R version 2.8.0 (2008-10-20)
Copyright (C) 2008 The R Foundation for Statistical Computing
ISBN 3-900051-07-0
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> x <- array(list(7.5,0,7.2,0,6.9,0,6.7,0,6.4,0,6.3,0,6.8,0,7.3,0,7.1,0,7.1,0,6.8,0,6.5,0,6.3,0,6.1,0,6.1,0,6.3,0,6.3,0,6,0,6.2,0,6.4,0,6.8,0,7.5,0,7.5,0,7.6,0,7.6,0,7.4,0,7.3,0,7.1,0,6.9,0,6.8,0,7.5,0,7.6,0,7.8,0,8.0,0,8.1,0,8.2,0,8.3,0,8.2,0,8.0,0,7.9,0,7.6,0,7.6,0,8.2,0,8.3,0,8.4,0,8.4,0,8.4,0,8.6,0,8.9,0,8.8,0,8.3,0,7.5,0,7.2,0,7.5,0,8.8,0,9.3,0,9.3,0,8.7,1,8.2,1,8.3,1,8.5,1,8.6,1,8.6,1,8.2,1,8.1,1,8.0,1,8.6,1,8.7,1,8.8,1,8.5,1,8.4,1,8.5,1,8.7,1,8.7,1,8.6,1,8.5,1,8.3,1,8.1,1,8.2,1,8.1,1,8.1,1,7.9,1,7.9,1,7.9,1,8.0,1,8.0,1,7.9,1,8.0,1,7.7,1,7.2,1,7.5,1,7.3,1,7.0,1,7.0,1,7.0,1,7.2,1,7.3,1,7.1,1,6.8,1,6.6,1,6.2,1,6.2,1,6.8,1,6.9,1,6.8,1),dim=c(2,105),dimnames=list(c('w','d'),1:105))
> y <- array(NA,dim=c(2,105),dimnames=list(c('w','d'),1:105))
> 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
w d M1 M2 M3 M4 M5 M6 M7 M8 M9 M10 M11 t
1 7.5 0 1 0 0 0 0 0 0 0 0 0 0 1
2 7.2 0 0 1 0 0 0 0 0 0 0 0 0 2
3 6.9 0 0 0 1 0 0 0 0 0 0 0 0 3
4 6.7 0 0 0 0 1 0 0 0 0 0 0 0 4
5 6.4 0 0 0 0 0 1 0 0 0 0 0 0 5
6 6.3 0 0 0 0 0 0 1 0 0 0 0 0 6
7 6.8 0 0 0 0 0 0 0 1 0 0 0 0 7
8 7.3 0 0 0 0 0 0 0 0 1 0 0 0 8
9 7.1 0 0 0 0 0 0 0 0 0 1 0 0 9
10 7.1 0 0 0 0 0 0 0 0 0 0 1 0 10
11 6.8 0 0 0 0 0 0 0 0 0 0 0 1 11
12 6.5 0 0 0 0 0 0 0 0 0 0 0 0 12
13 6.3 0 1 0 0 0 0 0 0 0 0 0 0 13
14 6.1 0 0 1 0 0 0 0 0 0 0 0 0 14
15 6.1 0 0 0 1 0 0 0 0 0 0 0 0 15
16 6.3 0 0 0 0 1 0 0 0 0 0 0 0 16
17 6.3 0 0 0 0 0 1 0 0 0 0 0 0 17
18 6.0 0 0 0 0 0 0 1 0 0 0 0 0 18
19 6.2 0 0 0 0 0 0 0 1 0 0 0 0 19
20 6.4 0 0 0 0 0 0 0 0 1 0 0 0 20
21 6.8 0 0 0 0 0 0 0 0 0 1 0 0 21
22 7.5 0 0 0 0 0 0 0 0 0 0 1 0 22
23 7.5 0 0 0 0 0 0 0 0 0 0 0 1 23
24 7.6 0 0 0 0 0 0 0 0 0 0 0 0 24
25 7.6 0 1 0 0 0 0 0 0 0 0 0 0 25
26 7.4 0 0 1 0 0 0 0 0 0 0 0 0 26
27 7.3 0 0 0 1 0 0 0 0 0 0 0 0 27
28 7.1 0 0 0 0 1 0 0 0 0 0 0 0 28
29 6.9 0 0 0 0 0 1 0 0 0 0 0 0 29
30 6.8 0 0 0 0 0 0 1 0 0 0 0 0 30
31 7.5 0 0 0 0 0 0 0 1 0 0 0 0 31
32 7.6 0 0 0 0 0 0 0 0 1 0 0 0 32
33 7.8 0 0 0 0 0 0 0 0 0 1 0 0 33
34 8.0 0 0 0 0 0 0 0 0 0 0 1 0 34
35 8.1 0 0 0 0 0 0 0 0 0 0 0 1 35
36 8.2 0 0 0 0 0 0 0 0 0 0 0 0 36
37 8.3 0 1 0 0 0 0 0 0 0 0 0 0 37
38 8.2 0 0 1 0 0 0 0 0 0 0 0 0 38
39 8.0 0 0 0 1 0 0 0 0 0 0 0 0 39
40 7.9 0 0 0 0 1 0 0 0 0 0 0 0 40
41 7.6 0 0 0 0 0 1 0 0 0 0 0 0 41
42 7.6 0 0 0 0 0 0 1 0 0 0 0 0 42
43 8.2 0 0 0 0 0 0 0 1 0 0 0 0 43
44 8.3 0 0 0 0 0 0 0 0 1 0 0 0 44
45 8.4 0 0 0 0 0 0 0 0 0 1 0 0 45
46 8.4 0 0 0 0 0 0 0 0 0 0 1 0 46
47 8.4 0 0 0 0 0 0 0 0 0 0 0 1 47
48 8.6 0 0 0 0 0 0 0 0 0 0 0 0 48
49 8.9 0 1 0 0 0 0 0 0 0 0 0 0 49
50 8.8 0 0 1 0 0 0 0 0 0 0 0 0 50
51 8.3 0 0 0 1 0 0 0 0 0 0 0 0 51
52 7.5 0 0 0 0 1 0 0 0 0 0 0 0 52
53 7.2 0 0 0 0 0 1 0 0 0 0 0 0 53
54 7.5 0 0 0 0 0 0 1 0 0 0 0 0 54
55 8.8 0 0 0 0 0 0 0 1 0 0 0 0 55
56 9.3 0 0 0 0 0 0 0 0 1 0 0 0 56
57 9.3 0 0 0 0 0 0 0 0 0 1 0 0 57
58 8.7 1 0 0 0 0 0 0 0 0 0 1 0 58
59 8.2 1 0 0 0 0 0 0 0 0 0 0 1 59
