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.
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Type 'license()' or 'licence()' for distribution details.
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Type 'contributors()' for more information and
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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(8587
+ ,9743
+ ,9084
+ ,9081
+ ,9700
+ ,9731
+ ,8587
+ ,9743
+ ,9084
+ ,9081
+ ,9563
+ ,9731
+ ,8587
+ ,9743
+ ,9084
+ ,9998
+ ,9563
+ ,9731
+ ,8587
+ ,9743
+ ,9437
+ ,9998
+ ,9563
+ ,9731
+ ,8587
+ ,10038
+ ,9437
+ ,9998
+ ,9563
+ ,9731
+ ,9918
+ ,10038
+ ,9437
+ ,9998
+ ,9563
+ ,9252
+ ,9918
+ ,10038
+ ,9437
+ ,9998
+ ,9737
+ ,9252
+ ,9918
+ ,10038
+ ,9437
+ ,9035
+ ,9737
+ ,9252
+ ,9918
+ ,10038
+ ,9133
+ ,9035
+ ,9737
+ ,9252
+ ,9918
+ ,9487
+ ,9133
+ ,9035
+ ,9737
+ ,9252
+ ,8700
+ ,9487
+ ,9133
+ ,9035
+ ,9737
+ ,9627
+ ,8700
+ ,9487
+ ,9133
+ ,9035
+ ,8947
+ ,9627
+ ,8700
+ ,9487
+ ,9133
+ ,9283
+ ,8947
+ ,9627
+ ,8700
+ ,9487
+ ,8829
+ ,9283
+ ,8947
+ ,9627
+ ,8700
+ ,9947
+ ,8829
+ ,9283
+ ,8947
+ ,9627
+ ,9628
+ ,9947
+ ,8829
+ ,9283
+ ,8947
+ ,9318
+ ,9628
+ ,9947
+ ,8829
+ ,9283
+ ,9605
+ ,9318
+ ,9628
+ ,9947
+ ,8829
+ ,8640
+ ,9605
+ ,9318
+ ,9628
+ ,9947
+ ,9214
+ ,8640
+ ,9605
+ ,9318
+ ,9628
+ ,9567
+ ,9214
+ ,8640
+ ,9605
+ ,9318
+ ,8547
+ ,9567
+ ,9214
+ ,8640
+ ,9605
+ ,9185
+ ,8547
+ ,9567
+ ,9214
+ ,8640
+ ,9470
+ ,9185
+ ,8547
+ ,9567
+ ,9214
+ ,9123
+ ,9470
+ ,9185
+ ,8547
+ ,9567
+ ,9278
+ ,9123
+ ,9470
+ ,9185
+ ,8547
+ ,10170
+ ,9278
+ ,9123
+ ,9470
+ ,9185
+ ,9434
+ ,10170
+ ,9278
+ ,9123
+ ,9470
+ ,9655
+ ,9434
+ ,10170
+ ,9278
+ ,9123
+ ,9429
+ ,9655
+ ,9434
+ ,10170
+ ,9278
+ ,8739
+ ,9429
+ ,9655
+ ,9434
+ ,10170
+ ,9552
+ ,8739
+ ,9429
+ ,9655
+ ,9434
+ ,9687
+ ,9552
+ ,8739
+ ,9429
+ ,9655
+ ,9019
+ ,9687
+ ,9552
+ ,8739
+ ,9429
+ ,9672
+ ,9019
+ ,9687
+ ,9552
+ ,8739
+ ,9206
+ ,9672
+ ,9019
+ ,9687
+ ,9552
+ ,9069
+ ,9206
+ ,9672
+ ,9019
+ ,9687
+ ,9788
+ ,9069
+ ,9206
+ ,9672
+ ,9019
+ ,10312
+ ,9788
+ ,9069
+ ,9206
+ ,9672
+ ,10105
+ ,10312
+ ,9788
+ ,9069
+ ,9206
+ ,9863
+ ,10105
+ ,10312
+ ,9788
+ ,9069
+ ,9656
+ ,9863
+ ,10105
+ ,10312
+ ,9788
+ ,9295
+ ,9656
+ ,9863
+ ,10105
+ ,10312
+ ,9946
+ ,9295
+ ,9656
+ ,9863
+ ,10105
+ ,9701
+ ,9946
+ ,9295
+ ,9656
+ ,9863
+ ,9049
+ ,9701
+ ,9946
+ ,9295
+ ,9656
+ ,10190
+ ,9049
+ ,9701
+ ,9946
+ ,9295
+ ,9706
+ ,10190
+ ,9049
+ ,9701
+ ,9946
+ ,9765
+ ,9706
+ ,10190
+ ,9049
+ ,9701
+ ,9893
+ ,9765
+ ,9706
+ ,10190
+ ,9049
+ ,9994
+ ,9893
+ ,9765
+ ,9706
+ ,10190
+ ,10433
+ ,9994
+ ,9893
+ ,9765
+ ,9706
+ ,10073
+ ,10433
+ ,9994
+ ,9893
+ ,9765
+ ,10112
+ ,10073
+ ,10433
+ ,9994
+ ,9893
+ ,9266
+ ,10112
+ ,10073
+ ,10433
+ ,9994
+ ,9820
+ ,9266
+ ,10112
+ ,10073
+ ,10433
+ ,10097
+ ,9820
+ ,9266
+ ,10112
+ ,10073
+ ,9115
+ ,10097
+ ,9820
+ ,9266
+ ,10112
+ ,10411
+ ,9115
+ ,10097
+ ,9820
+ ,9266
+ ,9678
+ ,10411
+ ,9115
