MRLM 2

*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, 21 Dec 2010 15:18:59 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/21/t1292945262yp1xe8bqpvitcpq.htm/, Retrieved Tue, 21 Dec 2010 16:27:45 +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/2010/Dec/21/t1292945262yp1xe8bqpvitcpq.htm/}, year = {2010}, } @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 = {2010}, 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 «

1 216.234 627 1,59 2 213.586 696 1,26 3 209.465 825 1,13 4 204.045 677 1,92 5 200.237 656 2,61 6 203.666 785 2,26 7 241.476 412 2,41 8 260.307 352 2,26 9 243.324 839 2,03 10 244.460 729 2,86 11 233.575 696 2,55 12 237.217 641 2,27 1 235.243 695 2,26 2 230.354 638 2,57 3 227.184 762 3,07 4 221.678 635 2,76 5 217.142 721 2,51 6 219.452 854 2,87 7 256.446 418 3,14 8 265.845 367 3,11 9 248.624 824 3,16 10 241.114 687 2,47 11 229.245 601 2,57 12 231.805 676 2,89 1 219.277 740 2,63 2 219.313 691 2,38 3 212.610 683 1,69 4 214.771 594 1,96 5 211.142 729 2,19 6 211.457 731 1,87 7 240.048 386 1,6 8 240.636 331 1,63 9 230.580 707 1,22 10 208.795 715 1,21 11 197.922 657 1,49 12 194.596 653 1,64 1 194.581 642 1,66 2 185.686 643 1,77 3 178.106 718 1,82 4 172.608 654 1,78 5 167.302 632 1,28 6 168.053 731 1,29 7 202.300 392 1,37 8 202.388 344 1,12 9 182.516 792 1,51 10 173.476 852 2,24 11 166.444 649 2,94 12 171.297 629 3,09 1 169.701 685 3,46 2 164.182 617 3,64 3 161.914 715 etc...

