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.
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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(6.5
+ ,15.8
+ ,6.8
+ ,7.5
+ ,8
+ ,8.2
+ ,6.6
+ ,15.8
+ ,6.5
+ ,6.8
+ ,7.5
+ ,8
+ ,7.6
+ ,23.2
+ ,6.6
+ ,6.5
+ ,6.8
+ ,7.5
+ ,8
+ ,23.2
+ ,7.6
+ ,6.6
+ ,6.5
+ ,6.8
+ ,8.1
+ ,23.2
+ ,8
+ ,7.6
+ ,6.6
+ ,6.5
+ ,7.7
+ ,20.9
+ ,8.1
+ ,8
+ ,7.6
+ ,6.6
+ ,7.5
+ ,20.9
+ ,7.7
+ ,8.1
+ ,8
+ ,7.6
+ ,7.6
+ ,20.9
+ ,7.5
+ ,7.7
+ ,8.1
+ ,8
+ ,7.8
+ ,19.8
+ ,7.6
+ ,7.5
+ ,7.7
+ ,8.1
+ ,7.8
+ ,19.8
+ ,7.8
+ ,7.6
+ ,7.5
+ ,7.7
+ ,7.8
+ ,19.8
+ ,7.8
+ ,7.8
+ ,7.6
+ ,7.5
+ ,7.5
+ ,20.6
+ ,7.8
+ ,7.8
+ ,7.8
+ ,7.6
+ ,7.5
+ ,20.6
+ ,7.5
+ ,7.8
+ ,7.8
+ ,7.8
+ ,7.1
+ ,20.6
+ ,7.5
+ ,7.5
+ ,7.8
+ ,7.8
+ ,7.5
+ ,21.1
+ ,7.1
+ ,7.5
+ ,7.5
+ ,7.8
+ ,7.5
+ ,21.1
+ ,7.5
+ ,7.1
+ ,7.5
+ ,7.5
+ ,7.6
+ ,21.1
+ ,7.5
+ ,7.5
+ ,7.1
+ ,7.5
+ ,7.7
+ ,22.4
+ ,7.6
+ ,7.5
+ ,7.5
+ ,7.1
+ ,7.7
+ ,22.4
+ ,7.7
+ ,7.6
+ ,7.5
+ ,7.5
+ ,7.9
+ ,22.4
+ ,7.7
+ ,7.7
+ ,7.6
+ ,7.5
+ ,8.1
+ ,20.5
+ ,7.9
+ ,7.7
+ ,7.7
+ ,7.6
+ ,8.2
+ ,20.5
+ ,8.1
+ ,7.9
+ ,7.7
+ ,7.7
+ ,8.2
+ ,20.5
+ ,8.2
+ ,8.1
+ ,7.9
+ ,7.7
+ ,8.2
+ ,18.4
+ ,8.2
+ ,8.2
+ ,8.1
+ ,7.9
+ ,7.9
+ ,18.4
+ ,8.2
+ ,8.2
+ ,8.2
+ ,8.1
+ ,7.3
+ ,18.4
+ ,7.9
+ ,8.2
+ ,8.2
+ ,8.2
+ ,6.9
+ ,17.6
+ ,7.3
+ ,7.9
+ ,8.2
+ ,8.2
+ ,6.6
+ ,17.6
+ ,6.9
+ ,7.3
+ ,7.9
+ ,8.2
+ ,6.7
+ ,17.6
+ ,6.6
+ ,6.9
+ ,7.3
+ ,7.9
+ ,6.9
+ ,18.5
+ ,6.7
+ ,6.6
+ ,6.9
+ ,7.3
+ ,7
+ ,18.5
+ ,6.9
+ ,6.7
+ ,6.6
+ ,6.9
+ ,7.1
+ ,18.5
+ ,7
+ ,6.9
+ ,6.7
+ ,6.6
+ ,7.2
+ ,17.3
+ ,7.1
+ ,7
+ ,6.9
+ ,6.7
+ ,7.1
+ ,17.3
+ ,7.2
+ ,7.1
+ ,7
+ ,6.9
+ ,6.9
+ ,17.3
+ ,7.1
+ ,7.2
+ ,7.1
+ ,7
+ ,7
+ ,16.2
+ ,6.9
+ ,7.1
+ ,7.2
+ ,7.1
+ ,6.8
+ ,16.2
+ ,7
+ ,6.9
+ ,7.1
+ ,7.2
+ ,6.4
+ ,16.2
+ ,6.8
+ ,7
+ ,6.9
+ ,7.1
+ ,6.7
+ ,18.5
+ ,6.4
+ ,6.8
+ ,7
+ ,6.9
+ ,6.6
+ ,18.5
+ ,6.7
+ ,6.4
+ ,6.8
+ ,7
+ ,6.4
+ ,18.5
+ ,6.6
+ ,6.7
+ ,6.4
+ ,6.8
+ ,6.3
+ ,16.3
+ ,6.4
+ ,6.6
+ ,6.7
+ ,6.4
+ ,6.2
+ ,16.3
+ ,6.3
+ ,6.4