60 8.3 1 0 0 0 0 0 0 0 0 0 0 0 60
61 8.5 1 1 0 0 0 0 0 0 0 0 0 0 61
62 8.6 1 0 1 0 0 0 0 0 0 0 0 0 62
63 8.6 1 0 0 1 0 0 0 0 0 0 0 0 63
64 8.2 1 0 0 0 1 0 0 0 0 0 0 0 64
65 8.1 1 0 0 0 0 1 0 0 0 0 0 0 65
66 8.0 1 0 0 0 0 0 1 0 0 0 0 0 66
67 8.6 1 0 0 0 0 0 0 1 0 0 0 0 67
68 8.7 1 0 0 0 0 0 0 0 1 0 0 0 68
69 8.8 1 0 0 0 0 0 0 0 0 1 0 0 69
70 8.5 1 0 0 0 0 0 0 0 0 0 1 0 70
71 8.4 1 0 0 0 0 0 0 0 0 0 0 1 71
72 8.5 1 0 0 0 0 0 0 0 0 0 0 0 72
73 8.7 1 1 0 0 0 0 0 0 0 0 0 0 73
74 8.7 1 0 1 0 0 0 0 0 0 0 0 0 74
75 8.6 1 0 0 1 0 0 0 0 0 0 0 0 75
76 8.5 1 0 0 0 1 0 0 0 0 0 0 0 76
77 8.3 1 0 0 0 0 1 0 0 0 0 0 0 77
78 8.1 1 0 0 0 0 0 1 0 0 0 0 0 78
79 8.2 1 0 0 0 0 0 0 1 0 0 0 0 79
80 8.1 1 0 0 0 0 0 0 0 1 0 0 0 80
81 8.1 1 0 0 0 0 0 0 0 0 1 0 0 81
82 7.9 1 0 0 0 0 0 0 0 0 0 1 0 82
83 7.9 1 0 0 0 0 0 0 0 0 0 0 1 83
84 7.9 1 0 0 0 0 0 0 0 0 0 0 0 84
85 8.0 1 1 0 0 0 0 0 0 0 0 0 0 85
86 8.0 1 0 1 0 0 0 0 0 0 0 0 0 86
87 7.9 1 0 0 1 0 0 0 0 0 0 0 0 87
88 8.0 1 0 0 0 1 0 0 0 0 0 0 0 88
89 7.7 1 0 0 0 0 1 0 0 0 0 0 0 89
90 7.2 1 0 0 0 0 0 1 0 0 0 0 0 90
91 7.5 1 0 0 0 0 0 0 1 0 0 0 0 91
92 7.3 1 0 0 0 0 0 0 0 1 0 0 0 92
93 7.0 1 0 0 0 0 0 0 0 0 1 0 0 93
94 7.0 1 0 0 0 0 0 0 0 0 0 1 0 94
95 7.0 1 0 0 0 0 0 0 0 0 0 0 1 95
96 7.2 1 0 0 0 0 0 0 0 0 0 0 0 96
97 7.3 1 1 0 0 0 0 0 0 0 0 0 0 97
98 7.1 1 0 1 0 0 0 0 0 0 0 0 0 98
99 6.8 1 0 0 1 0 0 0 0 0 0 0 0 99
100 6.6 1 0 0 0 1 0 0 0 0 0 0 0 100
101 6.2 1 0 0 0 0 1 0 0 0 0 0 0 101
102 6.2 1 0 0 0 0 0 1 0 0 0 0 0 102
103 6.8 1 0 0 0 0 0 0 1 0 0 0 0 103
104 6.9 1 0 0 0 0 0 0 0 1 0 0 0 104
105 6.8 1 0 0 0 0 0 0 0 0 1 0 0 105
> k <- length(x[1,])
> df <- as.data.frame(x)
> (mylm <- lm(df))
Call:
lm(formula = df)
Coefficients:
(Intercept) d M1 M2 M3 M4
7.415278 -0.118472 0.089155 -0.031103 -0.218029 -0.416065
M5 M6 M7 M8 M9 M10
-0.658546 -0.778804 -0.243507 -0.108210 -0.095135 0.055795
M11 t
-0.053353 0.009147
> (mysum <- summary(mylm))
Call:
lm(formula = df)
Residuals:
Min 1Q Median 3Q Max
-1.4122377 -0.4358025 0.0002160 0.5793364 1.4806790
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 7.415278 0.322124 23.020 <2e-16 ***
d -0.118472 0.309809 -0.382 0.7031
M1 0.089155 0.383647 0.232 0.8168
M2 -0.031103 0.383540 -0.081 0.9355
M3 -0.218029 0.383501 -0.569 0.5711
M4 -0.416065 0.383530 -1.085 0.2809
M5 -0.658546 0.383626 -1.717 0.0894 .
M6 -0.778804 0.383790 -2.029 0.0454 *
M7 -0.243507 0.384023 -0.634 0.5276
M8 -0.108210 0.384322 -0.282 0.7789
M9 -0.095135 0.384689 -0.247 0.8052
M10 0.055795 0.394652 0.141 0.8879
M11 -0.053353 0.394553 -0.135 0.8927
t 0.009147 0.005101 1.793 0.0763 .
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 0.789 on 91 degrees of freedom
Multiple R-squared: 0.1832, Adjusted R-squared: 0.06648
F-statistic: 1.57 on 13 and 91 DF, p-value: 0.1087
> 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,] 0.15158514 0.3031702896 0.8484148552
[2,] 0.08814373 0.1762874690 0.9118562655
[3,] 0.04479730 0.0895945917 0.9552027041
[4,] 0.02709102 0.0541820301 0.9729089850
[5,] 0.01941560 0.0388312084 0.9805843958
