Investeringen met dummy variabele

*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: Thu, 27 Nov 2008 13:00:49 -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/Nov/27/t1227816570ntoagqivt7ok4wv.htm/, Retrieved Thu, 27 Nov 2008 20:09:39 +0000

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/Nov/27/t1227816570ntoagqivt7ok4wv.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}, }

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

Feedback Forum:

2008-11-27 13:41:43 [a2386b643d711541400692649981f2dc]  [reply]  test Post a new message

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

119,5 0 125 0 145 0 105,3 0 116,9 0 120,1 0 88,9 0 78,4 0 114,6 0 113,3 0 117 0 99,6 0 99,4 0 101,9 0 115,2 0 108,5 0 113,8 0 121 0 92,2 0 90,2 0 101,5 0 126,6 0 93,9 0 89,8 0 93,4 0 101,5 0 110,4 0 105,9 0 108,4 0 113,9 0 86,1 0 69,4 0 101,2 0 100,5 0 98 0 106,6 0 90,1 0 96,9 0 109,9 0 99 0 106,3 0 128,9 0 111,1 0 102,9 0 130 0 87 0 87,5 0 117,6 0 103,4 0 110,8 0 112,6 0 102,5 1 112,4 1 135,6 1 105,1 1 127,7 1 137 1 91 1 90,5 1 122,4 1 123,3 1 124,3 1 120 1 118,1 1 119 1 142,7 1 123,6 1 129,6 1 151,6 1 110,4 1 99,2 1 130,5 1 136,2 1 129,7 1 128 1 121,6 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 24 seconds R Server 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation invest[t] = + 107.824598610113 + 18.7627965492451dummyvar[t] -1.21790621113053M1[t] + 2.39627309346937M2[t] + 9.75330954092637M3[t] -4.31291066150878M4[t] + 1.21741153446764M5[t] + 15.5220670295437M6[t] -10.2732774753803M7[t] -11.6686219803042M8[t] + 11.3527001814385M9[t] -6.42597765681877M10[t] -13.4713221617427M11[t] -0.0713221617427219t + 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) 107.824598610113 6.17454 17.4628 0 0 dummyvar 18.7627965492451 5.313156 3.5314 0.000786 0.000393 M1 -1.21790621113053 6.955825 -0.1751 0.861578 0.430789 M2 2.39627309346937 6.950823 0.3447 0.731452 0.365726 M3 9.75330954092637 6.947683 1.4038 0.165361 0.082681 M4 -4.31291066150878 6.980498 -0.6179 0.538936 0.269468 M5 1.21741153446764 7.250954 0.1679 0.867211 0.433605 M6 15.5220670295437 7.239322 2.1441 0.035951 0.017975 M7 -10.2732774753803 7.229465 -1.421 0.160319 0.080159 M8 -11.6686219803042 7.22139 -1.6158 0.111206 0.055603 M9 11.3527001814385 7.215104 1.5735 0.120701 0.060351 M10 -6.42597765681877 7.21061 -0.8912 0.376276 0.188138 M11 -13.4713221617427 7.207912 -1.869 0.066353 0.033177 t -0.0713221617427219 0.113866 -0.6264 0.533374 0.266687 Multiple Linear Regression - Regression Statistics Multiple R 0.713721327038836 R-squared 0.509398132670077 Adjusted R-squared 0.406529999197674 F-TEST (value) 4.95195271339044 F-TEST (DF numerator) 13 F-TEST (DF denominator) 62 p-value 7.17369109004551e-06 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 12.4829117508561 Sum Squared Residuals 9661.03131833897 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 119.5 106.535370237240 12.9646297627604 2 125 110.078227380097 14.9217726199035 3 145 117.363941665811 27.6360583341892 4 105.3 103.226399301633 2.07360069836706 5 116.9 108.685399335867 8.21460066413341 6 120.1 122.9187326692 -2.81873266919994 7 88.9 97.0520660025333 -8.1520660025333 8 78.4 95.5853993358666 -17.1853993358666 9 114.6 118.535399335867 -3.93539933586661 10 113.3 100.685399335867 12.6146006641334 11 117 93.5687326692 23.4312673308000 12 99.6 106.9687326692 -7.36873266919994 13 99.4 105.679504296327 -6.27950429632668 14 101.9 109.222361439184 -7.32236143918386 15 115.2 116.508075724898 -1.30807572489815 16 108.5 102.370533360720 6.12946663927973 17 113.8 107.829533394954 5.97046660504604 18 121 122.062866728287 -1.06286672828728 19 92.2 96.1962000616206 -3.99620006162062 20 90.2 94.729533394954 -4.52953339495395 21 101.5 117.679533394954 -16.1795333949539 22 126.6 99.829533394954 26.7704666050460 23 93.9 92.7128667282873 1.18713327171272 24 89.8 106.112866728287 -16.3128667282873 25 93.4 104.823638355414 -11.423638355414 26 101.5 108.366495498271 -6.8664954982712 27 110.4 115.652209783985 -5.25220978398549 28 105.9 101.514667419808 4.3853325801924 29 108.4 106.973667454041 1.42633254595871 30 113.9 121.207000787375 -7.30700078737462 31 86.1 95.340334120708 -9.24033412070796 32 69.4 93.8736674540413 -24.4736674540413 33 101.2 116.823667454041 -15.6236674540413 34 100.5 98.9736674540413 1.52633254595872 35 98 91.8570007873746 6.14299921262538 36 106.6 105.257000787375 1.34299921262538 37 90.1 103.967772414501 -13.8677724145014 38 96.9 107.510629557359 -10.6106295573585 39 