+ ,6.6
+ ,6.7
+ ,6.5
+ ,16.3
+ ,6.2
+ ,6.3
+ ,6.4
+ ,6.6
+ ,6.8
+ ,16.8
+ ,6.5
+ ,6.2
+ ,6.3
+ ,6.4
+ ,6.8
+ ,16.8
+ ,6.8
+ ,6.5
+ ,6.2
+ ,6.3
+ ,6.4
+ ,16.8
+ ,6.8
+ ,6.8
+ ,6.5
+ ,6.2
+ ,6.1
+ ,14.8
+ ,6.4
+ ,6.8
+ ,6.8
+ ,6.5
+ ,5.8
+ ,14.8
+ ,6.1
+ ,6.4
+ ,6.8
+ ,6.8
+ ,6.1
+ ,14.8
+ ,5.8
+ ,6.1
+ ,6.4
+ ,6.8
+ ,7.2
+ ,21.4
+ ,6.1
+ ,5.8
+ ,6.1
+ ,6.4
+ ,7.3
+ ,21.4
+ ,7.2
+ ,6.1
+ ,5.8
+ ,6.1
+ ,6.9
+ ,21.4
+ ,7.3
+ ,7.2
+ ,6.1
+ ,5.8
+ ,6.1
+ ,16.1
+ ,6.9
+ ,7.3
+ ,7.2
+ ,6.1
+ ,5.8
+ ,16.1
+ ,6.1
+ ,6.9
+ ,7.3
+ ,7.2
+ ,6.2
+ ,16.1
+ ,5.8
+ ,6.1
+ ,6.9
+ ,7.3
+ ,7.1
+ ,19.6
+ ,6.2
+ ,5.8
+ ,6.1
+ ,6.9
+ ,7.7
+ ,19.6
+ ,7.1
+ ,6.2
+ ,5.8
+ ,6.1
+ ,7.9
+ ,19.6
+ ,7.7
+ ,7.1
+ ,6.2
+ ,5.8
+ ,7.7
+ ,18.9
+ ,7.9
+ ,7.7
+ ,7.1
+ ,6.2
+ ,7.4
+ ,18.9
+ ,7.7
+ ,7.9
+ ,7.7
+ ,7.1
+ ,7.5
+ ,18.9
+ ,7.4
+ ,7.7
+ ,7.9
+ ,7.7
+ ,8
+ ,21.9
+ ,7.5
+ ,7.4
+ ,7.7
+ ,7.9
+ ,8.1
+ ,21.9
+ ,8
+ ,7.5
+ ,7.4
+ ,7.7
+ ,8
+ ,21.9
+ ,8.1
+ ,8
+ ,7.5
+ ,7.4)
+ ,dim=c(6
+ ,65)
+ ,dimnames=list(c('Y'
+ ,'X'
+ ,'Y(t-1)'
+ ,'Y(t-2)'
+ ,'Y(t-3)'
+ ,'Y(t-4)')
+ ,1:65))
> y <- array(NA,dim=c(6,65),dimnames=list(c('Y','X','Y(t-1)','Y(t-2)','Y(t-3)','Y(t-4)'),1:65))
> for (i in 1:dim(x)[1])
+ {
+ for (j in 1:dim(x)[2])
+ {
+ y[i,j] <- as.numeric(x[i,j])
+ }
+ }
> par3 = 'Linear Trend'
> par2 = 'Include Monthly 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)
> library(lmtest)
Loading required package: zoo
Attaching package: 'zoo'
The following object(s) are masked from package:base :
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
Y X Y(t-1) Y(t-2) Y(t-3) Y(t-4) M1 M2 M3 M4 M5 M6 M7 M8 M9 M10 M11 t
1 6.5 15.8 6.8 7.5 8.0 8.2 1 0 0 0 0 0 0 0 0 0 0 1
2 6.6 15.8 6.5 6.8 7.5 8.0 0 1 0 0 0 0 0 0 0 0 0 2
3 7.6 23.2 6.6 6.5 6.8 7.5 0 0 1 0 0 0 0 0 0 0 0 3
4 8.0 23.2 7.6 6.6 6.5 6.8 0 0 0 1 0 0 0 0 0 0 0 4
5 8.1 23.2 8.0 7.6 6.6 6.5 0 0 0 0 1 0 0 0 0 0 0 5
6 7.7 20.9 8.1 8.0 7.6 6.6 0 0 0 0 0 1 0 0 0 0 0 6
7 7.5 20.9 7.7 8.1 8.0 7.6 0 0 0 0 0 0 1 0 0 0 0 7
