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(493.000,0,481.000,0,462.000,0,457.000,0,442.000,0,439.000,0,488.000,0,521.000,0,501.000,0,485.000,0,464.000,0,460.000,0,467.000,0,460.000,0,448.000,0,443.000,0,436.000,0,431.000,0,484.000,0,510.000,0,513.000,0,503.000,0,471.000,0,471.000,0,476.000,0,475.000,0,470.000,0,461.000,0,455.000,0,456.000,0,517.000,1,525.000,1,523.000,1,519.000,1,509.000,1,512.000,1,519.000,1,517.000,1,510.000,1,509.000,1,501.000,1,507.000,1,569.000,1,580.000,1,578.000,1,565.000,1,547.000,1,555.000,1,562.000,1,561.000,1,555.000,1,544.000,1,537.000,1,543.000,1,594.000,1,611.000,1,613.000,1,611.000,1,594.000,1,595.000,1),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
1 493 0
2 481 0
3 462 0
4 457 0
5 442 0
6 439 0
7 488 0
8 521 0
9 501 0
10 485 0
11 464 0
12 460 0
13 467 0
14 460 0
15 448 0
16 443 0
17 436 0
18 431 0
19 484 0
20 510 0
21 513 0
22 503 0
23 471 0
24 471 0
25 476 0
26 475 0
27 470 0
28 461 0
29 455 0
30 456 0
31 517 1
32 525 1
33 523 1
34 519 1
35 509 1
36 512 1
37 519 1
38 517 1
39 510 1
40 509 1
41 501 1
42 507 1
43 569 1
44 580 1
45 578 1
46 565 1
47 547 1
48 555 1
49 562 1
50 561 1
51 555 1
52 544 1
53 537 1
54 543 1
55 594 1
56 611 1
57 613 1
58 611 1
59 594 1
60 595 1
> k <- length(x[1,])
> df <- as.data.frame(x)
> (mylm <- lm(df))
Call:
lm(formula = df)
Coefficients:
(Intercept) x
470.77 78.63
> (mysum <- summary(mylm))
Call:
lm(formula = df)
Residuals:
Min 1Q Median 3Q Max
-48.400 -26.742 -3.083 17.825 63.600
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 470.767 5.488 85.78 < 2e-16 ***
x 78.633 7.762 10.13 1.91e-14 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 30.06 on 58 degrees of freedom
Multiple R-squared: 0.6389, Adjusted R-squared: 0.6327
F-statistic: 102.6 on 1 and 58 DF, p-value: 1.911e-14
> postscript(file="/var/www/html/rcomp/tmp/1gi551229082490.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/2mw171229082490.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556)
> plot(mysum$resid, type='b', pch=19, main='Residuals', ylab='value of Residuals', xlab='time or index')
> grid()
> dev.off()
null device
1
> postscript(file="/var/www/html/rcomp/tmp/3qg701229082490.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556)
> hist(mysum$resid, main='Residual Histogram', xlab='values of Residuals')
> grid()
> dev.off()
null device
1
> postscript(file="/var/www/html/rcomp/tmp/4euhr1229082490.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556)
> densityplot(~mysum$resid,col='black',main='Residual Density Plot', xlab='values of Residuals')
> dev.off()
null device
1
> postscript(file="/var/www/html/rcomp/tmp/5qh0f1229082490.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556)
> qqnorm(mysum$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
22.2333333 10.2333333 -8.7666667 -13.7666667 -28.7666667 -31.7666667
7 8 9 10 11 12
17.2333333 50.2333333 30.2333333 14.2333333 -6.7666667 -10.7666667
13 14 15 16 17 18
-3.7666667 -10.7666667 -22.7666667 -27.7666667 -34.7666667 -39.7666667
19 20 21 22 23 24
13.2333333 39.2333333 42.2333333 32.2333333 0.2333333 0.2333333
25 26 27 28 29 30
5.2333333 4.2333333 -0.7666667 -9.7666667 -15.7666667 -14.7666667
31 32 33 34 35 36
-32.4000000 -24.4000000 -26.4000000 -30.4000000 -40.4000000 -37.4000000
37 38 39 40 41 42
-30.4000000 -32.4000000 -39.4000000 -40.4000000 -48.4000000 -42.4000000
43 44 45 46 47 48
19.6000000 30.6000000 28.6000000 15.6000000 -2.4000000 5.6000000
49 50 51 52 53 54
12.6000000 11.6000000 5.6000000 -5.4000000 -12.4000000 -6.4000000
55 56 57 58 59 60
44.6000000 61.6000000 63.6000000 61.6000000 44.6000000 45.6000000
