimnames=list(c('FOB','Weight','Brass','Finish','Aerator','Drain','Box'),1:15))
> 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
FOB Weight Brass Finish Aerator Drain Box
1 913 730 2 2 0 0 1
2 773 730 1 1 0 0 2
3 992 904 1 1 3 0 2
4 977 904 2 2 0 0 1
5 691 550 1 1 2 1 2
6 686 460 1 1 2 1 1
7 632 590 1 1 2 0 1
8 683 670 1 1 2 1 1
9 731 670 1 3 2 1 1
10 776 715 1 1 3 1 1
11 820 715 1 3 3 1 1
12 736 612 1 1 3 1 1
13 827 612 1 3 3 1 1
14 841 746 1 1 3 1 1
15 556 441 1 1 2 0 1
> k <- length(x[1,])
> df <- as.data.frame(x)
> (mylm <- lm(df))
Call:
lm(formula = df)
Coefficients:
(Intercept) Weight Brass Finish Aerator Drain
-92.4679 0.5526 226.9168 21.1741 45.5608 15.5384
Box
89.8235
> (mysum <- summary(mylm))
Call:
lm(formula = df)
Residuals:
Min 1Q Median 3Q Max
-54.85 -27.43 -15.12 25.81 79.70
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -92.4679 130.7717 -0.707 0.49958
Weight 0.5526 0.1325 4.170 0.00312 **
Brass 226.9168 76.1073 2.982 0.01756 *
Finish 21.1741 18.1321 1.168 0.27652
Aerator 45.5608 21.4906 2.120 0.06682 .
Drain 15.5384 36.2576 0.429 0.67955
Box 89.8235 43.5276 2.064 0.07295 .
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 49.43 on 8 degrees of freedom
Multiple R-squared: 0.9075, Adjusted R-squared: 0.8382
F-statistic: 13.08 on 6 and 8 DF, p-value: 0.0009411
> 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/1d0yy1383307107.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=16.666666666667,height=11.111111111111)
> plot(x[,1], type='l', main='Actuals and Interpolation', ylab='value of Actuals and Interpolation (dots)', xlab='time or index')
> points(x[,1]-mysum$resid)
> grid()
> dev.off()
null device
1
> postscript(file="/var/fisher/rcomp/tmp/2hrei1383307107.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=16.666666666667,height=11.111111111111)
> plot(mysum$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/3i85c1383307107.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=16.666666666667,height=11.111111111111)
> hist(mysum$resid, main='Residual Histogram', xlab='values of Residuals')
> grid()
> dev.off()
null device
1
> postscript(file="/var/fisher/rcomp/tmp/47j8f1383307107.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=16.666666666667,height=11.111111111111)
> densityplot(~mysum$resid,col='black',main='Residual Density Plot', xlab='values of Residuals')
> dev.off()
null device
1
> postscript(file="/var/fisher/rcomp/tmp/5lh9b1383307107.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=16.666666666667,height=11.111111111111)
> 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 = 15
Frequency = 1
1 2 3 4 5 6
16.0749619 34.3423430 20.5099469 -16.0749619 -54.8522899 79.7039422
7 8 9 10 11 12
-30.5937847 -39.3390691 -33.6873222 -16.7662528 -15.1145059 0.1500813
13 14 15
48.8018282 31.1035883 -24.2585052
> postscript(file="/var/fisher/rcomp/tmp/6pz9b1383307107.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=16.666666666667,height=11.111111111111)
> dum <- cbind(lag(myerror,k=1),myerror)
> dum
Time Series:
Start = 0
End = 15
Frequency = 1
lag(myerror, k = 1) myerror
0 16.0749619 NA
1 34.3423430 16.0749619
2 20.5099469 34.3423430
3 -16.0749619 20.5099469
4 -54.8522899 -16.0749619
5 79.7039422 -54.8522899
6 -30.5937847 79.7039422
7 -39.3390691 -30.5937847
8 -33.6873222 -39.3390691
9 -16.7662528 -33.6873222
10 -15.1145059 -16.7662528
11 0.1500813 -15.1145059
12 48.8018282 0.1500813
13 31.1035883 48.8018282
14 -24.2585052 31.1035883
15 NA -24.2585052
> dum1 <- dum[2:length(myerror),]
> dum1
lag(myerror, k = 1) myerror
[1,] 34.3423430 16.0749619
[2,] 20.5099469 34.3423430
[3,] -16.0749619 20.5099469
[4,] -54.8522899 -16.0749619
[5,] 79.7039422 -54.8522899
[6,] -30.5937847 79.7039422
[7,] -39.3390691 -30.5937847
[8,] -33.6873222 -39.3390691
[9,] -16.7662528 -33.6873222
[10,] -15.1145059 -16.7662528
[11,] 0.1500813 -15.1145059
[12,] 48.8018282 0.1500813
[13,] 31.1035883 48.8018282