[6,] 0.05518194 0.1103638794 0.9448180603
[7,] 0.13673521 0.2734704241 0.8632647880
[8,] 0.31861273 0.6372254570 0.6813872715
[9,] 0.42535667 0.8507133319 0.5746433340
[10,] 0.50627750 0.9874449986 0.4937224993
[11,] 0.56646419 0.8670716152 0.4335358076
[12,] 0.58323158 0.8335368442 0.4167684221
[13,] 0.59615597 0.8076880619 0.4038440310
[14,] 0.63586361 0.7282727809 0.3641363904
[15,] 0.72145612 0.5570877697 0.2785438848
[16,] 0.77872058 0.4425588480 0.2212794240
[17,] 0.82535588 0.3492882478 0.1746441239
[18,] 0.81247964 0.3750407189 0.1875203594
[19,] 0.80428653 0.3914269461 0.1957134731
[20,] 0.81637735 0.3672452941 0.1836226471
[21,] 0.81921572 0.3615685590 0.1807842795
[22,] 0.83809962 0.3238007531 0.1619003766
[23,] 0.85137476 0.2972504722 0.1486252361
[24,] 0.84919156 0.3016168753 0.1508084376
[25,] 0.84787711 0.3042457862 0.1521228931
[26,] 0.84941298 0.3011740485 0.1505870242
[27,] 0.86080811 0.2783837801 0.1391918900
[28,] 0.86565462 0.2686907581 0.1343453791
[29,] 0.85936395 0.2812721044 0.1406360522
[30,] 0.82376252 0.3524749549 0.1762374774
[31,] 0.77865477 0.4426904537 0.2213452269
[32,] 0.73229019 0.5354196166 0.2677098083
[33,] 0.68901543 0.6219691324 0.3109845662
[34,] 0.64679999 0.7064000139 0.3532000069
[35,] 0.59328554 0.8134289267 0.4067144634
[36,] 0.72830085 0.5433983036 0.2716991518
[37,] 0.90968629 0.1806274176 0.0903137088
[38,] 0.96663108 0.0667378416 0.0333689208
[39,] 0.96837954 0.0632409241 0.0316204620
[40,] 0.96694645 0.0661070936 0.0330535468
[41,] 0.96044390 0.0791121991 0.0395560996
[42,] 0.94672439 0.1065512284 0.0532756142
[43,] 0.96053838 0.0789232435 0.0394616218
[44,] 0.97390590 0.0521881929 0.0260940965
[45,] 0.98379849 0.0324030138 0.0162015069
[46,] 0.98766670 0.0246665907 0.0123332953
[47,] 0.98855260 0.0228947980 0.0114473990
[48,] 0.99719028 0.0056194346 0.0028097173
[49,] 0.99921659 0.0015668184 0.0007834092
[50,] 0.99977925 0.0004415030 0.0002207515
[51,] 0.99982853 0.0003429417 0.0001714709
[52,] 0.99977752 0.0004449596 0.0002224798
[53,] 0.99954853 0.0009029469 0.0004514734
[54,] 0.99929714 0.0014057287 0.0007028643
[55,] 0.99907106 0.0018578760 0.0009289380
[56,] 0.99877056 0.0024588866 0.0012294433
[57,] 0.99805545 0.0038891055 0.0019445527
[58,] 0.99640356 0.0071928708 0.0035964354
[59,] 0.99317398 0.0136520452 0.0068260226
[60,] 0.98741972 0.0251605515 0.0125802757
[61,] 0.97844794 0.0431041246 0.0215520623
[62,] 0.96667744 0.0666451191 0.0333225596
[63,] 0.95528268 0.0894346408 0.0447173204
[64,] 0.95286647 0.0942670675 0.0471335337
[65,] 0.93934114 0.1213177229 0.0606588614
[66,] 0.92624190 0.1475162082 0.0737581041
[67,] 0.89803752 0.2039249590 0.1019624795
[68,] 0.86235525 0.2752894945 0.1376447473
[69,] 0.81485713 0.3702857372 0.1851428686
[70,] 0.72787575 0.5442484980 0.2721242490
[71,] 0.61997976 0.7600404824 0.3800202412
[72,] 0.57572910 0.8485418059 0.4242709029
> postscript(file="/var/www/html/rcomp/tmp/1b5zg1227789279.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$resid)
> grid()
> dev.off()