8 7.6 20.9 7.5 7.7 8.1 8.0 0 0 0 0 0 0 0 1 0 0 0 8
9 7.8 19.8 7.6 7.5 7.7 8.1 0 0 0 0 0 0 0 0 1 0 0 9
10 7.8 19.8 7.8 7.6 7.5 7.7 0 0 0 0 0 0 0 0 0 1 0 10
11 7.8 19.8 7.8 7.8 7.6 7.5 0 0 0 0 0 0 0 0 0 0 1 11
12 7.5 20.6 7.8 7.8 7.8 7.6 0 0 0 0 0 0 0 0 0 0 0 12
13 7.5 20.6 7.5 7.8 7.8 7.8 1 0 0 0 0 0 0 0 0 0 0 13
14 7.1 20.6 7.5 7.5 7.8 7.8 0 1 0 0 0 0 0 0 0 0 0 14
15 7.5 21.1 7.1 7.5 7.5 7.8 0 0 1 0 0 0 0 0 0 0 0 15
16 7.5 21.1 7.5 7.1 7.5 7.5 0 0 0 1 0 0 0 0 0 0 0 16
17 7.6 21.1 7.5 7.5 7.1 7.5 0 0 0 0 1 0 0 0 0 0 0 17
18 7.7 22.4 7.6 7.5 7.5 7.1 0 0 0 0 0 1 0 0 0 0 0 18
19 7.7 22.4 7.7 7.6 7.5 7.5 0 0 0 0 0 0 1 0 0 0 0 19
20 7.9 22.4 7.7 7.7 7.6 7.5 0 0 0 0 0 0 0 1 0 0 0 20
21 8.1 20.5 7.9 7.7 7.7 7.6 0 0 0 0 0 0 0 0 1 0 0 21
22 8.2 20.5 8.1 7.9 7.7 7.7 0 0 0 0 0 0 0 0 0 1 0 22
23 8.2 20.5 8.2 8.1 7.9 7.7 0 0 0 0 0 0 0 0 0 0 1 23
24 8.2 18.4 8.2 8.2 8.1 7.9 0 0 0 0 0 0 0 0 0 0 0 24
25 7.9 18.4 8.2 8.2 8.2 8.1 1 0 0 0 0 0 0 0 0 0 0 25
26 7.3 18.4 7.9 8.2 8.2 8.2 0 1 0 0 0 0 0 0 0 0 0 26
27 6.9 17.6 7.3 7.9 8.2 8.2 0 0 1 0 0 0 0 0 0 0 0 27
28 6.6 17.6 6.9 7.3 7.9 8.2 0 0 0 1 0 0 0 0 0 0 0 28
29 6.7 17.6 6.6 6.9 7.3 7.9 0 0 0 0 1 0 0 0 0 0 0 29
30 6.9 18.5 6.7 6.6 6.9 7.3 0 0 0 0 0 1 0 0 0 0 0 30
31 7.0 18.5 6.9 6.7 6.6 6.9 0 0 0 0 0 0 1 0 0 0 0 31
32 7.1 18.5 7.0 6.9 6.7 6.6 0 0 0 0 0 0 0 1 0 0 0 32
33 7.2 17.3 7.1 7.0 6.9 6.7 0 0 0 0 0 0 0 0 1 0 0 33
34 7.1 17.3 7.2 7.1 7.0 6.9 0 0 0 0 0 0 0 0 0 1 0 34
35 6.9 17.3 7.1 7.2 7.1 7.0 0 0 0 0 0 0 0 0 0 0 1 35
36 7.0 16.2 6.9 7.1 7.2 7.1 0 0 0 0 0 0 0 0 0 0 0 36
37 6.8 16.2 7.0 6.9 7.1 7.2 1 0 0 0 0 0 0 0 0 0 0 37
38 6.4 16.2 6.8 7.0 6.9 7.1 0 1 0 0 0 0 0 0 0 0 0 38
39 6.7 18.5 6.4 6.8 7.0 6.9 0 0 1 0 0 0 0 0 0 0 0 39
40 6.6 18.5 6.7 6.4 6.8 7.0 0 0 0 1 0 0 0 0 0 0 0 40
41 6.4 18.5 6.6 6.7 6.4 6.8 0 0 0 0 1 0 0 0 0 0 0 41
42 6.3 16.3 6.4 6.6 6.7 6.4 0 0 0 0 0 1 0 0 0 0 0 42
43 6.2 16.3 6.3 6.4 6.6 6.7 0 0 0 0 0 0 1 0 0 0 0 43
44 6.5 16.3 6.2 6.3 6.4 6.6 0 0 0 0 0 0 0 1 0 0 0 44
