R version 2.9.0 (2009-04-17)
Copyright (C) 2009 The R Foundation for Statistical Computing
ISBN 3-900051-07-0
R is free software and comes with ABSOLUTELY NO WARRANTY.
You are welcome to redistribute it under certain conditions.
Type 'license()' or 'licence()' for distribution details.
R is a collaborative project with many contributors.
Type 'contributors()' for more information and
'citation()' on how to cite R or R packages in publications.
Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.
> x <- array(list(318672
+ ,441977
+ ,326225
+ ,327532
+ ,338653
+ ,344744
+ ,317756
+ ,439148
+ ,318672
+ ,326225
+ ,327532
+ ,338653
+ ,337302
+ ,488180
+ ,317756
+ ,318672
+ ,326225
+ ,327532
+ ,349420
+ ,520564
+ ,337302
+ ,317756
+ ,318672
+ ,326225
+ ,336923
+ ,501492
+ ,349420
+ ,337302
+ ,317756
+ ,318672
+ ,330758
+ ,485025
+ ,336923
+ ,349420
+ ,337302
+ ,317756
+ ,321002
+ ,464196
+ ,330758
+ ,336923
+ ,349420
+ ,337302
+ ,320820
+ ,460170
+ ,321002
+ ,330758
+ ,336923
+ ,349420
+ ,327032
+ ,467037
+ ,320820
+ ,321002
+ ,330758
+ ,336923
+ ,324047
+ ,460070
+ ,327032
+ ,320820
+ ,321002
+ ,330758
+ ,316735
+ ,447988
+ ,324047
+ ,327032
+ ,320820
+ ,321002
+ ,315710
+ ,442867
+ ,316735
+ ,324047
+ ,327032
+ ,320820
+ ,313427
+ ,436087
+ ,315710
+ ,316735
+ ,324047
+ ,327032
+ ,310527
+ ,431328
+ ,313427
+ ,315710
+ ,316735
+ ,324047
+ ,330962
+ ,484015
+ ,310527
+ ,313427
+ ,315710
+ ,316735
+ ,339015
+ ,509673
+ ,330962
+ ,310527
+ ,313427
+ ,315710
+ ,341332
+ ,512927
+ ,339015
+ ,330962
+ ,310527
+ ,313427
+ ,339092
+ ,502831
+ ,341332
+ ,339015
+ ,330962
+ ,310527
+ ,323308
+ ,470984
+ ,339092
+ ,341332
+ ,339015
+ ,330962
+ ,325849
+ ,471067
+ ,323308
+ ,339092
+ ,341332
+ ,339015
+ ,330675
+ ,476049
+ ,325849
+ ,323308
+ ,339092
+ ,341332
+ ,332225
+ ,474605
+ ,330675
+ ,325849
+ ,323308
+ ,339092
+ ,331735
+ ,470439
+ ,332225
+ ,330675
+ ,325849
+ ,323308
+ ,328047
+ ,461251
+ ,331735
+ ,332225
+ ,330675
+ ,325849
+ ,326165
+ ,454724
+ ,328047
+ ,331735
+ ,332225
+ ,330675
+ ,327081
+ ,455626
+ ,326165
+ ,328047
+ ,331735
+ ,332225
+ ,346764
+ ,516847
+ ,327081
+ ,326165
+ ,328047
+ ,331735
+ ,344190
+ ,525192
+ ,346764
+ ,327081
+ ,326165
+ ,328047
+ ,343333
+ ,522975
+ ,344190
+ ,346764
+ ,327081
+ ,326165
+ ,345777
+ ,518585
+ ,343333
+ ,344190
+ ,346764
+ ,327081
+ ,344094
+ ,509239
+ ,345777
+ ,343333
+ ,344190
+ ,346764
+ ,348609
+ ,512238
+ ,344094
+ ,345777
+ ,343333
+ ,344190
+ ,354846
+ ,519164
+ ,348609
+ ,344094
+ ,345777
+ ,343333
+ ,356427
+ ,517009
+ ,354846
+ ,348609
+ ,344094
+ ,345777
+ ,353467
+ ,509933
+ ,356427
+ ,354846
+ ,348609
+ ,344094
+ ,355996
+ ,509127
+ ,353467
+ ,356427
+ ,354846
