Case Q3

*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: Sat, 22 Nov 2008 10:58:30 -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/22/t122737698694otquffmbyhrnp.htm/, Retrieved Sat, 22 Nov 2008 18:03:06 +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/22/t122737698694otquffmbyhrnp.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)

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

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0,9059 0 0,8883 0 0,8924 0 0,8833 0 0,8700 0 0,8758 0 0,8858 0 0,9170 0 0,9554 0 0,9922 0 0,9778 0 0,9808 0 0,9811 0 1,0014 0 1,0183 0 1,0622 0 1,0773 0 1,0807 0 1,0848 0 1,1582 0 1,1663 0 1,1372 0 1,1139 0 1,1222 0 1,1692 0 1,1702 0 1,2286 0 1,2613 0 1,2646 0 1,2262 0 1,1985 0 1,2007 0 1,2138 0 1,2266 0 1,2176 0 1,2218 0 1,2490 0 1,2991 0 1,3408 0 1,3119 0 1,3014 0 1,3201 0 1,2938 0 1,2694 0 1,2165 1 1,2037 1 1,2292 1 1,2256 1 1,2015 1 1,1786 1 1,1856 1 1,2103 1 1,1938 1 1,2020 1 1,2271 1 1,2770 1 1,2650 1 1,2684 1 1,2811 1 1,2727 1 1,2611 1 1,2881 1 1,3213 1 1,2999 1 1,3074 1 1,3242 1 1,3516 1 1,3511 1 1,3419 1 1,3716 1 1,3622 1 1,3896 1 1,4227 1 1,4684 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 6 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Multiple Linear Regression - Estimated Regression Equation y[t] = + 0.87139195945946 -0.219908603603604x[t] + 0.00470879129129134M1[t] + 0.0090164339339339M2[t] + 0.0201631156156156M3[t] + 0.0166540915915916M4[t] + 0.00376173423423416M5[t] -0.00431395645645647M6[t] -0.0127063138138138M7[t] -0.00123200450450454M8[t] + 0.0225104054054054M9[t] + 0.018818048048048M10[t] + 0.00534235735735734M11[t] + 0.0104923573573574t + 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) 0.87139195945946 0.019239 45.292 0 0 x -0.219908603603604 0.017887 -12.2943 0 0 M1 0.00470879129129134 0.021846 0.2155 0.830071 0.415036 M2 0.0090164339339339 0.021832 0.413 0.681079 0.340539 M3 0.0201631156156156 0.022721 0.8874 0.378392 0.189196 M4 0.0166540915915916 0.022704 0.7335 0.466088 0.233044 M5 0.00376173423423416 0.022694 0.1658 0.868905 0.434453 M6 -0.00431395645645647 0.022692 -0.1901 0.849865 0.424933 M7 -0.0127063138138138 0.022697 -0.5598 0.577686 0.288843 M8 -0.00123200450450454 0.02271 -0.0543 0.956916 0.478458 M9 0.0225104054054054 0.022671 0.9929 0.32474 0.16237 M10 0.018818048048048 0.022653 0.8307 0.409423 0.204712 M11 0.00534235735735734 0.022641 0.236 0.814272 0.407136 t 0.0104923573573574 0.000409 25.6266 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.971111121424003 R-squared 0.943056810153385 Adjusted R-squared 0.930719119019952 F-TEST (value) 76.4370577893495 F-TEST (DF numerator) 13 F-TEST (DF denominator) 60 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.0392097818050764 Sum Squared Residuals 0.092244419352102 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 0.9059 0.886593108108108 0.019306891891892 2 0.8883 0.901393108108108 -0.0130931081081081 3 0.8924 0.923032147147147 -0.0306321471471471 4 0.8833 0.93001548048048 -0.0467154804804805 5 0.87 0.92761548048048 -0.0576154804804805 6 0.8758 0.930032147147147 -0.0542321471471472 7 0.8858 0.932132147147147 -0.0463321471471471 8 0.917 0.954098813813814 -0.0370988138138138 9 0.9554 0.988333581081081 -0.032933581081081 10 0.9922 0.995133581081081 -0.00293358108108105 11 0.9778 0.992150247747748 -0.0143502477477477 12 0.9808 0.997300247747748 -0.0165002477477478 13 0.9811 1.01250139639640 -0.0314013963963965 14 1.0014 1.02730139639640 -0.0259013963963964 15 1.0183 1.04894043543544 -0.0306404354354354 16 1.0622 1.05592376876877 0.00627623123123125 17 1.0773 1.05352376876877 0.0237762312312312 18 1.0807 1.05594043543544 0.0247595645645646 19 1.0848 1.05804043543544 0.0267595645645646 20 1.1582 1.08000710210210 0.0781928978978978 21 1.1663 1.11424186936937 0.0520581306306306 22 1.1372 1.12104186936937 0.0161581306306307 23 1.1139 1.11805853603604 -0.00415853603603617 24 1.1222 1.12320853603604 -0.00100853603603597 25 1.1692 1.13840968468468 0.0307903153153153 26 1.1702 1.15320968468468 0.0169903153153152 27 1.2286 1.17484872372372 0.0537512762762763 28 1.2613 1.18183205705706 0.079467942942943 29 1.2646 1.17943205705706 0.085167942942943 30 1.2262 1.18184872372372 0.0443512762762762 31 1.1985 1.18394872372372 0.0145512762762761 32 1.2007 1.20591539039039 -0.00521539039039029 33 1.2138 1.24015015765766 -0.0263501576576576 34 1.2266 1.24695015765766 -0.0203501576576577 35 1.2176 1.24396682432432 -0.0263668243243243 36 1.2218 1.24911682432432 -0.0273168243243244 37 1.249 1.26431797297297 -0.0153179729729730 38 1.2991 1.27911797297297 0.0199820270270269 39 1.3408 1.30075701201201 0.0400429879879880 40 1.3119 1.30774034534535 0.00415965465465466 41 1.3014 1.30534034534535 -0.00394034534534534 42 1.3201 1.30775701201201 0.0123429879879880 43 1.2938 1.30985701201201 -0.0160570120120120 44 1.2694 1.33182367867868 -0.0624236786786786 45 1.2165 1.14614984234234 0.0703501576576576 46 1.2037 1.15294984234234 0.0507501576576577 47 1.2292 1.14996650900901 0.079233490990991 48 1.2256 1.15511650900901 0.070483490990991 49 1.2015 1.17031765765766 0.0311823423423423 50 1.1786 1.18511765765766 -0.00651765765765753 51 1.1856 1.20675669669670 -0.0211566966966967 52 1.2103 1.21374003003003 -0.0034400300300301 53 1.1938 1.21134003003003 -0.0175400300300300 54 1.202 1.21375669669670 -0.0117566966966967 55 1.2271 1.21585669669670 0.0112433033033034 56 1.277 1.23782336336336 0.0391766366366366 57 1.265 1.27205813063063 -0.00705813063063069 58 1.2684 1.27885813063063 -0.0104581306306306 59 1.2811 1.27587479729730 0.00522520270270262 60 1.2727 1.28102479729730 -0.00832479729729737 61 1.2611 1.29622594594595 -0.0351259459459459 62 1.2881 1.31102594594595 -0.0229259459459459 63 1.3213 1.33266498498498 -0.011364984984985 64 1.2999 1.33964831831832 -0.0397483183183183 65 1.3074 1.33724831831832 -0.0298483183183183 66 1.3242 1.33966498498498 -0.0154649849849849 67 1.3516 1.34176498498498 0.00983501501501497 68 1.3511 1.36373165165165 -0.0126316516516517 69 1.3419 1.39796641891892 -0.0560664189189188 70 1.3716 1.40476641891892 -0.0331664189189190 71 1.3622 1.40178308558559 -0.0395830855855855 72 1.3896 1.40693308558559 -0.0173330855855856 73 1.4227 1.42213423423423 0.000565765765765759 74 1.4684 1.43693423423423 0.0314657657657657 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.834853433359285 0.330293133281431 0.165146566640715 18 0.840734560636967 0.318530878726067 0.159265439363033 19 0.807857048139482 0.384285903721037 0.192142951860518 20 0.87398044016244 0.25203911967512 0.12601955983756 21 0.841893042764985 0.31621391447003 0.158106957235015 22 0.782599579626534 0.434800840746932 0.217400420373466 23 0.744567540175759 0.510864919648482 0.255432459824241 24 0.695264360503676 0.609471278992647 0.304735639496324 25 0.616662025984595 0.76667594803081 0.383337974015405 26 0.542646331590855 0.91470733681829 0.457353668409145 27 0.494108116252392 0.988216232504783 0.505891883747608 28 0.547364082213997 0.905271835572006 0.452635917786003 29 0.648060892258001 0.703878215483997 0.351939107741999 30 0.587974210084417 0.824051579831166 0.412025789915583 31 0.554796748361433 0.890406503277134 0.445203251638567 32 0.681315383040557 0.637369233918886 0.318684616959443 33 0.782377359298165 0.435245281403671 0.217622640701835 34 0.811124839529923 0.377750320940154 0.188875160470077 35 0.834554172443095 0.33089165511381 0.165445827556905 36 0.86451655050172 0.270966898996561 0.135483449498281 37 0.876411278204378 0.247177443591244 0.123588721795622 38 0.828652888011325 0.342694223977349 0.171347111988675 39 0.832325906179283 0.335348187641434 0.167674093820717 40 0.824180448018083 0.351639103963834 0.175819551981917 41 0.828740716795482 0.342518566409037 0.171259283204518 42 0.859551813282003 0.280896373435994 0.140448186717997 43 0.848139614851265 0.303720770297471 0.151860385148735 44 0.868987297073484 0.262025405853032 0.131012702926516 45 0.88929032060847 0.221419358783061 0.110709679391530 46 0.86812387772602 0.263752244547959 0.131876122273979 47 0.917541914125293 0.164916171749413 0.0824580858747066 48 0.953082089449244 0.0938358211015123 0.0469179105507562 49 0.951247319368865 0.0975053612622706 0.0487526806311353 50 0.944773144068598 0.110453711862804 0.0552268559314018 51 0.93310861531337 0.133782769373261 0.0668913846866303 52 0.908026229190126 0.183947541619749 0.0919737708098744 53 0.858519636481011 0.282960727037977 0.141480363518988 54 0.779969017766288 0.440061964467423 0.220030982233712 55 0.664088496268144 0.671823007463711 0.335911503731856 56 0.604054795064208 0.791890409871585 0.395945204935792 57 0.562422084885932 0.875155830228135 0.437577915114068 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 0 0 OK 10% type I error level 2 0.0487804878048781 OK

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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