*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: Fri, 20 Nov 2009 07:38:06 -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/Nov/20/t125872809769krb8m4jvy2x38.htm/, Retrieved Fri, 20 Nov 2009 15:41:49 +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/Nov/20/t125872809769krb8m4jvy2x38.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:

Dataseries X:

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613 0 611 611 0 613 594 0 611 595 0 594 591 0 595 589 0 591 584 0 589 573 0 584 567 0 573 569 0 567 621 0 569 629 0 621 628 0 629 612 0 628 595 0 612 597 0 595 593 0 597 590 0 593 580 0 590 574 0 580 573 0 574 573 0 573 620 0 573 626 0 620 620 0 626 588 0 620 566 0 588 557 0 566 561 0 557 549 0 561 532 0 549 526 0 532 511 0 526 499 0 511 555 0 499 565 0 555 542 0 565 527 0 542 510 0 527 514 0 510 517 0 514 508 0 517 493 0 508 490 0 493 469 0 490 478 0 469 528 0 478 534 0 528 518 1 534 506 1 518 502 1 506 516 1 502 528 1 516 533 1 528 536 1 533 537 1 536 524 1 537 536 1 524 587 1 536 597 1 587 581 1 597

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 5 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation WklBe[t] = + 78.3799061515617 + 14.6195874973145X[t] + 0.898113780807656Y1[t] -20.7234367469645M1[t] -27.0811350164046M2[t] -28.2616920464878M3[t] -11.6422490765710M4[t] -11.2092314050304M5[t] -16.9965909773283M6[t] -21.6360223524573M7[t] -18.3441303358710M8[t] -24.6650706863537M9[t] -12.0177055958290M10[t] + 37.5949348318731M11[t] -0.388490745478934t + 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) 78.3799061515617 26.479551 2.96 0.00485 0.002425 X 14.6195874973145 3.288852 4.4452 5.5e-05 2.8e-05 Y1 0.898113780807656 0.039915 22.5009 0 0 M1 -20.7234367469645 3.953963 -5.2412 4e-06 2e-06 M2 -27.0811350164046 4.204585 -6.4409 0 0 M3 -28.2616920464878 4.32882 -6.5287 0 0 M4 -11.6422490765710 4.511667 -2.5805 0.013123 0.006562 M5 -11.2092314050304 4.428655 -2.5311 0.014855 0.007427 M6 -16.9965909773283 4.356003 -3.9019 0.000309 0.000155 M7 -21.6360223524573 4.377076 -4.943 1.1e-05 5e-06 M8 -18.3441303358710 4.473265 -4.1008 0.000166 8.3e-05 M9 -24.6650706863537 4.515308 -5.4625 2e-06 1e-06 M10 -12.0177055958290 4.67794 -2.569 0.013508 0.006754 M11 37.5949348318731 4.590183 8.1903 0 0 t -0.388490745478934 0.11461 -3.3897 0.001445 0.000722 Multiple Linear Regression - Regression Statistics Multiple R 0.991014050333522 R-squared 0.982108847958452 Adjusted R-squared 0.976663714728416 F-TEST (value) 180.364521209686 F-TEST (DF numerator) 14 F-TEST (DF denominator) 46 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 6.42361458238997 Sum Squared Residuals 1898.08991794228 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 613 606.015498732596 6.98450126740352 2 611 601.065537279292 9.934462720708 3 594 597.700261942114 -3.70026194211452 4 595 598.663279892822 -3.66327989282235 5 591 599.605920599692 -8.6059205996916 6 589 589.837615158684 -0.837615158684151 7 584 583.013465476461 0.986534523539002 8 573 581.42629784353 -8.42629784353008 9 567 564.837615158684 2.16238484131586 10 569 571.707806818884 -2.70780681888394 11 621 622.728184062722 -1.72818406272239 12 629 631.446675087369 -2.44667508736856 13 628 617.519657841386 10.4803421586136 14 612 609.87535504566 2.12464495434040 15 595 593.936486777175 1.06351322282496 16 597 594.899504727883 2.10049527211723 17 593 596.74025921556 -3.74025921555972 18 590 586.971953774552 3.02804622544775 19 580 579.249690311521 0.750309688478562 20 574 573.171953774552 0.828046225447751 21 573 561.073839993745 11.9261600062554 22 573 572.434600557983 0.565399442017315 23 620 621.658750240206 -1.65875024020584 24 626 625.886672360814 0.113327639186318 25 620 610.163427553216 9.83657244678383 26 588 598.028555853451 -10.0285558534512 27 566 567.719867092044 -1.71986709204409 28 557 564.192316138714 -7.19231613871355 29 561 556.153819037506 4.84618096249371 30 549 553.57042384296 -4.57042384296006 31 532 537.76513635266 -5.76513635266034 32 526 525.400603350038 0.599396649962425 33 511 513.30248956923 -2.30248956922991 34 499 512.089657202161 -13.0896572021608 35 555 550.536441514692 4.46355848530787 36 565 562.847387662569 2.15261233743114 37 542 550.716597978202 -8.71659797820196 38 527 523.313792004707 3.68620799529316 39 510 508.27303751703 1.72696248297010 40 514 509.236055467738 4.76394453226237 41 517 512.87303751703 4.12696248297012 42 508 509.391528541676 -1.39152854167601 43 493 496.280582393799 -3.28058239379926 44 490 485.712276952792 4.2877230472082 