+ ,348609
+ ,352487
+ ,500857
+ ,355996
+ ,353467
+ ,356427
+ ,354846
+ ,355178
+ ,506971
+ ,352487
+ ,355996
+ ,353467
+ ,356427
+ ,374556
+ ,569323
+ ,355178
+ ,352487
+ ,355996
+ ,353467
+ ,375021
+ ,579714
+ ,374556
+ ,355178
+ ,352487
+ ,355996
+ ,375787
+ ,577992
+ ,375021
+ ,374556
+ ,355178
+ ,352487
+ ,372720
+ ,565464
+ ,375787
+ ,375021
+ ,374556
+ ,355178
+ ,364431
+ ,547344
+ ,372720
+ ,375787
+ ,375021
+ ,374556
+ ,370490
+ ,554788
+ ,364431
+ ,372720
+ ,375787
+ ,375021
+ ,376974
+ ,562325
+ ,370490
+ ,364431
+ ,372720
+ ,375787
+ ,377632
+ ,560854
+ ,376974
+ ,370490
+ ,364431
+ ,372720
+ ,378205
+ ,555332
+ ,377632
+ ,376974
+ ,370490
+ ,364431
+ ,370861
+ ,543599
+ ,378205
+ ,377632
+ ,376974
+ ,370490
+ ,369167
+ ,536662
+ ,370861
+ ,378205
+ ,377632
+ ,376974
+ ,371551
+ ,542722
+ ,369167
+ ,370861
+ ,378205
+ ,377632
+ ,382842
+ ,593530
+ ,371551
+ ,369167
+ ,370861
+ ,378205
+ ,381903
+ ,610763
+ ,382842
+ ,371551
+ ,369167
+ ,370861
+ ,384502
+ ,612613
+ ,381903
+ ,382842
+ ,371551
+ ,369167
+ ,392058
+ ,611324
+ ,384502
+ ,381903
+ ,382842
+ ,371551
+ ,384359
+ ,594167
+ ,392058
+ ,384502
+ ,381903
+ ,382842
+ ,388884
+ ,595454
+ ,384359
+ ,392058
+ ,384502
+ ,381903
+ ,386586
+ ,590865
+ ,388884
+ ,384359
+ ,392058
+ ,384502
+ ,387495
+ ,589379
+ ,386586
+ ,388884
+ ,384359
+ ,392058
+ ,385705
+ ,584428
+ ,387495
+ ,386586
+ ,388884
+ ,384359
+ ,378670
+ ,573100
+ ,385705
+ ,387495
+ ,386586
+ ,388884
+ ,377367
+ ,567456
+ ,378670
+ ,385705
+ ,387495
+ ,386586
+ ,376911
+ ,569028
+ ,377367
+ ,378670
+ ,385705
+ ,387495
+ ,389827
+ ,620735
+ ,376911
+ ,377367
+ ,378670
+ ,385705
+ ,387820
+ ,628884
+ ,389827
+ ,376911
+ ,377367
+ ,378670
+ ,387267
+ ,628232
+ ,387820
+ ,389827
+ ,376911
+ ,377367
+ ,380575
+ ,612117
+ ,387267
+ ,387820
+ ,389827
+ ,376911
+ ,372402
+ ,595404
+ ,380575
+ ,387267
+ ,387820
+ ,389827
+ ,376740
+ ,597141
+ ,372402
+ ,380575
+ ,387267
+ ,387820)
+ ,dim=c(6
+ ,68)
+ ,dimnames=list(c('Y'
+ ,'X'
+ ,'yt-1'
+ ,'yt-2'
+ ,'yt-3'
+ ,'yt-4')
+ ,1:68))
> y <- array(NA,dim=c(6,68),dimnames=list(c('Y','X','yt-1','yt-2','yt-3','yt-4'),1:68))
> 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 yt-1 yt-2 yt-3 yt-4 M1 M2 M3 M4 M5 M6 M7 M8 M9 M10 M11
1 318672 441977 326225 327532 338653 344744 1 0 0 0 0 0 0 0 0 0 0
2 317756 439148 318672 326225 327532 338653 0 1 0 0 0 0 0 0 0 0 0
3 337302 488180 317756 318672 326225 327532 0 0 1 0 0 0 0 0 0 0 0
4 349420 520564 337302 317756 318672 326225 0 0 0 1 0 0 0 0 0 0 0
5 336923 501492 349420 337302 317756 318672 0 0 0 0 1 0 0 0 0 0 0
6 330758 485025 336923 349420 337302 317756 0 0 0 0 0 1 0 0 0 0 0
7 321002 464196 330758 336923 349420 337302 0 0 0 0 0 0 1 0 0 0 0