45 6.8 16.8 6.5 6.2 6.3 6.4 0 0 0 0 0 0 0 0 1 0 0 45
46 6.8 16.8 6.8 6.5 6.2 6.3 0 0 0 0 0 0 0 0 0 1 0 46
47 6.4 16.8 6.8 6.8 6.5 6.2 0 0 0 0 0 0 0 0 0 0 1 47
48 6.1 14.8 6.4 6.8 6.8 6.5 0 0 0 0 0 0 0 0 0 0 0 48
49 5.8 14.8 6.1 6.4 6.8 6.8 1 0 0 0 0 0 0 0 0 0 0 49
50 6.1 14.8 5.8 6.1 6.4 6.8 0 1 0 0 0 0 0 0 0 0 0 50
51 7.2 21.4 6.1 5.8 6.1 6.4 0 0 1 0 0 0 0 0 0 0 0 51
52 7.3 21.4 7.2 6.1 5.8 6.1 0 0 0 1 0 0 0 0 0 0 0 52
53 6.9 21.4 7.3 7.2 6.1 5.8 0 0 0 0 1 0 0 0 0 0 0 53
54 6.1 16.1 6.9 7.3 7.2 6.1 0 0 0 0 0 1 0 0 0 0 0 54
55 5.8 16.1 6.1 6.9 7.3 7.2 0 0 0 0 0 0 1 0 0 0 0 55
56 6.2 16.1 5.8 6.1 6.9 7.3 0 0 0 0 0 0 0 1 0 0 0 56
57 7.1 19.6 6.2 5.8 6.1 6.9 0 0 0 0 0 0 0 0 1 0 0 57
58 7.7 19.6 7.1 6.2 5.8 6.1 0 0 0 0 0 0 0 0 0 1 0 58
59 7.9 19.6 7.7 7.1 6.2 5.8 0 0 0 0 0 0 0 0 0 0 1 59
60 7.7 18.9 7.9 7.7 7.1 6.2 0 0 0 0 0 0 0 0 0 0 0 60
61 7.4 18.9 7.7 7.9 7.7 7.1 1 0 0 0 0 0 0 0 0 0 0 61
62 7.5 18.9 7.4 7.7 7.9 7.7 0 1 0 0 0 0 0 0 0 0 0 62
63 8.0 21.9 7.5 7.4 7.7 7.9 0 0 1 0 0 0 0 0 0 0 0 63
64 8.1 21.9 8.0 7.5 7.4 7.7 0 0 0 1 0 0 0 0 0 0 0 64
65 8.0 21.9 8.1 8.0 7.5 7.4 0 0 0 0 1 0 0 0 0 0 0 65
> k <- length(x[1,])
> df <- as.data.frame(x)
> (mylm <- lm(df))
Call:
lm(formula = df)
Coefficients:
(Intercept) X `Y(t-1)` `Y(t-2)` `Y(t-3)` `Y(t-4)`
0.043844 0.091191 1.102428 -0.486419 -0.188442 0.342364
M1 M2 M3 M4 M5 M6
-0.189339 -0.248582 0.003343 -0.535099 -0.353680 -0.188467
M7 M8 M9 M10 M11 t
-0.259621 -0.046703 -0.013266 -0.113339 -0.086442 0.001888
> (mysum <- summary(mylm))
Call:
lm(formula = df)
Residuals:
Min 1Q Median 3Q Max
-0.42089 -0.08001 0.03089 0.08638 0.31174
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 0.043844 0.401943 0.109 0.913603
X 0.091191 0.021500 4.241 0.000103 ***
`Y(t-1)` 1.102428 0.156443 7.047 6.94e-09 ***
`Y(t-2)` -0.486419 0.229403 -2.120 0.039281 *
`Y(t-3)` -0.188442 0.221128 -0.852 0.398434
`Y(t-4)` 0.342364 0.118904 2.879 0.005982 **
M1 -0.189339 0.106143 -1.784 0.080911 .
