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cs.shw.ws7.v2

*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: Thu, 26 Nov 2009 09:07:10 -0700
 
Cite this page as follows:
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Nov/26/t125925190026zba80duvrixrw.htm/, Retrieved Thu, 26 Nov 2009 17:11:52 +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/26/t125925190026zba80duvrixrw.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:
» Textbox « » Textfile « » CSV «
8.9 1.9 9 1.6 9 1.7 9 2 9 2.5 9 2.4 9 2.3 9 2.3 9 2.1 9 2.4 9 2.2 9.1 2.4 9 1.9 9 2.1 9.1 2.1 9 2.1 9 2 9 2.1 9 2.2 8.9 2.2 8.9 2.6 8.9 2.5 8.9 2.3 8.8 2.2 8.8 2.4 8.7 2.3 8.7 2.2 8.5 2.5 8.5 2.5 8.4 2.5 8.2 2.4 8.2 2.3 8.1 1.7 8.1 1.6 8 1.9 7.9 1.9 7.8 1.8 7.7 1.8 7.6 1.9 7.5 1.9 7.5 1.9 7.5 1.9 7.5 1.8 7.5 1.7 7.4 2.1 7.4 2.6 7.3 3.1 7.3 3.1 7.3 3.2 7.2 3.3 7.2 3.6 7.3 3.3 7.4 3.7 7.4 4 7.5 4 7.6 3.8 7.7 3.6 7.9 3.2 8 2.1 8.2 1.6
 
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
R Framework
error message
The field 'Names of X columns' contains a hard return which cannot be interpreted.
Please, resubmit your request without hard returns in the 'Names of X columns'.


Multiple Linear Regression - Estimated Regression Equation
werkl[t] = + 9.34448245145198 -0.484143951541065`infl `[t] + 0.0999999999999908M1[t] + 0.0503171209691788M2[t] + 0.0890486370924635M3[t] + 0.0580972741849276M4[t] + 0.155560306431498M5[t] + 0.164608943523962M6[t] + 0.125243185462319M7[t] + 0.0865116693390339M8[t] + 0.0471459112773918M9[t] + 0.106511669339034M10[t] + 0.0187315161232850M11[t] + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)9.344482451451980.45010920.760500
`infl `-0.4841439515410650.145973-3.31670.0017630.000881
M10.09999999999999080.4374530.22860.8201740.410087
M20.05031712096917880.4374620.1150.9089190.454459
M30.08904863709246350.437540.20350.8396060.419803
M40.05809727418492760.4378030.13270.8949960.447498
M50.1555603064314980.4393580.35410.7248750.362438
M60.1646089435239620.4402590.37390.7101670.355083
M70.1252431854623190.4396390.28490.776990.388495
M80.08651166933903390.438630.19720.8444970.422248
M90.04714591127739180.4382410.10760.9147870.457393
M100.1065116693390340.438630.24280.8091950.404598
M110.01873151612328500.4376080.04280.9660390.483019


Multiple Linear Regression - Regression Statistics
Multiple R0.438622344152539
R-squared0.192389560789868
Adjusted R-squared-0.0138088492212289
F-TEST (value)0.933031252663462
F-TEST (DF numerator)12
F-TEST (DF denominator)47
p-value0.523093765381267
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.691673198671604
Sum Squared Residuals22.4853552467486


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
18.98.5246089435240.375391056476
298.620169249955460.379830750044541
398.610486370924640.389513629075362
498.434291822554780.565708177445217
598.289682879030820.710317120969179
698.34714591127740.652854088722608
798.356194548369860.643805451630144
898.317463032246570.682536967753429
998.374926064493140.625073935506859
1098.289048637092460.710951362907536
1198.298097274184930.701902725815072
129.18.182536967753430.91746303224657
1398.524608943523950.475391056476048
1498.378097274184930.621902725815072
159.18.416828790308210.683171209691787
1698.385877427400680.614122572599323
1798.531754854801350.468245145198646
1898.492389096739710.507610903260289
1998.404608943523960.595391056476038
208.98.365877427400680.534122572599324
218.98.132854088722610.767145911277392
228.98.240634241938360.659365758061643
238.98.249682879030820.650317120969179
248.88.279365758061640.520634241938358
258.88.282536967753420.51746303224658
268.78.281268483876720.418731516123284
278.78.36841439515410.331585604845893
288.58.192219846784250.307780153215749
298.58.289682879030820.210317120969178
308.48.298731516123280.101268483876715
318.28.30778015321575-0.10778015321575
328.28.31746303224657-0.117463032246571
338.18.56858364510957-0.468583645109567
348.18.67636379832532-0.576363798325316
3588.44334045964725-0.443340459647247
367.98.42460894352396-0.524608943523962
377.88.57302333867806-0.77302333867806
387.78.52334045964725-0.823340459647247
397.68.51365758061642-0.913657580616426
407.58.48270621770889-0.98270621770889
417.58.58016924995546-1.08016924995546
427.58.58921788704792-1.08921788704792
437.58.59826652414039-1.09826652414039
447.58.6079494031712-1.10794940317121
457.48.37492606449314-0.97492606449314
467.48.19221984678425-0.79221984678425
477.37.86236771779797-0.56236771779797
487.37.84363620167469-0.543636201674685
497.37.89522180652057-0.595221806520569
507.27.79712453233565-0.59712453233565
517.27.69061286299662-0.490612862996616
527.37.8049046855514-0.504904685551399
537.47.70871013718154-0.308710137181544
547.47.57251558881169-0.172515588811688
557.57.53314983075005-0.0331498307500458
567.67.591247104934970.0087528950650263
577.77.648710137181540.0512898628184562
587.97.90173347585961-0.00173347585961171
5988.34651166933903-0.346511669339034
608.28.56985212898628-0.369852128986282


