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final

*Unverified author*
R Software Module: rwasp_multipleregression.wasp (opens new window with default values)
Title produced by software: Multiple Regression
Date of computation: Thu, 27 Nov 2008 03:04:18 -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/27/t1227780335gk4c65wk8du7zs8.htm/, Retrieved Thu, 27 Nov 2008 10:05:35 +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/27/t1227780335gk4c65wk8du7zs8.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:
» Textbox « » Textfile « » CSV «
9492.49 0 9682.35 0 9762.12 0 10124.63 0 10540.05 0 10601.61 0 10323.73 0 10418.4 0 10092.96 0 10364.91 0 10152.09 0 10032.8 0 10204.59 0 10001.6 0 10411.75 0 10673.38 0 10539.51 0 10723.78 0 10682.06 0 10283.19 0 10377.18 0 10486.64 0 10545.38 0 10554.27 0 10532.54 0 10324.31 0 10695.25 0 10827.81 0 10872.48 0 10971.19 0 11145.65 0 11234.68 0 11333.88 0 10997.97 0 11036.89 0 11257.35 0 11533.59 0 11963.12 0 12185.15 0 12377.62 0 12512.89 0 12631.48 0 12268.53 0 12754.8 0 13407.75 1 13480.21 1 13673.28 1 13239.71 1 13557.69 1 13901.28 1 13200.58 1 13406.97 1 12538.12 1 12419.57 1 12193.88 1 12656.63 1 12812.48 1 12056.67 1 11322.38 1 11530.75 1 11114.08 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 Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time6 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24


Multiple Linear Regression - Estimated Regression Equation
X[t] = + 10528.8355454545 + 1985.35113636364Y[t] -118.122590909089M1[t] + 248.626227272727M2[t] + 325.064227272727M3[t] + 556.176227272727M4[t] + 474.704227272727M5[t] + 543.620227272727M6[t] + 396.864227272727M7[t] + 543.634227272727M8[t] + 281.874000000000M9[t] + 154.304000000000M10[t] + 23.0279999999997M11[t] + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)10528.8355454545406.63887925.892300
Y1985.35113636364256.8387857.7300
M1-118.122590909089533.004943-0.22160.8255530.412776
M2248.626227272727558.7842440.44490.6583620.329181
M3325.064227272727558.7842440.58170.5634680.281734
M4556.176227272727558.7842440.99530.3245660.162283
M5474.704227272727558.7842440.84950.3998040.199902
M6543.620227272727558.7842440.97290.3354990.167749
M7396.864227272727558.7842440.71020.4809990.2405
M8543.634227272727558.7842440.97290.3354870.167743
M9281.874000000000556.4181740.50660.6147640.307382
M10154.304000000000556.4181740.27730.7827280.391364
M1123.0279999999997556.4181740.04140.967160.48358


Multiple Linear Regression - Regression Statistics
Multiple R0.749292474625416
R-squared0.561439212530279
Adjusted R-squared0.451799015662849
F-TEST (value)5.12074247011007
F-TEST (DF numerator)12
F-TEST (DF denominator)48
p-value1.99781687993950e-05
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation879.774381340634
Sum Squared Residuals37152142.1790382


