Home » date » 2010 » Nov » 28 »

W8 - Yt-5 en Yt-6

*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, 28 Nov 2010 13:13:37 +0000
 
Cite this page as follows:
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Nov/28/t1290949989zdpv2krt4jy0wht.htm/, Retrieved Sun, 28 Nov 2010 14:13:20 +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/2010/Nov/28/t1290949989zdpv2krt4jy0wht.htm/},
    year = {2010},
}
@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 = {2010},
    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 «
9081 9700 9084 9081 9743 9084 8587 9743 9731 8587 9563 9731 9998 9563 9437 9998 10038 9437 9918 10038 9252 9918 9737 9252 9035 9737 9133 9035 9487 9133 8700 9487 9627 8700 8947 9627 9283 8947 8829 9283 9947 8829 9628 9947 9318 9628 9605 9318 8640 9605 9214 8640 9567 9214 8547 9567 9185 8547 9470 9185 9123 9470 9278 9123 10170 9278 9434 10170 9655 9434 9429 9655 8739 9429 9552 8739 9687 9552 9019 9687 9672 9019 9206 9672 9069 9206 9788 9069 10312 9788 10105 10312 9863 10105 9656 9863 9295 9656 9946 9295 9701 9946 9049 9701 10190 9049 9706 10190 9765 9706 9893 9765 9994 9893 10433 9994 10073 10433 10112 10073 9266 10112 9820 9266 10097 9820 9115 10097 10411 9115 9678 10411 10408 9678 10153 10408 10368 10153
 
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
Yt-5[t] = + 7020.47641726063 + 0.250863300117026`Yt-6`[t] -679.47273995534M1[t] -63.2724898724251M2[t] + 72.1050849430458M3[t] -877.017102218858M4[t] + 302.088829651828M5[t] -322.230497226616M6[t] -56.5172825314797M7[t] -153.698715001137M8[t] + 425.146565088753M9[t] + 95.456109910176M10[t] -136.157685669757M11[t] + 7.52661398200408t + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)7020.476417260631206.1062065.820800
`Yt-6`0.2508633001170260.1290661.94370.0570570.028528
M1-679.47273995534166.985747-4.0690.0001527.6e-05
M2-63.2724898724251182.470663-0.34680.7300990.36505
M372.1050849430458167.153120.43140.6678840.333942
M4-877.017102218858166.567529-5.26522e-061e-06
M5302.088829651828194.5984021.55240.1263090.063155
M6-322.230497226616167.476942-1.9240.0595320.029766
M7-56.5172825314797168.305294-0.33580.7382980.369149
M8-153.698715001137166.155366-0.9250.3589910.179496
M9425.146565088753166.5832862.55220.0135140.006757
M1095.456109910176184.1419590.51840.606270.303135
M11-136.157685669757177.169138-0.76850.4454670.222733
t7.526613982004082.0821573.61480.0006530.000326


Multiple Linear Regression - Regression Statistics
Multiple R0.855889471630712
R-squared0.7325467876483
Adjusted R-squared0.669330573819716
F-TEST (value)11.5879573179543
F-TEST (DF numerator)13
F-TEST (DF denominator)55
p-value1.81126225129447e-11
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation274.182074467497
Sum Squared Residuals4134669.5477615


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
190818781.90430242245299.095697577554
290849250.34678371493-166.346783714931
397439394.00356241276348.996437587244
485878617.72690400998-30.7269040099772
597319514.36147492739216.638525072615
695639184.55637736483378.443622635174
799989415.6511716223582.348828377696
894379435.121888685561.87811131444258
9100389880.7594713918157.240528608201
1099189709.36447356556208.635526434441
1192529455.1736959536-203.173695953588
1297379431.7830377274305.216962272592
1390358881.50561231083153.49438768917
1491339329.1264396936-196.126439693597
1594879496.61523190254-9.61523190254031
1687008643.8252669640756.1747330359326
1796279633.02839562466-6.02839562465827
1889479248.7859619367-301.785961936702
1992839351.43874653426-68.4387465342645
2088299346.07399688593-517.073996885932
2199479818.5539527047128.446047295304
2296289776.85528103896-148.855281038959
2393189472.7427067037-154.742706703698
2496059538.6593833191866.3406166808187
2586408938.71102447943-298.711024479432
2692149320.35480393142-106.354803931420
2795679607.25452699607-40.2545269960684
2885478754.21369875748-207.213698757478
2991859684.9656784908-499.965678490802
3094709228.22375106902241.776248930975
3191239572.95962027952-449.959620279518
3292789396.25523665126-118.255236651257
331017010021.5109422413148.489057758711
3494349923.1171647491-489.117164749105
3596559514.39459426504140.605405734956
3694299713.51968324267-284.519683242668
3787398984.87845144288-245.878451442884
3895529435.50963842705116.490361572945
3996879782.36569021967-95.3656902196723
4090198874.63666255557144.363337444430
4196729893.69252393009-221.692523930088
4292069440.71354601007-234.713546010066
4390699597.05107683267-528.051076832672
4497889473.02798622899314.972013771014
451031210239.770593085072.229406914978
461010510049.059121149855.9408788502284
4798639773.0432364276289.956763572382
4896569856.01861745106-200.018617451059
4992959132.1437883535162.856211646502
5099469665.30900107617280.690998923829
5197019971.52519824983-270.52519824983
5290498968.4681165412680.5318834587424
53101909991.53779071765198.462209282353
5497069660.9801032547345.0198967452653
5597659812.80209467523-47.8020946752344
5698939737.94821089448155.051789105514
57999410356.4306073814-362.430607381359
581043310059.6039594966373.396040503394
59100739945.64576665005127.354233349948
60101129999.01927825968112.980721740317
6192669336.8568209909-70.8568209909108
6298209748.3533331568371.6466668431742
631009710030.235790219166.7642097808667
6491159158.12935117165-43.129351171649
651041110098.4141363094312.58586369058
6696789806.74026036465-128.740260364646
67104089896.097290056511.902709943993
68101539989.57268065378163.427319346218
691036810511.9744331958-143.974433195834