+ ,10097
+ ,9820
+ ,10408
+ ,9678
+ ,10411
+ ,9115
+ ,10097
+ ,10153
+ ,10408
+ ,9678
+ ,10411
+ ,9115
+ ,10368
+ ,10153
+ ,10408
+ ,9678
+ ,10411
+ ,10581
+ ,10368
+ ,10153
+ ,10408
+ ,9678
+ ,10597
+ ,10581
+ ,10368
+ ,10153
+ ,10408
+ ,10680
+ ,10597
+ ,10581
+ ,10368
+ ,10153
+ ,9738
+ ,10680
+ ,10597
+ ,10581
+ ,10368
+ ,9556
+ ,9738
+ ,10680
+ ,10597
+ ,10581)
+ ,dim=c(5
+ ,71)
+ ,dimnames=list(c('MontlyBirths'
+ ,'Y1'
+ ,'Y2'
+ ,'Y3'
+ ,'Y4')
+ ,1:71))
> y <- array(NA,dim=c(5,71),dimnames=list(c('MontlyBirths','Y1','Y2','Y3','Y4'),1:71))
> 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
MontlyBirths Y1 Y2 Y3 Y4 M1 M2 M3 M4 M5 M6 M7 M8 M9 M10 M11 t
1 8587 9743 9084 9081 9700 1 0 0 0 0 0 0 0 0 0 0 1
2 9731 8587 9743 9084 9081 0 1 0 0 0 0 0 0 0 0 0 2
3 9563 9731 8587 9743 9084 0 0 1 0 0 0 0 0 0 0 0 3
4 9998 9563 9731 8587 9743 0 0 0 1 0 0 0 0 0 0 0 4
5 9437 9998 9563 9731 8587 0 0 0 0 1 0 0 0 0 0 0 5
6 10038 9437 9998 9563 9731 0 0 0 0 0 1 0 0 0 0 0 6
7 9918 10038 9437 9998 9563 0 0 0 0 0 0 1 0 0 0 0 7
8 9252 9918 10038 9437 9998 0 0 0 0 0 0 0 1 0 0 0 8
9 9737 9252 9918 10038 9437 0 0 0 0 0 0 0 0 1 0 0 9
10 9035 9737 9252 9918 10038 0 0 0 0 0 0 0 0 0 1 0 10
11 9133 9035 9737 9252 9918 0 0 0 0 0 0 0 0 0 0 1 11
12 9487 9133 9035 9737 9252 0 0 0 0 0 0 0 0 0 0 0 12
13 8700 9487 9133 9035 9737 1 0 0 0 0 0 0 0 0 0 0 13
14 9627 8700 9487 9133 9035 0 1 0 0 0 0 0 0 0 0 0 14
15 8947 9627 8700 9487 9133 0 0 1 0 0 0 0 0 0 0 0 15
16 9283 8947 9627 8700 9487 0 0 0 1 0 0 0 0 0 0 0 16
17 8829 9283 8947 9627 8700 0 0 0 0 1 0 0 0 0 0 0 17
18 9947 8829 9283 8947 9627 0 0 0 0 0 1 0 0 0 0 0 18
19 9628 9947 8829 9283 8947 0 0 0 0 0 0 1 0 0 0 0 19
20 9318 9628 9947 8829 9283 0 0 0 0 0 0 0 1 0 0 0 20
21 9605 9318 9628 9947 8829 0 0 0 0 0 0 0 0 1 0 0 21
22 8640 9605 9318 9628 9947 0 0 0 0 0 0 0 0 0 1 0 22
23 9214 8640 9605 9318 9628 0 0 0 0 0 0 0 0 0 0 1 23
24 9567 9214 8640 9605 9318 0 0 0 0 0 0 0 0 0 0 0 24
25 8547 9567 9214 8640 9605 1 0 0 0 0 0 0 0 0 0 0 25
26 9185 8547 9567 9214 8640 0 1 0 0 0 0 0 0 0 0 0 26
27 9470 9185 8547 9567 9214 0 0 1 0 0 0 0 0 0 0 0 27
28 9123 9470 9185 8547 9567 0 0 0 1 0 0 0 0 0 0 0 28
29 9278 9123 9470 9185 8547 0 0 0 0 1 0 0 0 0 0 0 29
30 10170 9278 9123 9470 9185 0 0 0 0 0 1 0 0 0 0 0 30
31 9434 10170 9278 9123 9470 0 0 0 0 0 0 1 0 0 0 0 31
32 9655 9434 10170 9278 9123 0 0 0 0 0 0 0 1 0 0 0 32
33 9429 9655 9434 10170 9278 0 0 0 0 0 0 0 0 1 0 0 33
34 8739 9429 9655 9434 10170 0 0 0 0 0 0 0 0 0 1 0 34
35 9552 8739 9429 9655 9434 0 0 0 0 0 0 0 0 0 0 1 35
36 9687 9552 8739 9429 9655 0 0 0 0 0 0 0 0 0 0 0 36
37 9019 9687 9552 8739 9429 1 0 0 0 0 0 0 0 0 0 0 37
38 9672 9019 9687 9552 8739 0 1 0 0 0 0 0 0 0 0 0 38
39 9206 9672 9019 9687 9552 0 0 1 0 0 0 0 0 0 0 0 39
40 9069 9206 9672 9019 9687 0 0 0 1 0 0 0 0 0 0 0 40
41 9788 9069 9206 9672 9019 0 0 0 0 1 0 0 0 0 0 0 41
42 10312 9788 9069 9206 9672 0 0 0 0 0 1 0 0 0 0 0 42
43 10105 10312 9788 9069 9206 0 0 0 0 0 0 1 0 0 0 0 43