M2 -0.248582 0.111660 -2.226 0.030829 *
M3 0.003343 0.140870 0.024 0.981168
M4 -0.535099 0.126357 -4.235 0.000106 ***
M5 -0.353680 0.143484 -2.465 0.017413 *
M6 -0.188467 0.119133 -1.582 0.120358
M7 -0.259621 0.121117 -2.144 0.037274 *
M8 -0.046703 0.121031 -0.386 0.701326
M9 -0.013266 0.117847 -0.113 0.910850
M10 -0.113339 0.117581 -0.964 0.340021
M11 -0.086442 0.111035 -0.779 0.440173
t 0.001888 0.001441 1.310 0.196590
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 0.1696 on 47 degrees of freedom
Multiple R-squared: 0.9517, Adjusted R-squared: 0.9343
F-statistic: 54.5 on 17 and 47 DF, p-value: < 2.2e-16
> 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
+ }
[,1] [,2] [,3]
[1,] 0.4909449 0.9818899 0.5090551
[2,] 0.5095054 0.9809892 0.4904946
[3,] 0.4933360 0.9866719 0.5066640
[4,] 0.6925896 0.6148208 0.3074104
[5,] 0.6257946 0.7484107 0.3742054
[6,] 0.6244046 0.7511908 0.3755954
[7,] 0.8470317 0.3059366 0.1529683
[8,] 0.7885944 0.4228112 0.2114056
[9,] 0.7475941 0.5048119 0.2524059
[10,] 0.7332660 0.5334680 0.2667340
[11,] 0.6506798 0.6986404 0.3493202
[12,] 0.5580440 0.8839120 0.4419560
[13,] 0.4995484 0.9990967 0.5004516
[14,] 0.3936543 0.7873086 0.6063457
[15,] 0.3241271 0.6482543 0.6758729
[16,] 0.3421524 0.6843048 0.6578476
[17,] 0.2585591 0.5171183 0.7414409
[18,] 0.4562748 0.9125497 0.5437252
[19,] 0.4100851 0.8201701 0.5899149
[20,] 0.3977337 0.7954674 0.6022663
[21,] 0.3400304 0.6800607 0.6599696
[22,] 0.3019276 0.6038552 0.6980724
[23,] 0.1881431 0.3762862 0.8118569
[24,] 0.2682375 0.5364750 0.7317625
> postscript(file="/var/www/html/rcomp/tmp/126lx1258667848.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$resid)
> grid()
> dev.off()
null device
1
> postscript(file="/var/www/html/rcomp/tmp/2ukfb1258667848.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556)
> plot(mysum$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/3fvyl1258667848.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556)
> hist(mysum$resid, main='Residual Histogram', xlab='values of Residuals')
> grid()
> dev.off()
null device
1
> postscript(file="/var/www/html/rcomp/tmp/44dm31258667848.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556)
> densityplot(~mysum$resid,col='black',main='Residual Density Plot', xlab='values of Residuals')
> dev.off()
null device
1
> postscript(file="/var/www/html/rcomp/tmp/591a81258667848.ps",horizontal=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 = 65
Frequency = 1
1 2 3 4 5
0.0545659900 0.1764081565 0.0308855639 0.0967764553 0.1804707870
6 7 8 9 10
0.0616400574 0.1535311062 -0.0534577193 -0.1056123632 -0.0800140127
11 12 13 14 15
0.0758021106 -0.3820283630 0.0676784769 -0.4208921244 0.0641381940
16 17 18 19 20
0.0678631344 0.1037469850 0.0201777712 -0.1091032778 -0.0564223683
21 22 23 24 25
0.0456377895 0.0863841834 0.0823287832 0.2033579820 0.0411805688
26 27 28 29 30
-0.2049723022 -0.2703011289 0.0588405923 0.1013385389 -0.0739605236
31 32 33 34 35
0.0038746460 -0.0023360024 0.1136192873 0.0005743116 -0.0847180072
36 37 38 39 40
0.1837141461 -0.0894418208 -0.1664110559 0.1010410570 -0.0596253363
41 42 43 44 45
-0.1936676967 0.1051742952 -0.0341546089 0.1091891891 -0.0014730518
46 47 48 49 50
