Paper: Multiple Regression met dummy: Toetreding van Slovenië tot de EU zonder seasonal dummies en linear 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: Sun, 14 Dec 2008 06:58:55 -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/14/t12292632210b664cjxb0npe68.htm/, Retrieved Sun, 14 Dec 2008 15:00:31 +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/14/t12292632210b664cjxb0npe68.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:

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17.3 0 15.4 0 16.9 0 20.8 0 16.4 0 11.3 0 17.5 0 16.6 0 17.5 0 19.5 0 18.8 0 20.2 0 19.2 0 14.4 0 24.5 0 25.7 0 27.1 0 21 0 18.6 0 20 0 21.8 0 20.4 0 18 1 21.5 1 19.1 1 19.7 1 26 1 26.3 1 24.6 1 22.4 1 32 1 24 1 30 1 24.1 1 26.3 1 29.8 1 21.9 1 22.8 1 29.2 1 27.5 1 27.4 1 31 1 26.1 1 22.2 1 34 1 26.9 1 31.9 1 34.2 1 31.2 1 28.5 1 37.1 1 36 1 34.8 1 32.1 1 37.2 1 36.3 1 39.5 1 37.1 1 35.6 1 36.2 1 35.9 1 32.5 1 39.2 1 39.4 1 42.8 1 34.5 1 43.7 1 46.3 1 40.8 1 48.4 1 43.2 1 48.1 1 42.8 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 Input view raw input (R code) Raw Output view raw output of R engine Computing time 4 seconds R Server 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation Aantal_werklozen[t] = + 19.1318181818182 + 12.9877896613191Dummyvariabele[t] + e[t] Multiple Linear Regression - Ordinary Least Squares Variable Parameter S.D. T-STAT H0: parameter = 0 2-tail p-value 1-tail p-value (Intercept) 19.1318181818182 1.462771 13.0792 0 0 Dummyvariabele 12.9877896613191 1.750059 7.4213 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.66094575496907 R-squared 0.436849291011634 Adjusted R-squared 0.428917590885037 F-TEST (value) 55.076375056942 F-TEST (DF numerator) 1 F-TEST (DF denominator) 71 p-value 1.96981209121816e-10 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 6.8610023899415 Sum Squared Residuals 3342.20811942959 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 17.3 19.1318181818180 -1.83181818181804 2 15.4 19.1318181818182 -3.73181818181822 3 16.9 19.1318181818182 -2.23181818181819 4 20.8 19.1318181818182 1.66818181818181 5 16.4 19.1318181818182 -2.73181818181819 6 11.3 19.1318181818182 -7.83181818181819 7 17.5 19.1318181818182 -1.63181818181819 8 16.6 19.1318181818182 -2.53181818181819 9 17.5 19.1318181818182 -1.63181818181819 10 19.5 19.1318181818182 0.368181818181813 11 18.8 19.1318181818182 -0.331818181818186 12 20.2 19.1318181818182 1.06818181818181 13 19.2 19.1318181818182 0.0681818181818123 14 14.4 19.1318181818182 -4.73181818181819 15 24.5 19.1318181818182 5.36818181818181 16 25.7 19.1318181818182 6.56818181818181 17 27.1 19.1318181818182 7.96818181818181 18 21 19.1318181818182 1.86818181818181 19 18.6 19.1318181818182 -0.531818181818186 20 20 19.1318181818182 0.868181818181813 21 21.8 19.1318181818182 2.66818181818181 22 20.4 19.1318181818182 1.26818181818181 23 18 32.1196078431373 -14.1196078431373 24 21.5 32.1196078431373 -10.6196078431373 25 19.1 32.1196078431373 -13.0196078431373 26 19.7 32.1196078431373 -12.4196078431373 27 26 32.1196078431373 -6.11960784313725 28 26.3 32.1196078431373 -5.81960784313725 29 24.6 32.1196078431373 -7.51960784313725 30 22.4 32.1196078431373 -9.71960784313726 31 32 32.1196078431373 -0.119607843137254 32 24 32.1196078431373 -8.11960784313725 33 30 32.1196078431373 -2.11960784313725 34 24.1 32.1196078431373 -8.01960784313725 35 26.3 32.1196078431373 -5.81960784313725 36 29.8 32.1196078431373 -2.31960784313725 37 21.9 32.1196078431373 -10.2196078431373 38 22.8 32.1196078431373 -9.31960784313725 39 29.2 32.1196078431373 -2.91960784313726 40 27.5 32.1196078431373 -4.61960784313725 41 27.4 32.1196078431373 -4.71960784313726 42 31 32.1196078431373 -1.11960784313725 43 26.1 32.1196078431373 -6.01960784313725 44 22.2 32.1196078431373 -9.91960784313726 45 34 32.1196078431373 1.88039215686275 46 26.9 32.1196078431373 -5.21960784313726 47 31.9 32.1196078431373 -0.219607843137256 48 34.2 32.1196078431373 2.08039215686275 49 31.2 32.1196078431373 -0.919607843137255 50 28.5 32.1196078431373 -3.61960784313725 51 37.1 32.1196078431373 4.98039215686275 52 36 32.1196078431373 3.88039215686275 53 34.8 32.1196078431373 2.68039215686274 54 32.1 32.1196078431373 -0.0196078431372529 55 37.2 32.1196078431373 5.08039215686275 56 36.3 32.1196078431373 4.18039215686274 57 39.5 32.1196078431373 7.38039215686275 58 37.1 32.1196078431373 4.98039215686275 59 35.6 32.1196078431373 3.48039215686275 60 36.2 32.1196078431373 4.08039215686275 61 35.9 32.1196078431373 3.78039215686274 62 32.5 32.1196078431373 0.380392156862746 63 39.2 32.1196078431373 7.08039215686275 