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DSHW-WS7-MiltReg.T

*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 09:13:36 -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/t1258733685vowvbwn3vzililt.htm/, Retrieved Fri, 20 Nov 2009 17:14:58 +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/t1258733685vowvbwn3vzililt.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:
SDHW, DSHW
 
Dataseries X:
» Textbox « » Textfile « » CSV «
2,0 0,0 2,0 1,7 1,6 1,4 2,1 0,0 2,0 2,0 1,7 1,6 2,5 0,0 2,1 2,0 2,0 1,7 2,5 0,0 2,5 2,1 2,0 2,0 2,6 0,0 2,5 2,5 2,1 2,0 2,7 0,0 2,6 2,5 2,5 2,1 3,7 0,0 2,7 2,6 2,5 2,5 4,0 0,0 3,7 2,7 2,6 2,5 5,0 0,0 4,0 3,7 2,7 2,6 5,1 0,0 5,0 4,0 3,7 2,7 5,1 0,0 5,1 5,0 4,0 3,7 5,0 0,0 5,1 5,1 5,0 4,0 5,1 0,0 5,0 5,1 5,1 5,0 4,7 0,0 5,1 5,0 5,1 5,1 4,5 0,0 4,7 5,1 5,0 5,1 4,5 0,0 4,5 4,7 5,1 5,0 4,6 0,0 4,5 4,5 4,7 5,1 4,6 0,0 4,6 4,5 4,5 4,7 4,6 0,0 4,6 4,6 4,5 4,5 4,6 0,0 4,6 4,6 4,6 4,5 5,3 0,0 4,6 4,6 4,6 4,6 5,4 0,0 5,3 4,6 4,6 4,6 5,3 0,0 5,4 5,3 4,6 4,6 5,2 0,0 5,3 5,4 5,3 4,6 5,0 0,0 5,2 5,3 5,4 5,3 4,2 0,0 5,0 5,2 5,3 5,4 4,3 0,0 4,2 5,0 5,2 5,3 4,3 0,0 4,3 4,2 5,0 5,2 4,3 0,0 4,3 4,3 4,2 5,0 4,0 0,0 4,3 4,3 4,3 4,2 4,0 0,0 4,0 4,3 4,3 4,3 4,1 0,0 4,0 4,0 4,3 4,3 4,4 0,0 4,1 4,0 4,0 4,3 3,6 0,0 4,4 4,1 4,0 4,0 3,7 0,0 3,6 4,4 4,1 4,0 3,8 0,0 3,7 3,6 4,4 4,1 3,3 0,0 3,8 3,7 3,6 4,4 3,3 0,0 3,3 3,8 3,7 3,6 3,3 0,0 3,3 3,3 3,8 3,7 3,5 0,0 3,3 3,3 3,3 3,8 3,3 0,0 3,5 3,3 3,3 3,3 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 Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time6 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135


Multiple Linear Regression - Estimated Regression Equation
IndGez[t] = + 0.680001490026424 -0.109916882560442InvlMex[t] + 0.829083916174935`Yt-1`[t] + 0.0406279848806237`Yt-2`[t] + 0.102037061011512`Yt-3`[t] -0.109824058538842`Yt-4`[t] -0.199444656948999M1[t] -0.252551856372627M2[t] -0.2362239526388M3[t] -0.0226862977284185M4[t] -0.0745510928749468M5[t] -0.161684153029778M6[t] + 0.160657728882051M7[t] + 0.0429349888681616M8[t] + 0.906708489222317M9[t] -0.040782689573798M10[t] -0.0505139202881374M11[t] -0.00275273476324471t + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)0.6800014900264240.4192061.62210.1140160.057008
InvlMex-0.1099168825604420.225445-0.48760.6289940.314497
`Yt-1`0.8290839161749350.1694894.89172.4e-051.2e-05
`Yt-2`0.04062798488062370.2478350.16390.8707560.435378
`Yt-3`0.1020370610115120.2589430.39410.6960030.348001
`Yt-4`-0.1098240585388420.189244-0.58030.5655190.28276
M1-0.1994446569489990.307899-0.64780.5214910.260745
M2-0.2525518563726270.310744-0.81270.4220260.211013
M3-0.23622395263880.295468-0.79950.4295570.214778
M4-0.02268629772841850.330934-0.06860.9457470.472874
M5-0.07455109287494680.344289-0.21650.8298640.414932
M6-0.1616841530297780.302225-0.5350.5961460.298073
M70.1606577288820510.3039480.52860.6005370.300269
M80.04293498886816160.3097320.13860.8905680.445284
M90.9067084892223170.3180132.85120.0073540.003677
M10-0.0407826895737980.32261-0.12640.9001480.450074
M11-0.05051392028813740.349013-0.14470.8857760.442888
t-0.002752734763244710.004832-0.56970.5726340.286317