44 9863 10105 10312 9788 9069 0 0 0 0 0 0 0 1 0 0 0 44
45 9656 9863 10105 10312 9788 0 0 0 0 0 0 0 0 1 0 0 45
46 9295 9656 9863 10105 10312 0 0 0 0 0 0 0 0 0 1 0 46
47 9946 9295 9656 9863 10105 0 0 0 0 0 0 0 0 0 0 1 47
48 9701 9946 9295 9656 9863 0 0 0 0 0 0 0 0 0 0 0 48
49 9049 9701 9946 9295 9656 1 0 0 0 0 0 0 0 0 0 0 49
50 10190 9049 9701 9946 9295 0 1 0 0 0 0 0 0 0 0 0 50
51 9706 10190 9049 9701 9946 0 0 1 0 0 0 0 0 0 0 0 51
52 9765 9706 10190 9049 9701 0 0 0 1 0 0 0 0 0 0 0 52
53 9893 9765 9706 10190 9049 0 0 0 0 1 0 0 0 0 0 0 53
54 9994 9893 9765 9706 10190 0 0 0 0 0 1 0 0 0 0 0 54
55 10433 9994 9893 9765 9706 0 0 0 0 0 0 1 0 0 0 0 55
56 10073 10433 9994 9893 9765 0 0 0 0 0 0 0 1 0 0 0 56
57 10112 10073 10433 9994 9893 0 0 0 0 0 0 0 0 1 0 0 57
58 9266 10112 10073 10433 9994 0 0 0 0 0 0 0 0 0 1 0 58
59 9820 9266 10112 10073 10433 0 0 0 0 0 0 0 0 0 0 1 59
60 10097 9820 9266 10112 10073 0 0 0 0 0 0 0 0 0 0 0 60
61 9115 10097 9820 9266 10112 1 0 0 0 0 0 0 0 0 0 0 61
62 10411 9115 10097 9820 9266 0 1 0 0 0 0 0 0 0 0 0 62
63 9678 10411 9115 10097 9820 0 0 1 0 0 0 0 0 0 0 0 63
64 10408 9678 10411 9115 10097 0 0 0 1 0 0 0 0 0 0 0 64
65 10153 10408 9678 10411 9115 0 0 0 0 1 0 0 0 0 0 0 65
66 10368 10153 10408 9678 10411 0 0 0 0 0 1 0 0 0 0 0 66
67 10581 10368 10153 10408 9678 0 0 0 0 0 0 1 0 0 0 0 67
68 10597 10581 10368 10153 10408 0 0 0 0 0 0 0 1 0 0 0 68
69 10680 10597 10581 10368 10153 0 0 0 0 0 0 0 0 1 0 0 69
70 9738 10680 10597 10581 10368 0 0 0 0 0 0 0 0 0 1 0 70
71 9556 9738 10680 10597 10581 0 0 0 0 0 0 0 0 0 0 1 71
> k <- length(x[1,])
> df <- as.data.frame(x)
> (mylm <- lm(df))
Call:
lm(formula = df)
Coefficients:
(Intercept) Y1 Y2 Y3 Y4 M1
3873.0530 0.1248 0.1649 0.2438 0.0617 -777.0071
M2 M3 M4 M5 M6 M7
184.9309 -260.9220 -1.6281 -194.0146 383.2153 170.9164
M8 M9 M10 M11 t
-137.9781 -156.2182 -891.3542 -335.8468 5.5708
> (mysum <- summary(mylm))
Call:
lm(formula = df)
Residuals:
Min 1Q Median 3Q Max
-589.67 -125.36 30.63 145.79 611.40
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 3873.0530 1593.6498 2.430 0.018439 *
Y1 0.1248 0.1435 0.870 0.388305
Y2 0.1649 0.1364 1.209 0.231842
Y3 0.2438 0.1370 1.780 0.080728 .
Y4 0.0617 0.1454 0.424 0.673079
M1 -777.0071 209.2133 -3.714 0.000485 ***
M2 184.9309 235.6375 0.785 0.435994
M3 -260.9220 173.8839 -1.501 0.139296
M4 -1.6281 239.6472 -0.007 0.994605
M5 -194.0146 219.0306 -0.886 0.379660
M6 383.2153 190.3282 2.013 0.049063 *
M7 170.9164 207.8565 0.822 0.414533
M8 -137.9781 234.7006 -0.588 0.559057
M9 -156.2182 214.4775 -0.728 0.469536
M10 -891.3542 190.6922 -4.674 2.01e-05 ***
M11 -335.8468 219.2813 -1.532 0.131464
t 5.5708 2.5409 2.192 0.032678 *
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 271.2 on 54 degrees of freedom
Multiple R-squared: 0.7811, Adjusted R-squared: 0.7162
F-statistic: 12.04 on 16 and 54 DF, p-value: 1.578e-12
> 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,] 0.8333408 0.3333185 0.16665924