64 39.4 32.1196078431373 7.28039215686274 65 42.8 32.1196078431373 10.6803921568627 66 34.5 32.1196078431373 2.38039215686275 67 43.7 32.1196078431373 11.5803921568627 68 46.3 32.1196078431373 14.1803921568627 69 40.8 32.1196078431373 8.68039215686274 70 48.4 32.1196078431373 16.2803921568627 71 43.2 32.1196078431373 11.0803921568627 72 48.1 32.1196078431373 15.9803921568627 73 42.8 32.1196078431373 10.6803921568627 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 0.047150717330194 0.094301434660388 0.952849282669806 6 0.0844085911136645 0.168817182227329 0.915591408886336 7 0.0357548428020319 0.0715096856040638 0.964245157197968 8 0.0134953099653019 0.0269906199306039 0.986504690034698 9 0.0049851193727975 0.009970238745595 0.995014880627203 10 0.00268565893957283 0.00537131787914566 0.997314341060427 11 0.00111010430721115 0.00222020861442229 0.998889895692789 12 0.000656107029286813 0.00131221405857363 0.999343892970713 13 0.000267419560271404 0.000534839120542808 0.999732580439729 14 0.000172736499336287 0.000345472998672575 0.999827263500664 15 0.000774828434484736 0.00154965686896947 0.999225171565515 16 0.00252929328788521 0.00505858657577043 0.997470706712115 17 0.00745468767812649 0.0149093753562530 0.992545312321873 18 0.00420302980792010 0.00840605961584019 0.99579697019208 19 0.00210177590320141 0.00420355180640281 0.997898224096799 20 0.00103812406432330 0.00207624812864661 0.998961875935677 21 0.000589857392246785 0.00117971478449357 0.999410142607753 22 0.000280654258193369 0.000561308516386739 0.999719345741807 23 0.000212245340172568 0.000424490680345137 0.999787754659827 24 0.000159567081989379 0.000319134163978758 0.99984043291801 25 0.000129300944972526 0.000258601889945053 0.999870699055027 26 0.000108126040270982 0.000216252080541965 0.999891873959729 27 0.000157143803300465 0.000314287606600930 0.9998428561967 28 0.000174152165435566 0.000348304330871133 0.999825847834564 29 0.000137655161417148 0.000275310322834296 0.999862344838583 30 0.000116110690934502 0.000232221381869003 0.999883889309066 31 0.000437904634079134 0.000875809268158269 0.999562095365921 32 0.000361947020377221 0.000723894040754441 0.999638052979623 33 0.000461522791788585 0.00092304558357717 0.999538477208211 34 0.000412265969820459 0.000824531939640917 0.99958773403018 35 0.000346801615742914 0.000693603231485827 0.999653198384257 36 0.000373878491650229 0.000747756983300457 0.99962612150835 37 0.000631641182916792 0.00126328236583358 0.999368358817083 38 0.00101588054785126 0.00203176109570251 0.998984119452149 39 0.00113387628724458 0.00226775257448916 0.998866123712755 40 0.00122200046084166 0.00244400092168333 0.998777999539158 41 0.00139864527489922 0.00279729054979844 0.9986013547251 42 0.00179060962084616 0.00358121924169233 0.998209390379154 43 0.00265163568940001 0.00530327137880002 0.9973483643106 44 0.0130790818819194 0.0261581637638388 0.98692091811808 45 0.0222862605320097 0.0445725210640193 0.97771373946799 46 0.0426879731787146 0.0853759463574292 0.957312026821285 47 0.057955089660455 0.11591017932091 0.942044910339545 48 0.0783451861683431 0.156690372336686 0.921654813831657 49 0.103986008850350 0.207972017700700 0.89601399114965 50 0.195684724933596 0.391369449867193 0.804315275066404 51 0.251991188136812 0.503982376273625 0.748008811863188 52 0.285966408045606 0.571932816091212 0.714033591954394 53 0.314515122597718 0.629030245195435 0.685484877402282 54 0.397877599032449 0.795755198064898 0.602122400967551 55 0.419308731615379 0.838617463230757 0.580691268384621 56 0.434526164104986 0.869052328209971 0.565473835895014 57 0.444455682995552 0.888911365991105 0.555544317004448 58 0.436577798012384 0.873155596024768 0.563422201987616 59 0.448200274798821 0.896400549597642 0.551799725201179 60 0.45444832991361 0.90889665982722 0.54555167008639 61 0.477183298654176 0.954366597308353 0.522816701345824 62 0.705577173848764 0.588845652302472 0.294422826151236 63 0.692200983907411 0.615598032185179 0.307799016092589 64 0.674526749439473 0.650946501121053 0.325473250560527 65 0.608776696774342 0.782446606451317 0.391223303225658 66 0.89941079599885 0.201178408002302 0.100589204001151 67 0.834492709344457 0.331014581311086 0.165507290655543 68 0.739033786475502 0.521932427048996 0.260966213524498 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 34 0.53125 NOK 5% type I error level 38 0.59375 NOK 10% type I error level 41 0.640625 NOK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No 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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