8 320820 460170 321002 330758 336923 349420 0 0 0 0 0 0 0 1 0 0 0
9 327032 467037 320820 321002 330758 336923 0 0 0 0 0 0 0 0 1 0 0
10 324047 460070 327032 320820 321002 330758 0 0 0 0 0 0 0 0 0 1 0
11 316735 447988 324047 327032 320820 321002 0 0 0 0 0 0 0 0 0 0 1
12 315710 442867 316735 324047 327032 320820 0 0 0 0 0 0 0 0 0 0 0
13 313427 436087 315710 316735 324047 327032 1 0 0 0 0 0 0 0 0 0 0
14 310527 431328 313427 315710 316735 324047 0 1 0 0 0 0 0 0 0 0 0
15 330962 484015 310527 313427 315710 316735 0 0 1 0 0 0 0 0 0 0 0
16 339015 509673 330962 310527 313427 315710 0 0 0 1 0 0 0 0 0 0 0
17 341332 512927 339015 330962 310527 313427 0 0 0 0 1 0 0 0 0 0 0
18 339092 502831 341332 339015 330962 310527 0 0 0 0 0 1 0 0 0 0 0
19 323308 470984 339092 341332 339015 330962 0 0 0 0 0 0 1 0 0 0 0
20 325849 471067 323308 339092 341332 339015 0 0 0 0 0 0 0 1 0 0 0
21 330675 476049 325849 323308 339092 341332 0 0 0 0 0 0 0 0 1 0 0
22 332225 474605 330675 325849 323308 339092 0 0 0 0 0 0 0 0 0 1 0
23 331735 470439 332225 330675 325849 323308 0 0 0 0 0 0 0 0 0 0 1
24 328047 461251 331735 332225 330675 325849 0 0 0 0 0 0 0 0 0 0 0
25 326165 454724 328047 331735 332225 330675 1 0 0 0 0 0 0 0 0 0 0
26 327081 455626 326165 328047 331735 332225 0 1 0 0 0 0 0 0 0 0 0
27 346764 516847 327081 326165 328047 331735 0 0 1 0 0 0 0 0 0 0 0
28 344190 525192 346764 327081 326165 328047 0 0 0 1 0 0 0 0 0 0 0
29 343333 522975 344190 346764 327081 326165 0 0 0 0 1 0 0 0 0 0 0
30 345777 518585 343333 344190 346764 327081 0 0 0 0 0 1 0 0 0 0 0
31 344094 509239 345777 343333 344190 346764 0 0 0 0 0 0 1 0 0 0 0
32 348609 512238 344094 345777 343333 344190 0 0 0 0 0 0 0 1 0 0 0
33 354846 519164 348609 344094 345777 343333 0 0 0 0 0 0 0 0 1 0 0
34 356427 517009 354846 348609 344094 345777 0 0 0 0 0 0 0 0 0 1 0
35 353467 509933 356427 354846 348609 344094 0 0 0 0 0 0 0 0 0 0 1
36 355996 509127 353467 356427 354846 348609 0 0 0 0 0 0 0 0 0 0 0
37 352487 500857 355996 353467 356427 354846 1 0 0 0 0 0 0 0 0 0 0
38 355178 506971 352487 355996 353467 356427 0 1 0 0 0 0 0 0 0 0 0
39 374556 569323 355178 352487 355996 353467 0 0 1 0 0 0 0 0 0 0 0
40 375021 579714 374556 355178 352487 355996 0 0 0 1 0 0 0 0 0 0 0
41 375787 577992 375021 374556 355178 352487 0 0 0 0 1 0 0 0 0 0 0
42 372720 565464 375787 375021 374556 355178 0 0 0 0 0 1 0 0 0 0 0
43 364431 547344 372720 375787 375021 374556 0 0 0 0 0 0 1 0 0 0 0
44 370490 554788 364431 372720 375787 375021 0 0 0 0 0 0 0 1 0 0 0
45 376974 562325 370490 364431 372720 375787 0 0 0 0 0 0 0 0 1 0 0
46 377632 560854 376974 370490 364431 372720 0 0 0 0 0 0 0 0 0 1 0
47 378205 555332 377632 376974 370490 364431 0 0 0 0 0 0 0 0 0 0 1