-0.0726988420 -0.2647888906 -0.0759417388 -0.1550390029 0.3117421090
51 52 53 54 55
0.1598270518 -0.2241868236 -0.2234337845 -0.1130316001 -0.0141478655
56 57 58 59 60
0.0030269009 -0.0521716618 0.0657543597 0.1913760041 0.0708979737
61 62 63 64 65
0.0810557879 0.3041252169 -0.0855907378 0.0603319778 0.0315451702
> postscript(file="/var/www/html/rcomp/tmp/6q97j1258667848.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 = 65
Frequency = 1
lag(myerror, k = 1) myerror
0 0.0545659900 NA
1 0.1764081565 0.0545659900
2 0.0308855639 0.1764081565
3 0.0967764553 0.0308855639
4 0.1804707870 0.0967764553
5 0.0616400574 0.1804707870
6 0.1535311062 0.0616400574
7 -0.0534577193 0.1535311062
8 -0.1056123632 -0.0534577193
9 -0.0800140127 -0.1056123632
10 0.0758021106 -0.0800140127
11 -0.3820283630 0.0758021106
12 0.0676784769 -0.3820283630
13 -0.4208921244 0.0676784769
14 0.0641381940 -0.4208921244
15 0.0678631344 0.0641381940
16 0.1037469850 0.0678631344
17 0.0201777712 0.1037469850
18 -0.1091032778 0.0201777712
19 -0.0564223683 -0.1091032778
20 0.0456377895 -0.0564223683
21 0.0863841834 0.0456377895
22 0.0823287832 0.0863841834
23 0.2033579820 0.0823287832
24 0.0411805688 0.2033579820
25 -0.2049723022 0.0411805688
26 -0.2703011289 -0.2049723022
27 0.0588405923 -0.2703011289
28 0.1013385389 0.0588405923
29 -0.0739605236 0.1013385389
30 0.0038746460 -0.0739605236
31 -0.0023360024 0.0038746460
32 0.1136192873 -0.0023360024
33 0.0005743116 0.1136192873
34 -0.0847180072 0.0005743116
35 0.1837141461 -0.0847180072
36 -0.0894418208 0.1837141461
37 -0.1664110559 -0.0894418208
38 0.1010410570 -0.1664110559
39 -0.0596253363 0.1010410570
40 -0.1936676967 -0.0596253363
41 0.1051742952 -0.1936676967
42 -0.0341546089 0.1051742952
43 0.1091891891 -0.0341546089
44 -0.0014730518 0.1091891891
45 -0.0726988420 -0.0014730518
46 -0.2647888906 -0.0726988420
47 -0.0759417388 -0.2647888906
48 -0.1550390029 -0.0759417388
49 0.3117421090 -0.1550390029
50 0.1598270518 0.3117421090
51 -0.2241868236 0.1598270518
52 -0.2234337845 -0.2241868236
53 -0.1130316001 -0.2234337845
54 -0.0141478655 -0.1130316001
55 0.0030269009 -0.0141478655
56 -0.0521716618 0.0030269009
57 0.0657543597 -0.0521716618
58 0.1913760041 0.0657543597
59 0.0708979737 0.1913760041
60 0.0810557879 0.0708979737
61 0.3041252169 0.0810557879
62 -0.0855907378 0.3041252169
63 0.0603319778 -0.0855907378
64 0.0315451702 0.0603319778
65 NA 0.0315451702
> dum1 <- dum[2:length(myerror),]
> dum1
lag(myerror, k = 1) myerror
[1,] 0.1764081565 0.0545659900
[2,] 0.0308855639 0.1764081565
[3,] 0.0967764553 0.0308855639
[4,] 0.1804707870 0.0967764553
[5,] 0.0616400574 0.1804707870
[6,] 0.1535311062 0.0616400574
[7,] -0.0534577193 0.1535311062
[8,] -0.1056123632 -0.0534577193
[9,] -0.0800140127 -0.1056123632
[10,] 0.0758021106 -0.0800140127
[11,] -0.3820283630 0.0758021106
[12,] 0.0676784769 -0.3820283630
[13,] -0.4208921244 0.0676784769
[14,] 0.0641381940 -0.4208921244
[15,] 0.0678631344 0.0641381940
[16,] 0.1037469850 0.0678631344
[17,] 0.0201777712 0.1037469850
[18,] -0.1091032778 0.0201777712
[19,] -0.0564223683 -0.1091032778
[20,] 0.0456377895 -0.0564223683
[21,] 0.0863841834 0.0456377895
[22,] 0.0823287832 0.0863841834
[23,] 0.2033579820 0.0823287832
[24,] 0.0411805688 0.2033579820