null device
1
> postscript(file="/var/www/html/rcomp/tmp/27l221227789279.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556)
> plot(mysum$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/38h2b1227789279.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556)
> hist(mysum$resid, main='Residual Histogram', xlab='values of Residuals')
> grid()
> dev.off()
null device
1
> postscript(file="/var/www/html/rcomp/tmp/4icuf1227789279.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556)
> densityplot(~mysum$resid,col='black',main='Residual Density Plot', xlab='values of Residuals')
> dev.off()
null device
1
> postscript(file="/var/www/html/rcomp/tmp/54o0l1227789279.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 = 105
Frequency = 1
1 2 3 4 5
-0.0135802469 -0.2024691358 -0.3246913580 -0.3358024691 -0.4024691358
6 7 8 9 10
-0.3913580247 -0.4358024691 -0.0802469136 -0.3024691358 -0.4625462963
11 12 13 14 15
-0.6625462963 -1.0250462963 -1.3233487654 -1.4122376543 -1.2344598765
16 17 18 19 20
-0.8455709877 -0.6122376543 -0.8011265432 -1.1455709877 -1.0900154321
21 22 23 24 25
-0.7122376543 -0.1723148148 -0.0723148148 -0.0348148148 -0.1331172840
26 27 28 29 30
-0.2220061728 -0.1442283951 -0.1553395062 -0.1220061728 -0.1108950617
31 32 33 34 35
0.0446604938 0.0002160494 0.1779938272 0.2179166667 0.4179166667
36 37 38 39 40
0.4554166667 0.4571141975 0.4682253086 0.4460030864 0.5348919753
41 42 43 44 45
0.4682253086 0.5793364198 0.6348919753 0.5904475309 0.6682253086
46 47 48 49 50
0.5081481481 0.6081481481 0.7456481481 0.9473456790 0.9584567901
51 52 53 54 55
0.6362345679 0.0251234568 -0.0415432099 0.3695679012 1.1251234568
56 57 58 59 60
1.4806790123 1.4584567901 0.8168518519 0.4168518519 0.4543518519
61 62 63 64 65
0.5560493827 0.7671604938 0.9449382716 0.7338271605 0.8671604938
66 67 68 69 70
0.8782716049 0.9338271605 0.8893827160 0.9671604938 0.5070833333
71 72 73 74 75
0.5070833333 0.5445833333 0.6462808642 0.7573919753 0.8351697531
76 77 78 79 80
0.9240586420 0.9573919753 0.8685030864 0.4240586420 0.1796141975
81 82 83 84 85
0.1573919753 -0.2026851852 -0.1026851852 -0.1651851852 -0.1634876543
86 87 88 89 90
-0.0523765432 0.0254012346 0.3142901235 0.2476234568 -0.1412654321
91 92 93 94 95
-0.3857098765 -0.7301543210 -1.0523765432 -1.2124537037 -1.1124537037
96 97 98 99 100
-0.9749537037 -0.9732561728 -1.0621450617 -1.1843672840 -1.1954783951
101 102 103 104 105
-1.3621450617 -1.2510339506 -1.1954783951 -1.2399228395 -1.3621450617
> postscript(file="/var/www/html/rcomp/tmp/6euvj1227789279.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 = 105
Frequency = 1
lag(myerror, k = 1) myerror
0 -0.0135802469 NA
1 -0.2024691358 -0.0135802469
2 -0.3246913580 -0.2024691358
3 -0.3358024691 -0.3246913580
4 -0.4024691358 -0.3358024691
5 -0.3913580247 -0.4024691358
6 -0.4358024691 -0.3913580247
7 -0.0802469136 -0.4358024691
8 -0.3024691358 -0.0802469136
9 -0.4625462963 -0.3024691358
10 -0.6625462963 -0.4625462963
11 -1.0250462963 -0.6625462963