48 370861 543599 378205 377632 376974 370490 0 0 0 0 0 0 0 0 0 0 0
49 369167 536662 370861 378205 377632 376974 1 0 0 0 0 0 0 0 0 0 0
50 371551 542722 369167 370861 378205 377632 0 1 0 0 0 0 0 0 0 0 0
51 382842 593530 371551 369167 370861 378205 0 0 1 0 0 0 0 0 0 0 0
52 381903 610763 382842 371551 369167 370861 0 0 0 1 0 0 0 0 0 0 0
53 384502 612613 381903 382842 371551 369167 0 0 0 0 1 0 0 0 0 0 0
54 392058 611324 384502 381903 382842 371551 0 0 0 0 0 1 0 0 0 0 0
55 384359 594167 392058 384502 381903 382842 0 0 0 0 0 0 1 0 0 0 0
56 388884 595454 384359 392058 384502 381903 0 0 0 0 0 0 0 1 0 0 0
57 386586 590865 388884 384359 392058 384502 0 0 0 0 0 0 0 0 1 0 0
58 387495 589379 386586 388884 384359 392058 0 0 0 0 0 0 0 0 0 1 0
59 385705 584428 387495 386586 388884 384359 0 0 0 0 0 0 0 0 0 0 1
60 378670 573100 385705 387495 386586 388884 0 0 0 0 0 0 0 0 0 0 0
61 377367 567456 378670 385705 387495 386586 1 0 0 0 0 0 0 0 0 0 0
62 376911 569028 377367 378670 385705 387495 0 1 0 0 0 0 0 0 0 0 0
63 389827 620735 376911 377367 378670 385705 0 0 1 0 0 0 0 0 0 0 0
64 387820 628884 389827 376911 377367 378670 0 0 0 1 0 0 0 0 0 0 0
65 387267 628232 387820 389827 376911 377367 0 0 0 0 1 0 0 0 0 0 0
66 380575 612117 387267 387820 389827 376911 0 0 0 0 0 1 0 0 0 0 0
67 372402 595404 380575 387267 387820 389827 0 0 0 0 0 0 1 0 0 0 0
68 376740 597141 372402 380575 387267 387820 0 0 0 0 0 0 0 1 0 0 0
t
1 1
2 2
3 3
4 4
5 5
6 6
7 7
8 8
9 9
10 10
11 11
12 12
13 13
14 14
15 15
16 16
17 17
18 18
19 19
20 20
21 21
22 22
23 23
24 24
25 25
26 26
27 27
28 28
29 29
30 30
31 31
32 32
33 33
34 34
35 35
36 36
37 37
38 38
39 39
40 40
41 41
42 42
43 43
44 44
45 45
46 46
47 47
48 48
49 49
50 50
51 51
52 52
53 53
54 54
55 55
56 56
57 57
58 58
59 59
60 60
61 61
62 62
63 63
64 64
65 65
66 66
67 67
68 68
> k <- length(x[1,])
> df <- as.data.frame(x)
> (mylm <- lm(df))
Call:
lm(formula = df)
Coefficients:
(Intercept) X `yt-1` `yt-2` `yt-3` `yt-4`
4.516e+04 4.920e-01 4.691e-01 -7.892e-02 8.727e-02 -2.897e-01
M1 M2 M3 M4 M5 M6
3.347e+03 4.680e+03 -5.912e+03 -2.011e+04 -2.037e+04 -1.701e+04
M7 M8 M9 M10 M11 t
-1.061e+04 -2.692e+03 -2.070e+03 -1.154e+03 -2.543e+03 -3.112e+02
> (mysum <- summary(mylm))
Call:
lm(formula = df)
Residuals:
Min 1Q Median 3Q Max
-5753.3 -2055.0 151.1 1857.2 4559.8
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 4.516e+04 1.465e+04 3.082 0.003341 **
X 4.920e-01 6.991e-02 7.039 5.22e-09 ***
`yt-1` 4.691e-01 1.239e-01 3.786 0.000411 ***
`yt-2` -7.892e-02 1.378e-01 -0.573 0.569312
`yt-3` 8.727e-02 1.382e-01 0.631 0.530666
`yt-4` -2.897e-01 1.022e-01 -2.834 0.006616 **
M1 3.347e+03 1.934e+03 1.731 0.089674 .
