Home » date » 2008 » Dec » 16 »

Consumptiegoederen met seizoenale en lange termijn trend

*The author of this computation has been verified*
R Software Module: rwasp_multipleregression.wasp (opens new window with default values)
Title produced by software: Multiple Regression
Date of computation: Tue, 16 Dec 2008 05:45:53 -0700
 
Cite this page as follows:
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Dec/16/t122943160544qsydouvh0m9on.htm/, Retrieved Tue, 16 Dec 2008 13:46:55 +0100
 
BibTeX entries for LaTeX users:
@Manual{KEY,
    author = {{YOUR NAME}},
    publisher = {Office for Research Development and Education},
    title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2008/Dec/16/t122943160544qsydouvh0m9on.htm/},
    year = {2008},
}
@Manual{R,
    title = {R: A Language and Environment for Statistical Computing},
    author = {{R Development Core Team}},
    organization = {R Foundation for Statistical Computing},
    address = {Vienna, Austria},
    year = {2008},
    note = {{ISBN} 3-900051-07-0},
    url = {http://www.R-project.org},
}
 
Original text written by user:
 
IsPrivate?
No (this computation is public)
 
User-defined keywords:
 
Dataseries X:
» Textbox « » Textfile « » CSV «
98.5 0 97.0 0 103.3 0 99.6 0 100.1 0 102.9 0 95.9 0 94.5 0 107.4 0 116.0 0 102.8 0 99.8 0 109.6 0 103.0 0 111.6 0 106.3 0 97.9 0 108.8 0 103.9 0 101.2 0 122.9 0 123.9 0 111.7 0 120.9 0 99.6 0 103.3 0 119.4 0 106.5 0 101.9 0 124.6 0 106.5 0 107.8 0 127.4 0 120.1 0 118.5 0 127.7 0 107.7 0 104.5 0 118.8 0 110.3 0 109.6 0 119.1 0 96.5 0 106.7 0 126.3 0 116.2 0 118.8 0 115.2 0 110.0 0 111.4 0 129.6 0 108.1 0 117.8 0 122.9 0 100.6 0 111.8 0 127.0 0 128.6 0 124.8 0 118.5 0 114.7 0 112.6 0 128.7 0 111.0 0 115.8 0 126.0 0 111.1 1 113.2 1 120.1 1 130.6 1 124.0 1 119.4 1 116.7 1 116.5 1 119.6 1 126.5 1 111.3 1 123.5 1 114.2 1 103.7 1 129.5 1
 
Output produced by software:

Enter (or paste) a matrix (table) containing all data (time) series. Every column represents a different variable and must be delimited by a space or Tab. Every row represents a period in time (or category) and must be delimited by hard returns. The easiest way to enter data is to copy and paste a block of spreadsheet cells. Please, do not use commas or spaces to seperate groups of digits!


Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135


Multiple Linear Regression - Estimated Regression Equation
Y[t] = + 101.931799517928 -4.85601080442307X[t] + 0.291678530898587t + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)101.9317995179281.98663151.308900
X-4.856010804423073.09841-1.56730.1211020.060551
t0.2916785308985870.0514775.666200


Multiple Linear Regression - Regression Statistics
Multiple R0.58846223881155
R-squared0.346287806507102
Adjusted R-squared0.329525955391900
F-TEST (value)20.6592818494271
F-TEST (DF numerator)2
F-TEST (DF denominator)78
p-value6.3106899927945e-08
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation8.01326014010615
Sum Squared Residuals5008.5623696951