[2,] 0.7267811 0.5464379 0.27321894
[3,] 0.6275789 0.7448423 0.37242113
[4,] 0.6541686 0.6916628 0.34583140
[5,] 0.6226066 0.7547868 0.37739338
[6,] 0.5452219 0.9095562 0.45477810
[7,] 0.5028409 0.9943183 0.49715913
[8,] 0.7292019 0.5415961 0.27079807
[9,] 0.6900551 0.6198897 0.30994486
[10,] 0.6321827 0.7356346 0.36781729
[11,] 0.8009910 0.3980181 0.19900904
[12,] 0.7845360 0.4309280 0.21546399
[13,] 0.7732045 0.4535909 0.22679545
[14,] 0.7070788 0.5858423 0.29292116
[15,] 0.7030583 0.5938834 0.29694172
[16,] 0.7014823 0.5970353 0.29851766
[17,] 0.6845584 0.6308831 0.31544156
[18,] 0.6780457 0.6439086 0.32195428
[19,] 0.5970055 0.8059890 0.40299450
[20,] 0.5180592 0.9638816 0.48194078
[21,] 0.7352855 0.5294290 0.26471451
[22,] 0.8182628 0.3634745 0.18173723
[23,] 0.8078586 0.3842828 0.19214141
[24,] 0.7940648 0.4118704 0.20593518
[25,] 0.7512177 0.4975647 0.24878233
[26,] 0.6903204 0.6193592 0.30967961
[27,] 0.6069083 0.7861834 0.39309172
[28,] 0.8392603 0.3214793 0.16073967
[29,] 0.7494196 0.5011608 0.25058039
[30,] 0.9240691 0.1518618 0.07593088
[31,] 0.8492059 0.3015882 0.15079411
[32,] 0.7518977 0.4962046 0.24810229
> postscript(file="/var/www/html/rcomp/tmp/1ff401290800775.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$resid)
> grid()
> dev.off()
null device
1
> postscript(file="/var/www/html/rcomp/tmp/2ff401290800775.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556)
> plot(mysum$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/3ff401290800775.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556)
> hist(mysum$resid, main='Residual Histogram', xlab='values of Residuals')
> grid()
> dev.off()
null device
1
> postscript(file="/var/www/html/rcomp/tmp/48pll1290800775.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556)
> densityplot(~mysum$resid,col='black',main='Residual Density Plot', xlab='values of Residuals')
> dev.off()
null device
1
> postscript(file="/var/www/html/rcomp/tmp/58pll1290800775.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 = 71
Frequency = 1
1 2 3 4 5 6
-41.081269 208.521986 367.754904 611.396727 3.035196 -10.083550
7 8 9 10 11 12
-1.565477 -338.429657 150.261830 219.269341 -66.373787 -27.422962
13 14 15 16 17 18
37.880000 56.669361 -261.355964 -88.158142 -462.603065 182.454235
19 20 21 22 23 24
-34.486336 -95.731591 50.688152 -160.669706 20.655069 68.854422
25 26 27 28 29 30
-100.870090 -441.646805 250.699577 -275.053359 -29.518023 208.702640
31 32 33 34 35 36
-390.469923 62.277355 -284.311544 -128.577440 238.278689 85.601328
37 38 39 40 41 42
220.292264 -188.715315 -268.880843 -565.718585 316.055656 263.403981
43 44 45 46 47 48
141.315178 -24.753540 -326.850288 125.593563 366.482304 -176.284540
49 50 51 52 53 54
-32.823569 126.023597 66.935266 -92.575051 56.741548 -403.169657
55 56 57 58 59 60
224.322895 61.344033 53.049347 -122.151058 30.631862 49.251752
61 62 63 64 65 66
