Workshop 7 - regression model

*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: Tue, 23 Nov 2010 14:55:54 +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/23/t1290524074deeysgbtfsyziad.htm/, Retrieved Tue, 23 Nov 2010 15:54:48 +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/23/t1290524074deeysgbtfsyziad.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 «

70,5 4 370 74 53,5 315 6166 53 65 4 684 68 76,5 17 449 80 70 8 643 72 71 56 1551 74 60,5 15 616 61 51,5 503 36660 53 78 26 403 82 76 26 346 79 57,5 44 2471 58 61 24 7427 63 64,5 23 2992 65 78,5 38 233 82 79 18 609 82 61 96 7615 63 70 90 370 73 70 49 1066 73 72 66 600 76 64,5 21 4873 66 54,5 592 3485 56 56,5 73 2364 57 64,5 14 1016 67 64,5 88 1062 67 73 39 480 77 72 6 559 75 69 32 259 74 64 11 1340 67 78,5 26 275 82 53 23 12550 54 75 32 965 78 52,5 NA 25229 55 68,5 11 4883 71 70 5 1189 72 70,5 3 226 75 76 3 611 79 75,5 13 404 79 74,5 56 576 78 65 29 3096 67 54 NA 23193 56

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 Input view raw input (R code) Raw Output view raw output of R engine Computing time 6 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation X2t[t] = + 25578.1303782642 -990.437503041272Yt[t] + 18.5570105455728X1t[t] + 615.08893959725X3t[t] + e[t] Multiple Linear Regression - Ordinary Least Squares Variable Parameter S.D. T-STAT H0: parameter = 0 2-tail p-value 1-tail p-value (Intercept) 25578.1303782642 10607.785665 2.4113 0.021448 0.010724 Yt -990.437503041272 1127.032157 -0.8788 0.385678 0.192839 X1t 18.5570105455728 7.513409 2.4699 0.018694 0.009347 X3t 615.08893959725 990.827211 0.6208 0.538882 0.269441 Multiple Linear Regression - Regression Statistics Multiple R 0.676420411214375 R-squared 0.457544572707424 Adjusted R-squared 0.40968085853455 F-TEST (value) 9.55932026200189 F-TEST (DF numerator) 3 F-TEST (DF denominator) 34 p-value 0.000101194092399060 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 4776.13028631606 Sum Squared Residuals 775588297.403426 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 370 1343.09598623306 -973.09598623306 2 6166 11034.8960860658 -4868.89608606576 3 684 3099.96861537675 -2415.96861537675 4 449 -667.754257338434 1116.75425733843 5 643 682.364900741679 -39.3649007416788 6 1551 1812.8417830824 -261.8417830824 7 616 3455.44191788303 -2839.44191788303 8 36660 16504.489074716 20155.510925284 9 403 -756.21953779569 1159.21953779569 10 346 -620.611350504895 966.611350504895 11 2471 5119.6409140367 -2648.64091403670 12 7427 4357.41414046704 3069.58585953296 13 2992 2102.50374847152 889.49625152848 14 233 -1028.75416276945 1261.75416276945 15 609 -1895.11312520154 2504.11312520154 16 7615 5693.51889974829 1921.48110025171 17 370 2819.12870507590 -2449.12870507590 18 1066 2058.29127270741 -992.291272707413 19 600 2238.15226469135 -1638.15226469135 20 4873 2680.47866697762 2192.52133302238 21 3485 17030.0173229399 -13545.0173229399 22 2364 6033.14278330234 -3669.14278330234 23 1016 3165.66853275586 -2149.66853275586 24 1062 4538.88731312825 -3476.88731312825 25 480 1361.76441651687 -881.764416516867 26 559 509.642692359738 49.3573076402622 27 259 3348.34853607119 -3089.34853607119 28 1340 3605.21625263978 -2265.21625263978 29 275 -1251.43828931633 1526.43828931633 30 12550 6726.5566978764 5823.4433021236 31 965 -133.920723787436 1098.92072378744 32 25229 21954.6032473431 3274.39675265694 33 4883 4320.69386910496 562.306130895039 34 1189 2902.62791528493 -1713.62791528493 35 226 -1432.42259305307 1658.42259305307 36 611 -159.633736076705 770.633736076705 37 404 634.666280826947 -230.666280826947 38 576 428.804939418818 147.195060581182 39 3096 NA NA 40 23193 NA NA Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 7 7.35156510979815e-05 0.000147031302195963 0.999926484348902 8 0.99903156164834 0.00193687670332126 0.000968438351660631 9 0.997575271976056 0.00484945604788706 0.00242472802394353 10 0.99476906169955 0.0104618766008989 0.00523093830044946 11 0.995472090476433 0.00905581904713299 0.00452790952356649 12 0.996043718430613 0.00791256313877326 0.00395628156938663 13 0.998441174702988 0.00311765059402503 0.00155882529701251 14 0.99658806116768 0.00682387766464167 0.00341193883232083 