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
198.5102.223478048827-3.72347804882674
297102.515156579725-5.51515657972479
3103.3102.8068351106230.493164889376648
499.6103.098513641522-3.49851364152198
5100.1103.390192172421-3.29019217242057
6102.9103.681870703319-0.78187070331914
795.9103.973549234218-8.07354923421773
894.5104.265227765116-9.76522776511632
9107.4104.5569062960152.8430937039851
10116104.84858482691311.1514151730865
11102.8105.140263357812-2.34026335781209
1299.8105.431941888711-5.63194188871067
13109.6105.7236204196093.87637958039074
14103106.015298950508-3.01529895050784
15111.6106.3069774814065.29302251859356
16106.3106.598656012305-0.298656012305021
1797.9106.890334543204-8.9903345432036
18108.8107.1820130741021.61798692589780
19103.9107.473691605001-3.57369160500077
20101.2107.765370135899-6.56537013589937
21122.9108.05704866679814.8429513332021
22123.9108.34872719769715.5512728023035
23111.7108.6404057285953.05959427140487
24120.9108.93208425949411.9679157405063
2599.6109.223762790392-9.6237627903923
26103.3109.515441321291-6.21544132129089
27119.4109.8071198521899.59288014781053
28106.5110.098798383088-3.59879838308806
29101.9110.390476913987-8.49047691398665
30124.6110.68215544488513.9178445551148
31106.5110.973833975784-4.47383397578383
32107.8111.265512506682-3.46551250668242
33127.4111.55719103758115.842808962419
34120.1111.8488695684808.2511304315204
35118.5112.1405480993786.35945190062182
36127.7112.43222663027715.2677733697232
37107.7112.723905161175-5.02390516117535
38104.5113.015583692074-8.51558369207394
39118.8113.3072622229735.49273777702747
40110.3113.598940753871-3.29894075387111
41109.6113.890619284770-4.29061928476971
42119.1114.1822978156684.91770218433171
4396.5114.473976346567-17.9739763465669
44106.7114.765654877465-8.06565487746546
45126.3115.05733340836411.2426665916359
46116.2115.3490119392630.850988060737367
47118.8115.6406904701613.15930952983877
48115.2115.932369001060-0.732369001059807
49110116.224047531958-6.2240475319584
50111.4116.515726062857-5.11572606285698
51129.6116.80740459375612.7925954062444
52108.1117.099083124654-8.99908312465416
53117.8117.3907616555530.40923834444725
54122.9117.6824401864515.21755981354867
55100.6117.97411871735-17.3741187173499
56111.8118.265797248249-6.46579724824851
57127118.5574757791478.4425242208529
58128.6118.8491543100469.75084568995431
59124.8119.1408328409445.65916715905573
60118.5119.432511371843-0.932511371842858
61114.7119.724189902741-5.02418990274144
62112.6120.01586843364-7.41586843364004
63128.7120.3075469645398.39245303546137
64111120.599225495437-9.5992254954372
65115.8120.890904026336-5.09090402633579
66126121.1825825572344.81741744276562
67111.1116.61825028371-5.51825028370989
68113.2116.909928814608-3.70992881460847
69120.1117.2016073455072.89839265449293
70130.6117.49328587640613.1067141235943
71124117.7849644073046.21503559269576
72119.4118.0766429382031.32335706179718
73116.7118.368321469101-1.66832146910141
74116.5118.66-2.16
75119.6118.9516785308990.648321469101408
76126.5119.2433570617977.25664293820283
77111.3119.535035592696-8.23503559269576
78123.5119.8267141235943.67328587640565
79114.2120.118392654493-5.91839265449293
80103.7120.410071185392-16.7100711853915
81129.5120.701749716298.79825028370989


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
60.03753730492662290.07507460985324580.962462695073377
70.04738029378313050.0947605875662610.95261970621687
80.03317251432862850.0663450286572570.966827485671371
90.07227029727860040.1445405945572010.9277297027214
100.2210212363432530.4420424726865060.778978763656747
110.1618258338820350.3236516677640710.838174166117965
120.1429816562188310.2859633124376630.857018343781169
130.1012315559359370.2024631118718740.898768444064063
140.07226864626313690.1445372925262740.927731353736863
150.052303006406840.104606012813680.94769699359316
160.03242905346628560.06485810693257120.967570946533714
170.05623539605691820.1124707921138360.943764603943082
180.03563541419034590.07127082838069180.964364585809654
190.02555206825761330.05110413651522660.974447931742387
200.02413312237368040.04826624474736090.97586687762632
210.09154742333084370.1830948466616870.908452576669156
220.1674871014191070.3349742028382150.832512898580893
230.1240917697835440.2481835395670890.875908230216456
240.1240192501600130.2480385003200260.875980749839987
250.2378493109973120.4756986219946250.762150689002688
260.2641372168957360.5282744337914720.735862783104264
270.2447447044530990.4894894089061990.7552552955469
280.2319907135365960.4639814270731930.768009286463404
290.2894162786018010.5788325572036010.7105837213982
300.3483845780328240.6967691560656490.651615421967175
310.3399849925232150.679969985046430.660015007476785
320.3149205069371480.6298410138742960.685079493062852
330.4173293787446830.8346587574893660.582670621255317
340.3811051498002570.7622102996005150.618894850199743
350.3336198264516880.6672396529033760.666380173548312
360.4341822491178230.8683644982356470.565817750882177
370.4456477155880550.891295431176110.554352284411945
380.5064905223892110.9870189552215770.493509477610789
390.4617178655528150.923435731105630.538282134447185
400.4289667700115860.8579335400231720.571033229988414
410.4022581124967030.8045162249934050.597741887503297
420.3577728862385600.7155457724771190.64222711376144
430.6495236332428660.7009527335142690.350476366757134
440.6717154702048420.6565690595903160.328284529795158
450.699415181899920.6011696362001620.300584818100081
460.6394253698380280.7211492603239450.360574630161972
470.5814126322442840.8371747355114310.418587367755716
480.517909981598280.964180036803440.48209001840172
490.4998364065375270.9996728130750540.500163593462473
500.4706570474506880.9413140949013770.529342952549312
510.5505633589901190.8988732820197630.449436641009881
520.5745201172696010.8509597654607990.425479882730399
530.5052848796149130.9894302407701750.494715120385087
540.4597232620396650.919446524079330.540276737960335
550.7331520689167210.5336958621665580.266847931083279
560.7442650252674360.5114699494651280.255734974732564
570.7242384584702770.5515230830594450.275761541529723
580.7387003924824360.5225992150351280.261299607517564
590.7102040234250950.5795919531498090.289795976574905
600.6411476624230140.7177046751539720.358852337576986
610.5860908638712770.8278182722574470.413909136128723
620.5685360993346630.8629278013306740.431463900665337
630.5946947801028410.8106104397943180.405305219897159
640.6026363074906940.7947273850186110.397363692509306
650.5800275024567460.8399449950865090.419972497543254
660.4951900812342780.9903801624685550.504809918765722
670.4953652298933340.9907304597866690.504634770106666
680.5036824733806630.9926350532386740.496317526619337
690.4270710043902880.8541420087805760.572928995609712
700.4470770907187050.8941541814374090.552922909281295
710.3683367571037130.7366735142074250.631663242896287
720.2653369589433890.5306739178867790.734663041056611
730.1774544545856920.3549089091713830.822545545414308
740.1093860234818170.2187720469636340.890613976518183
750.05490915049328510.1098183009865700.945090849506715