-83.397336 239.147176 -155.152940 410.108410 116.288687 -241.307649
67 68 69 70 71
60.883663 335.293401 357.162503 66.535300 -589.674138
> postscript(file="/var/www/html/rcomp/tmp/68pll1290800775.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 = 71
Frequency = 1
lag(myerror, k = 1) myerror
0 -41.081269 NA
1 208.521986 -41.081269
2 367.754904 208.521986
3 611.396727 367.754904
4 3.035196 611.396727
5 -10.083550 3.035196
6 -1.565477 -10.083550
7 -338.429657 -1.565477
8 150.261830 -338.429657
9 219.269341 150.261830
10 -66.373787 219.269341
11 -27.422962 -66.373787
12 37.880000 -27.422962
13 56.669361 37.880000
14 -261.355964 56.669361
15 -88.158142 -261.355964
16 -462.603065 -88.158142
17 182.454235 -462.603065
18 -34.486336 182.454235
19 -95.731591 -34.486336
20 50.688152 -95.731591
21 -160.669706 50.688152
22 20.655069 -160.669706
23 68.854422 20.655069
24 -100.870090 68.854422
25 -441.646805 -100.870090
26 250.699577 -441.646805
27 -275.053359 250.699577
28 -29.518023 -275.053359
29 208.702640 -29.518023
30 -390.469923 208.702640
31 62.277355 -390.469923
32 -284.311544 62.277355
33 -128.577440 -284.311544
34 238.278689 -128.577440
35 85.601328 238.278689
36 220.292264 85.601328
37 -188.715315 220.292264
38 -268.880843 -188.715315
39 -565.718585 -268.880843
40 316.055656 -565.718585
41 263.403981 316.055656
42 141.315178 263.403981
43 -24.753540 141.315178
44 -326.850288 -24.753540
45 125.593563 -326.850288
46 366.482304 125.593563
47 -176.284540 366.482304
48 -32.823569 -176.284540
49 126.023597 -32.823569
50 66.935266 126.023597
51 -92.575051 66.935266
52 56.741548 -92.575051
53 -403.169657 56.741548
54 224.322895 -403.169657
55 61.344033 224.322895
56 53.049347 61.344033
57 -122.151058 53.049347
58 30.631862 -122.151058
59 49.251752 30.631862
60 -83.397336 49.251752
61 239.147176 -83.397336
62 -155.152940 239.147176
63 410.108410 -155.152940
64 116.288687 410.108410
65 -241.307649 116.288687
66 60.883663 -241.307649
67 335.293401 60.883663
68 357.162503 335.293401
69 66.535300 357.162503
70 -589.674138 66.535300
71 NA -589.674138
> dum1 <- dum[2:length(myerror),]
> dum1
lag(myerror, k = 1) myerror
[1,] 208.521986 -41.081269
[2,] 367.754904 208.521986
[3,] 611.396727 367.754904
[4,] 3.035196 611.396727
[5,] -10.083550 3.035196
[6,] -1.565477 -10.083550
[7,] -338.429657 -1.565477
[8,] 150.261830 -338.429657
[9,] 219.269341 150.261830
[10,] -66.373787 219.269341
[11,] -27.422962 -66.373787
[12,] 37.880000 -27.422962
[13,] 56.669361 37.880000
[14,] -261.355964 56.669361
[15,] -88.158142 -261.355964
[16,] -462.603065 -88.158142
[17,] 182.454235 -462.603065
[18,] -34.486336 182.454235
[19,] -95.731591 -34.486336
[20,] 50.688152 -95.731591
[21,] -160.669706 50.688152
[22,] 20.655069 -160.669706
[23,] 68.854422 20.655069
[24,] -100.870090 68.854422
[25,] -441.646805 -100.870090
[26,] 250.699577 -441.646805
[27,] -275.053359 250.699577
[28,] -29.518023 -275.053359
[29,] 208.702640 -29.518023