M2 4.680e+03 1.974e+03 2.371 0.021626 *
M3 -5.912e+03 4.091e+03 -1.445 0.154636
M4 -2.011e+04 4.439e+03 -4.530 3.68e-05 ***
M5 -2.037e+04 4.237e+03 -4.809 1.43e-05 ***
M6 -1.701e+04 3.546e+03 -4.796 1.50e-05 ***
M7 -1.061e+04 1.998e+03 -5.313 2.50e-06 ***
M8 -2.692e+03 2.419e+03 -1.113 0.271104
M9 -2.070e+03 2.473e+03 -0.837 0.406544
M10 -1.154e+03 2.414e+03 -0.478 0.634603
M11 -2.543e+03 1.988e+03 -1.279 0.206776
t -3.112e+02 8.490e+01 -3.666 0.000597 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 2934 on 50 degrees of freedom
Multiple R-squared: 0.9896, Adjusted R-squared: 0.9861
F-statistic: 281.2 on 17 and 50 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,] 0.2134646 0.4269293 0.78653537
[2,] 0.1772989 0.3545978 0.82270110
[3,] 0.3265507 0.6531014 0.67344928
[4,] 0.2986866 0.5973733 0.70131335
[5,] 0.3647815 0.7295630 0.63521851
[6,] 0.3020137 0.6040274 0.69798632
[7,] 0.9106133 0.1787733 0.08938667
[8,] 0.9371435 0.1257129 0.06285645
[9,] 0.9055472 0.1889055 0.09445275
[10,] 0.8625601 0.2748798 0.13743991
[11,] 0.7995053 0.4009893 0.20049467
[12,] 0.8592967 0.2814066 0.14070330
[13,] 0.8221988 0.3556025 0.17780123
[14,] 0.7488434 0.5023131 0.25115656
[15,] 0.7747290 0.4505421 0.22527104
[16,] 0.7591796 0.4816408 0.24082038
[17,] 0.7493460 0.5013081 0.25065403
[18,] 0.7287258 0.5425484 0.27127418
[19,] 0.8398721 0.3202558 0.16012792
[20,] 0.7865630 0.4268741 0.21343704
[21,] 0.7016745 0.5966509 0.29832546
[22,] 0.5925124 0.8149752 0.40748759
[23,] 0.5040558 0.9918883 0.49594417
[24,] 0.3968839 0.7937678 0.60311610
[25,] 0.2985531 0.5971063 0.70144685
[26,] 0.2656545 0.5313090 0.73434550
[27,] 0.1612793 0.3225585 0.83872075
> postscript(file="/var/www/html/rcomp/tmp/1t5el1258561298.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$resid)
> grid()
> dev.off()
null device
1
> postscript(file="/var/www/html/rcomp/tmp/2uoop1258561298.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556)
> plot(mysum$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/3imqo1258561298.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556)
> hist(mysum$resid, main='Residual Histogram', xlab='values of Residuals')
> grid()
> dev.off()
null device
1
> postscript(file="/var/www/html/rcomp/tmp/4j7lu1258561298.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556)
> densityplot(~mysum$resid,col='black',main='Residual Density Plot', xlab='values of Residuals')
> dev.off()
null device
1
> postscript(file="/var/www/html/rcomp/tmp/5c1j91258561298.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 = 68
Frequency = 1
1 2 3 4 5 6
-3846.863376 -1747.035591 1302.865382 3031.785023 -5753.301539 -2024.090400
7 8 9 10 11 12
-1101.957927 1777.109427 532.433956 -3491.857996 -4078.810032 -2216.674916
13 14 15 16 17 18
-2235.944143 -3052.779902 1513.108288 1534.753791 255.080655 -3147.484502
19 20 21 22 23 24
-2891.727030 1355.411813 1848.444094 2169.747708 289.177594 -442.820457
25 26 27 28 29 30
804.645116 1338.576760 1403.794565 -835.373348 2111.556025 2406.696733
31 32 33 34 35 36
