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q3a

*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: Sun, 23 Nov 2008 08:53:10 -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/23/t12274556220w53llgqw0a7wye.htm/, Retrieved Sun, 23 Nov 2008 15:53:51 +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/23/t12274556220w53llgqw0a7wye.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 «
1515 0 1510 0 1225 0 1577 0 1417 0 1224 0 1693 0 1633 0 1639 0 1914 0 1586 0 1552 0 2081 0 1500 0 1437 0 1470 0 1849 0 1387 0 1592 0 1589 0 1798 0 1935 0 1887 0 2027 0 2080 0 1556 0 1682 0 1785 0 1869 0 1781 0 2082 0 2570 1 1862 1 1936 1 1504 1 1765 1 1607 1 1577 1 1493 1 1615 1 1700 1 1335 1 1523 1 1623 1 1540 1 1637 1 1524 1 1419 1 1821 1 1593 1 1357 1 1263 1 1750 1 1405 1 1393 1 1639 1 1679 1 1551 1 1744 1 1429 1 1784 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 time3 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135


Multiple Linear Regression - Estimated Regression Equation
Gebouwen[t] = + 1622.60475938657 -148.643010752688Dummy[t] + 3.16784769962981t + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)1622.6047593865770.70537522.948800
Dummy-148.643010752688123.204227-1.20650.2325320.116266
t3.167847699629813.4982950.90550.3689260.184463


Multiple Linear Regression - Regression Statistics
Multiple R0.160479702443966
R-squared0.0257537348965038
Adjusted R-squared-0.00784096390016864
F-TEST (value)0.766601154913609
F-TEST (DF numerator)2
F-TEST (DF denominator)58
p-value0.469238606944363
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation240.531615479265
Sum Squared Residuals3355616.56661378


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
115151625.77260708619-110.772607086191
215101628.94045478583-118.940454785828
312251632.10830248546-407.108302485458
415771635.27615018509-58.2761501850878
514171638.44399788472-221.443997884718
612241641.61184558435-417.611845584347
716931644.7796932839848.2203067160228
816331647.94754098361-14.9475409836070
916391651.11538868324-12.1153886832368
1019141654.28323638287259.716763617133
1115861657.45108408250-71.4510840824964
1215521660.61893178213-108.618931782126
1320811663.78677948176417.213220518244
1415001666.95462718139-166.954627181386
1514371670.12247488102-233.122474881016
1614701673.29032258065-203.290322580645
1718491676.45817028028172.541829719725
1813871679.62601797991-292.626017979905
1915921682.79386567953-90.7938656795348
2015891685.96171337916-96.9617133791646
2117981689.12956107879108.870438921206
2219351692.29740877842242.702591221576
2318871695.46525647805191.534743521946
2420271698.63310417768328.366895822316
2520801701.80095187731378.199048122686
2615561704.96879957694-148.968799576943
2716821708.13664727657-26.1366472765733
2817851711.3044949762073.695505023797
2918691714.47234267583154.527657324167
3017811717.6401903754663.3598096245373
3120821720.80803807509361.191961924908
3225701575.33287502203994.667124977965
3318621578.50072272166283.499277278336
3419361581.66857042129354.331429578706
3515041584.83641812092-80.836418120924
3617651588.00426582055176.995734179446
3716071591.1721135201815.8278864798165
3815771594.33996121981-17.3399612198133
3914931597.50780891944-104.507808919443
4016151600.6756566190714.3243433809271
4117001603.8435043187096.1564956812973
4213351607.01135201833-272.011352018333
4315231610.17919971796-87.1791997179623
4416231613.347047417599.65295258240786
4515401616.51489511722-76.514895117222
4616371619.6827428168517.3172571831483
4715241622.85059051648-98.8505905164816
4814191626.01843821611-207.018438216111
4918211629.18628591574191.813714084259
5015931632.35413361537-39.354133615371
5113571635.521981315-278.521981315001
5212631638.68982901463-375.689829014631
5317501641.85767671426108.142323285740
5414051645.02552441389-240.02552441389
5513931648.19337211352-255.19337211352
5616391651.36121981315-12.3612198131498
5716791654.5290675127824.4709324872204
5815511657.69691521241-106.696915212409
5917441660.8647629120483.1352370879608
6014291664.03261061167-235.032610611669
6117841667.2004583113116.799541688701


