R version 2.8.0 (2008-10-20)
Copyright (C) 2008 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(120.3,0,133.4,0,109.4,0,93.2,0,91.2,0,99.2,0,108.2,0,101.5,0,106.9,0,104.4,0,77.9,0,60,0,99.5,0,95,0,105.6,0,102.5,0,93.3,0,97.3,0,127,0,111.7,0,96.4,0,133,0,72.2,0,95.8,0,124.1,0,127.6,0,110.7,0,104.6,0,112.7,0,115.3,0,139.4,0,119,0,97.4,0,154,0,81.5,0,88.8,0,127.7,1,105.1,1,114.9,1,106.4,1,104.5,1,121.6,1,141.4,1,99,1,126.7,1,134.1,1,81.3,1,88.6,1,132.7,1,132.9,1,134.4,1,103.7,1,119.7,1,115,1,132.9,1,108.5,1,113.9,1,142.9,1,95.2,1,93,1),dim=c(2,60),dimnames=list(c('Y','X'),1:60))
> y <- array(NA,dim=c(2,60),dimnames=list(c('Y','X'),1:60))
> 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'
> #'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 X
1 120.3 0
2 133.4 0
3 109.4 0
4 93.2 0
5 91.2 0
6 99.2 0
7 108.2 0
8 101.5 0
9 106.9 0
10 104.4 0
11 77.9 0
12 60.0 0
13 99.5 0
14 95.0 0
15 105.6 0
16 102.5 0
17 93.3 0
18 97.3 0
19 127.0 0
20 111.7 0
21 96.4 0
22 133.0 0
23 72.2 0
24 95.8 0
25 124.1 0
26 127.6 0
27 110.7 0
28 104.6 0
29 112.7 0
30 115.3 0
31 139.4 0
32 119.0 0
33 97.4 0
34 154.0 0
35 81.5 0
36 88.8 0
37 127.7 1
38 105.1 1
39 114.9 1
40 106.4 1
41 104.5 1
42 121.6 1
43 141.4 1
44 99.0 1
45 126.7 1
46 134.1 1
47 81.3 1
48 88.6 1
49 132.7 1
50 132.9 1
51 134.4 1
52 103.7 1
53 119.7 1
54 115.0 1
55 132.9 1
56 108.5 1
57 113.9 1
58 142.9 1
59 95.2 1
60 93.0 1
> k <- length(x[1,])
> df <- as.data.frame(x)
> (mylm <- lm(df))
Call:
lm(formula = df)
Coefficients:
(Intercept) X
105.833 9.838
> (mysum <- summary(mylm))
Call:
lm(formula = df)
Residuals:
Min 1Q Median 3Q Max
-45.833 -10.918 -1.002 13.492 48.167
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 105.833 3.074 34.427 <2e-16 ***
X 9.838 4.861 2.024 0.0476 *
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 18.45 on 58 degrees of freedom
Multiple R-squared: 0.06596, Adjusted R-squared: 0.04986
F-statistic: 4.096 on 1 and 58 DF, p-value: 0.0476
> postscript(file="/var/www/html/rcomp/tmp/1v3e01229682050.ps",horizontal=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/28sak1229682050.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556)
> plot(mysum$resid, type='b', pch=19, main='Residuals', ylab='value of Residuals', xlab='time or index')
> grid()
> dev.off()
null device
1
> postscript(file="/var/www/html/rcomp/tmp/3tp7r1229682050.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556)
> hist(mysum$resid, main='Residual Histogram', xlab='values of Residuals')
> grid()
> dev.off()
null device
1
> postscript(file="/var/www/html/rcomp/tmp/4xf0m1229682050.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556)
> densityplot(~mysum$resid,col='black',main='Residual Density Plot', xlab='values of Residuals')
> dev.off()
null device
1
> postscript(file="/var/www/html/rcomp/tmp/5o79b1229682050.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556)
> qqnorm(mysum$resid, main='Residual Normal Q-Q Plot')
> grid()
> dev.off()
null device
1
> (myerror <- as.ts(mysum$resid))
Time Series:
Start = 1
End = 60
Frequency = 1
1 2 3 4 5 6
14.4666667 27.5666667 3.5666667 -12.6333333 -14.6333333 -6.6333333
7 8 9 10 11 12
2.3666667 -4.3333333 1.0666667 -1.4333333 -27.9333333 -45.8333333
13 14 15 16 17 18
-6.3333333 -10.8333333 -0.2333333 -3.3333333 -12.5333333 -8.5333333
19 20 21 22 23 24
21.1666667 5.8666667 -9.4333333 27.1666667 -33.6333333 -10.0333333
25 26 27 28 29 30
18.2666667 21.7666667 4.8666667 -1.2333333 6.8666667 9.4666667
31 32 33 34 35 36
33.5666667 13.1666667 -8.4333333 48.1666667 -24.3333333 -17.0333333
37 38 39 40 41 42
12.0291667 -10.5708333 -0.7708333 -9.2708333 -11.1708333 5.9291667
43 44 45 46 47 48