45 469 476.308504514407 -7.30850451440711 46 478 469.706989462492 8.2930105375079 47 528 527.014163171984 0.985836828015844 48 534 533.936426635015 0.063573364985062 49 518 532.832769324732 -14.8327693247320 50 506 511.71675981689 -5.71675981689042 51 502 499.370346671636 2.62965332836356 52 516 512.008843772844 3.99115622715631 53 528 524.626963630213 3.37303636978748 54 533 529.228478682128 3.77152131787247 55 536 528.691125465558 7.30887453444203 56 537 534.288868079088 2.71113192091170 57 524 528.477550763934 -4.47755076393423 58 536 529.06094595848 6.93905404151954 59 587 589.062461010396 -2.06246101039548 60 597 596.882838254234 0.117161745766061 61 581 584.752048569867 -3.75204856986706 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 18 0.184311703662680 0.368623407325359 0.81568829633732 19 0.112462404175104 0.224924808350208 0.887537595824896 20 0.0590282321957096 0.118056464391419 0.94097176780429 21 0.0665574323850992 0.133114864770198 0.9334425676149 22 0.0307951655398725 0.0615903310797449 0.969204834460128 23 0.0173572421928665 0.0347144843857331 0.982642757807134 24 0.00890413147933768 0.0178082629586754 0.991095868520662 25 0.0397428852502019 0.0794857705004039 0.960257114749798 26 0.663342193988467 0.673315612023067 0.336657806011533 27 0.567097597544108 0.865804804911784 0.432902402455892 28 0.566784307602038 0.866431384795925 0.433215692397962 29 0.627546103508796 0.744907792982408 0.372453896491204 30 0.587205140439537 0.825589719120926 0.412794859560463 31 0.550303074322729 0.899393851354543 0.449696925677271 32 0.471488502244588 0.942977004489176 0.528511497755412 33 0.498841453065955 0.99768290613191 0.501158546934045 34 0.93063954398019 0.138720912039621 0.0693604560198104 35 0.94409004578764 0.111819908424721 0.0559099542123607 36 0.93986246051344 0.120275078973122 0.0601375394865612 37 0.953888264595582 0.0922234708088362 0.0461117354044181 38 0.982939448518759 0.0341211029624829 0.0170605514812415 39 0.96637143545757 0.0672571290848587 0.0336285645424294 40 0.95903041019747 0.081939179605061 0.0409695898025305 41 0.9805407502295 0.0389184995410022 0.0194592497705011 42 0.980583891790982 0.0388322164180356 0.0194161082090178 43 0.9710323120147 0.0579353759706005 0.0289676879853002 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 5 0.192307692307692 NOK 10% type I error level 11 0.423076923076923 NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Nov/20/t125872809769krb8m4jvy2x38/10h9pf1258727879.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/20/t125872809769krb8m4jvy2x38/10h9pf1258727879.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/20/t125872809769krb8m4jvy2x38/1umsw1258727879.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/20/t125872809769krb8m4jvy2x38/1umsw1258727879.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/20/t125872809769krb8m4jvy2x38/274go1258727879.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/20/t125872809769krb8m4jvy2x38/274go1258727879.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/20/t125872809769krb8m4jvy2x38/3a2o21258727879.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/20/t125872809769krb8m4jvy2x38/3a2o21258727879.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/20/t125872809769krb8m4jvy2x38/4raop1258727879.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/20/t125872809769krb8m4jvy2x38/4raop1258727879.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/20/t125872809769krb8m4jvy2x38/5x77e1258727879.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/20/t125872809769krb8m4jvy2x38/5x77e1258727879.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/20/t125872809769krb8m4jvy2x38/6i6pp1258727879.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/20/t125872809769krb8m4jvy2x38/6i6pp1258727879.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/20/t125872809769krb8m4jvy2x38/71sgd1258727879.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/20/t125872809769krb8m4jvy2x38/71sgd1258727879.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/20/t125872809769krb8m4jvy2x38/8qpia1258727879.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/20/t125872809769krb8m4jvy2x38/8qpia1258727879.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/20/t125872809769krb8m4jvy2x38/90fjy1258727879.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/20/t125872809769krb8m4jvy2x38/90fjy1258727879.ps (open in new window)

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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