12 -1.3233487654 -1.0250462963
13 -1.4122376543 -1.3233487654
14 -1.2344598765 -1.4122376543
15 -0.8455709877 -1.2344598765
16 -0.6122376543 -0.8455709877
17 -0.8011265432 -0.6122376543
18 -1.1455709877 -0.8011265432
19 -1.0900154321 -1.1455709877
20 -0.7122376543 -1.0900154321
21 -0.1723148148 -0.7122376543
22 -0.0723148148 -0.1723148148
23 -0.0348148148 -0.0723148148
24 -0.1331172840 -0.0348148148
25 -0.2220061728 -0.1331172840
26 -0.1442283951 -0.2220061728
27 -0.1553395062 -0.1442283951
28 -0.1220061728 -0.1553395062
29 -0.1108950617 -0.1220061728
30 0.0446604938 -0.1108950617
31 0.0002160494 0.0446604938
32 0.1779938272 0.0002160494
33 0.2179166667 0.1779938272
34 0.4179166667 0.2179166667
35 0.4554166667 0.4179166667
36 0.4571141975 0.4554166667
37 0.4682253086 0.4571141975
38 0.4460030864 0.4682253086
39 0.5348919753 0.4460030864
40 0.4682253086 0.5348919753
41 0.5793364198 0.4682253086
42 0.6348919753 0.5793364198
43 0.5904475309 0.6348919753
44 0.6682253086 0.5904475309
45 0.5081481481 0.6682253086
46 0.6081481481 0.5081481481
47 0.7456481481 0.6081481481
48 0.9473456790 0.7456481481
49 0.9584567901 0.9473456790
50 0.6362345679 0.9584567901
51 0.0251234568 0.6362345679
52 -0.0415432099 0.0251234568
53 0.3695679012 -0.0415432099
54 1.1251234568 0.3695679012
55 1.4806790123 1.1251234568
56 1.4584567901 1.4806790123
57 0.8168518519 1.4584567901
58 0.4168518519 0.8168518519
59 0.4543518519 0.4168518519
60 0.5560493827 0.4543518519
61 0.7671604938 0.5560493827
62 0.9449382716 0.7671604938
63 0.7338271605 0.9449382716
64 0.8671604938 0.7338271605
65 0.8782716049 0.8671604938
66 0.9338271605 0.8782716049
67 0.8893827160 0.9338271605
68 0.9671604938 0.8893827160
69 0.5070833333 0.9671604938
70 0.5070833333 0.5070833333
71 0.5445833333 0.5070833333
72 0.6462808642 0.5445833333
73 0.7573919753 0.6462808642
74 0.8351697531 0.7573919753
75 0.9240586420 0.8351697531
76 0.9573919753 0.9240586420
77 0.8685030864 0.9573919753
78 0.4240586420 0.8685030864
79 0.1796141975 0.4240586420
80 0.1573919753 0.1796141975
81 -0.2026851852 0.1573919753
82 -0.1026851852 -0.2026851852
83 -0.1651851852 -0.1026851852
84 -0.1634876543 -0.1651851852
85 -0.0523765432 -0.1634876543
86 0.0254012346 -0.0523765432
87 0.3142901235 0.0254012346
88 0.2476234568 0.3142901235
89 -0.1412654321 0.2476234568
90 -0.3857098765 -0.1412654321
91 -0.7301543210 -0.3857098765
92 -1.0523765432 -0.7301543210
93 -1.2124537037 -1.0523765432
94 -1.1124537037 -1.2124537037
95 -0.9749537037 -1.1124537037
96 -0.9732561728 -0.9749537037
97 -1.0621450617 -0.9732561728
98 -1.1843672840 -1.0621450617
99 -1.1954783951 -1.1843672840
100 -1.3621450617 -1.1954783951
101 -1.2510339506 -1.3621450617
102 -1.1954783951 -1.2510339506
103 -1.2399228395 -1.1954783951
104 -1.3621450617 -1.2399228395
105 NA -1.3621450617
> dum1 <- dum[2:length(myerror),]
> dum1
lag(myerror, k = 1) myerror
[1,] -0.2024691358 -0.0135802469
[2,] -0.3246913580 -0.2024691358
[3,] -0.3358024691 -0.3246913580
[4,] -0.4024691358 -0.3358024691