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
170.0565043027884640.1130086055769280.943495697211536
180.5416184379564190.9167631240871620.458381562043581
190.5545582752056890.8908834495886230.445441724794311
200.4408542081025660.8817084162051320.559145791897434
210.5140104576934920.9719790846130170.485989542306508
220.4158006229000550.8316012458001110.584199377099945
230.4188750949574920.8377501899149850.581124905042508
240.3546589285606690.7093178571213390.64534107143933
250.2917306995647320.5834613991294650.708269300435268
260.4246916671808910.8493833343617820.575308332819109
270.3573329583489750.714665916697950.642667041651025
280.2768200392331620.5536400784663240.723179960766838
290.3391842935399720.6783685870799440.660815706460028
300.5235353198046690.952929360390660.47646468019533
310.5179307575541880.9641384848916240.482069242445812
320.5364366450076890.9271267099846210.463563354992311
330.6356770508221060.7286458983557890.364322949177894
340.6609640928789090.6780718142421830.339035907121091
350.7139335498169120.5721329003661750.286066450183088
360.6381413904421390.7237172191157220.361858609557861
370.573225523970430.853548952059140.42677447602957
380.6434885721210760.7130228557578470.356511427878924
390.5928520137459460.8142959725081080.407147986254054
400.6712825834563280.6574348330873440.328717416543672
410.6246042401331780.7507915197336440.375395759866822
420.5452671983252760.9094656033494480.454732801674724
430.8814784074230370.2370431851539250.118521592576963
440.8981339915384570.2037320169230860.101866008461543
450.9532422686439020.09351546271219680.0467577313560984
460.9299389992232430.1401220015535140.0700610007767572
470.891044831640160.2179103367196810.108955168359841
480.8614113324929430.2771773350141140.138588667507057
490.8159956375297660.3680087249404670.184004362470234
500.9091348330551710.1817303338896580.0908651669448288
510.8192599069898930.3614801860202140.180740093010107
520.7080941311891670.5838117376216670.291905868810833


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level00OK
5% type I error level00OK
10% type I error level10.0277777777777778OK
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Nov/28/t1290949989zdpv2krt4jy0wht/10b2u71290950009.png (open in new window)
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http://www.freestatistics.org/blog/date/2010/Nov/28/t1290949989zdpv2krt4jy0wht/24jfv1290950009.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Nov/28/t1290949989zdpv2krt4jy0wht/24jfv1290950009.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Nov/28/t1290949989zdpv2krt4jy0wht/3xseg1290950009.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Nov/28/t1290949989zdpv2krt4jy0wht/3xseg1290950009.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Nov/28/t1290949989zdpv2krt4jy0wht/4xseg1290950009.png (open in new window)
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http://www.freestatistics.org/blog/date/2010/Nov/28/t1290949989zdpv2krt4jy0wht/5xseg1290950009.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Nov/28/t1290949989zdpv2krt4jy0wht/5xseg1290950009.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Nov/28/t1290949989zdpv2krt4jy0wht/6qjv11290950009.png (open in new window)
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http://www.freestatistics.org/blog/date/2010/Nov/28/t1290949989zdpv2krt4jy0wht/70bu41290950009.png (open in new window)
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http://www.freestatistics.org/blog/date/2010/Nov/28/t1290949989zdpv2krt4jy0wht/80bu41290950009.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Nov/28/t1290949989zdpv2krt4jy0wht/80bu41290950009.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Nov/28/t1290949989zdpv2krt4jy0wht/90bu41290950009.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Nov/28/t1290949989zdpv2krt4jy0wht/90bu41290950009.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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Software written by Ed van Stee & Patrick Wessa


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