3953.855228 -306.242056 -500.157803 -177.638623 913.343476 3883.819047
37 38 39 40 41 42
1656.857589 2879.583869 -135.807855 1883.532219 4134.076423 2941.856722
43 44 45 46 47 48
4559.784314 3059.091854 2517.081627 565.937329 2829.184463 -1.073411
49 50 51 52 53 54
3993.113836 2729.186571 -520.683150 -2521.438555 377.496665 3924.356787
55 56 57 58 59 60
-1400.162812 -1410.450617 -4397.801873 933.811583 47.104499 -1223.250263
61 62 63 64 65 66
-371.809023 -2147.531706 -3563.277231 -3093.259130 -1124.908228 -4101.335340
67 68
-3119.791773 -4474.920421
> postscript(file="/var/www/html/rcomp/tmp/69ej81258561298.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 = 68
Frequency = 1
lag(myerror, k = 1) myerror
0 -3846.863376 NA
1 -1747.035591 -3846.863376
2 1302.865382 -1747.035591
3 3031.785023 1302.865382
4 -5753.301539 3031.785023
5 -2024.090400 -5753.301539
6 -1101.957927 -2024.090400
7 1777.109427 -1101.957927
8 532.433956 1777.109427
9 -3491.857996 532.433956
10 -4078.810032 -3491.857996
11 -2216.674916 -4078.810032
12 -2235.944143 -2216.674916
13 -3052.779902 -2235.944143
14 1513.108288 -3052.779902
15 1534.753791 1513.108288
16 255.080655 1534.753791
17 -3147.484502 255.080655
18 -2891.727030 -3147.484502
19 1355.411813 -2891.727030
20 1848.444094 1355.411813
21 2169.747708 1848.444094
22 289.177594 2169.747708
23 -442.820457 289.177594
24 804.645116 -442.820457
25 1338.576760 804.645116
26 1403.794565 1338.576760
27 -835.373348 1403.794565
28 2111.556025 -835.373348
29 2406.696733 2111.556025
30 3953.855228 2406.696733
31 -306.242056 3953.855228
32 -500.157803 -306.242056
33 -177.638623 -500.157803
34 913.343476 -177.638623
35 3883.819047 913.343476
36 1656.857589 3883.819047
37 2879.583869 1656.857589
38 -135.807855 2879.583869
39 1883.532219 -135.807855
40 4134.076423 1883.532219
41 2941.856722 4134.076423
42 4559.784314 2941.856722
43 3059.091854 4559.784314
44 2517.081627 3059.091854
45 565.937329 2517.081627
46 2829.184463 565.937329
47 -1.073411 2829.184463
48 3993.113836 -1.073411
49 2729.186571 3993.113836
50 -520.683150 2729.186571
51 -2521.438555 -520.683150
52 377.496665 -2521.438555
53 3924.356787 377.496665
54 -1400.162812 3924.356787
55 -1410.450617 -1400.162812
56 -4397.801873 -1410.450617
57 933.811583 -4397.801873
58 47.104499 933.811583
59 -1223.250263 47.104499
60 -371.809023 -1223.250263
61 -2147.531706 -371.809023
62 -3563.277231 -2147.531706
63 -3093.259130 -3563.277231
64 -1124.908228 -3093.259130
65 -4101.335340 -1124.908228
66 -3119.791773 -4101.335340
67 -4474.920421 -3119.791773
68 NA -4474.920421
> dum1 <- dum[2:length(myerror),]
> dum1
lag(myerror, k = 1) myerror
[1,] -1747.035591 -3846.863376
[2,] 1302.865382 -1747.035591
[3,] 3031.785023 1302.865382
[4,] -5753.301539 3031.785023
[5,] -2024.090400 -5753.301539
[6,] -1101.957927 -2024.090400
[7,] 1777.109427 -1101.957927
[8,] 532.433956 1777.109427
[9,] -3491.857996 532.433956
[10,] -4078.810032 -3491.857996
[11,] -2216.674916 -4078.810032
[12,] -2235.944143 -2216.674916
[13,] -3052.779902 -2235.944143
