Multiple Linear Regression 4 lags

*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, 19 Dec 2009 07:11:07 -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/Dec/19/t126123207942zbvsf5xoz2rnn.htm/, Retrieved Sat, 19 Dec 2009 15:14:51 +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/Dec/19/t126123207942zbvsf5xoz2rnn.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:

kvn paper

Dataseries X:

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9283 4359 8947 9627 8700 9487 8829 5382 9283 8947 9627 8700 9947 4459 8829 9283 8947 9627 9628 6398 9947 8829 9283 8947 9318 4596 9628 9947 8829 9283 9605 3024 9318 9628 9947 8829 8640 1887 9605 9318 9628 9947 9214 2070 8640 9605 9318 9628 9567 1351 9214 8640 9605 9318 8547 2218 9567 9214 8640 9605 9185 2461 8547 9567 9214 8640 9470 3028 9185 8547 9567 9214 9123 4784 9470 9185 8547 9567 9278 4975 9123 9470 9185 8547 10170 4607 9278 9123 9470 9185 9434 6249 10170 9278 9123 9470 9655 4809 9434 10170 9278 9123 9429 3157 9655 9434 10170 9278 8739 1910 9429 9655 9434 10170 9552 2228 8739 9429 9655 9434 9784 1594 9552 8739 9429 9655 9089 2467 9784 9552 8739 9429 9763 2222 9089 9784 9552 8739 9330 3607 9763 9089 9784 9552 9144 4685 9330 9763 9089 9784 9895 4962 9144 9330 9763 9089 10404 5770 9895 9144 9330 9763 10195 5480 10404 9895 9144 9330 9987 5000 10195 10404 9895 9144 9789 3228 9987 10195 10404 9895 9437 1993 9789 9987 10195 10404 10096 2288 9437 9789 9987 10195 9776 1580 10096 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 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Y[t] = + 9650.17770595167 -0.201647556215484X[t] -0.0389229420967999Y1[t] -0.0649419763446213Y2[t] + 0.130119737931372Y3[t] -0.0348300325060855Y4[t] + 588.596073150179M1[t] + 539.994539376167M2[t] + 1241.94351360937M3[t] + 1205.54423971928M4[t] + 886.023163317046M5[t] + 402.968909355954M6[t] -630.329686093159M7[t] -130.216474778553M8[t] -10.7569367020101M9[t] -626.183201456473M10[t] + 131.905261924072M11[t] + 18.9641357712519t + 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) 9650.17770595167 2414.05101 3.9975 0.000173 8.6e-05 X -0.201647556215484 0.085524 -2.3578 0.021553 0.010777 Y1 -0.0389229420967999 0.132496 -0.2938 0.769917 0.384958 Y2 -0.0649419763446213 0.124208 -0.5228 0.602944 0.301472 Y3 0.130119737931372 0.121458 1.0713 0.288182 0.144091 Y4 -0.0348300325060855 0.126155 -0.2761 0.783398 0.391699 M1 588.596073150179 229.691129 2.5626 0.012833 0.006417 M2 539.994539376167 268.726694 2.0095 0.048847 0.024423 M3 1241.94351360937 245.015123 5.0688 4e-06 2e-06 M4 1205.54423971928 293.603861 4.106 0.00012 6e-05 M5 886.023163317046 276.020084 3.21 0.002104 0.001052 M6 402.968909355954 203.633901 1.9789 0.052274 0.026137 M7 -630.329686093159 235.277945 -2.6791 0.009441 0.00472 M8 -130.216474778553 205.540882 -0.6335 0.528717 0.264359 M9 -10.7569367020101 213.222487 -0.0504 0.959926 0.479963 M10 -626.183201456473 208.917126 -2.9973 0.003915 0.001957 M11 131.905261924072 196.311343 0.6719 0.504132 0.252066 t 18.9641357712519 4.916013 3.8576 0.000275 0.000138 Multiple Linear Regression - Regression Statistics Multiple R 0.930235134326687 R-squared 0.86533740513579 Adjusted R-squared 0.828413790414957 F-TEST (value) 23.4358800371615 F-TEST (DF numerator) 17 F-TEST (DF denominator) 62 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 241.611366286730 Sum Squared Residuals 3619315.24377429 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 9283 9206.9254497378 76.0745502622092 2 8829 9150.11726974106 -321.117269741056 3 9947 9932.23272386608 14.7672761339165 4 9628 9577.17543629074 50.8245637092603 5 9318 9509.02142899276 -191.02142899276 6 9605 9555.99057344264 49.0094265573605 7 8640 8699.44234072492 -59.4423407249226 8 9214 9171.31413854657 42.6858614534297 9 9567 9543.19131858548 23.8086814145163 10 8547 8585.32249894844 -38.3224989484443 11 9185 9438.45133616994 -253.451336169944 12 9470 9278.52385328798 191.476146712019 13 9123 9334.44779992492 -211.447799924919 14 9278 9379.8365422908 -101.836542290796 15 10170 10206.3203273207 -36.3203273206869 16 9434 9757.91652288585 -323.916522885846 17 9655 9750.70568634797 -95.705686347974 18 9429 9769.6008066087 -340.600806608701 19 8739 8874.32874156035 -135.328741560346 20 9552 9425.20724847767 126.792751522331 21 9784 9667.53658676284 116.463413237164 22 9089 8751.2971600426 337.702839957398 23 9763 9719.55838607992 43.4416139200791 24 9330 9348.10696792755 -18.1069679275543 25 9144 9612.86006771662 -468.860067716619 26 9895 9674.63341558687 220.366584413131 27 10404 10135.6460898212 268.353910178770 28 10195 10098.9846740627 96.0153259372952 29 9987 9974.49629858656 