[5,] -0.3913580247 -0.4024691358
[6,] -0.4358024691 -0.3913580247
[7,] -0.0802469136 -0.4358024691
[8,] -0.3024691358 -0.0802469136
[9,] -0.4625462963 -0.3024691358
[10,] -0.6625462963 -0.4625462963
[11,] -1.0250462963 -0.6625462963
[12,] -1.3233487654 -1.0250462963
[13,] -1.4122376543 -1.3233487654
[14,] -1.2344598765 -1.4122376543
[15,] -0.8455709877 -1.2344598765
[16,] -0.6122376543 -0.8455709877
[17,] -0.8011265432 -0.6122376543
[18,] -1.1455709877 -0.8011265432
[19,] -1.0900154321 -1.1455709877
[20,] -0.7122376543 -1.0900154321
[21,] -0.1723148148 -0.7122376543
[22,] -0.0723148148 -0.1723148148
[23,] -0.0348148148 -0.0723148148
[24,] -0.1331172840 -0.0348148148
[25,] -0.2220061728 -0.1331172840
[26,] -0.1442283951 -0.2220061728
[27,] -0.1553395062 -0.1442283951
[28,] -0.1220061728 -0.1553395062
[29,] -0.1108950617 -0.1220061728
[30,] 0.0446604938 -0.1108950617
[31,] 0.0002160494 0.0446604938
[32,] 0.1779938272 0.0002160494
[33,] 0.2179166667 0.1779938272
[34,] 0.4179166667 0.2179166667
[35,] 0.4554166667 0.4179166667
[36,] 0.4571141975 0.4554166667
[37,] 0.4682253086 0.4571141975
[38,] 0.4460030864 0.4682253086
[39,] 0.5348919753 0.4460030864
[40,] 0.4682253086 0.5348919753
[41,] 0.5793364198 0.4682253086
[42,] 0.6348919753 0.5793364198
[43,] 0.5904475309 0.6348919753
[44,] 0.6682253086 0.5904475309
[45,] 0.5081481481 0.6682253086
[46,] 0.6081481481 0.5081481481
[47,] 0.7456481481 0.6081481481
[48,] 0.9473456790 0.7456481481
[49,] 0.9584567901 0.9473456790
[50,] 0.6362345679 0.9584567901
[51,] 0.0251234568 0.6362345679
[52,] -0.0415432099 0.0251234568
[53,] 0.3695679012 -0.0415432099
[54,] 1.1251234568 0.3695679012
[55,] 1.4806790123 1.1251234568
[56,] 1.4584567901 1.4806790123
[57,] 0.8168518519 1.4584567901
[58,] 0.4168518519 0.8168518519
[59,] 0.4543518519 0.4168518519
[60,] 0.5560493827 0.4543518519
[61,] 0.7671604938 0.5560493827
[62,] 0.9449382716 0.7671604938
[63,] 0.7338271605 0.9449382716
[64,] 0.8671604938 0.7338271605
[65,] 0.8782716049 0.8671604938
[66,] 0.9338271605 0.8782716049
[67,] 0.8893827160 0.9338271605
[68,] 0.9671604938 0.8893827160
[69,] 0.5070833333 0.9671604938
[70,] 0.5070833333 0.5070833333
[71,] 0.5445833333 0.5070833333
[72,] 0.6462808642 0.5445833333
[73,] 0.7573919753 0.6462808642
[74,] 0.8351697531 0.7573919753
[75,] 0.9240586420 0.8351697531
[76,] 0.9573919753 0.9240586420
[77,] 0.8685030864 0.9573919753
[78,] 0.4240586420 0.8685030864
[79,] 0.1796141975 0.4240586420
[80,] 0.1573919753 0.1796141975
[81,] -0.2026851852 0.1573919753
[82,] -0.1026851852 -0.2026851852
[83,] -0.1651851852 -0.1026851852
[84,] -0.1634876543 -0.1651851852
[85,] -0.0523765432 -0.1634876543
[86,] 0.0254012346 -0.0523765432
[87,] 0.3142901235 0.0254012346
[88,] 0.2476234568 0.3142901235
[89,] -0.1412654321 0.2476234568
[90,] -0.3857098765 -0.1412654321
[91,] -0.7301543210 -0.3857098765
[92,] -1.0523765432 -0.7301543210
[93,] -1.2124537037 -1.0523765432
[94,] -1.1124537037 -1.2124537037
[95,] -0.9749537037 -1.1124537037
[96,] -0.9732561728 -0.9749537037
