R version 2.9.0 (2009-04-17)
Copyright (C) 2009 The R Foundation for Statistical Computing
ISBN 3-900051-07-0
R is free software and comes with ABSOLUTELY NO WARRANTY.
You are welcome to redistribute it under certain conditions.
Type 'license()' or 'licence()' for distribution details.
R is a collaborative project with many contributors.
Type 'contributors()' for more information and
'citation()' on how to cite R or R packages in publications.
Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.
> x <- array(list(9,911,8,915,9,452,9,112,8,472,8,230,8,384,8,625,8,221,8,649,8,625,10,443,10,357,8,586,8,892,8,329,8,101,7,922,8,120,7,838,7,735,8,406,8,209,9,451),dim=c(2,24),dimnames=list(c('y',''),1:24))
> y <- array(NA,dim=c(2,24),dimnames=list(c('y',''),1:24))
> for (i in 1:dim(x)[1])
+ {
+ for (j in 1:dim(x)[2])
+ {
+ y[i,j] <- as.numeric(x[i,j])
+ }
+ }
> par20 = ''
> par19 = ''
> par18 = ''
> par17 = ''
> par16 = ''
> par15 = ''
> par14 = ''
> par13 = ''
> par12 = ''
> par11 = ''
> par10 = ''
> par9 = ''
> par8 = ''
> par7 = ''
> par6 = ''
> par5 = ''
> par4 = ''
> par3 = 'Linear Trend'
> par2 = 'Include Monthly Dummies'
> par1 = '1'
> ylab = ''
> xlab = ''
> main = ''
> #'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)
> 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
y M1 M2 M3 M4 M5 M6 M7 M8 M9 M10 M11 t
1 9 911 1 0 0 0 0 0 0 0 0 0 0 1
2 8 915 0 1 0 0 0 0 0 0 0 0 0 2
3 9 452 0 0 1 0 0 0 0 0 0 0 0 3
4 9 112 0 0 0 1 0 0 0 0 0 0 0 4
5 8 472 0 0 0 0 1 0 0 0 0 0 0 5
6 8 230 0 0 0 0 0 1 0 0 0 0 0 6
7 8 384 0 0 0 0 0 0 1 0 0 0 0 7
8 8 625 0 0 0 0 0 0 0 1 0 0 0 8
9 8 221 0 0 0 0 0 0 0 0 1 0 0 9
10 8 649 0 0 0 0 0 0 0 0 0 1 0 10
11 8 625 0 0 0 0 0 0 0 0 0 0 1 11
12 10 443 0 0 0 0 0 0 0 0 0 0 0 12
13 10 357 1 0 0 0 0 0 0 0 0 0 0 13
14 8 586 0 1 0 0 0 0 0 0 0 0 0 14
15 8 892 0 0 1 0 0 0 0 0 0 0 0 15
16 8 329 0 0 0 1 0 0 0 0 0 0 0 16
17 8 101 0 0 0 0 1 0 0 0 0 0 0 17
18 7 922 0 0 0 0 0 1 0 0 0 0 0 18
19 8 120 0 0 0 0 0 0 1 0 0 0 0 19
20 7 838 0 0 0 0 0 0 0 1 0 0 0 20
21 7 735 0 0 0 0 0 0 0 0 1 0 0 21
22 8 406 0 0 0 0 0 0 0 0 0 1 0 22
23 8 209 0 0 0 0 0 0 0 0 0 0 1 23
24 9 451 0 0 0 0 0 0 0 0 0 0 0 24
> k <- length(x[1,])
> df <- as.data.frame(x)
> (mylm <- lm(df))
Call:
lm(formula = df)
Coefficients:
(Intercept) V2 M1 M2 M3 M4
10.776931 -0.001421 -0.126224 -1.424981 -1.000927 -1.607089
M5 M6 M7 M8 M9 M10
-1.977631 -2.030469 -1.955392 -1.738147 -2.062855 -1.456851
M11 t
-1.578285 -0.035640
> (mysum <- summary(mylm))
Call:
lm(formula = df)
Residuals:
Min 1Q Median 3Q Max
-3.201e-01 -7.983e-02 2.429e-17 7.983e-02 3.201e-01
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 10.776931 0.247092 43.615 9.64e-13 ***
V2 -0.001422 0.000243 -5.850 0.000162 ***
M1 -0.126224 0.255499 -0.494 0.631955
M2 -1.424981 0.259282 -5.496 0.000263 ***
M3 -1.000927 0.252254 -3.968 0.002652 **
M4 -1.607090 0.250740 -6.409 7.74e-05 ***
M5 -1.977631 0.245652 -8.051 1.11e-05 ***
M6 -2.030470 0.242539 -8.372 7.89e-06 ***
M7 -1.955392 0.243953 -8.015 1.16e-05 ***
M8 -1.738147 0.247601 -7.020 3.63e-05 ***
M9 -2.062855 0.237094 -8.701 5.60e-06 ***
M10 -1.456851 0.237092 -6.145 0.000109 ***