[30,] -390.469923 208.702640
[31,] 62.277355 -390.469923
[32,] -284.311544 62.277355
[33,] -128.577440 -284.311544
[34,] 238.278689 -128.577440
[35,] 85.601328 238.278689
[36,] 220.292264 85.601328
[37,] -188.715315 220.292264
[38,] -268.880843 -188.715315
[39,] -565.718585 -268.880843
[40,] 316.055656 -565.718585
[41,] 263.403981 316.055656
[42,] 141.315178 263.403981
[43,] -24.753540 141.315178
[44,] -326.850288 -24.753540
[45,] 125.593563 -326.850288
[46,] 366.482304 125.593563
[47,] -176.284540 366.482304
[48,] -32.823569 -176.284540
[49,] 126.023597 -32.823569
[50,] 66.935266 126.023597
[51,] -92.575051 66.935266
[52,] 56.741548 -92.575051
[53,] -403.169657 56.741548
[54,] 224.322895 -403.169657
[55,] 61.344033 224.322895
[56,] 53.049347 61.344033
[57,] -122.151058 53.049347
[58,] 30.631862 -122.151058
[59,] 49.251752 30.631862
[60,] -83.397336 49.251752
[61,] 239.147176 -83.397336
[62,] -155.152940 239.147176
[63,] 410.108410 -155.152940
[64,] 116.288687 410.108410
[65,] -241.307649 116.288687
[66,] 60.883663 -241.307649
[67,] 335.293401 60.883663
[68,] 357.162503 335.293401
[69,] 66.535300 357.162503
[70,] -589.674138 66.535300
> z <- as.data.frame(dum1)
> z
lag(myerror, k = 1) myerror
1 208.521986 -41.081269
2 367.754904 208.521986
3 611.396727 367.754904
4 3.035196 611.396727
5 -10.083550 3.035196
6 -1.565477 -10.083550
7 -338.429657 -1.565477
8 150.261830 -338.429657
9 219.269341 150.261830
10 -66.373787 219.269341
11 -27.422962 -66.373787
12 37.880000 -27.422962
13 56.669361 37.880000
14 -261.355964 56.669361
15 -88.158142 -261.355964
16 -462.603065 -88.158142
17 182.454235 -462.603065
18 -34.486336 182.454235
19 -95.731591 -34.486336
20 50.688152 -95.731591
21 -160.669706 50.688152
22 20.655069 -160.669706
23 68.854422 20.655069
24 -100.870090 68.854422
25 -441.646805 -100.870090
26 250.699577 -441.646805
27 -275.053359 250.699577
28 -29.518023 -275.053359
29 208.702640 -29.518023
30 -390.469923 208.702640
31 62.277355 -390.469923
32 -284.311544 62.277355
33 -128.577440 -284.311544
34 238.278689 -128.577440
35 85.601328 238.278689
36 220.292264 85.601328
37 -188.715315 220.292264
38 -268.880843 -188.715315
39 -565.718585 -268.880843
40 316.055656 -565.718585
41 263.403981 316.055656
42 141.315178 263.403981
43 -24.753540 141.315178
44 -326.850288 -24.753540
45 125.593563 -326.850288
46 366.482304 125.593563
47 -176.284540 366.482304
48 -32.823569 -176.284540
49 126.023597 -32.823569
50 66.935266 126.023597
51 -92.575051 66.935266
52 56.741548 -92.575051
53 -403.169657 56.741548
54 224.322895 -403.169657
55 61.344033 224.322895
56 53.049347 61.344033
57 -122.151058 53.049347
58 30.631862 -122.151058
59 49.251752 30.631862
60 -83.397336 49.251752
61 239.147176 -83.397336
62 -155.152940 239.147176
63 410.108410 -155.152940
64 116.288687 410.108410
65 -241.307649 116.288687
66 60.883663 -241.307649
67 335.293401 60.883663
68 357.162503 335.293401