[14,] 1513.108288 -3052.779902
[15,] 1534.753791 1513.108288
[16,] 255.080655 1534.753791
[17,] -3147.484502 255.080655
[18,] -2891.727030 -3147.484502
[19,] 1355.411813 -2891.727030
[20,] 1848.444094 1355.411813
[21,] 2169.747708 1848.444094
[22,] 289.177594 2169.747708
[23,] -442.820457 289.177594
[24,] 804.645116 -442.820457
[25,] 1338.576760 804.645116
[26,] 1403.794565 1338.576760
[27,] -835.373348 1403.794565
[28,] 2111.556025 -835.373348
[29,] 2406.696733 2111.556025
[30,] 3953.855228 2406.696733
[31,] -306.242056 3953.855228
[32,] -500.157803 -306.242056
[33,] -177.638623 -500.157803
[34,] 913.343476 -177.638623
[35,] 3883.819047 913.343476
[36,] 1656.857589 3883.819047
[37,] 2879.583869 1656.857589
[38,] -135.807855 2879.583869
[39,] 1883.532219 -135.807855
[40,] 4134.076423 1883.532219
[41,] 2941.856722 4134.076423
[42,] 4559.784314 2941.856722
[43,] 3059.091854 4559.784314
[44,] 2517.081627 3059.091854
[45,] 565.937329 2517.081627
[46,] 2829.184463 565.937329
[47,] -1.073411 2829.184463
[48,] 3993.113836 -1.073411
[49,] 2729.186571 3993.113836
[50,] -520.683150 2729.186571
[51,] -2521.438555 -520.683150
[52,] 377.496665 -2521.438555
[53,] 3924.356787 377.496665
[54,] -1400.162812 3924.356787
[55,] -1410.450617 -1400.162812
[56,] -4397.801873 -1410.450617
[57,] 933.811583 -4397.801873
[58,] 47.104499 933.811583
[59,] -1223.250263 47.104499
[60,] -371.809023 -1223.250263
[61,] -2147.531706 -371.809023
[62,] -3563.277231 -2147.531706
[63,] -3093.259130 -3563.277231
[64,] -1124.908228 -3093.259130
[65,] -4101.335340 -1124.908228
[66,] -3119.791773 -4101.335340
[67,] -4474.920421 -3119.791773
> z <- as.data.frame(dum1)
> z
lag(myerror, k = 1) myerror
1 -1747.035591 -3846.863376
2 1302.865382 -1747.035591
3 3031.785023 1302.865382
4 -5753.301539 3031.785023
5 -2024.090400 -5753.301539
6 -1101.957927 -2024.090400
7 1777.109427 -1101.957927
8 532.433956 1777.109427
9 -3491.857996 532.433956
10 -4078.810032 -3491.857996
11 -2216.674916 -4078.810032
12 -2235.944143 -2216.674916
13 -3052.779902 -2235.944143
14 1513.108288 -3052.779902
15 1534.753791 1513.108288
16 255.080655 1534.753791
17 -3147.484502 255.080655
18 -2891.727030 -3147.484502
19 1355.411813 -2891.727030
20 1848.444094 1355.411813
21 2169.747708 1848.444094
22 289.177594 2169.747708
23 -442.820457 289.177594
24 804.645116 -442.820457
25 1338.576760 804.645116
26 1403.794565 1338.576760
27 -835.373348 1403.794565
28 2111.556025 -835.373348
29 2406.696733 2111.556025
30 3953.855228 2406.696733
31 -306.242056 3953.855228
32 -500.157803 -306.242056
33 -177.638623 -500.157803
34 913.343476 -177.638623
35 3883.819047 913.343476
36 1656.857589 3883.819047
37 2879.583869 1656.857589
38 -135.807855 2879.583869
39 1883.532219 -135.807855
40 4134.076423 1883.532219
41 2941.856722 4134.076423
42 4559.784314 2941.856722
43 3059.091854 4559.784314
44 2517.081627 3059.091854
45 565.937329 2517.081627
46 2829.184463 565.937329
47 -1.073411 2829.184463
48 3993.113836 -1.073411
49 2729.186571 3993.113836
50 -520.683150 2729.186571