> postscript(file="/var/www/html/rcomp/tmp/61yz81229082490.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 22.2333333 NA
1 10.2333333 22.2333333
2 -8.7666667 10.2333333
3 -13.7666667 -8.7666667
4 -28.7666667 -13.7666667
5 -31.7666667 -28.7666667
6 17.2333333 -31.7666667
7 50.2333333 17.2333333
8 30.2333333 50.2333333
9 14.2333333 30.2333333
10 -6.7666667 14.2333333
11 -10.7666667 -6.7666667
12 -3.7666667 -10.7666667
13 -10.7666667 -3.7666667
14 -22.7666667 -10.7666667
15 -27.7666667 -22.7666667
16 -34.7666667 -27.7666667
17 -39.7666667 -34.7666667
18 13.2333333 -39.7666667
19 39.2333333 13.2333333
20 42.2333333 39.2333333
21 32.2333333 42.2333333
22 0.2333333 32.2333333
23 0.2333333 0.2333333
24 5.2333333 0.2333333
25 4.2333333 5.2333333
26 -0.7666667 4.2333333
27 -9.7666667 -0.7666667
28 -15.7666667 -9.7666667
29 -14.7666667 -15.7666667
30 -32.4000000 -14.7666667
31 -24.4000000 -32.4000000
32 -26.4000000 -24.4000000
33 -30.4000000 -26.4000000
34 -40.4000000 -30.4000000
35 -37.4000000 -40.4000000
36 -30.4000000 -37.4000000
37 -32.4000000 -30.4000000
38 -39.4000000 -32.4000000
39 -40.4000000 -39.4000000
40 -48.4000000 -40.4000000
41 -42.4000000 -48.4000000
42 19.6000000 -42.4000000
43 30.6000000 19.6000000
44 28.6000000 30.6000000
45 15.6000000 28.6000000
46 -2.4000000 15.6000000
47 5.6000000 -2.4000000
48 12.6000000 5.6000000
49 11.6000000 12.6000000
50 5.6000000 11.6000000
51 -5.4000000 5.6000000
52 -12.4000000 -5.4000000
53 -6.4000000 -12.4000000
54 44.6000000 -6.4000000
55 61.6000000 44.6000000
56 63.6000000 61.6000000
57 61.6000000 63.6000000
58 44.6000000 61.6000000
59 45.6000000 44.6000000
60 NA 45.6000000
> dum1 <- dum[2:length(myerror),]
> dum1
lag(myerror, k = 1) myerror
[1,] 10.2333333 22.2333333
[2,] -8.7666667 10.2333333
[3,] -13.7666667 -8.7666667
[4,] -28.7666667 -13.7666667
[5,] -31.7666667 -28.7666667
[6,] 17.2333333 -31.7666667
[7,] 50.2333333 17.2333333
[8,] 30.2333333 50.2333333
[9,] 14.2333333 30.2333333
[10,] -6.7666667 14.2333333
[11,] -10.7666667 -6.7666667
[12,] -3.7666667 -10.7666667
[13,] -10.7666667 -3.7666667
[14,] -22.7666667 -10.7666667
[15,] -27.7666667 -22.7666667
[16,] -34.7666667 -27.7666667
[17,] -39.7666667 -34.7666667
[18,] 13.2333333 -39.7666667
[19,] 39.2333333 13.2333333
[20,] 42.2333333 39.2333333
[21,] 32.2333333 42.2333333
[22,] 0.2333333 32.2333333
[23,] 0.2333333 0.2333333
[24,] 5.2333333 0.2333333
[25,] 4.2333333 5.2333333
[26,] -0.7666667 4.2333333
[27,] -9.7666667 -0.7666667
[28,] -15.7666667 -9.7666667
[29,] -14.7666667 -15.7666667
[30,] -32.4000000 -14.7666667
[31,] -24.4000000 -32.4000000
[32,] -26.4000000 -24.4000000
[33,] -30.4000000 -26.4000000
[34,] -40.4000000 -30.4000000
[35,] -37.4000000 -40.4000000
[36,] -30.4000000 -37.4000000
[37,] -32.4000000 -30.4000000
[38,] -39.4000000 -32.4000000
[39,] -40.4000000 -39.4000000
[40,] -48.4000000 -40.4000000
[41,] -42.4000000 -48.4000000
[42,] 19.6000000 -42.4000000
[43,] 30.6000000 19.6000000
[44,] 28.6000000 30.6000000
[45,] 15.6000000 28.6000000
[46,] -2.4000000 15.6000000
[47,] 5.6000000 -2.4000000
[48,] 12.6000000 5.6000000
[49,] 11.6000000 12.6000000
[50,] 5.6000000 11.6000000
[51,] -5.4000000 5.6000000
[52,] -12.4000000 -5.4000000
[53,] -6.4000000 -12.4000000
[54,] 44.6000000 -6.4000000
[55,] 61.6000000 44.6000000
[56,] 63.6000000 61.6000000
[57,] 61.6000000 63.6000000
[58,] 44.6000000 61.6000000
[59,] 45.6000000 44.6000000
> z <- as.data.frame(dum1)
> z
lag(myerror, k = 1) myerror
1 10.2333333 22.2333333
2 -8.7666667 10.2333333
3 -13.7666667 -8.7666667
4 -28.7666667 -13.7666667
