*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: Tue, 15 Dec 2009 06:56:39 -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/15/t1260885497fy7j97lssjvcqal.htm/, Retrieved Tue, 15 Dec 2009 14:58:30 +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/15/t1260885497fy7j97lssjvcqal.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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2440.25 0 2350.44 2408.64 0 2440.25 2472.81 0 2408.64 2407.6 0 2472.81 2454.62 0 2407.6 2448.05 0 2454.62 2497.84 0 2448.05 2645.64 0 2497.84 2756.76 0 2645.64 2849.27 0 2756.76 2921.44 0 2849.27 2981.85 0 2921.44 3080.58 0 2981.85 3106.22 0 3080.58 3119.31 0 3106.22 3061.26 0 3119.31 3097.31 0 3061.26 3161.69 0 3097.31 3257.16 0 3161.69 3277.01 0 3257.16 3295.32 0 3277.01 3363.99 0 3295.32 3494.17 0 3363.99 3667.03 0 3494.17 3813.06 0 3667.03 3917.96 0 3813.06 3895.51 0 3917.96 3801.06 0 3895.51 3570.12 0 3801.06 3701.61 0 3570.12 3862.27 0 3701.61 3970.1 0 3862.27 4138.52 0 3970.1 4199.75 0 4138.52 4290.89 0 4199.75 4443.91 0 4290.89 4502.64 0 4443.91 4356.98 0 4502.64 4591.27 0 4356.98 4696.96 0 4591.27 4621.4 0 4696.96 4562.84 0 4621.4 4202.52 0 4562.84 4296.49 0 4202.52 4435.23 0 4296.49 4105.18 0 4435.23 4116.68 0 4105.18 3844.49 0 4116.68 3720.98 0 3844.49 3674.4 0 3720.98 3857.62 0 3674.4 3801.06 0 3857.62 3504.37 0 3801.06 3032.6 0 3504.37 3047.03 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] = + 227.039845124434 -97.252462831136X[t] + 0.945504547175353Y1[t] -0.78610162790592t + 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) 227.039845124434 132.04536 1.7194 0.090227 0.045114 X -97.252462831136 139.774326 -0.6958 0.489008 0.244504 Y1 0.945504547175353 0.048001 19.6977 0 0 t -0.78610162790592 2.146013 -0.3663 0.715307 0.357653 Multiple Linear Regression - Regression Statistics Multiple R 0.981200998591577 R-squared 0.962755399637109 Adjusted R-squared 0.961062463256977 F-TEST (value) 568.689651268741 F-TEST (DF numerator) 3 F-TEST (DF denominator) 66 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 167.074407875857 Sum Squared Residuals 1842314.61262650 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 2440.25 2448.60545135936 -8.35545135936304 2 2408.64 2532.73511311328 -124.095113113279 3 2472.81 2502.06161274916 -29.2516127491589 4 2407.6 2561.94853791350 -154.348537913496 5 2454.62 2499.50608476428 -44.8860847642851 6 2448.05 2543.17760694456 -95.127606944564 7 2497.84 2536.17954044172 -38.3395404417162 8 2645.64 2582.47011021767 63.1698897823285 9 2756.76 2721.42958066228 35.3304193377178 10 2849.27 2825.7079443165 23.5620556834978 11 2921.44 2912.39046834779 9.04953165221215 12 2981.85 2979.84142988953 2.00857011047251 13 3080.58 3036.17325795648 44.4067420435156 14 3106.22 3128.7368202712 -22.5168202712014 15 3119.31 3152.19345523287 -32.8834552328712 16 3061.26 3163.78400812749 -102.524008127491 17 3097.31 3108.11136753606 -10.8013675360559 18 3161.69 3141.41070483382 20.2792951661789 19 3257.16 3201.49618595306 55.6638140469353 20 3277.01 3290.97740344399 -13.9674034439893 21 3295.32 3308.95956707751 -13.6395670775145 22 3363.99 3325.48565370839 38.5043462916103 23 3494.17 3389.62734933501 104.542650664985 24 3667.03 3511.92702965840 155.102970341604 25 3813.06 3674.58084405522 138.479155944778 26 3917.96 3811.86677145133 106.093228548667 27 3895.51 3910.26409682212 -14.7540968221217 28 3801.06 3888.25141811013 -87.1914181101295 29 3570.12 3798.16241200151 -228.042412001511 30 3701.61 3579.02149024893 122.588509751071 31 3862.27 3702.55978152911 159.710218470889 32 3970.1 3853.6784404504 116.421559549603 33 4138.52 3954.84609414441 183.673905855591 34 4199.75 4113.30186835178 86.4481316482232 35 4290.89 4170.40901014742 120.480989852583 36 4443.91 4255.79619294907 188.113807050926 37 4502.64 4399.69119712994 102.948802870061 38 4356.98 4454.43457755764 -97.4545775576433 39 4591.27 4315.92628358817 275.343716411826 40 4696.96 4536.66244231798 160.297557682017 41 4621.4 4635.80671628104 -14.4067162810398 42 4562.84 4563.57829106856 -0.738291068563195 43 4202.52 4507.42344315807 -304.903443158069 44 4296.49 4165.95314309194 130.536856908060 45 4435.23 4254.0161037621 181.213896237898 46 4105.18 4384.40930300930 -279.229303009304 47 4116.68 4071.55942558617 45.1205744138270 48 3844.49 4081.64662625078 -237.156626250784 49 3720.98 3823.50364192722 -102.523641927218 50 3674.4 3705.93827367768 -31.5382736776845 51 3857.62 3661.11057024235 196.509429757649 52 3801.06 3833.55981174791 -32.499811747913 53 3504.37 3779.29597293177 -274.925972931769 54 3032.6 3497.98812720241 -465.388127202408 55 3047.03 3051.14134535359 -4.11134535358478 56 2962.34 2966.74641151028 -4.4064115102838 57 2197.82 2885.8855297821 -688.065529782097 58 2014.45 2162.24229174769 -147.79229174769 59 1862.83 1988.07902130424 -125.249021304240 60 1905.41 1843.93552023361 61.4744797663938 61 1810.99 1883.40900222443 -72.419002224427 62 1670.07 1793.34836125222 -123.278361252224 63 1864.44 1659.32175883637 205.118241163633 64 2052.02 1842.31337604294 209.706623957065 65 2029.6 2018.88501737418 10.714982625818 66 2070.83 1996.90070379860 73.9292962013954 67 2293.41 2035.09775465074 258.312245349261 68 2443.27 2244.76205513312 198.507944866877 69 2513.17 2385.66926494492 127.500735055085 70 2466.92 2450.97393116457 15.9460688354334 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 7 0.00436997205751246 0.00873994411502492 0.995630027942488 8 0.0447049107775033 0.0894098215550066 0.955295089222497 9 0.0358279626223361 0.0716559252446722 0.964172037377664 10 0.0138310404379099 0.0276620808758197 0.98616895956209 11 0.00484381497398504 0.00968762994797008 0.995156185026015 12 0.00162683951957476 0.00325367903914951 0.998373160480425 13 0.000519198981312534 0.00103839796262507 0.999480801018688 14 0.000209695223304542 0.000419390446609084 0.999790304776695 15 9.19898580263282e-05 0.000183979716052656 0.999908010141974 16 0.000153439033691687 0.000306878067383375 0.999846560966308 17 5.64214273901768e-05 0.000112842854780354 0.99994357857261 18 1.77480496866038e-05 3.54960993732076e-05 0.999982251950313 19 5.86728816088942e-06 1.17345763217788e-05 0.99999413271184 20 2.15687405336657e-06 4.31374810673314e-06 0.999997843125947 21 8.13616181000394e-07 1.62723236200079e-06 0.999999186383819 22 2.34280832501783e-07 4.68561665003566e-07 0.999999765719167 23 1.20123152761869e-07 2.40246305523739e-07 0.999999879876847 24 1.78601221051951e-07 3.57202442103902e-07 0.99999982139878 25 1.23915243810773e-07 2.47830487621545e-07 0.999999876084756 26 4.06655233399634e-08 8.13310466799267e-08 0.999999959334477 27 2.69797558612951e-08 5.39595117225902e-08 0.999999973020244 28 7.93435862365834e-08 1.58687172473167e-07 0.999999920656414 29 1.55058372478887e-05 3.10116744957774e-05 0.999984494162752 30 6.80578369277434e-06 1.36115673855487e-05 0.999993194216307 31 3.46386010073290e-06 6.92772020146579e-06 0.9999965361399 32 1.43172668297632e-06 2.86345336595265e-06 0.999998568273317 33 1.01785187752707e-06 2.03570375505413e-06 0.999998982148123 34 3.868120218297e-07 7.736240436594e-07 0.999999613187978 35 1.65294207754987e-07 3.30588415509975e-07 0.999999834705792 36 1.49933500641581e-07 2.99867001283162e-07 0.9999998500665 37 6.61412462175626e-08 1.32282492435125e-07 0.999999933858754 38 1.15583504528919e-07 2.31167009057838e-07 0.999999884416495 39 4.73207841751131e-07 9.46415683502262e-07 0.999999526792158 40 5.82163448665894e-07 1.16432689733179e-06 0.99999941783655 41 4.82113099288891e-07 9.64226198577783e-07 0.9999995178869 42 5.25044569782968e-07 1.05008913956594e-06 0.99999947495543 43 6.83806499226659e-05 0.000136761299845332 0.999931619350077 44 8.9659646447785e-05 0.00017931929289557 0.999910340353552 45 0.000326969066855951 0.000653938133711903 0.999673030933144 46 0.00252570917956236 0.00505141835912471 0.997474290820438 47 0.00369272286360572 0.00738544572721144 0.996307277136394 48 0.00556596651534672 0.0111319330306934 0.994434033484653 49 0.00379507509201423 0.00759015018402846 0.996204924907986 50 0.00286056826299607 0.00572113652599215 0.997139431737004 51 0.0221055396926093 0.0442110793852186 0.97789446030739 52 0.0439194317478808 0.0878388634957616 0.95608056825212 53 0.0491552518244991 0.0983105036489983 0.950844748175501 54 0.112118092355505 0.22423618471101 0.887881907644495 55 0.0884559440984547 0.176911888196909 0.911544055901545 56 0.826876001136514 0.346247997726973 0.173123998863486 57 0.87716690765118 0.245666184697639 0.122833092348819 58 0.853048796579507 0.293902406840987 0.146951203420493 59 0.791992454995627 0.416015090008746 0.208007545004373 60 0.88098527087576 0.238029458248482 0.119014729124241 61 0.894300419425571 0.211399161148857 0.105699580574428 62 0.836337679623903 0.327324640752193 0.163662320376097 63 0.725621684569723 0.548756630860554 0.274378315430277 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 40 0.701754385964912 NOK 5% type I error level 43 0.75438596491228 NOK 10% type I error level 47 0.824561403508772 NOK

Charts produced by software:

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Parameters (Session):

Parameters (R input):

par1 = 1 ; 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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