Ws 7

*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: Fri, 20 Nov 2009 11:21:24 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Nov/20/t1258741333hwcv7k15g0l4pra.htm/, Retrieved Fri, 20 Nov 2009 19:22:25 +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/2009/Nov/20/t1258741333hwcv7k15g0l4pra.htm/}, year = {2009}, } @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 = {2009}, 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 «

18.0 16.4 19.6 17.8 23.3 22.3 23.7 22.8 20.3 18.3 22.8 22.4 24.3 23.9 21.5 21.3 23.5 23.0 22.2 21.4 20.9 21.2 22.2 20.9 19.5 17.9 21.1 20.7 22.0 22.2 19.2 19.8 17.8 17.7 19.2 19.6 19.9 20.8 19.6 19.8 18.1 18.6 20.4 21. 18.1 18.6 18.6 18.9 17.6 17.3 19.4 20.0 19.3 19.9 18.6 19.5 16.9 16.2 16.4 17.6 19.0 19.8 18.7 19.4 17.1 17.2 21.5 21.1 17.8 17.8 18.1 17.5 19.0 18.0 18.9 19.1 16.8 17.7 18.1 19.2 15.7 15.1 15.1 16.3 18.3 18.6 16.5 17.2 16.9 17.8 18.4 19.1 16.4 16.6 15.7 16.0 16.9 16.7 16.6 17.4 16.7 17.9 16.6 17.8 14.4 13.9 14.5 15.9 17.5 17.9 14.3 15.4 15.4 16.4 17.2 17.9 14.6 15.3 14.2 14.6 14.9 14.9 14.1 15.0 15.6 16.7 14.6 16.3 11.9 11.7 13.5 15.1 14.2 15.5 13.7 15.0 14.4 15.4 15.3 16.0 14.3 14.7 14.5 14.8