M11 -1.578285 0.236018 -6.687 5.45e-05 ***
t -0.035640 0.008022 -4.443 0.001249 **
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 0.2358 on 10 degrees of freedom
Multiple R-squared: 0.9602, Adjusted R-squared: 0.9084
F-statistic: 18.55 on 13 and 10 DF, p-value: 2.866e-05
> postscript(file="/var/www/html/rcomp/tmp/1oc3x1291062331.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/www/html/rcomp/tmp/2oc3x1291062331.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556)
> plot(mysum$resid, type='b', pch=19, main='Residuals', ylab='value of Residuals', xlab='time or index')
> grid()
> dev.off()
null device
1
> postscript(file="/var/www/html/rcomp/tmp/3oc3x1291062331.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556)
> hist(mysum$resid, main='Residual Histogram', xlab='values of Residuals')
> grid()
> dev.off()
null device
1
> postscript(file="/var/www/html/rcomp/tmp/4oc3x1291062331.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556)
> densityplot(~mysum$resid,col='black',main='Residual Density Plot', xlab='values of Residuals')
> dev.off()
null device
1
> postscript(file="/var/www/html/rcomp/tmp/5oc3x1291062331.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556)
> qqnorm(mysum$resid, main='Residual Normal Q-Q Plot')
> grid()
> dev.off()
null device
1
> (myerror <- as.ts(mysum$resid))
Time Series:
Start = 1
End = 24
Frequency = 1
1 2 3 4 5 6
-0.32008907 0.01999339 -0.02656925 0.13192681 0.04984466 -0.20567690
7 8 9 10 11 12
-0.02620502 0.13476978 -0.07916435 -0.04113065 0.08182817 0.28047244
13 14 15 16 17 18
0.32008907 -0.01999339 0.02656925 -0.13192681 -0.04984466 0.20567690
19 20 21 22 23 24
0.02620502 -0.13476978 0.07916435 0.04113065 -0.08182817 -0.28047244
> postscript(file="/var/www/html/rcomp/tmp/6g32i1291062331.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 -0.32008907 NA
1 0.01999339 -0.32008907
2 -0.02656925 0.01999339
3 0.13192681 -0.02656925
4 0.04984466 0.13192681
5 -0.20567690 0.04984466
6 -0.02620502 -0.20567690
7 0.13476978 -0.02620502
8 -0.07916435 0.13476978
9 -0.04113065 -0.07916435
10 0.08182817 -0.04113065
11 0.28047244 0.08182817
12 0.32008907 0.28047244
13 -0.01999339 0.32008907
14 0.02656925 -0.01999339
15 -0.13192681 0.02656925
16 -0.04984466 -0.13192681
17 0.20567690 -0.04984466
18 0.02620502 0.20567690
19 -0.13476978 0.02620502
20 0.07916435 -0.13476978
21 0.04113065 0.07916435
22 -0.08182817 0.04113065
23 -0.28047244 -0.08182817
24 NA -0.28047244
> dum1 <- dum[2:length(myerror),]
> dum1
lag(myerror, k = 1) myerror
[1,] 0.01999339 -0.32008907
[2,] -0.02656925 0.01999339
[3,] 0.13192681 -0.02656925
[4,] 0.04984466 0.13192681
[5,] -0.20567690 0.04984466
[6,] -0.02620502 -0.20567690
[7,] 0.13476978 -0.02620502
[8,] -0.07916435 0.13476978
[9,] -0.04113065 -0.07916435
[10,] 0.08182817 -0.04113065
[11,] 0.28047244 0.08182817
[12,] 0.32008907 0.28047244
[13,] -0.01999339 0.32008907
[14,] 0.02656925 -0.01999339
[15,] -0.13192681 0.02656925
[16,] -0.04984466 -0.13192681
[17,] 0.20567690 -0.04984466
[18,] 0.02620502 0.20567690
[19,] -0.13476978 0.02620502
[20,] 0.07916435 -0.13476978
[21,] 0.04113065 0.07916435
[22,] -0.08182817 0.04113065