[25,] -0.2049723022 0.0411805688
[26,] -0.2703011289 -0.2049723022
[27,] 0.0588405923 -0.2703011289
[28,] 0.1013385389 0.0588405923
[29,] -0.0739605236 0.1013385389
[30,] 0.0038746460 -0.0739605236
[31,] -0.0023360024 0.0038746460
[32,] 0.1136192873 -0.0023360024
[33,] 0.0005743116 0.1136192873
[34,] -0.0847180072 0.0005743116
[35,] 0.1837141461 -0.0847180072
[36,] -0.0894418208 0.1837141461
[37,] -0.1664110559 -0.0894418208
[38,] 0.1010410570 -0.1664110559
[39,] -0.0596253363 0.1010410570
[40,] -0.1936676967 -0.0596253363
[41,] 0.1051742952 -0.1936676967
[42,] -0.0341546089 0.1051742952
[43,] 0.1091891891 -0.0341546089
[44,] -0.0014730518 0.1091891891
[45,] -0.0726988420 -0.0014730518
[46,] -0.2647888906 -0.0726988420
[47,] -0.0759417388 -0.2647888906
[48,] -0.1550390029 -0.0759417388
[49,] 0.3117421090 -0.1550390029
[50,] 0.1598270518 0.3117421090
[51,] -0.2241868236 0.1598270518
[52,] -0.2234337845 -0.2241868236
[53,] -0.1130316001 -0.2234337845
[54,] -0.0141478655 -0.1130316001
[55,] 0.0030269009 -0.0141478655
[56,] -0.0521716618 0.0030269009
[57,] 0.0657543597 -0.0521716618
[58,] 0.1913760041 0.0657543597
[59,] 0.0708979737 0.1913760041
[60,] 0.0810557879 0.0708979737
[61,] 0.3041252169 0.0810557879
[62,] -0.0855907378 0.3041252169
[63,] 0.0603319778 -0.0855907378
[64,] 0.0315451702 0.0603319778
> z <- as.data.frame(dum1)
> z
lag(myerror, k = 1) myerror
1 0.1764081565 0.0545659900
2 0.0308855639 0.1764081565
3 0.0967764553 0.0308855639
4 0.1804707870 0.0967764553
5 0.0616400574 0.1804707870
6 0.1535311062 0.0616400574
7 -0.0534577193 0.1535311062
8 -0.1056123632 -0.0534577193
9 -0.0800140127 -0.1056123632
10 0.0758021106 -0.0800140127
11 -0.3820283630 0.0758021106
12 0.0676784769 -0.3820283630
13 -0.4208921244 0.0676784769
14 0.0641381940 -0.4208921244
15 0.0678631344 0.0641381940
16 0.1037469850 0.0678631344
17 0.0201777712 0.1037469850
18 -0.1091032778 0.0201777712
19 -0.0564223683 -0.1091032778
20 0.0456377895 -0.0564223683
21 0.0863841834 0.0456377895
22 0.0823287832 0.0863841834
23 0.2033579820 0.0823287832
24 0.0411805688 0.2033579820
25 -0.2049723022 0.0411805688
26 -0.2703011289 -0.2049723022
27 0.0588405923 -0.2703011289
28 0.1013385389 0.0588405923
29 -0.0739605236 0.1013385389
30 0.0038746460 -0.0739605236
31 -0.0023360024 0.0038746460
32 0.1136192873 -0.0023360024
33 0.0005743116 0.1136192873
34 -0.0847180072 0.0005743116
35 0.1837141461 -0.0847180072
36 -0.0894418208 0.1837141461
37 -0.1664110559 -0.0894418208
38 0.1010410570 -0.1664110559
39 -0.0596253363 0.1010410570
40 -0.1936676967 -0.0596253363
41 0.1051742952 -0.1936676967
42 -0.0341546089 0.1051742952
43 0.1091891891 -0.0341546089
44 -0.0014730518 0.1091891891
45 -0.0726988420 -0.0014730518
46 -0.2647888906 -0.0726988420
47 -0.0759417388 -0.2647888906
48 -0.1550390029 -0.0759417388
49 0.3117421090 -0.1550390029
50 0.1598270518 0.3117421090
51 -0.2241868236 0.1598270518
52 -0.2234337845 -0.2241868236
53 -0.1130316001 -0.2234337845
54 -0.0141478655 -0.1130316001
55 0.0030269009 -0.0141478655
56 -0.0521716618 0.0030269009
57 0.0657543597 -0.0521716618
58 0.1913760041 0.0657543597
59 0.0708979737 0.1913760041
60 0.0810557879 0.0708979737
61 0.3041252169 0.0810557879
62 -0.0855907378 0.3041252169