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
160.0006979899673635150.001395979934727030.999302010032636
175.78564290888853e-050.0001157128581777710.99994214357091
184.23915078926217e-068.47830157852434e-060.99999576084921
193.08190685036631e-076.16381370073261e-070.999999691809315
208.79520420503894e-081.75904084100779e-070.999999912047958
214.27369409037339e-088.54738818074678e-080.99999995726306
221.40184697940510e-082.80369395881021e-080.99999998598153
235.14919880119734e-091.02983976023947e-080.999999994850801
241.16246869537657e-072.32493739075314e-070.99999988375313
251.23130353760903e-072.46260707521805e-070.999999876869646
267.7283795597078e-071.54567591194156e-060.999999227162044
277.19839503419977e-061.43967900683995e-050.999992801604966
280.0001214038444011100.0002428076888022210.999878596155599
290.001586874460969170.003173748921938340.99841312553903
300.01812160078532520.03624320157065050.981878399214675
310.1448984103313700.2897968206627390.85510158966863
320.3845416314986020.7690832629972050.615458368501398
330.72082630376320.55834739247360.2791736962368
340.7998585937847430.4002828124305140.200141406215257
350.8437289624286150.3125420751427690.156271037571385
360.8545084034583030.2909831930833940.145491596541697
370.8831221148875750.2337557702248500.116877885112425
380.9046814766112470.1906370467775070.0953185233887533
390.9139926609920470.1720146780159060.0860073390079531
400.8919796019124670.2160407961750660.108020398087533
410.8438831492510650.3122337014978700.156116850748935
420.7660153354700250.4679693290599510.233984664529975
430.6542188213527350.691562357294530.345781178647265
440.5429558387714190.9140883224571630.457044161228581


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level140.482758620689655NOK
5% type I error level150.517241379310345NOK
10% type I error level150.517241379310345NOK
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2009/Nov/26/t125925190026zba80duvrixrw/10jyxu1259251626.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/26/t125925190026zba80duvrixrw/10jyxu1259251626.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/26/t125925190026zba80duvrixrw/1pkss1259251626.png (open in new window)
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http://www.freestatistics.org/blog/date/2009/Nov/26/t125925190026zba80duvrixrw/20kon1259251626.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/26/t125925190026zba80duvrixrw/20kon1259251626.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/26/t125925190026zba80duvrixrw/3zafx1259251626.png (open in new window)
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http://www.freestatistics.org/blog/date/2009/Nov/26/t125925190026zba80duvrixrw/4ngy91259251626.png (open in new window)
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http://www.freestatistics.org/blog/date/2009/Nov/26/t125925190026zba80duvrixrw/53lvv1259251626.png (open in new window)
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http://www.freestatistics.org/blog/date/2009/Nov/26/t125925190026zba80duvrixrw/6vyhx1259251626.png (open in new window)
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http://www.freestatistics.org/blog/date/2009/Nov/26/t125925190026zba80duvrixrw/7zczl1259251626.png (open in new window)
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http://www.freestatistics.org/blog/date/2009/Nov/26/t125925190026zba80duvrixrw/8jphy1259251626.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/26/t125925190026zba80duvrixrw/8jphy1259251626.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/26/t125925190026zba80duvrixrw/9xezp1259251626.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/26/t125925190026zba80duvrixrw/9xezp1259251626.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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