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SHW WS7

*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 05:47:50 -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/t125872130794q9ttq63pxi267.htm/, Retrieved Fri, 20 Nov 2009 13:48:40 +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/t125872130794q9ttq63pxi267.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 «
8.3 0 8.5 8.6 7.8 0 8.3 8.5 7.8 0 7.8 8.3 8 0 7.8 7.8 8.6 0 8 7.8 8.9 0 8.6 8 8.9 0 8.9 8.6 8.6 0 8.9 8.9 8.3 0 8.6 8.9 8.3 0 8.3 8.6 8.3 0 8.3 8.3 8.4 0 8.3 8.3 8.5 0 8.4 8.3 8.4 0 8.5 8.4 8.6 0 8.4 8.5 8.5 0 8.6 8.4 8.5 0 8.5 8.6 8.5 0 8.5 8.5 8.5 0 8.5 8.5 8.5 0 8.5 8.5 8.5 0 8.5 8.5 8.5 0 8.5 8.5 8.5 0 8.5 8.5 8.5 0 8.5 8.5 8.5 0 8.5 8.5 8.5 0 8.5 8.5 8.6 0 8.5 8.5 8.4 0 8.6 8.5 8.1 0 8.4 8.6 8 0 8.1 8.4 8 0 8 8.1 8 0 8 8 8 0 8 8 7.9 0 8 8 7.8 0 7.9 8 7.8 0 7.8 7.9 7.9 0 7.8 7.8 8.1 0 7.9 7.8 8 0 8.1 7.9 7.6 0 8 8.1 7.3 0 7.6 8 7 0 7.3 7.6 6.8 0 7 7.3 7 0 6.8 7 7.1 0 7 6.8 7.2 0 7.1 7 7.1 1 7.2 7.1 6.9 1 7.1 7.2 6.7 1 6.9 7.1 6.7 1 6.7 6.9 6.6 1 6.7 6.7 6.9 1 6.6 6.7 7.3 1 6.9 6.6 7.5 1 7.3 6.9 7.3 1 7.5 7.3 7.1 1 7.3 7.5 6.9 1 7.1 7.3 7.1 1 6.9 7.1
 
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
Y[t] = + 2.06927334447505 -0.0797015328416982X[t] + 1.39881716350103Y1[t] -0.633441242873896Y2[t] -0.0335768798788945M1[t] -0.0768525073841112M2[t] + 0.0358245516507144M3[t] -0.0767177553795189M4[t] + 0.078013091687698M5[t] -0.0331205954376406M6[t] -0.0843123036080516M7[t] -0.0136287700007924M8[t] -0.0542657039509433M9[t] + 0.0657425302264035M10[t] -0.0510501938447505M11[t] -0.00610933566969867t + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)2.069273344475050.5871253.52440.001040.00052
X-0.07970153284169820.084142-0.94720.3489410.174471
Y11.398817163501030.12177511.486900
Y2-0.6334412428738960.124017-5.10777e-064e-06
M1-0.03357687987889450.113042-0.2970.7679070.383954
M2-0.07685250738411120.112984-0.68020.5001050.250053
M30.03582455165071440.1130910.31680.7529830.376491
M4-0.07671775537951890.11335-0.67680.5022310.251116
M50.0780130916876980.1129860.69050.49370.24685
M6-0.03312059543764060.113996-0.29050.7728320.386416
M7-0.08431230360805160.113241-0.74450.4606950.230348
M8-0.01362877000079240.113018-0.12060.9045910.452296
M9-0.05426570395094330.113129-0.47970.6339450.316973
M100.06574253022640350.113410.57970.5652210.282611
M11-0.05105019384475050.119009-0.4290.6701440.335072
t-0.006109335669698670.00245-2.4940.0166510.008326


Multiple Linear Regression - Regression Statistics
Multiple R0.975611291691286
R-squared0.95181739247554
Adjusted R-squared0.934609318359662
F-TEST (value)55.3122555183133
F-TEST (DF numerator)15
F-TEST (DF denominator)42
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.168088897767444
Sum Squared Residuals1.18666285721232