63 0.0603319778 -0.0855907378
64 0.0315451702 0.0603319778
> 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/764os1258667848.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556)
> acf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Autocorrelation Function')
> grid()
> dev.off()
null device
1
> postscript(file="/var/www/html/rcomp/tmp/8nue01258667848.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556)
> pacf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Partial Autocorrelation Function')
> grid()
> dev.off()
null device
1
> postscript(file="/var/www/html/rcomp/tmp/9jk481258667848.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556)
> opar <- par(mfrow = c(2,2), oma = c(0, 0, 1.1, 0))
> plot(mylm, las = 1, sub='Residual Diagnostics')
> par(opar)
> dev.off()
null device
1
> if (n > n25) {
+ postscript(file="/var/www/html/rcomp/tmp/10lxwz1258667848.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556)
+ plot(kp3:nmkm3,gqarr[,2], main='Goldfeld-Quandt test',ylab='2-sided p-value',xlab='breakpoint')
+ grid()
+ dev.off()
+ }
null device
1
>
> #Note: the /var/www/html/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab
> load(file="/var/www/html/rcomp/createtable")
>
> a<-table.start()
> a<-table.row.start(a)
> a<-table.element(a, 'Multiple Linear Regression - Estimated Regression Equation', 1, TRUE)
> a<-table.row.end(a)
> myeq <- colnames(x)[1]
> myeq <- paste(myeq, '[t] = ', sep='')
> for (i in 1:k){
+ if (mysum$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/11u8l21258667848.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/12cb801258667848.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/13dz7i1258667848.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/14se6r1258667848.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,gqarr[mypoint-kp3+1,1])
+ a<-table.element(a,gqarr[mypoint-kp3+1,2])
+ a<-table.element(a,gqarr[mypoint-kp3+1,3])
+ a<-table.row.end(a)
+ }
+ a<-table.end(a)
+ table.save(a,file="/var/www/html/rcomp/tmp/154dui1258667848.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,numsignificant1)
+ a<-table.element(a,numsignificant1/numgqtests)
+ 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,numsignificant5)
+ a<-table.element(a,numsignificant5/numgqtests)
+ 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,numsignificant10)
+ a<-table.element(a,numsignificant10/numgqtests)
+ 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/www/html/rcomp/tmp/1609ij1258667848.tab")
+ }
>
> system("convert tmp/126lx1258667848.ps tmp/126lx1258667848.png")
> system("convert tmp/2ukfb1258667848.ps tmp/2ukfb1258667848.png")
> system("convert tmp/3fvyl1258667848.ps tmp/3fvyl1258667848.png")
> system("convert tmp/44dm31258667848.ps tmp/44dm31258667848.png")
> system("convert tmp/591a81258667848.ps tmp/591a81258667848.png")
> system("convert tmp/6q97j1258667848.ps tmp/6q97j1258667848.png")
> system("convert tmp/764os1258667848.ps tmp/764os1258667848.png")
> system("convert tmp/8nue01258667848.ps tmp/8nue01258667848.png")
> system("convert tmp/9jk481258667848.ps tmp/9jk481258667848.png")
> system("convert tmp/10lxwz1258667848.ps tmp/10lxwz1258667848.png")
>
>
> proc.time()
user system elapsed
2.373 1.586 2.941