Multiple Regression met monthly dummies en een lineaire 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: Fri, 20 Nov 2009 10:26:11 -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/t1258738054bkgxt2i6mpwzovh.htm/, Retrieved Fri, 20 Nov 2009 18:27:47 +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/t1258738054bkgxt2i6mpwzovh.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:

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7.3 7.9 7.6 9.1 7.5 9.4 7.6 9.4 7.9 9.1 7.9 9 8.1 9.3 8.2 9.9 8 9.8 7.5 9.3 6.8 8.3 6.5 8 6.6 8.5 7.6 10.4 8 11.1 8.1 10.9 7.7 10 7.5 9.2 7.6 9.2 7.8 9.5 7.8 9.6 7.8 9.5 7.5 9.1 7.5 8.9 7.1 9 7.5 10.1 7.5 10.3 7.6 10.2 7.7 9.6 7.7 9.2 7.9 9.3 8.1 9.4 8.2 9.4 8.2 9.2 8.2 9 7.9 9 7.3 9 6.9 9.8 6.6 10 6.7 9.8 6.9 9.3 7 9 7.1 9 7.2 9.1 7.1 9.1 6.9 9.1 7 9.2 6.8 8.8 6.4 8.3 6.7 8.4 6.6 8.1 6.4 7.7 6.3 7.9 6.2 7.9 6.5 8 6.8 7.9 6.8 7.6 6.4 7.1 6.1 6.8 5.8 6.5 6.1 6.9 7.2 8.2 7.3 8.7 6.9 8.3 6.1 7.9 5.8 7.5 6.2 7.8 7.1 8.3 7.7 8.4 7.9 8.2 7.7 7.7 7.4 7.2 7.5 7.3

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 3 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation WGM[t] = + 3.77933636549804 + 0.421915736108744WGV[t] -0.133196764232351M1[t] -0.315249607827085M2[t] -0.423011503247149M3[t] -0.36018079288132M4[t] -0.296300268627076M5[t] -0.234246055715227M6[t] -0.0690858529874588M7[t] + 0.130184180527623M8[t] + 0.215663672606848M9[t] + 0.175891574176302M10[t] + 0.109041573893588M11[t] -0.00474896754226758t + 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) 3.77933636549804 0.891344 4.24 8e-05 4e-05 WGV 0.421915736108744 0.093426 4.516 3.1e-05 1.5e-05 M1 -0.133196764232351 0.267267 -0.4984 0.620079 0.31004 M2 -0.315249607827085 0.293183 -1.0753 0.286633 0.143317 M3 -0.423011503247149 0.302757 -1.3972 0.167586 0.083793 M4 -0.36018079288132 0.295994 -1.2169 0.228506 0.114253 M5 -0.296300268627076 0.285283 -1.0386 0.30322 0.15161 M6 -0.234246055715227 0.279891 -0.8369 0.406015 0.203007 M7 -0.0690858529874588 0.282155 -0.2449 0.807422 0.403711 M8 0.130184180527623 0.287996 0.452 0.652902 0.326451 M9 0.215663672606848 0.287764 0.7494 0.456566 0.228283 M10 0.175891574176302 0.282786 0.622 0.536341 0.26817 M11 0.109041573893588 0.277947 0.3923 0.696242 0.348121 t -0.00474896754226758 0.003732 -1.2726 0.208137 0.104068 Multiple Linear Regression - Regression Statistics Multiple R 0.739960868005558 R-squared 0.547542086179539 Adjusted R-squared 0.447847969575031 F-TEST (value) 5.49222065281612 F-TEST (DF numerator) 13 F-TEST (DF denominator) 59 p-value 2.18836094234565e-06 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.47961414642234 Sum Squared Residuals 13.5717540374574 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 7.3 6.97452494898247 0.325475051017533 2 7.6 7.29402202117599 0.305977978824011 3 7.5 7.30808587904628 0.191914120953721 4 7.6 7.36616762186984 0.233832378130160 5 7.9 7.2987244577492 0.601275542250807 6 7.9 7.3138381295079 0.5861618704921 7 8.1 7.60082408552602 0.499175914473975 8 8.2 8.04849459316408 0.151505406835915 9 8 8.08703354409017 -0.0870335440901684 10 7.5 7.83155461006298 -0.331554610062982 11 6.8 7.33803990612926 -0.538039906129257 12 6.5 7.09767464386078 -0.597674643860778 13 6.6 7.17068678014053 -0.570686780140531 14 7.6 7.78552486761014 -0.185524867610144 15 8 7.96835501992393 0.0316449800760681 16 8.1 7.94205361552574 0.157946384474255 17 7.7 7.62146100973985 0.0785389902601484 18 7.5 7.34123366622244 0.158766333777562 19 7.6 7.50164490140794 0.0983550985920613 20 7.8 7.82274068821338 -0.0227406882133760 21 7.8 7.9456627863612 -0.145662786361208 22 7.8 7.85895014677752 -0.0589501467775205 23 7.5 7.61858488450904 -0.118584884509041 24 7.5 7.42041119585144 0.0795888041485634 25 7.1 7.3246570376877 -0.224657037687692 26 7.5 7.60196253627031 -0.101962536270309 27 7.5 7.57383482052973 -0.0738348205297264 28 7.6 7.58972498974241 0.010275010257587 29 7.7 7.39570710478914 0.304292895210857 30 7.7 7.28424605571523 0.415753944284773 31 7.9 7.4868488645116 0.413151135488398 32 8.1 7.72356150409529 0.376438495904709 33 8.2 7.80429202863225 0.395707971367751 34 8.2 7.67538781543769 0.524612184562313 35 8.2 7.51940570039096 0.680594299609044 36 7.9 7.4056151589551 0.4943848410449 37 7.3 