[97,] -1.0621450617 -0.9732561728
[98,] -1.1843672840 -1.0621450617
[99,] -1.1954783951 -1.1843672840
[100,] -1.3621450617 -1.1954783951
[101,] -1.2510339506 -1.3621450617
[102,] -1.1954783951 -1.2510339506
[103,] -1.2399228395 -1.1954783951
[104,] -1.3621450617 -1.2399228395
> z <- as.data.frame(dum1)
> z
lag(myerror, k = 1) myerror
1 -0.2024691358 -0.0135802469
2 -0.3246913580 -0.2024691358
3 -0.3358024691 -0.3246913580
4 -0.4024691358 -0.3358024691
5 -0.3913580247 -0.4024691358
6 -0.4358024691 -0.3913580247
7 -0.0802469136 -0.4358024691
8 -0.3024691358 -0.0802469136
9 -0.4625462963 -0.3024691358
10 -0.6625462963 -0.4625462963
11 -1.0250462963 -0.6625462963
12 -1.3233487654 -1.0250462963
13 -1.4122376543 -1.3233487654
14 -1.2344598765 -1.4122376543
15 -0.8455709877 -1.2344598765
16 -0.6122376543 -0.8455709877
17 -0.8011265432 -0.6122376543
18 -1.1455709877 -0.8011265432
19 -1.0900154321 -1.1455709877
20 -0.7122376543 -1.0900154321
21 -0.1723148148 -0.7122376543
22 -0.0723148148 -0.1723148148
23 -0.0348148148 -0.0723148148
24 -0.1331172840 -0.0348148148
25 -0.2220061728 -0.1331172840
26 -0.1442283951 -0.2220061728
27 -0.1553395062 -0.1442283951
28 -0.1220061728 -0.1553395062
29 -0.1108950617 -0.1220061728
30 0.0446604938 -0.1108950617
31 0.0002160494 0.0446604938
32 0.1779938272 0.0002160494
33 0.2179166667 0.1779938272
34 0.4179166667 0.2179166667
35 0.4554166667 0.4179166667
36 0.4571141975 0.4554166667
37 0.4682253086 0.4571141975
38 0.4460030864 0.4682253086
39 0.5348919753 0.4460030864
40 0.4682253086 0.5348919753
41 0.5793364198 0.4682253086
42 0.6348919753 0.5793364198
43 0.5904475309 0.6348919753
44 0.6682253086 0.5904475309
45 0.5081481481 0.6682253086
46 0.6081481481 0.5081481481
47 0.7456481481 0.6081481481
48 0.9473456790 0.7456481481
49 0.9584567901 0.9473456790
50 0.6362345679 0.9584567901
51 0.0251234568 0.6362345679
52 -0.0415432099 0.0251234568
53 0.3695679012 -0.0415432099
54 1.1251234568 0.3695679012
55 1.4806790123 1.1251234568
56 1.4584567901 1.4806790123
57 0.8168518519 1.4584567901
58 0.4168518519 0.8168518519
59 0.4543518519 0.4168518519
60 0.5560493827 0.4543518519
61 0.7671604938 0.5560493827
62 0.9449382716 0.7671604938
63 0.7338271605 0.9449382716
64 0.8671604938 0.7338271605
65 0.8782716049 0.8671604938
66 0.9338271605 0.8782716049
67 0.8893827160 0.9338271605
68 0.9671604938 0.8893827160
69 0.5070833333 0.9671604938
70 0.5070833333 0.5070833333
71 0.5445833333 0.5070833333
72 0.6462808642 0.5445833333
73 0.7573919753 0.6462808642
74 0.8351697531 0.7573919753
75 0.9240586420 0.8351697531
76 0.9573919753 0.9240586420
77 0.8685030864 0.9573919753
78 0.4240586420 0.8685030864
79 0.1796141975 0.4240586420
80 0.1573919753 0.1796141975
81 -0.2026851852 0.1573919753
82 -0.1026851852 -0.2026851852
83 -0.1651851852 -0.1026851852
84 -0.1634876543 -0.1651851852
85 -0.0523765432 -0.1634876543
86 0.0254012346 -0.0523765432
87 0.3142901235 0.0254012346
88 0.2476234568 0.3142901235
89 -0.1412654321 0.2476234568
90 -0.3857098765 -0.1412654321