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
18.38.4719383299697-0.171938329969697
27.88.20613405838197-0.406134058381967
37.87.739981448571360.0600185514286436
487.938050427308370.0619495726916263
58.68.36643537140610.233564628593901
68.98.9617943981369-0.0617943981368987
78.98.94407375762276-0.0440737576227613
88.68.81861558269815-0.218615582698153
98.38.352224164028-0.0522241640279928
108.38.23651028634750.0634897136524972
118.38.30364059946882-0.00364059946881829
128.48.348581457643870.0514185423561296
138.58.448776958445380.0512230415546199
148.48.47592958733318-0.0759295873331775
158.68.379271470060810.220728529939187
168.58.60372738434848-0.103727384348475
178.58.485778930821110.0142210691788878
188.58.431880032313460.0681199676865357
198.58.374578988473350.125421011526645
208.58.439153186410910.0608468135890848
218.58.392406916791070.107593083208934
228.58.50630581529871-0.00630581529871382
238.58.383403755557860.116596244442139
248.58.428344613732910.071655386267087
258.58.388658398184320.111341601815680
268.58.33927343500940.160726564990596
278.68.445841158374530.154158841625468
288.48.4670712320247-0.0670712320247015
298.18.27258518643463-0.172585186434626
3087.862385263164060.137614736835943
3187.855234875836010.144765124163985
3287.983153198060960.0168468019390354
3387.936406928441110.063593071558885
347.98.05030582694876-0.150305826948763
357.87.78752205085780.0124779491421919
367.87.755925316970150.0440746830298544
377.97.779583225708940.120416774291058
388.17.870079978884130.229920021115869
3988.19306701066207-0.193067010662073
407.67.80784540303726-0.20784540303726
417.37.46028417332175-0.160284173321755
4277.17677249862597-0.176772498625967
436.86.88985867859772-0.089858678597718
4476.864701816697240.135298183302759
457.17.22440722835238-0.124407228352377
467.27.35149959463535-0.151499594635348
477.17.22543359411551-0.125433594115513
486.97.06714861165307-0.16714861165307
496.76.81104308769166-0.111043087691662
506.76.608582940391320.0914170596086807
516.66.84183891233123-0.241838912331226
526.96.583305553281190.31669444671881
537.37.214916338016410.0850836619835917
547.57.467167807759610.0328321922403873
557.37.43625369947015-0.136253699470151
567.17.094376216132730.0056237838672736
576.96.894554762387450.00544523761255068
587.16.855378476769670.244621523230327


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
190.2508790219104220.5017580438208440.749120978089578
200.1387788693489120.2775577386978240.861221130651088
210.1026485906343570.2052971812687140.897351409365643
220.1303751253729070.2607502507458140.869624874627093
230.07408067701647210.1481613540329440.925919322983528
240.03817957499978230.07635914999956450.961820425000218
250.01764408460808400.03528816921616790.982355915391916
260.02626796677065430.05253593354130860.973732033229346
270.03255804128270490.06511608256540970.967441958717295
280.02234774949532550.04469549899065110.977652250504675
290.08406542975278960.1681308595055790.91593457024721
300.05661652904713220.1132330580942640.943383470952868
310.07879018126801950.1575803625360390.92120981873198
320.07052607963826110.1410521592765220.92947392036174
330.08144326418037830.1628865283607570.918556735819622
340.1011210099887810.2022420199775620.898878990011219
350.08378835917980340.1675767183596070.916211640820197
360.08058352470695330.1611670494139070.919416475293047
370.0923152710541840.1846305421083680.907684728945816
380.1469246350793850.2938492701587700.853075364920615
390.7403308922655720.5193382154688550.259669107734428


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level00OK
5% type I error level20.0952380952380952NOK
10% type I error level50.238095238095238NOK
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2009/Nov/20/t125872130794q9ttq63pxi267/10k33s1258721265.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t125872130794q9ttq63pxi267/10k33s1258721265.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t125872130794q9ttq63pxi267/19ef11258721265.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t125872130794q9ttq63pxi267/19ef11258721265.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t125872130794q9ttq63pxi267/2jzb51258721265.png (open in new window)
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http://www.freestatistics.org/blog/date/2009/Nov/20/t125872130794q9ttq63pxi267/3d65c1258721265.png (open in new window)
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http://www.freestatistics.org/blog/date/2009/Nov/20/t125872130794q9ttq63pxi267/4xj9z1258721265.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t125872130794q9ttq63pxi267/4xj9z1258721265.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t125872130794q9ttq63pxi267/5h5uy1258721265.png (open in new window)
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http://www.freestatistics.org/blog/date/2009/Nov/20/t125872130794q9ttq63pxi267/6xzbp1258721265.png (open in new window)
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http://www.freestatistics.org/blog/date/2009/Nov/20/t125872130794q9ttq63pxi267/7gnaz1258721265.png (open in new window)
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http://www.freestatistics.org/blog/date/2009/Nov/20/t125872130794q9ttq63pxi267/8dhic1258721265.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t125872130794q9ttq63pxi267/8dhic1258721265.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t125872130794q9ttq63pxi267/96zp61258721265.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t125872130794q9ttq63pxi267/96zp61258721265.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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