25.7291667 -16.6708333 11.0291667 18.4291667 -34.3708333 -27.0708333
49 50 51 52 53 54
17.0291667 17.2291667 18.7291667 -11.9708333 4.0291667 -0.6708333
55 56 57 58 59 60
17.2291667 -7.1708333 -1.7708333 27.2291667 -20.4708333 -22.6708333
> postscript(file="/var/www/html/rcomp/tmp/6uce61229682050.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556)
> dum <- cbind(lag(myerror,k=1),myerror)
> dum
Time Series:
Start = 0
End = 60
Frequency = 1
lag(myerror, k = 1) myerror
0 14.4666667 NA
1 27.5666667 14.4666667
2 3.5666667 27.5666667
3 -12.6333333 3.5666667
4 -14.6333333 -12.6333333
5 -6.6333333 -14.6333333
6 2.3666667 -6.6333333
7 -4.3333333 2.3666667
8 1.0666667 -4.3333333
9 -1.4333333 1.0666667
10 -27.9333333 -1.4333333
11 -45.8333333 -27.9333333
12 -6.3333333 -45.8333333
13 -10.8333333 -6.3333333
14 -0.2333333 -10.8333333
15 -3.3333333 -0.2333333
16 -12.5333333 -3.3333333
17 -8.5333333 -12.5333333
18 21.1666667 -8.5333333
19 5.8666667 21.1666667
20 -9.4333333 5.8666667
21 27.1666667 -9.4333333
22 -33.6333333 27.1666667
23 -10.0333333 -33.6333333
24 18.2666667 -10.0333333
25 21.7666667 18.2666667
26 4.8666667 21.7666667
27 -1.2333333 4.8666667
28 6.8666667 -1.2333333
29 9.4666667 6.8666667
30 33.5666667 9.4666667
31 13.1666667 33.5666667
32 -8.4333333 13.1666667
33 48.1666667 -8.4333333
34 -24.3333333 48.1666667
35 -17.0333333 -24.3333333
36 12.0291667 -17.0333333
37 -10.5708333 12.0291667
38 -0.7708333 -10.5708333
39 -9.2708333 -0.7708333
40 -11.1708333 -9.2708333
41 5.9291667 -11.1708333
42 25.7291667 5.9291667
43 -16.6708333 25.7291667
44 11.0291667 -16.6708333
45 18.4291667 11.0291667
46 -34.3708333 18.4291667
47 -27.0708333 -34.3708333
48 17.0291667 -27.0708333
49 17.2291667 17.0291667
50 18.7291667 17.2291667
51 -11.9708333 18.7291667
52 4.0291667 -11.9708333
53 -0.6708333 4.0291667
54 17.2291667 -0.6708333
55 -7.1708333 17.2291667
56 -1.7708333 -7.1708333
57 27.2291667 -1.7708333
58 -20.4708333 27.2291667
59 -22.6708333 -20.4708333
60 NA -22.6708333
> dum1 <- dum[2:length(myerror),]
> dum1
lag(myerror, k = 1) myerror
[1,] 27.5666667 14.4666667
[2,] 3.5666667 27.5666667
[3,] -12.6333333 3.5666667
[4,] -14.6333333 -12.6333333
[5,] -6.6333333 -14.6333333
[6,] 2.3666667 -6.6333333
[7,] -4.3333333 2.3666667
[8,] 1.0666667 -4.3333333
[9,] -1.4333333 1.0666667
[10,] -27.9333333 -1.4333333
[11,] -45.8333333 -27.9333333
[12,] -6.3333333 -45.8333333
[13,] -10.8333333 -6.3333333
[14,] -0.2333333 -10.8333333
[15,] -3.3333333 -0.2333333
[16,] -12.5333333 -3.3333333
[17,] -8.5333333 -12.5333333
[18,] 21.1666667 -8.5333333
[19,] 5.8666667 21.1666667
[20,] -9.4333333 5.8666667
[21,] 27.1666667 -9.4333333
[22,] -33.6333333 27.1666667
[23,] -10.0333333 -33.6333333
[24,] 18.2666667 -10.0333333
[25,] 21.7666667 18.2666667
[26,] 4.8666667 21.7666667
[27,] -1.2333333 4.8666667
[28,] 6.8666667 -1.2333333
[29,] 9.4666667 6.8666667
[30,] 33.5666667 9.4666667
[31,] 13.1666667 33.5666667
[32,] -8.4333333 13.1666667
[33,] 48.1666667 -8.4333333
[34,] -24.3333333 48.1666667
[35,] -17.0333333 -24.3333333
[36,] 12.0291667 -17.0333333
[37,] -10.5708333 12.0291667
[38,] -0.7708333 -10.5708333
[39,] -9.2708333 -0.7708333
[40,] -11.1708333 -9.2708333
[41,] 5.9291667 -11.1708333
[42,] 25.7291667 5.9291667
[43,] -16.6708333 25.7291667
[44,] 11.0291667 -16.6708333
[45,] 18.4291667 11.0291667
[46,] -34.3708333 18.4291667
[47,] -27.0708333 -34.3708333
[48,] 17.0291667 -27.0708333
[49,] 17.2291667 17.0291667
[50,] 18.7291667 17.2291667
[51,] -11.9708333 18.7291667
[52,] 4.0291667 -11.9708333
[53,] -0.6708333 4.0291667
[54,] 17.2291667 -0.6708333
[55,] -7.1708333 17.2291667
[56,] -1.7708333 -7.1708333
[57,] 27.2291667 -1.7708333
[58,] -20.4708333 27.2291667