91 -0.7301543210 -0.3857098765
92 -1.0523765432 -0.7301543210
93 -1.2124537037 -1.0523765432
94 -1.1124537037 -1.2124537037
95 -0.9749537037 -1.1124537037
96 -0.9732561728 -0.9749537037
97 -1.0621450617 -0.9732561728
98 -1.1843672840 -1.0621450617
99 -1.1954783951 -1.1843672840
100 -1.3621450617 -1.1954783951
101 -1.2510339506 -1.3621450617
102 -1.1954783951 -1.2510339506
103 -1.2399228395 -1.1954783951
104 -1.3621450617 -1.2399228395
> 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/7sy5a1227789280.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556)
> acf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Autocorrelation Function')
> grid()
> dev.off()
null device
1
> postscript(file="/var/www/html/rcomp/tmp/8cy8u1227789280.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556)
> pacf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Partial Autocorrelation Function')
> grid()
> dev.off()
null device
1
> postscript(file="/var/www/html/rcomp/tmp/9t2q01227789280.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556)
> opar <- par(mfrow = c(2,2), oma = c(0, 0, 1.1, 0))
> plot(mylm, las = 1, sub='Residual Diagnostics')
> par(opar)
> dev.off()
null device
1
> if (n > n25) {
+ postscript(file="/var/www/html/rcomp/tmp/102e3o1227789280.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556)
+ plot(kp3:nmkm3,gqarr[,2], main='Goldfeld-Quandt test',ylab='2-sided p-value',xlab='breakpoint')
+ grid()
+ dev.off()
+ }
null device
1
>
> #Note: the /var/www/html/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab
> load(file="/var/www/html/rcomp/createtable")
>
> a<-table.start()
> a<-table.row.start(a)
> a<-table.element(a, 'Multiple Linear Regression - Estimated Regression Equation', 1, TRUE)
> a<-table.row.end(a)
> myeq <- colnames(x)[1]
> myeq <- paste(myeq, '[t] = ', sep='')
> for (i in 1:k){
+ if (mysum$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/111o1x1227789280.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/12c5wz1227789280.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/13nfe51227789280.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/14gkld1227789280.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/15hf5u1227789280.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/169mjy1227789280.tab")
+ }
>
> system("convert tmp/1b5zg1227789279.ps tmp/1b5zg1227789279.png")
> system("convert tmp/27l221227789279.ps tmp/27l221227789279.png")
> system("convert tmp/38h2b1227789279.ps tmp/38h2b1227789279.png")
> system("convert tmp/4icuf1227789279.ps tmp/4icuf1227789279.png")
> system("convert tmp/54o0l1227789279.ps tmp/54o0l1227789279.png")
> system("convert tmp/6euvj1227789279.ps tmp/6euvj1227789279.png")
> system("convert tmp/7sy5a1227789280.ps tmp/7sy5a1227789280.png")
> system("convert tmp/8cy8u1227789280.ps tmp/8cy8u1227789280.png")
> system("convert tmp/9t2q01227789280.ps tmp/9t2q01227789280.png")
> system("convert tmp/102e3o1227789280.ps tmp/102e3o1227789280.png")
>
>
> proc.time()
user system elapsed
3.050 1.593 3.559