7.26766942718048 0.0323305728195192 38 6.9 7.41840020493047 -0.518400204930474 39 6.6 7.39027248918989 -0.790272489189893 40 6.7 7.3639710847917 -0.663971084791704 41 6.9 7.21214477344931 -0.312144773449309 42 7 7.14287529798627 -0.142875297986267 43 7.1 7.30328653317177 -0.203286533171769 44 7.2 7.53999917275546 -0.339999172755456 45 7.1 7.62072969729241 -0.520729697292415 46 6.9 7.5762086313196 -0.6762086313196 47 7 7.54680123710549 -0.546801237105493 48 6.8 7.26424440122614 -0.464244401226141 49 6.4 6.91534080139715 -0.515340801397149 50 6.7 6.77073056387102 -0.0707305638710222 51 6.6 6.53164498007607 0.0683550199239323 52 6.4 6.42096042845613 -0.0209604284561309 53 6.3 6.56447513238986 -0.264475132389857 54 6.2 6.62178037775944 -0.421780377759438 55 6.5 6.82438318655581 -0.324383186555813 56 6.8 6.97671267891775 -0.176712678917753 57 6.8 6.93086848262209 -0.130868482622087 58 6.4 6.6753895485949 -0.275389548594902 59 6.1 6.4772158599373 -0.377215859937297 60 5.8 6.23685059766882 -0.436850597668818 61 6.1 6.2676711603377 -0.167671160337697 62 7.2 6.62935980614206 0.570640193857938 63 7.3 6.7278068112341 0.572193188765897 64 6.9 6.61712225961417 0.282877740385833 65 6.1 6.50748752188265 -0.407487521882646 66 5.8 6.39602647280873 -0.59602647280873 67 6.2 6.68301242882685 -0.483012428826853 68 7.1 7.08849136285404 0.0115086371459601 69 7.7 7.21141346100187 0.488586538998128 70 7.9 7.08250924780731 0.817490752192691 71 7.7 6.79995241192796 0.900047588072044 72 7.4 6.47520400243773 0.924795997562272 73 7.5 6.37944984427398 1.12055015572602 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.0108565084167496 0.0217130168334991 0.98914349158325 18 0.0269382514862981 0.0538765029725962 0.973061748513702 19 0.0156433548323487 0.0312867096646975 0.984356645167651 20 0.0123195385030918 0.0246390770061836 0.987680461496908 21 0.00799308904667122 0.0159861780933424 0.992006910953329 22 0.0131684553923789 0.0263369107847579 0.986831544607621 23 0.0231243998115581 0.0462487996231161 0.976875600188442 24 0.0499987874198401 0.0999975748396801 0.95000121258016 25 0.0279890172490723 0.0559780344981446 0.972010982750928 26 0.0144559241305373 0.0289118482610747 0.985544075869463 27 0.00708106707902634 0.0141621341580527 0.992918932920974 28 0.0033507122859542 0.0067014245719084 0.996649287714046 29 0.00205506939335989 0.00411013878671978 0.99794493060664 30 0.00168004337804248 0.00336008675608495 0.998319956621958 31 0.00161369904296645 0.0032273980859329 0.998386300957034 32 0.00193215697277083 0.00386431394554165 0.99806784302723 33 0.00326891369825959 0.00653782739651918 0.99673108630174 34 0.0106190710572643 0.0212381421145286 0.989380928942736 35 0.090066673523805 0.18013334704761 0.909933326476195 36 0.227486550166677 0.454973100333355 0.772513449833323 37 0.219400352198726 0.438800704397452 0.780599647801274 38 0.260183802940998 0.520367605881996 0.739816197059002 39 0.421429995308535 0.84285999061707 0.578570004691465 40 0.480168876232437 0.960337752464874 0.519831123767563 41 0.478762680792592 0.957525361585185 0.521237319207408 42 0.591469486444178 0.817061027111645 0.408530513555822 43 0.71096294858278 0.578074102834439 0.289037051417220 44 0.705404767956064 0.589190464087873 0.294595232043936 45 0.632537259181718 0.734925481636564 0.367462740818282 46 0.585242499347217 0.829515001305566 0.414757500652783 47 0.529137055280010 0.94172588943998 0.47086294471999 48 0.476244669339331 0.952489338678662 0.523755330660669 49 0.741394605140251 0.517210789719498 0.258605394859749 50 0.812475667540899 0.375048664918203 0.187524332459101 51 0.767253432522072 0.465493134955857 0.232746567477928 52 0.753463937192558 0.493072125614884 0.246536062807442 53 0.692967895906969 0.614064208186062 0.307032104093031 54 0.573465736403466 0.85306852719307 0.426534263596534 55 0.484324858167296 0.968649716334593 0.515675141832704 56 0.744724298601338 0.510551402797325 0.255275701398662 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 6 0.15 NOK 5% type I error level 15 0.375 NOK 10% type I error level 18 0.45 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 = Include Monthly 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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