[59,] -22.6708333 -20.4708333
> z <- as.data.frame(dum1)
> z
lag(myerror, k = 1) myerror
1 27.5666667 14.4666667
2 3.5666667 27.5666667
3 -12.6333333 3.5666667
4 -14.6333333 -12.6333333
5 -6.6333333 -14.6333333
6 2.3666667 -6.6333333
7 -4.3333333 2.3666667
8 1.0666667 -4.3333333
9 -1.4333333 1.0666667
10 -27.9333333 -1.4333333
11 -45.8333333 -27.9333333
12 -6.3333333 -45.8333333
13 -10.8333333 -6.3333333
14 -0.2333333 -10.8333333
15 -3.3333333 -0.2333333
16 -12.5333333 -3.3333333
17 -8.5333333 -12.5333333
18 21.1666667 -8.5333333
19 5.8666667 21.1666667
20 -9.4333333 5.8666667
21 27.1666667 -9.4333333
22 -33.6333333 27.1666667
23 -10.0333333 -33.6333333
24 18.2666667 -10.0333333
25 21.7666667 18.2666667
26 4.8666667 21.7666667
27 -1.2333333 4.8666667
28 6.8666667 -1.2333333
29 9.4666667 6.8666667
30 33.5666667 9.4666667
31 13.1666667 33.5666667
32 -8.4333333 13.1666667
33 48.1666667 -8.4333333
34 -24.3333333 48.1666667
35 -17.0333333 -24.3333333
36 12.0291667 -17.0333333
37 -10.5708333 12.0291667
38 -0.7708333 -10.5708333
39 -9.2708333 -0.7708333
40 -11.1708333 -9.2708333
41 5.9291667 -11.1708333
42 25.7291667 5.9291667
43 -16.6708333 25.7291667
44 11.0291667 -16.6708333
45 18.4291667 11.0291667
46 -34.3708333 18.4291667
47 -27.0708333 -34.3708333
48 17.0291667 -27.0708333
49 17.2291667 17.0291667
50 18.7291667 17.2291667
51 -11.9708333 18.7291667
52 4.0291667 -11.9708333
53 -0.6708333 4.0291667
54 17.2291667 -0.6708333
55 -7.1708333 17.2291667
56 -1.7708333 -7.1708333
57 27.2291667 -1.7708333
58 -20.4708333 27.2291667
59 -22.6708333 -20.4708333
> 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/7rm6f1229682050.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556)
> acf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Autocorrelation Function')
> grid()
> dev.off()
null device
1
> postscript(file="/var/www/html/rcomp/tmp/8rckw1229682050.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556)
> pacf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Partial Autocorrelation Function')
> grid()
> dev.off()
null device
1
> postscript(file="/var/www/html/rcomp/tmp/98ndu1229682050.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556)
> opar <- par(mfrow = c(2,2), oma = c(0, 0, 1.1, 0))
> plot(mylm, las = 1, sub='Residual Diagnostics')
> par(opar)
> dev.off()
null device
1
>
> #Note: the /var/www/html/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab
> load(file="/var/www/html/rcomp/createtable")
>
> a<-table.start()
> a<-table.row.start(a)
> a<-table.element(a, 'Multiple Linear Regression - Estimated Regression Equation', 1, TRUE)
> a<-table.row.end(a)
> myeq <- colnames(x)[1]
> myeq <- paste(myeq, '[t] = ', sep='')
> for (i in 1:k){
+ if (mysum$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/10cpp11229682050.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/11bhl61229682050.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/127vlk1229682051.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/135s4u1229682051.tab")
>
> system("convert tmp/1v3e01229682050.ps tmp/1v3e01229682050.png")
> system("convert tmp/28sak1229682050.ps tmp/28sak1229682050.png")
> system("convert tmp/3tp7r1229682050.ps tmp/3tp7r1229682050.png")
> system("convert tmp/4xf0m1229682050.ps tmp/4xf0m1229682050.png")
> system("convert tmp/5o79b1229682050.ps tmp/5o79b1229682050.png")
> system("convert tmp/6uce61229682050.ps tmp/6uce61229682050.png")
> system("convert tmp/7rm6f1229682050.ps tmp/7rm6f1229682050.png")
> system("convert tmp/8rckw1229682050.ps tmp/8rckw1229682050.png")
> system("convert tmp/98ndu1229682050.ps tmp/98ndu1229682050.png")
>
>
> proc.time()
user system elapsed
1.927 1.411 2.416