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
19492.4910410.7129545454-918.222954545446
29682.3510777.4617727273-1095.11177272727
39762.1210853.8997727273-1091.77977272727
410124.6311085.0117727273-960.381772727274
510540.0511003.5397727273-463.489772727273
610601.6111072.4557727273-470.845772727272
710323.7310925.6997727273-601.969772727273
810418.411072.4697727273-654.069772727273
910092.9610810.7095454545-717.749545454546
1010364.9110683.1395454545-318.229545454545
1110152.0910551.8635454545-399.773545454545
1210032.810528.8355454545-496.035545454546
1310204.5910410.7129545455-206.122954545457
1410001.610777.4617727273-775.861772727272
1510411.7510853.8997727273-442.149772727273
1610673.3811085.0117727273-411.631772727273
1710539.5111003.5397727273-464.029772727272
1810723.7811072.4557727273-348.675772727272
1910682.0610925.6997727273-243.639772727273
2010283.1911072.4697727273-789.279772727272
2110377.1810810.7095454545-433.529545454545
2210486.6410683.1395454545-196.499545454546
2310545.3810551.8635454545-6.48354545454617
2410554.2710528.835545454525.4344545454548
2510532.5410410.7129545455121.827045454544
2610324.3110777.4617727273-453.151772727273
2710695.2510853.8997727273-158.649772727273
2810827.8111085.0117727273-257.201772727273
2910872.4811003.5397727273-131.059772727273
3010971.1911072.4557727273-101.265772727273
3111145.6510925.6997727273219.950227272727
3211234.6811072.4697727273162.210227272727
3311333.8810810.7095454545523.170454545454
3410997.9710683.1395454545314.830454545454
3511036.8910551.8635454545485.026454545454
3611257.3510528.8355454545728.514454545455
3711533.5910410.71295454551122.87704545454
3811963.1210777.46177272731185.65822727273
3912185.1510853.89977272731331.25022727273
4012377.6211085.01177272731292.60822727273
4112512.8911003.53977272731509.35022727273
4212631.4811072.45577272731559.02422727273
4312268.5310925.69977272731342.83022727273
4412754.811072.46977272731682.33022727273
4513407.7512796.0606818182611.689318181819
4613480.2112668.4906818182811.719318181818
4713673.2812537.21468181821136.06531818182
4813239.7112514.1866818182725.523318181817
4913557.6912396.06409090911161.62590909091
5013901.2812762.81290909091138.46709090909
5113200.5812839.2509090909361.329090909091
5213406.9713070.3629090909336.607090909091
5312538.1212988.8909090909-450.770909090908
5412419.5713057.8069090909-638.236909090909
5512193.8812911.0509090909-717.170909090909
5612656.6313057.8209090909-401.190909090909
5712812.4812796.060681818216.4193181818184
5812056.6712668.4906818182-611.820681818181
5911322.3812537.2146818182-1214.83468181818
6011530.7512514.1866818182-983.436681818182
6111114.0812396.0640909091-1281.98409090909


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
160.1641074880835680.3282149761671360.835892511916432
170.07031207463482460.1406241492696490.929687925365175
180.02796239902540280.05592479805080550.972037600974597
190.01270195292409410.02540390584818820.987298047075906
200.005387242659401450.01077448531880290.994612757340599
210.002439599799143250.00487919959828650.997560400200857
220.0008541237619351790.001708247523870360.999145876238065
230.0003995446344408450.000799089268881690.99960045536556
240.0002482039412788060.0004964078825576110.999751796058721
250.0003228521288697550.0006457042577395110.99967714787113
260.0004039870338993770.0008079740677987540.9995960129661
270.0005162474808390780.001032494961678160.99948375251916
280.0004965993583818010.0009931987167636020.999503400641618
290.0003358092765119810.0006716185530239610.999664190723488
300.0002160322819922650.0004320645639845290.999783967718008
310.0002141511670239840.0004283023340479670.999785848832976
320.0004713617705724930.0009427235411449860.999528638229428
330.001369443368060410.002738886736120830.99863055663194
340.001257607609088080.002515215218176160.998742392390912
350.001178726236255860.002357452472511730.998821273763744
360.00146306277572430.00292612555144860.998536937224276
370.004267438453282220.008534876906564440.995732561546718
380.03031620664536430.06063241329072850.969683793354636
390.06016302925789940.1203260585157990.9398369707421
400.0902551657748870.1805103315497740.909744834225113
410.09494544357950470.1898908871590090.905054556420495
420.08840068951429270.1768013790285850.911599310485707
430.0649961413742210.1299922827484420.935003858625779
440.05342669134342380.1068533826868480.946573308656576
450.02549537537360840.05099075074721670.974504624626392


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level170.566666666666667NOK
5% type I error level190.633333333333333NOK
10% type I error level220.733333333333333NOK
 
Charts produced by software:
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/27/t1227780335gk4c65wk8du7zs8/10agk01227780247.png (open in new window)
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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/27/t1227780335gk4c65wk8du7zs8/4xh0c1227780247.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/27/t1227780335gk4c65wk8du7zs8/4xh0c1227780247.ps (open in new window)


http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/27/t1227780335gk4c65wk8du7zs8/5i7dk1227780247.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/27/t1227780335gk4c65wk8du7zs8/5i7dk1227780247.ps (open in new window)


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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/27/t1227780335gk4c65wk8du7zs8/6cbuc1227780247.ps (open in new window)


http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/27/t1227780335gk4c65wk8du7zs8/7bkn01227780247.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/27/t1227780335gk4c65wk8du7zs8/7bkn01227780247.ps (open in new window)


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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/27/t1227780335gk4c65wk8du7zs8/8sp8t1227780247.ps (open in new window)


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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/27/t1227780335gk4c65wk8du7zs8/9svmi1227780247.ps (open in new window)


 
Parameters (Session):
par1 = 1 ; par2 = Include Monthly Dummies ; par3 = No Linear Trend ;
 
Parameters (R input):
par1 = 1 ; par2 = Include Monthly Dummies ; par3 = No 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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Software written by Ed van Stee & Patrick Wessa


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