51 -2521.438555 -520.683150
52 377.496665 -2521.438555
53 3924.356787 377.496665
54 -1400.162812 3924.356787
55 -1410.450617 -1400.162812
56 -4397.801873 -1410.450617
57 933.811583 -4397.801873
58 47.104499 933.811583
59 -1223.250263 47.104499
60 -371.809023 -1223.250263
61 -2147.531706 -371.809023
62 -3563.277231 -2147.531706
63 -3093.259130 -3563.277231
64 -1124.908228 -3093.259130
65 -4101.335340 -1124.908228
66 -3119.791773 -4101.335340
67 -4474.920421 -3119.791773
> 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/7a5xp1258561298.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556)
> acf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Autocorrelation Function')
> grid()
> dev.off()
null device
1
> postscript(file="/var/www/html/rcomp/tmp/8uoqj1258561298.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556)
> pacf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Partial Autocorrelation Function')
> grid()
> dev.off()
null device
1
> postscript(file="/var/www/html/rcomp/tmp/9l37a1258561298.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556)
> opar <- par(mfrow = c(2,2), oma = c(0, 0, 1.1, 0))
> plot(mylm, las = 1, sub='Residual Diagnostics')
> par(opar)
> dev.off()
null device
1
> if (n > n25) {
+ postscript(file="/var/www/html/rcomp/tmp/10jmpu1258561298.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556)
+ plot(kp3:nmkm3,gqarr[,2], main='Goldfeld-Quandt test',ylab='2-sided p-value',xlab='breakpoint')
+ grid()
+ dev.off()
+ }
null device
1
>
> #Note: the /var/www/html/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab
> load(file="/var/www/html/rcomp/createtable")
>
> a<-table.start()
> a<-table.row.start(a)
> a<-table.element(a, 'Multiple Linear Regression - Estimated Regression Equation', 1, TRUE)
> a<-table.row.end(a)
> myeq <- colnames(x)[1]
> myeq <- paste(myeq, '[t] = ', sep='')
> for (i in 1:k){
+ if (mysum$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/115ufa1258561298.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/122i2v1258561298.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/133m1v1258561298.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/14qcfc1258561298.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/15ivxi1258561298.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/16rh2q1258561298.tab")
+ }
>
> system("convert tmp/1t5el1258561298.ps tmp/1t5el1258561298.png")
> system("convert tmp/2uoop1258561298.ps tmp/2uoop1258561298.png")
> system("convert tmp/3imqo1258561298.ps tmp/3imqo1258561298.png")
> system("convert tmp/4j7lu1258561298.ps tmp/4j7lu1258561298.png")
> system("convert tmp/5c1j91258561298.ps tmp/5c1j91258561298.png")
> system("convert tmp/69ej81258561298.ps tmp/69ej81258561298.png")
> system("convert tmp/7a5xp1258561298.ps tmp/7a5xp1258561298.png")
> system("convert tmp/8uoqj1258561298.ps tmp/8uoqj1258561298.png")
> system("convert tmp/9l37a1258561298.ps tmp/9l37a1258561298.png")
> system("convert tmp/10jmpu1258561298.ps tmp/10jmpu1258561298.png")
>
>
> proc.time()
user system elapsed
2.609 1.638 7.509