5 -31.7666667 -28.7666667
6 17.2333333 -31.7666667
7 50.2333333 17.2333333
8 30.2333333 50.2333333
9 14.2333333 30.2333333
10 -6.7666667 14.2333333
11 -10.7666667 -6.7666667
12 -3.7666667 -10.7666667
13 -10.7666667 -3.7666667
14 -22.7666667 -10.7666667
15 -27.7666667 -22.7666667
16 -34.7666667 -27.7666667
17 -39.7666667 -34.7666667
18 13.2333333 -39.7666667
19 39.2333333 13.2333333
20 42.2333333 39.2333333
21 32.2333333 42.2333333
22 0.2333333 32.2333333
23 0.2333333 0.2333333
24 5.2333333 0.2333333
25 4.2333333 5.2333333
26 -0.7666667 4.2333333
27 -9.7666667 -0.7666667
28 -15.7666667 -9.7666667
29 -14.7666667 -15.7666667
30 -32.4000000 -14.7666667
31 -24.4000000 -32.4000000
32 -26.4000000 -24.4000000
33 -30.4000000 -26.4000000
34 -40.4000000 -30.4000000
35 -37.4000000 -40.4000000
36 -30.4000000 -37.4000000
37 -32.4000000 -30.4000000
38 -39.4000000 -32.4000000
39 -40.4000000 -39.4000000
40 -48.4000000 -40.4000000
41 -42.4000000 -48.4000000
42 19.6000000 -42.4000000
43 30.6000000 19.6000000
44 28.6000000 30.6000000
45 15.6000000 28.6000000
46 -2.4000000 15.6000000
47 5.6000000 -2.4000000
48 12.6000000 5.6000000
49 11.6000000 12.6000000
50 5.6000000 11.6000000
51 -5.4000000 5.6000000
52 -12.4000000 -5.4000000
53 -6.4000000 -12.4000000
54 44.6000000 -6.4000000
55 61.6000000 44.6000000
56 63.6000000 61.6000000
57 61.6000000 63.6000000
58 44.6000000 61.6000000
59 45.6000000 44.6000000
> 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/7gxil1229082490.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556)
> acf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Autocorrelation Function')
> grid()
> dev.off()
null device
1
> postscript(file="/var/www/html/rcomp/tmp/8w6pt1229082490.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556)
> pacf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Partial Autocorrelation Function')
> grid()
> dev.off()
null device
1
> postscript(file="/var/www/html/rcomp/tmp/9u0w31229082490.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556)
> opar <- par(mfrow = c(2,2), oma = c(0, 0, 1.1, 0))
> plot(mylm, las = 1, sub='Residual Diagnostics')
hat values (leverages) are all = 0.03333333
and there are no factor predictors; no plot no. 5
> par(opar)
> dev.off()
null device
1
>
> #Note: the /var/www/html/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab
> load(file="/var/www/html/rcomp/createtable")
>
> a<-table.start()
> a<-table.row.start(a)
> a<-table.element(a, 'Multiple Linear Regression - Estimated Regression Equation', 1, TRUE)
> a<-table.row.end(a)
> myeq <- colnames(x)[1]
> myeq <- paste(myeq, '[t] = ', sep='')
> for (i in 1:k){
+ if (mysum$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/105yaq1229082490.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/11hiyo1229082490.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/12je7h1229082490.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/13pols1229082490.tab")
>
> system("convert tmp/1gi551229082490.ps tmp/1gi551229082490.png")
> system("convert tmp/2mw171229082490.ps tmp/2mw171229082490.png")
> system("convert tmp/3qg701229082490.ps tmp/3qg701229082490.png")
> system("convert tmp/4euhr1229082490.ps tmp/4euhr1229082490.png")
> system("convert tmp/5qh0f1229082490.ps tmp/5qh0f1229082490.png")
> system("convert tmp/61yz81229082490.ps tmp/61yz81229082490.png")
> system("convert tmp/7gxil1229082490.ps tmp/7gxil1229082490.png")
> system("convert tmp/8w6pt1229082490.ps tmp/8w6pt1229082490.png")
> system("convert tmp/9u0w31229082490.ps tmp/9u0w31229082490.png")
>
>
> proc.time()
user system elapsed
1.897 1.394 2.361