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 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Y[t] = -1.86988843332436 + 1.09005922831809X[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) -1.86988843332436 0.704185 -2.6554 0.009801 0.0049 X 1.09005922831809 0.038656 28.1987 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.958692162093623 R-squared 0.919090661659746 Adjusted R-squared 0.917934813969171 F-TEST (value) 795.16589352917 F-TEST (DF numerator) 1 F-TEST (DF denominator) 70 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.809424302599723 Sum Squared Residuals 45.8617391147334 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 18 16.0070829110923 1.9929170889077 2 19.6 17.5331658307376 2.06683416926241 3 23.3 22.4384323581690 0.861567641831023 4 23.7 22.9834619723280 0.716538027671978 5 20.3 18.0781954448966 2.22180455510337 6 22.8 22.5474382810008 0.252561718999217 7 24.3 24.1825271234779 0.117472876522087 8 21.5 21.3483731298509 0.151626870149109 9 23.5 23.2014738179916 0.298526182008362 10 22.2 21.4573790526827 0.742620947317302 11 20.9 21.2393672070191 -0.339367207019082 12 22.2 20.9123494385237 1.28765056147635 13 19.5 17.6421717535694 1.85782824643061 14 21.1 20.6943375928600 0.405662407139965 15 22 22.3294264353372 -0.329426435337167 16 19.2 19.7132842873738 -0.513284287373761 17 17.8 17.4241599079058 0.375840092094224 18 19.2 19.4952724417101 -0.295272441710145 19 19.9 20.8033435156918 -0.903343515691849 20 19.6 19.7132842873738 -0.113284287373759 21 18.1 18.4052132133921 -0.305213213392056 22 20.4 21.0213553613555 -0.621355361355466 23 18.1 18.4052132133921 -0.305213213392056 24 18.6 18.7322309818875 -0.132230981887479 25 17.6 16.9881362165785 0.611863783421458 26 19.4 19.9312961330374 -0.531296133037379 27 19.3 19.8222902102056 -0.522290210205566 28 18.6 19.3862665188783 -0.786266518878332 29 16.9 15.7890710654286 1.11092893457135 30 16.4 17.3151539850740 -0.915153985073972 31 19 19.7132842873738 -0.713284287373761 32 18.7 19.2772605960465 -0.577260596046524 33 17.1 16.8791302937467 0.220869706253268 34 21.5 21.1303612841873 0.369638715812726 35 17.8 17.5331658307376 0.266834169262414 36 18.1 17.2061480622422 0.893851937757841 37 19 17.7511776764012 1.24882232359880 38 18.9 18.9502428275511 -0.050242827551102 39 16.8 17.4241599079058 -0.624159907905776 40 18.1 19.0592487503829 -0.959248750382905 41 15.7 14.5900059142788 1.10999408572125 42 15.1 15.8980769882605 -0.798076988260457 43 18.3 18.4052132133921 -0.105213213392056 44 16.5 16.8791302937467 -0.379130293746733 45 16.9 17.5331658307376 -0.633165830737588 46 18.4 18.9502428275511 -0.550242827551102 47 16.4 16.2250947567559 0.174905243244115 48 15.7 15.5710592197650 0.128940780234969 49 16.9 16.3341006795877 0.565899320412309 50 16.6 17.0971421394104 -0.497142139410349 51 16.7 17.6421717535694 -0.942171753569394 52 16.6 17.5331658307376 -0.933165830737586 53 14.4 13.2819348402970 1.11806515970295 54 14.5 15.4620532969332 -0.962053296933222 55 17.5 17.6421717535694 -0.142171753569393 56 14.3 14.9170236827742 -0.617023682774178 57 15.4 16.0070829110923 -0.607082911092263 58 17.2 17.6421717535694 -0.442171753569394 59 14.6 14.8080177599424 -0.208017759942370 60 14.2 14.0449763001197 0.155023699880291 61 14.9 14.3719940686151 0.528005931384865 62 14.1 14.4809999914469 -0.380999991446944 63 15.6 16.3341006795877 -0.73410067958769 64 14.6 15.8980769882605 -1.29807698826046 65 11.9 10.8838045379973 1.01619546200274 66 13.5 14.5900059142788 -1.09000591427875 67 14.2 15.0260296056060 -0.826029605605987 68 13.7 14.4809999914469 -0.780999991446944 69 14.4 14.9170236827742 -0.517023682774178 70 15.3 15.5710592197650 -0.271059219765029 71 14.3 14.1539822229515 0.146017777048484 72 14.5 14.2629881457833 0.237011854216673 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 0.0879894781837294 0.175978956367459 0.91201052181627 6 0.109322579870755 0.218645159741510 0.890677420129245 7 0.0507323155755954 0.101464631151191 0.949267684424405 8 0.113619909266188 0.227239818532376 0.886380090733812 9 0.0620477901398665 0.124095580279733 0.937952209860134 10 0.0351613740771529 0.0703227481543059 0.964838625922847 11 0.179161988130851 0.358323976261702 0.82083801186915 12 0.186006978680771 0.372013957361541 0.81399302131923 13 0.209868177537428 0.419736355074855 0.790131822462573 14 0.216726225180914 0.433452450361828 0.783273774819086 15 0.258791453168791 0.517582906337581 0.741208546831209 16 0.647802691900097 0.704394616199807 0.352197308099903 17 0.763136528688076 0.473726942623848 0.236863471311924 18 0.837234631704201 0.325530736591597 0.162765368295799 19 0.91494819211673 0.17010361576654 0.08505180788327 20 0.914086116601828 0.171827766796344 0.0859138833981718 21 0.935069711949611 0.129860576100777 0.0649302880503887 22 0.936142795992415 0.127714408015170 0.0638572040075848 23 0.941778500336307 0.116442999327386 0.0582214996636932 24 0.934791671917591 0.130416656164817 0.0652083280824086 25 0.927093367780395 0.145813264439211 0.0729066322196055 26 0.923627841328919 0.152744317342163 0.0763721586710813 27 0.917823817153975 0.164352365692051 0.0821761828460255 28 0.927074320846162 0.145851358307676 0.072925679153838 29 0.938074196454099 0.123851607091802 0.0619258035459011 30 0.961860062909505 0.0762798741809903 0.0381399370904952 31 0.958885947538335 0.08222810492333 0.041114052461665 32 0.952060793599196 0.0958784128016079 0.0479392064008039 33 0.938178530522884 0.123642938954233 0.0618214694771164 34 0.940763328584768 0.118473342830465 0.0592366714152323 35 0.929322965609145 0.141354068781711 0.0706770343908553 36 0.949602332518056 0.100795334963888 0.0503976674819442 37 0.988930612053154 0.0221387758936918 0.0110693879468459 38 0.98912437014858 0.0217512597028385 0.0108756298514193 39 0.987764728761765 0.0244705424764693 0.0122352712382347 40 0.986983514079233 0.0260329718415347 0.0130164859207673 41 0.993594616860872 0.0128107662782570 0.00640538313912848 42 0.994477182713451 0.0110456345730975 0.00552281728654873 43 0.99413994364589 0.0117201127082176 0.00586005635410881 44 0.991632094851948 0.0167358102961042 0.0083679051480521 45 0.988576368605601 0.0228472627887976 0.0114236313943988 46 0.985945947975429 0.0281081040491426 0.0140540520245713 47 0.984337761654986 0.031324476690027 0.0156622383450135 48 0.979674404216127 0.0406511915677471 0.0203255957838736 49 0.990958164441276 0.0180836711174485 0.00904183555872425 50 0.987691432315885 0.0246171353682301 0.0123085676841151 51 0.98343437183381 0.0331312563323805 0.0165656281661902 52 0.977240465842374 0.0455190683152526 0.0227595341576263 53 0.988704463770273 0.0225910724594544 0.0112955362297272 54 0.988648926975736 0.0227021460485277 0.0113510730242639 55 0.992900772490808 0.0141984550183835 0.00709922750919175 56 0.989015899324737 0.0219682013505260 0.0109841006752630 57 0.980930894004468 0.0381382119910647 0.0190691059955323 58 0.988418878361802 0.023162243276397 0.0115811216381985 59 0.978871432309137 0.0422571353817269 0.0211285676908635 60 0.964269053394728 0.0714618932105432 0.0357309466052716 61 0.978410894608649 0.0431782107827015 0.0215891053913508 62 0.95739077607793 0.0852184478441398 0.0426092239220699 63 0.937536716759945 0.124926566480111 0.0624632832400554 64 0.912413782777501 0.175172434444999 0.0875862172224993 65 0.842089988387512 0.315820023224976 0.157910011612488 66 0.878297309615333 0.243405380769335 0.121702690384667 67 0.820148913214373 0.359702173571254 0.179851086785627 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 0 0 OK 5% type I error level 24 0.380952380952381 NOK 10% type I error level 30 0.476190476190476 NOK

Charts produced by software:

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Parameters (Session):

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