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level00OK
5% type I error level10.0142857142857143OK
10% type I error level70.1NOK
 
Charts produced by software:
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Parameters (Session):
par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ;
 
Parameters (R input):
par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ;
 
R code (references can be found in the software module):
library(lattice)
library(lmtest)
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
k <- length(x[1,])
df <- as.data.frame(x)
(mylm <- lm(df))
(mysum <- summary(mylm))
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)$p.value
}
if (gqarr[mypoint-kp3+1,2] < 0.01) numsignificant1 <- numsignificant1 + 1
if (gqarr[mypoint-kp3+1,2] < 0.05) numsignificant5 <- numsignificant5 + 1
if (gqarr[mypoint-kp3+1,2] < 0.10) numsignificant10 <- numsignificant10 + 1
}
gqarr
}
bitmap(file='test0.png')
plot(x[,1], type='l', main='Actuals and Interpolation', ylab='value of Actuals and Interpolation (dots)', xlab='time or index')
points(x[,1]-mysum$resid)
grid()
dev.off()
bitmap(file='test1.png')
plot(mysum$resid, type='b', pch=19, main='Residuals', ylab='value of Residuals', xlab='time or index')
grid()
dev.off()
bitmap(file='test2.png')
hist(mysum$resid, main='Residual Histogram', xlab='values of Residuals')
grid()
dev.off()
bitmap(file='test3.png')
densityplot(~mysum$resid,col='black',main='Residual Density Plot', xlab='values of Residuals')
dev.off()
bitmap(file='test4.png')
qqnorm(mysum$resid, main='Residual Normal Q-Q Plot')
qqline(mysum$resid)
grid()
dev.off()
(myerror <- as.ts(mysum$resid))
bitmap(file='test5.png')
dum <- cbind(lag(myerror,k=1),myerror)
dum
dum1 <- dum[2:length(myerror),]
dum1
z <- as.data.frame(dum1)
z
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()
bitmap(file='test6.png')
acf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Autocorrelation Function')
grid()
dev.off()
bitmap(file='test7.png')
pacf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Partial Autocorrelation Function')
grid()
dev.off()
bitmap(file='test8.png')
opar <- par(mfrow = c(2,2), oma = c(0, 0, 1.1, 0))
plot(mylm, las = 1, sub='Residual Diagnostics')
par(opar)
dev.off()
if (n > n25) {
bitmap(file='test9.png')
plot(kp3:nmkm3,gqarr[,2], main='Goldfeld-Quandt test',ylab='2-sided p-value',xlab='breakpoint')
grid()
dev.off()
}
load(file='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$coefficients)[i] != 't') myeq <- paste(myeq, '[t]', sep='')
}
}
myeq <- paste(myeq, ' + e[t]')
a<-table.row.start(a)
a<-table.element(a, myeq)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,hyperlink('http://www.xycoon.com/ols1.htm','Multiple Linear Regression - Ordinary Least Squares',''), 6, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Variable',header=TRUE)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'S.D.',header=TRUE)
a<-table.element(a,'T-STAT<br />H0: parameter = 0',header=TRUE)
a<-table.element(a,'2-tail p-value',header=TRUE)
a<-table.element(a,'1-tail p-value',header=TRUE)
a<-table.row.end(a)
for (i in 1:k){
a<-table.row.start(a)
a<-table.element(a,rownames(mysum$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$coefficients[i,4]/2,6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Regression Statistics', 2, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Multiple R',1,TRUE)
a<-table.element(a, sqrt(mysum$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$sigma)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Sum Squared Residuals',1,TRUE)
a<-table.element(a, sum(myerror*myerror))
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable3.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Actuals, Interpolation, and Residuals', 4, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Time or Index', 1, TRUE)
a<-table.element(a, 'Actuals', 1, TRUE)
a<-table.element(a, 'Interpolation<br />Forecast', 1, TRUE)
a<-table.element(a, 'Residuals<br />Prediction Error', 1, TRUE)
a<-table.row.end(a)
for (i in 1:n) {
a<-table.row.start(a)
a<-table.element(a,i, 1, TRUE)
a<-table.element(a,x[i])
a<-table.element(a,x[i]-mysum$resid[i])
a<-table.element(a,mysum$resid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable4.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='mytable5.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='mytable6.tab')
}
 





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Software written by Ed van Stee & Patrick Wessa


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