12.5037014134386 30 9789 9929.46808721772 -140.468087217717 31 9437 9140.45952130757 296.540478692428 32 10096 9606.82479754822 489.175202451783 33 9776 9866.70523667894 -90.705236678944 34 9106 9093.92103308954 12.0789669104557 35 10258 9999.50906256194 258.490937438062 36 9766 9536.52711699733 229.472883002666 37 9826 9797.83664285604 28.163357143959 38 9957 9928.50174620358 28.4982537964230 39 10036 10347.3325635295 -311.332563529519 40 10508 10388.4277269450 119.572273054962 41 10146 10131.3496947354 14.6503052646238 42 10166 10111.3306806103 54.6693193896712 43 9365 9394.75952908213 -29.7595290821262 44 9968 9818.8713356971 149.128664302907 45 10123 10162.1702624546 -39.17026245456 46 9144 9317.79349021288 -173.793490212879 47 10447 10129.4311610274 317.568838972646 48 9699 9826.26518705785 -127.26518705785 49 10451 10012.2282604761 438.771739523925 50 10192 10014.5817929343 177.41820706573 51 10404 10550.5984739469 -146.598473946882 52 10597 10629.9429337656 -32.9429337655865 53 10633 10164.3275863704 468.672413629586 54 10727 10366.3661555747 360.633844425286 55 9784 9581.94682654597 202.053173454034 56 9667 10004.9678868034 -337.967886803398 57 10297 10430.88489901 -133.884899010006 58 9426 9573.357123871 -147.357123871003 59 10274 10237.6105674034 36.3894325966067 60 9598 10186.4873256256 -588.487325625558 61 10400 10315.2395999948 84.7604000052414 62 9985 10094.5512485019 -109.551248501886 63 10761 10620.2960599048 140.703940095247 64 11081 10880.3576183082 200.642381691769 65 10297 10373.1111854933 -76.1111854932893 66 10751 10598.9974065614 152.002593438598 67 9760 9867.63770208635 -107.637702086347 68 10133 10196.9443311980 -63.9443311979532 69 10806 10682.5116965082 123.488303491829 70 9734 9724.30869383553 9.69130616447232 71 10083 10485.4394867574 -402.439486757449 72 10691 10378.0895491037 312.910450896277 73 10446 10393.4621792938 52.5378207062032 74 10517 10410.7779847415 106.222015258454 75 11353 11282.5737616108 70.4262383891544 76 10436 10546.1950877419 -110.195087741854 77 10721 10853.9881194736 -132.988119473625 78 10701 10836.2462899845 -135.246289984499 79 9793 9959.42533869272 -166.42533869272 80 10142 10547.8702617291 -405.870261729099 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 21 0.177311639169619 0.354623278339237 0.822688360830381 22 0.095188443457904 0.190376886915808 0.904811556542096 23 0.147302972846306 0.294605945692612 0.852697027153694 24 0.124853468019015 0.24970693603803 0.875146531980985 25 0.160554817275274 0.321109634550547 0.839445182724726 26 0.465150648800566 0.930301297601132 0.534849351199434 27 0.607915312021918 0.784169375956164 0.392084687978082 28 0.515047789966556 0.969904420066888 0.484952210033444 29 0.419280019813617 0.838560039627234 0.580719980186383 30 0.379131573536271 0.758263147072543 0.620868426463729 31 0.364702433443876 0.729404866887751 0.635297566556124 32 0.464003242005711 0.928006484011421 0.535996757994289 33 0.432003829268974 0.864007658537949 0.567996170731026 34 0.39745970761671 0.79491941523342 0.60254029238329 35 0.360431638129506 0.720863276259012 0.639568361870494 36 0.315452046474272 0.630904092948543 0.684547953525728 37 0.266867030055601 0.533734060111202 0.733132969944399 38 0.213008986389289 0.426017972778578 0.786991013610711 39 0.283056029769742 0.566112059539484 0.716943970230258 40 0.216374740666633 0.432749481333266 0.783625259333367 41 0.168077056324524 0.336154112649047 0.831922943675476 42 0.137698924931156 0.275397849862312 0.862301075068844 43 0.117694585951242 0.235389171902483 0.882305414048758 44 0.0962340391132418 0.192468078226484 0.903765960886758 45 0.0710266785407428 0.142053357081486 0.928973321459257 46 0.0915933939420233 0.183186787884047 0.908406606057977 47 0.0983995023811296 0.196799004762259 0.90160049761887 48 0.0890181910494305 0.178036382098861 0.91098180895057 49 0.107816061801698 0.215632123603397 0.892183938198302 50 0.0770598067747688 0.154119613549538 0.922940193225231 51 0.0789906558468244 0.157981311693649 0.921009344153176 52 0.0615693562271268 0.123138712454254 0.938430643772873 53 0.129763693493637 0.259527386987274 0.870236306506363 54 0.113443132859075 0.226886265718151 0.886556867140925 55 0.105630120081083 0.211260240162167 0.894369879918917 56 0.0953982097080467 0.190796419416093 0.904601790291953 57 0.0985547275245213 0.197109455049043 0.901445272475479 58 0.0975466556387092 0.195093311277418 0.90245334436129 59 0.070682316362739 0.141364632725478 0.929317683637261 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 0 0 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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