109.9 114.796343843073 -4.89634384307282 40 99 100.658801478895 -1.65880147889494 41 106.3 106.117801513129 0.182198486871365 42 128.9 120.351134846462 8.54886515353805 43 111.1 94.4844681797953 16.6155318202047 44 102.9 93.0178015131286 9.88219848687138 45 130 115.967801513129 14.0321984868714 46 87 98.1178015131286 -11.1178015131286 47 87.5 91.001134846462 -3.50113484646196 48 117.6 104.401134846462 13.1988651535380 49 103.4 103.111906473589 0.288093526411324 50 110.8 106.654763616446 4.14523638355412 51 112.6 113.940477902160 -1.34047790216017 52 102.5 118.565732087227 -16.0657320872274 53 112.4 124.024732121461 -11.6247321214611 54 135.6 138.258065454794 -2.65806545479442 55 105.1 112.391398788128 -7.29139878812776 56 127.7 110.924732121461 16.7752678785389 57 137 133.874732121461 3.12526787853891 58 91 116.024732121461 -25.0247321214611 59 90.5 108.908065454794 -18.4080654547944 60 122.4 122.308065454794 0.091934545205594 61 123.3 121.018837081921 2.28116291807885 62 124.3 124.561694224778 -0.261694224778342 63 120 131.847408510493 -11.8474085104926 64 118.1 117.709866146315 0.390133853685246 65 119 123.168866180548 -4.16886618054843 66 142.7 137.402199513882 5.29780048611823 67 123.6 111.535532847215 12.0644671527849 68 129.6 110.068866180548 19.5311338194516 69 151.6 133.018866180548 18.5811338194516 70 110.4 115.168866180548 -4.76886618054842 71 99.2 108.052199513882 -8.85219951388176 72 130.5 121.452199513882 9.04780048611825 73 136.2 120.162971141008 16.0370288589915 74 129.7 123.705828283866 5.99417171613431 75 128 130.99154256958 -2.99154256957996 76 121.6 116.854000205402 4.74599979459791 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.619793541266866 0.760412917466267 0.380206458733134 18 0.567334394472475 0.86533121105505 0.432665605527525 19 0.519792304373345 0.96041539125331 0.480207695626655 20 0.563551575152335 0.872896849695329 0.436448424847665 21 0.466497682025721 0.932995364051441 0.533502317974279 22 0.759600201464018 0.480799597071964 0.240399798535982 23 0.807707606608529 0.384584786782942 0.192292393391471 24 0.745494729179687 0.509010541640626 0.254505270820313 25 0.667873513606621 0.664252972786758 0.332126486393379 26 0.583599837597638 0.832800324804725 0.416400162402362 27 0.556430239344138 0.887139521311723 0.443569760655862 28 0.607391070362824 0.785217859274351 0.392608929637176 29 0.585000546172214 0.829998907655572 0.414999453827786 30 0.506304965978147 0.987390068043705 0.493695034021853 31 0.449923132938132 0.899846265876263 0.550076867061868 32 0.69758239305475 0.604835213890501 0.302417606945251 33 0.800104031187207 0.399791937625586 0.199895968812793 34 0.907748304079877 0.184503391840247 0.0922516959201233 35 0.987666714858377 0.0246665702832459 0.0123332851416230 36 0.994286050151472 0.0114278996970553 0.00571394984852764 37 0.996471290086895 0.00705741982621049 0.00352870991310524 38 0.995519161527222 0.00896167694555659 0.00448083847277829 39 0.99509291359678 0.00981417280643834 0.00490708640321917 40 0.99222796076275 0.0155440784745003 0.00777203923725013 41 0.988611349866815 0.0227773002663692 0.0113886501331846 42 0.993451664123005 0.0130966717539895 0.00654833587699477 43 0.999409685284575 0.00118062943084965 0.000590314715424824 44 0.9999312664861 0.000137467027799646 6.8733513899823e-05 45 0.99994265050265 0.000114698994698682 5.73494973493412e-05 46 0.999907234152227 0.000185531695545304 9.2765847772652e-05 47 0.999889504719784 0.000220990560432812 0.000110495280216406 48 0.999927040600243 0.000145918799514058 7.29593997570288e-05 49 0.999966796050926 6.64078981476907e-05 3.32039490738453e-05 50 0.999918231290367 0.000163537419265782 8.17687096328908e-05 51 0.999736760904845 0.000526478190310794 0.000263239095155397 52 0.9992833320968 0.00143333580639777 0.000716667903198886 53 0.998116145392065 0.00376770921587043 0.00188385460793521 54 0.995514690066112 0.00897061986777626 0.00448530993388813 55 0.994770953489274 0.0104580930214522 0.00522904651072609 56 0.995105059715168 0.00978988056966297 0.00489494028483149 57 0.988601019505621 0.0227979609887576 0.0113989804943788 58 0.996772367488711 0.00645526502257732 0.00322763251128866 59 0.984119511567851 0.031760976864297 0.0158804884321485 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 17 0.395348837209302 NOK 5% type I error level 25 0.581395348837209 NOK 10% type I error level 25 0.581395348837209 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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