Workshop 4

*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: Wed, 01 Dec 2010 17:47:50 +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/01/t129122561357786xfuv29y81v.htm/, Retrieved Wed, 01 Dec 2010 18:46:53 +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/01/t129122561357786xfuv29y81v.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:

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162556 807 213118 6282154 29790 444 81767 4321023 87550 412 153198 4111912 84738 428 -26007 223193 54660 315 126942 1491348 42634 168 157214 1629616 40949 263 129352 1398893 45187 267 234817 1926517 37704 228 60448 983660 16275 129 47818 1443586 25830 104 245546 1073089 12679 122 48020 984885 18014 393 -1710 1405225 43556 190 32648 227132 24811 280 95350 929118 6575 63 151352 1071292 7123 102 288170 638830 21950 265 114337 856956 37597 234 37884 992426 17821 277 122844 444477 12988 73 82340 857217 22330 67 79801 711969 13326 103 165548 702380 16189 290 116384 358589 7146 83 134028 297978 15824 56 63838 585715 27664 236 74996 657954 11920 73 31080 209458 8568 34 32168 786690 14416 139 49857 439798 3369 26 87161 688779 11819 70 106113 574339 6984 40 80570 741409 4519 42 102129 597793 2220 12 301670 644190 18562 211 102313 377934 10327 74 88577 640273 5336 80 112477 697458 2365 83 191778 550608 4069 131 79804 207393 8636 203 128294 301607 13718 56 96448 345783 4525 89 93 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 4 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Multiple Linear Regression - Estimated Regression Equation Wealth[t] = + 23546.9979632041 + 13.9716805944773Costs[t] + 2839.80734684669Orders[t] + 3.4504396643183Dividends[t] -9004.44968489971t + 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) 23546.9979632041 380044.053397 0.062 0.95087 0.475435 Costs 13.9716805944773 6.977434 2.0024 0.051289 0.025644 Orders 2839.80734684669 1296.710286 2.19 0.033748 0.016874 Dividends 3.4504396643183 1.427679 2.4168 0.019774 0.009887 t -9004.44968489971 8948.121956 -1.0063 0.319654 0.159827 Multiple Linear Regression - Regression Statistics Multiple R 0.819356821074545 R-squared 0.671345600241384 Adjusted R-squared 0.642131875818396 F-TEST (value) 22.9804865179431 F-TEST (DF numerator) 4 F-TEST (DF denominator) 45 p-value 2.15578666029614e-10 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 665198.538833598 Sum Squared Residuals 19912009322985.9 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 6282154 5312798.38827962 969355.611720383 2 4321023 1964761.02553513 2356261.97446487 3 4111912 2918355.36755006 1193556.63244994 4 223193 2297163.42953888 -2073970.42953888 5 1491348 2074761.83695743 -583413.836957434 6 1629616 1584733.98597513 44882.0140248697 7 1398893 1725832.80251174 -326939.802511736 8 1926517 2151300.18377095 -224783.183770947 9 983660 1325343.44784304 -341683.447843035 10 1443586 692219.87440092 751366.12559908 11 1073089 1427968.18307141 -354879.183071411 12 984885 604787.148997646 380097.851002354 13 1405225 1268319.04177319 136905.958226813 14 227132 1158248.57240919 -931116.572409195 15 929118 1359277.09902911 -430159.099029107 16 1071292 672478.409838741 398813.590161259 17 638830 1253965.18163934 -615135.181639337 18 856956 1315207.15949732 -458251.15949732 19 992426 1172987.10466583 -180561.104665831 20 444477 1302939.76933944 -858462.76933944 21 857217 507332.880421158 349884.119578842 22 711969 603052.36046108 108916.639538920 23 702380 866344.81308629 -163964.813086290 24 358589 1258747.84314716 -900158.843147165 25 297978 596436.922486374 -298458.922486374 26 585715 389817.558596986 195897.441403014 27 657954 1095903.13535757 -437949.135357565 28 209458 252510.440559002 -43052.4405590021 29 786690 89674.509349172 697015.490650828 30 439798 521591.046421804 -81793.0464218044 31 688779 166058.412253768 522720.587746232 32 574339 465458.919371616 108880.080628384 33 741409 215572.593261336 525836.406738664 34 597793 252195.594327781 345597.405672219 35 644190 814380.211608515 -170190.211608515 36 377934 910953.328061551 -533019.328061551 37 640273 350443.242934058 289829.757065942 38 697458 371210.48746041 326247.51253959 39 550608 602838.912589964 -52230.9125899638 40 207393 367593.428314317 -160200.428314317 41 301607 794175.592200152 -492568.592200152 42 345783 328840.841760041 16942.1582399590 43 501749 276009.565421245 225739.434578755 44 379983 378721.401704276 1261.5982957237 45 387475 32389.1432055677 355085.856794432 46 377305 83106.1801522993 294198.819847701 47 370837 534376.091792169 -163539.091792169 48 430866 591795.055993165 -160929.055993165 49 469107 236190.599987446 232916.400012554 50 194493 -14708.1249103702 209201.124910370 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 8 0.996507364156043 0.00698527168791362 0.00349263584395681 9 0.999999915575747 1.68848505856559e-07 8.44242529282793e-08 10 0.999999999962175 7.56497392957813e-11 3.78248696478907e-11 11 0.999999999921175 1.57649079762029e-10 7.88245398810143e-11 12 0.999999999907506 1.84987113470480e-10 9.24935567352399e-11 13 0.999999999988364 2.327196614098e-11 1.163598307049e-11 14 0.999999999999428 1.14480665504541e-12 5.72403327522705e-13 15 0.999999999998775 2.44957312459637e-12 1.22478656229818e-12 16 0.999999999999574 8.5281339558329e-13 4.26406697791645e-13 17 0.999999999999248 1.50442013722568e-12 7.52210068612842e-13 18 0.99999999999854 2.92152805809135e-12 1.46076402904568e-12 19 0.999999999999335 1.33023257481046e-12 6.65116287405231e-13 20 0.999999999997473 5.05368201986704e-12 2.52684100993352e-12 21 0.999999999998773 2.45336240116369e-12 1.22668120058185e-12 22 0.999999999996953 6.09438168460284e-12 3.04719084230142e-12 23 0.999999999983847 3.23059375217913e-11 1.61529687608957e-11 24 0.999999999935434 1.29132475870623e-10 6.45662379353113e-11 25 0.999999999967523 6.49539117069232e-11 3.24769558534616e-11 26 0.999999999904993 1.90013328470725e-10 9.50066642353624e-11 27 0.999999999734172 5.31656405211626e-10 2.65828202605813e-10 28 0.999999999986795 2.64092849132215e-11 1.32046424566108e-11 29 0.999999999966555 6.68891716037278e-11 3.34445858018639e-11 30 0.999999999852316 2.95368350504495e-10 1.47684175252247e-10 31 0.999999999159435 1.68113033363307e-09 8.40565166816536e-10 32 0.999999994893842 1.02123164506304e-08 5.10615822531519e-09 33 0.999999979319718 4.13605648519324e-08 2.06802824259662e-08 34 0.999999866628176 2.66743647837215e-07 1.33371823918608e-07 35 0.999999373897168 1.25220566479113e-06 6.26102832395563e-07 36 0.999996496292153 7.00741569405198e-06 3.50370784702599e-06 37 0.999986063702449 2.78725951024098e-05 1.39362975512049e-05 38 0.99998514311821 2.97137635789386e-05 1.48568817894693e-05 39 0.999931373997867 0.000137252004266326 6.8626002133163e-05 40 0.999740855189907 0.00051828962018701 0.000259144810093505 41 0.999411235106942 0.00117752978611604 0.000588764893058021 42 0.99571466189858 0.00857067620284053 0.00428533810142026 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 35 1 NOK 5% type I error level 35 1 NOK 10% type I error level 35 1 NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/01/t129122561357786xfuv29y81v/10ey321291225661.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/01/t129122561357786xfuv29y81v/10ey321291225661.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/01/t129122561357786xfuv29y81v/17f6r1291225661.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/01/t129122561357786xfuv29y81v/17f6r1291225661.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/01/t129122561357786xfuv29y81v/27f6r1291225661.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/01/t129122561357786xfuv29y81v/27f6r1291225661.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/01/t129122561357786xfuv29y81v/3i7nb1291225661.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/01/t129122561357786xfuv29y81v/3i7nb1291225661.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/01/t129122561357786xfuv29y81v/4i7nb1291225661.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/01/t129122561357786xfuv29y81v/4i7nb1291225661.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/01/t129122561357786xfuv29y81v/5i7nb1291225661.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/01/t129122561357786xfuv29y81v/5i7nb1291225661.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/01/t129122561357786xfuv29y81v/6tynw1291225661.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/01/t129122561357786xfuv29y81v/6tynw1291225661.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/01/t129122561357786xfuv29y81v/7374z1291225661.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/01/t129122561357786xfuv29y81v/7374z1291225661.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/01/t129122561357786xfuv29y81v/8374z1291225661.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/01/t129122561357786xfuv29y81v/8374z1291225661.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/01/t129122561357786xfuv29y81v/9374z1291225661.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/01/t129122561357786xfuv29y81v/9374z1291225661.ps (open in new window)

Parameters (Session):

par1 = 4 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 4 ; par2 = Do not include Seasonal 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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