[23,] -0.28047244 -0.08182817
> z <- as.data.frame(dum1)
> z
lag(myerror, k = 1) myerror
1 0.01999339 -0.32008907
2 -0.02656925 0.01999339
3 0.13192681 -0.02656925
4 0.04984466 0.13192681
5 -0.20567690 0.04984466
6 -0.02620502 -0.20567690
7 0.13476978 -0.02620502
8 -0.07916435 0.13476978
9 -0.04113065 -0.07916435
10 0.08182817 -0.04113065
11 0.28047244 0.08182817
12 0.32008907 0.28047244
13 -0.01999339 0.32008907
14 0.02656925 -0.01999339
15 -0.13192681 0.02656925
16 -0.04984466 -0.13192681
17 0.20567690 -0.04984466
18 0.02620502 0.20567690
19 -0.13476978 0.02620502
20 0.07916435 -0.13476978
21 0.04113065 0.07916435
22 -0.08182817 0.04113065
23 -0.28047244 -0.08182817
> 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/www/html/rcomp/tmp/79c2l1291062331.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556)
> acf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Autocorrelation Function')
> grid()
> dev.off()
null device
1
> postscript(file="/var/www/html/rcomp/tmp/89c2l1291062331.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556)
> pacf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Partial Autocorrelation Function')
> grid()
> dev.off()
null device
1
> postscript(file="/var/www/html/rcomp/tmp/99c2l1291062331.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556)
> opar <- par(mfrow = c(2,2), oma = c(0, 0, 1.1, 0))
> plot(mylm, las = 1, sub='Residual Diagnostics')
> par(opar)
> dev.off()
null device
1
>
> #Note: the /var/www/html/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab
> load(file="/var/www/html/rcomp/createtable")
>
> a<-table.start()
> a<-table.row.start(a)
> a<-table.element(a, 'Multiple Linear Regression - Estimated Regression Equation', 1, TRUE)
> a<-table.row.end(a)
> myeq <- colnames(x)[1]
> myeq <- paste(myeq, '[t] = ', sep='')
> for (i in 1:k){
+ if (mysum$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/www/html/rcomp/tmp/10n40u1291062331.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/www/html/rcomp/tmp/11gezx1291062331.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/www/html/rcomp/tmp/125we91291062331.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/www/html/rcomp/tmp/13xovc1291062331.tab")
>
> try(system("convert tmp/1oc3x1291062331.ps tmp/1oc3x1291062331.png",intern=TRUE))
character(0)
> try(system("convert tmp/2oc3x1291062331.ps tmp/2oc3x1291062331.png",intern=TRUE))
character(0)
> try(system("convert tmp/3oc3x1291062331.ps tmp/3oc3x1291062331.png",intern=TRUE))
character(0)
> try(system("convert tmp/4oc3x1291062331.ps tmp/4oc3x1291062331.png",intern=TRUE))
character(0)
> try(system("convert tmp/5oc3x1291062331.ps tmp/5oc3x1291062331.png",intern=TRUE))
character(0)
> try(system("convert tmp/6g32i1291062331.ps tmp/6g32i1291062331.png",intern=TRUE))
character(0)
> try(system("convert tmp/79c2l1291062331.ps tmp/79c2l1291062331.png",intern=TRUE))
character(0)
> try(system("convert tmp/89c2l1291062331.ps tmp/89c2l1291062331.png",intern=TRUE))
character(0)
> try(system("convert tmp/99c2l1291062331.ps tmp/99c2l1291062331.png",intern=TRUE))
character(0)
>
>
> proc.time()
user system elapsed
1.928 1.449 14.841