Multiple Linear Regression - Regression Statistics
Multiple R0.950462850624025
R-squared0.903379630416347
Adjusted R-squared0.85506944562452
F-TEST (value)18.6995689275274
F-TEST (DF numerator)17
F-TEST (DF denominator)34
p-value1.68287606072681e-12
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.342358847011439
Sum Squared Residuals3.98512572431807


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
122.21454512062515-0.214545120625151
22.12.15911247629585-0.0591124762958488
32.52.275224749333490.224775250666508
42.52.78875881687701-0.288758816877015
52.62.76059618702064-0.160596187020643
62.72.78345120227078-0.0834512022707805
73.73.146081916109380.553918083890616
843.86895686209640.131043137903601
955.01855208766768-0.0185520876676811
105.15.000635140905070.0993648590949268
115.15.032474611690220.0675253883097832
1255.15338843915303-0.153388439153031
135.14.76866230338560.331337696614397
144.74.78066555647428-0.0806655564742768
154.54.45646625136180.043533748638203
164.54.50636930627673-0.00636930627673205
174.64.391828949132350.208171050867654
184.64.4083737570450.191626242955003
194.64.75399051438941-0.153990514389412
204.64.64371874571343-0.0437187457134295
215.35.49375710545046-0.193757105450456
225.45.123871933213550.276128066786449
235.35.22273594876990.0772640512301022
245.25.26307748387342-0.0630774838734171
2554.907235767179580.0927642328204208
264.24.66031013931462-0.460310139314622
274.34.003271278121860.296728721878136
284.34.255037195633580.0449628043664231
294.34.144817627110420.155182372889575
3044.15299478512457-0.152994785124574
3144.21287635156679-0.212876351566793
324.14.080212481325470.0197875186745276
334.44.99353052023042-0.593530520230422
343.64.32902179757326-0.729021797573259
353.73.675662800721060.0243371992789359
363.83.793458702408520.00654129759147848
373.33.56365563443097-0.26365563443097
383.33.195379493576920.104620506423082
393.33.187861970354460.112138029645545
403.53.336645954141950.163354045858049
413.33.50275723673659-0.202757236736587
423.33.255180255559650.0448197444403515
433.43.58705121793441-0.187051217934410
443.43.5071119108647-0.107111910864699
455.24.394160286651440.80583971334856
465.34.946471128308120.353528871691883
474.84.96912663881882-0.169126638818821
4854.790075374565030.209924625434969
494.64.54590117437870.0540988256213028
504.64.104532334338330.495467665661665
513.54.17717575082839-0.677175750828391
523.53.413188727070730.0868112729292748


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
210.2368187704999090.4736375409998170.763181229500091
220.1635362218494350.3270724436988690.836463778150565
230.1579969645646090.3159939291292180.842003035435391
240.1212131008065500.2424262016131010.87878689919345
250.07088612486992190.1417722497398440.929113875130078
260.1214263732782150.2428527465564300.878573626721785
270.07906983222259950.1581396644451990.9209301677774
280.04477722141729690.08955444283459390.955222778582703
290.02884258550023100.05768517100046210.97115741449977
300.01115138035580300.02230276071160600.988848619644197
310.006911011430463160.01382202286092630.993088988569537


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level00OK
5% type I error level20.181818181818182NOK
10% type I error level40.363636363636364NOK
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258733685vowvbwn3vzililt/10j90z1258733609.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258733685vowvbwn3vzililt/10j90z1258733609.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t1258733685vowvbwn3vzililt/10s101258733609.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258733685vowvbwn3vzililt/10s101258733609.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t1258733685vowvbwn3vzililt/2orun1258733609.png (open in new window)
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http://www.freestatistics.org/blog/date/2009/Nov/20/t1258733685vowvbwn3vzililt/32inb1258733609.png (open in new window)
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http://www.freestatistics.org/blog/date/2009/Nov/20/t1258733685vowvbwn3vzililt/4rqik1258733609.png (open in new window)
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http://www.freestatistics.org/blog/date/2009/Nov/20/t1258733685vowvbwn3vzililt/5c5xs1258733609.png (open in new window)
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http://www.freestatistics.org/blog/date/2009/Nov/20/t1258733685vowvbwn3vzililt/6blim1258733609.png (open in new window)
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http://www.freestatistics.org/blog/date/2009/Nov/20/t1258733685vowvbwn3vzililt/74be11258733609.png (open in new window)
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http://www.freestatistics.org/blog/date/2009/Nov/20/t1258733685vowvbwn3vzililt/8t5bm1258733609.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258733685vowvbwn3vzililt/8t5bm1258733609.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t1258733685vowvbwn3vzililt/9qo611258733609.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258733685vowvbwn3vzililt/9qo611258733609.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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