[14,] -24.2585052 31.1035883
> z <- as.data.frame(dum1)
> z
lag(myerror, k = 1) myerror
1 34.3423430 16.0749619
2 20.5099469 34.3423430
3 -16.0749619 20.5099469
4 -54.8522899 -16.0749619
5 79.7039422 -54.8522899
6 -30.5937847 79.7039422
7 -39.3390691 -30.5937847
8 -33.6873222 -39.3390691
9 -16.7662528 -33.6873222
10 -15.1145059 -16.7662528
11 0.1500813 -15.1145059
12 48.8018282 0.1500813
13 31.1035883 48.8018282
14 -24.2585052 31.1035883
> 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/7g17j1383307107.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=16.666666666667,height=11.111111111111)
> acf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Autocorrelation Function')
> grid()
> dev.off()
null device
1
> postscript(file="/var/fisher/rcomp/tmp/8vtrp1383307107.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=16.666666666667,height=11.111111111111)
> pacf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Partial Autocorrelation Function')
> grid()
> dev.off()
null device
1
> postscript(file="/var/fisher/rcomp/tmp/900wn1383307107.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=16.666666666667,height=11.111111111111)
> opar <- par(mfrow = c(2,2), oma = c(0, 0, 1.1, 0))
> plot(mylm, las = 1, sub='Residual Diagnostics')
> par(opar)
> dev.off()
null device
1
> if (n > n25) {
+ postscript(file="/var/fisher/rcomp/tmp/10vphp1383307107.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=16.666666666667,height=11.111111111111)
+ plot(kp3:nmkm3,gqarr[,2], main='Goldfeld-Quandt test',ylab='2-sided p-value',xlab='breakpoint')
+ grid()
+ dev.off()
+ }
>
> #Note: the /var/fisher/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab
> load(file="/var/fisher/rcomp/createtable")
>
> a<-table.start()
> a<-table.row.start(a)
> a<-table.element(a, 'Multiple Linear Regression - Estimated Regression Equation', 1, TRUE)
> a<-table.row.end(a)
> myeq <- colnames(x)[1]
> myeq <- paste(myeq, '[t] = ', sep='')
> for (i in 1:k){
+ if (mysum$coefficients[i,1] > 0) myeq <- paste(myeq, '+', '')
+ myeq <- paste(myeq, 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/fisher/rcomp/tmp/11zgtg1383307107.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/fisher/rcomp/tmp/12cl8l1383307107.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/fisher/rcomp/tmp/13fh4t1383307107.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/fisher/rcomp/tmp/14yz1g1383307107.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/fisher/rcomp/tmp/15ebh91383307107.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/fisher/rcomp/tmp/16mmnt1383307107.tab")
+ }
>
> try(system("convert tmp/1d0yy1383307107.ps tmp/1d0yy1383307107.png",intern=TRUE))
character(0)
> try(system("convert tmp/2hrei1383307107.ps tmp/2hrei1383307107.png",intern=TRUE))
character(0)
> try(system("convert tmp/3i85c1383307107.ps tmp/3i85c1383307107.png",intern=TRUE))
character(0)
> try(system("convert tmp/47j8f1383307107.ps tmp/47j8f1383307107.png",intern=TRUE))
character(0)
> try(system("convert tmp/5lh9b1383307107.ps tmp/5lh9b1383307107.png",intern=TRUE))
character(0)
> try(system("convert tmp/6pz9b1383307107.ps tmp/6pz9b1383307107.png",intern=TRUE))
character(0)
> try(system("convert tmp/7g17j1383307107.ps tmp/7g17j1383307107.png",intern=TRUE))
character(0)
> try(system("convert tmp/8vtrp1383307107.ps tmp/8vtrp1383307107.png",intern=TRUE))
character(0)
> try(system("convert tmp/900wn1383307107.ps tmp/900wn1383307107.png",intern=TRUE))
character(0)
> try(system("convert tmp/10vphp1383307107.ps tmp/10vphp1383307107.png",intern=TRUE))
convert: unable to open image `tmp/10vphp1383307107.ps': @ error/blob.c/OpenBlob/2587.
convert: missing an image filename `tmp/10vphp1383307107.png' @ error/convert.c/ConvertImageCommand/3011.
character(0)
attr(,"status")
[1] 1
Warning message:
running command 'convert tmp/10vphp1383307107.ps tmp/10vphp1383307107.png' had status 1
>
>
> proc.time()
user system elapsed
6.725 1.105 7.817