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 6 seconds R Server 'RServer@AstonUniversity' @ vre.aston.ac.uk Multiple Linear Regression - Estimated Regression Equation werklozen[t] = + 252.407362663364 + 1.10477271192568month[t] -0.0641619305654837faillissementen[t] -5.07414212008297inflatie[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) 252.407362663364 15.739788 16.0363 0 0 month 1.10477271192568 0.868867 1.2715 0.207879 0.10394 faillissementen -0.0641619305654837 0.019362 -3.3138 0.001478 0.000739 inflatie -5.07414212008297 1.948364 -2.6043 0.011296 0.005648 Multiple Linear Regression - Regression Statistics Multiple R 0.461331452857874 R-squared 0.212826709395957 Adjusted R-squared 0.178098475986955 F-TEST (value) 6.1283482775945 F-TEST (DF numerator) 3 F-TEST (DF denominator) 68 p-value 0.000943453677627604 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 25.4245327686721 Sum Squared Residuals 43955.6669223591 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 216.234 205.214718939799 11.0192810602008 2 213.586 203.566785342334 10.0192146576655 3 209.465 197.054307486924 12.4106925130764 4 204.045 203.646473647675 0.398526352324688 5 200.237 202.597488838619 -2.36048883861889 6 203.666 197.201322249626 6.46467775037378 7 241.476 221.477373744465 19.9986262555351 8 260.307 227.192983608332 33.114016391668 9 243.324 198.217948822486 45.1060511775138 10 244.46 202.168995936946 42.2910040630538 11 233.575 206.964096414759 26.6109035852414 12 237.217 213.018535101409 24.1984648985909 13 235.243 197.452032440891 37.7909675591087 14 230.354 200.641051137824 29.7129488621762 15 227.184 191.252673399588 35.9313266004119 16 221.678 202.078995350556 19.5990046494441 17 217.142 198.934377563871 18.2076224361293 18 219.452 189.678922347357 29.7730776526428 19 256.446 217.388278413411 39.0577215865886 20 265.845 221.917533847779 43.9274661522208 21 248.624 193.446597185275 55.1774028147253 22 241.114 206.842712447529 34.2712875524711 23 229.245 212.957996976078 16.2870030239221 24 231.805 207.626899417166 24.1781005828342 25 219.277 192.687312981014 26.5896870189861 26 219.313 198.204555820669 21.108444179331 27 212.61 203.323782039976 9.28621796002422 28 214.771 208.768948199807 6.00205180019286 29 211.142 200.044807597773 11.0971924022266 30 211.457 202.644981926995 8.81201807300531 31 240.048 227.255639056435 12.7923609435653 32 240.636 231.737093685859 8.89890631414055 33 230.58 210.797378774397 19.7826212256027 34 208.795 211.439597463 -2.64459746299993 35 197.922 214.8450023541 -16.9230023541004 36 194.596 215.445301470276 -20.8493014702756 37 194.581 203.897100032912 -9.31610003291176 38 185.686 204.379555181063 -18.6935551810628 39 178.106 200.418475994573 -22.3124759945731 40 172.608 205.832577947493 -33.224577947493 41 167.302 210.885984191901 -43.5839841919009 42 168.053 205.587984356643 -37.5349843566428 43 202.3 228.037720160661 -25.7377201606608 44 202.388 233.49080106975 -31.1028010697505 45 182.516 203.872113461507 -21.3561134615071 46 173.476 197.423046591843 -23.9470465918432 47 166.444 208.000791724504 -41.556791724504 48 171.297 209.627681729727 -38.3306817297269 49 169.701 192.004681202447 -22.3036812024466 50 164.182 196.55911961121 -32.3771196112103 51 161.914 187.570416537656 -25.6564165376563 52 159.612 189.892983358402 -30.2809833584019 53 151.001 191.137091451671 -40.1360914516712 54 158.114 170.833646240454 -12.7196462404541 55 186.53 196.082606586882 -9.55260658688193 56 187.069 210.990109119645 -23.9211091196449 57 174.33 175.809010766494 -1.47901076649391 58 169.362 186.379060467609 -17.017060467609 59 166.827 203.200409397124 -36.3734093971239 60 178.037 197.268705005469 -19.2317050054693 61 186.413 192.014629468448 -5.60162946844765 62 189.226 194.456698301551 -5.23069830155086 63 191.563 188.028810535813 3.53418946418665 64 188.906 203.158205022851 -14.2522050228506 65 186.005 212.713801772358 -26.7088017723584 66 195.309 206.486846174681 -11.1778461746815 67 223.532 234.531183347746 -10.9991833477461 68 226.899 240.372708083592 -13.4737080835923 69 214.126 204.8040730032 9.32192699680015 70 206.903 214.41682403353 -7.51382403352985 71 204.442 207.936317484545 -3.49431748454533 72 220.375 214.170728553043 6.2042714469573 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 7 0.0121267963484816 0.0242535926969631 0.987873203651518 8 0.0028306964076284 0.00566139281525681 0.997169303592372 9 0.0117769496920269 0.0235538993840537 0.988223050307973 10 0.011729079958053 0.023458159916106 0.988270920041947 11 0.0125248439011688 0.0250496878023377 0.987475156098831 12 0.0199718014970202 0.0399436029940404 0.98002819850298 13 0.0780930128115917 0.156186025623183 0.921906987188408 14 0.0597569895640987 0.119513979128197 0.940243010435901 15 0.0443061101859512 0.0886122203719024 0.955693889814049 16 0.0286942574554904 0.0573885149109808 0.97130574254451 17 0.0182681360033423 0.0365362720066847 0.981731863996658 18 0.0121621846858964 0.0243243693717929 0.987837815314104 19 0.0113354029026939 0.0226708058053878 0.988664597097306 20 0.0149182470766779 0.0298364941533558 0.985081752923322 21 0.0377420864314571 0.0754841728629141 0.962257913568543 22 0.0426219769434131 0.0852439538868261 0.957378023056587 23 0.0539555648274618 0.107911129654924 0.946044435172538 24 0.0762162633703515 0.152432526740703 0.923783736629649 25 0.0831018111630231 0.166203622326046 0.916898188836977 26 0.0908225395247013 0.181645079049403 0.909177460475299 27 0.080724795089081 0.161449590178162 0.919275204910919 28 0.0819748259484244 0.163949651896849 0.918025174051576 29 0.092735602276983 0.185471204553966 0.907264397723017 30 0.0963412965995633 0.192682593199127 0.903658703400437 31 0.136127391512052 0.272254783024104 0.863872608487948 32 0.224360124784314 0.448720249568627 0.775639875215686 33 0.418430839027221 0.836861678054442 0.581569160972779 34 0.438993827800196 0.877987655600392 0.561006172199804 35 0.562537888764013 0.874924222471975 0.437462111235987 36 0.676805985726281 0.646388028547438 0.323194014273719 37 0.698537023995947 0.602925952008107 0.301462976004053 38 0.752457446094821 0.495085107810358 0.247542553905179 39 0.809590208263382 0.380819583473237 0.190409791736618 40 0.90048009306168 0.199039813876639 0.0995199069383197 41 0.964906551350072 0.070186897299857 0.0350934486499285 42 0.984539857092135 0.0309202858157306 0.0154601429078653 43 0.97889133605088 0.0422173278982399 0.0211086639491199 44 0.969688016125456 0.0606239677490874 0.0303119838745437 45 0.96303149183558 0.0739370163288402 0.0369685081644201 46 0.975288473630152 0.0494230527396953 0.0247115263698476 47 0.997503980173408 0.00499203965318335 0.00249601982659168 48 0.999535695496709 0.000928609006582237 0.000464304503291118 49 0.999638784717164 0.00072243056567203 0.000361215282836015 50 0.999758031895998 0.00048393620800481 0.000241968104002405 51 0.999726013556044 0.000547972887911743 0.000273986443955871 52 0.999731848692786 0.000536302614428577 0.000268151307214289 53 0.99990406248057 0.000191875038859129 9.59375194295647e-05 54 0.999759622435243 0.000480755129514613 0.000240377564757307 55 0.999621269367698 0.00075746126460457 0.000378730632302285 56 0.999198894881704 0.0016022102365914 0.000801105118295698 57 0.9989986420168 0.00200271596640022 0.00100135798320011 58 0.997686174833224 0.00462765033355282 0.00231382516677641 59 0.998230247410254 0.00353950517949258 0.00176975258974629 60 0.999094305842467 0.00181138831506612 0.000905694157533058 61 0.997153255555373 0.00569348888925318 0.00284674444462659 62 0.992317737187306 0.0153645256253881 0.00768226281269407 63 0.993373493762717 0.0132530124745667 0.00662650623728333 64 0.990038085894706 0.0199238282105886 0.00996191410529429 65 0.966412976599602 0.0671740468007953 0.0335870234003976 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 16 0.271186440677966 NOK 5% type I error level 31 0.525423728813559 NOK 10% type I error level 39 0.661016949152542 NOK

Charts produced by software:

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Parameters (Session):

par1 = 2 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 2 ; 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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