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
60.3624976092821430.7249952185642860.637502390717857
70.5045834141666260.9908331716667480.495416585833374
80.3974073768667170.7948147537334330.602592623133283
90.2826767694795540.5653535389591070.717323230520446
100.3043222214115990.6086444428231980.695677778588401
110.2493507791854920.4987015583709830.750649220814508
120.2138331729468330.4276663458936670.786166827053167
130.3101682313867350.620336462773470.689831768613265
140.3803511957314110.7607023914628220.619648804268589
150.4682604331351720.9365208662703440.531739566864828
160.4934804388084640.9869608776169280.506519561191536
170.4338709122222850.867741824444570.566129087777715
180.5633477309307320.8733045381385360.436652269069268
190.5256941719229770.9486116561540460.474305828077023
200.4993151456222910.9986302912445810.500684854377709
210.4429895586223490.8859791172446980.557010441377651
220.4184581885889870.8369163771779750.581541811411012
230.358130753547240.716261507094480.64186924645276
240.3454640405268910.6909280810537810.65453595947311
250.3503107808178840.7006215616357690.649689219182116
260.4201979673461840.8403959346923680.579802032653816
270.3957699248710020.7915398497420050.604230075128998
280.3360083172132370.6720166344264740.663991682786763
290.2705365223181900.5410730446363790.72946347768181
300.2407483518433870.4814967036867730.759251648156613
310.2086251558607500.4172503117215010.79137484413925
320.7834419992580570.4331160014838860.216558000741943
330.9047061017658550.1905877964682900.0952938982341448
340.9550242541409180.0899514917181640.044975745859082
350.9765219181896970.04695616362060620.0234780818103031
360.978912343100860.04217531379828130.0210876568991406
370.97635911078630.04728177842740010.0236408892137000
380.9714668560995660.05706628780086760.0285331439004338
390.9670765232088380.0658469535823250.0329234767911625
400.9559421277573650.08811574448526910.0440578722426346
410.9528905898794260.09421882024114820.0471094101205741
420.9628292237670660.07434155246586850.0371707762329343
430.9460908308774650.1078183382450700.0539091691225348
440.9246024546001580.1507950907996850.0753975453998423
450.8921471653325620.2157056693348770.107852834667438
460.8623493001403540.2753013997192910.137650699859646
470.8111511493149230.3776977013701530.188848850685077
480.7645049742244920.4709900515510170.235495025775508
490.8632554299334220.2734891401331570.136744570066578
500.8529869896522640.2940260206954730.147013010347736
510.7945059988185540.4109880023628920.205494001181446
520.8131580463519580.3736839072960850.186841953648042
530.8631306505507460.2737386988985080.136869349449254
540.770888503657270.4582229926854590.229111496342730
550.7172935201885720.5654129596228550.282706479811428


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level00OK
5% type I error level30.06NOK
10% type I error level90.18NOK
 
Charts produced by software:
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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/23/t12274556220w53llgqw0a7wye/132mf1227455586.ps (open in new window)


http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/23/t12274556220w53llgqw0a7wye/2kxsg1227455586.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/23/t12274556220w53llgqw0a7wye/2kxsg1227455586.ps (open in new window)


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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/23/t12274556220w53llgqw0a7wye/354oh1227455586.ps (open in new window)


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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/23/t12274556220w53llgqw0a7wye/45qsy1227455586.ps (open in new window)


http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/23/t12274556220w53llgqw0a7wye/5inmw1227455586.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/23/t12274556220w53llgqw0a7wye/5inmw1227455586.ps (open in new window)


http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/23/t12274556220w53llgqw0a7wye/6gjfc1227455586.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/23/t12274556220w53llgqw0a7wye/6gjfc1227455586.ps (open in new window)


http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/23/t12274556220w53llgqw0a7wye/7u5n81227455586.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/23/t12274556220w53llgqw0a7wye/7u5n81227455586.ps (open in new window)


http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/23/t12274556220w53llgqw0a7wye/8b5mm1227455586.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/23/t12274556220w53llgqw0a7wye/8b5mm1227455586.ps (open in new window)


http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/23/t12274556220w53llgqw0a7wye/91pwp1227455586.png (open in new window)
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Parameters (Session):
par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ;
 
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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Software written by Ed van Stee & Patrick Wessa


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