69 66.535300 357.162503
70 -589.674138 66.535300
> 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/7iylo1290800775.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556)
> acf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Autocorrelation Function')
> grid()
> dev.off()
null device
1
> postscript(file="/var/www/html/rcomp/tmp/8t72r1290800775.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556)
> pacf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Partial Autocorrelation Function')
> grid()
> dev.off()
null device
1
> postscript(file="/var/www/html/rcomp/tmp/9t72r1290800775.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556)
> opar <- par(mfrow = c(2,2), oma = c(0, 0, 1.1, 0))
> plot(mylm, las = 1, sub='Residual Diagnostics')
> par(opar)
> dev.off()
null device
1
> if (n > n25) {
+ postscript(file="/var/www/html/rcomp/tmp/10my1u1290800775.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556)
+ plot(kp3:nmkm3,gqarr[,2], main='Goldfeld-Quandt test',ylab='2-sided p-value',xlab='breakpoint')
+ grid()
+ dev.off()
+ }
null device
1
>
> #Note: the /var/www/html/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab
> load(file="/var/www/html/rcomp/createtable")
>
> a<-table.start()
> a<-table.row.start(a)
> a<-table.element(a, 'Multiple Linear Regression - Estimated Regression Equation', 1, TRUE)
> a<-table.row.end(a)
> myeq <- colnames(x)[1]
> myeq <- paste(myeq, '[t] = ', sep='')
> for (i in 1:k){
+ if (mysum$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/11pz001290800775.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/12iqhl1290800775.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/1379wf1290800775.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/14z0dz1290800775.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/153jun1290800775.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/16zbrw1290800775.tab")
+ }
>
> try(system("convert tmp/1ff401290800775.ps tmp/1ff401290800775.png",intern=TRUE))
character(0)
> try(system("convert tmp/2ff401290800775.ps tmp/2ff401290800775.png",intern=TRUE))
character(0)
> try(system("convert tmp/3ff401290800775.ps tmp/3ff401290800775.png",intern=TRUE))
character(0)
> try(system("convert tmp/48pll1290800775.ps tmp/48pll1290800775.png",intern=TRUE))
character(0)
> try(system("convert tmp/58pll1290800775.ps tmp/58pll1290800775.png",intern=TRUE))
character(0)
> try(system("convert tmp/68pll1290800775.ps tmp/68pll1290800775.png",intern=TRUE))
character(0)
> try(system("convert tmp/7iylo1290800775.ps tmp/7iylo1290800775.png",intern=TRUE))
character(0)
> try(system("convert tmp/8t72r1290800775.ps tmp/8t72r1290800775.png",intern=TRUE))
character(0)
> try(system("convert tmp/9t72r1290800775.ps tmp/9t72r1290800775.png",intern=TRUE))
character(0)
> try(system("convert tmp/10my1u1290800775.ps tmp/10my1u1290800775.png",intern=TRUE))
character(0)
>
>
> proc.time()
user system elapsed
2.554 1.630 6.858