15 0.994742702690276 0.0105145946194479 0.00525729730972396 16 0.994997802382926 0.0100043952341482 0.00500219761707409 17 0.995250705638012 0.0094985887239758 0.0047492943619879 18 0.99117201998372 0.0176559600325595 0.00882798001627974 19 0.988574037390353 0.0228519252192931 0.0114259626096466 20 0.983800541456962 0.032398917086075 0.0161994585430375 21 0.999774253441942 0.000451493116116514 0.000225746558058257 22 0.999844705909856 0.000310588180288354 0.000155294090144177 23 0.999845531849252 0.000308936301496924 0.000154468150748462 24 0.999881680196555 0.000236639606889891 0.000118319803444946 25 0.999565671762877 0.000868656474245455 0.000434328237122727 26 0.998587306966284 0.00282538606743157 0.00141269303371578 27 0.995725520155097 0.0085489596898066 0.0042744798449033 28 0.995886964045285 0.00822607190943098 0.00411303595471549 29 0.9900988838696 0.0198022322607982 0.00990111613039912 30 0.990908774963807 0.0181824500723856 0.00909122503619282 31 0.962570437927613 0.0748591241447737 0.0374295620723869 32 0.988556397195028 0.0228872056099445 0.0114436028049722 33 0.988733386529562 0.0225332269408753 0.0112666134704377 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 16 0.592592592592593 NOK 5% type I error level 26 0.962962962962963 NOK 10% type I error level 27 1 NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/23/t1290524074deeysgbtfsyziad/10b03r1290524147.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290524074deeysgbtfsyziad/10b03r1290524147.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290524074deeysgbtfsyziad/1nzog1290524147.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290524074deeysgbtfsyziad/1nzog1290524147.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290524074deeysgbtfsyziad/2nzog1290524147.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290524074deeysgbtfsyziad/2nzog1290524147.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290524074deeysgbtfsyziad/3xqni1290524147.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290524074deeysgbtfsyziad/3xqni1290524147.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290524074deeysgbtfsyziad/4xqni1290524147.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290524074deeysgbtfsyziad/4xqni1290524147.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290524074deeysgbtfsyziad/5xqni1290524147.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290524074deeysgbtfsyziad/5xqni1290524147.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290524074deeysgbtfsyziad/6qh4m1290524147.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290524074deeysgbtfsyziad/6qh4m1290524147.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290524074deeysgbtfsyziad/70qlo1290524147.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290524074deeysgbtfsyziad/70qlo1290524147.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290524074deeysgbtfsyziad/80qlo1290524147.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290524074deeysgbtfsyziad/80qlo1290524147.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290524074deeysgbtfsyziad/90qlo1290524147.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290524074deeysgbtfsyziad/90qlo1290524147.ps (open in new window)

Parameters (Session):

par1 = 3 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 3 ; par2 = Do not include Seasonal 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') }

Copyright

This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa

Disclaimer

Information provided on this web site is provided "AS IS" without warranty of any kind, either express or implied, including, without limitation, warranties of merchantability, fitness for a particular purpose, and noninfringement. We use reasonable efforts to include accurate and timely information and periodically update the information, and software without notice. However, we make no warranties or representations as to the accuracy or completeness of such information (or software), and we assume no liability or responsibility for errors or omissions in the content of this web site, or any software bugs in online applications. Your use of this web site is AT YOUR OWN RISK. Under no circumstances and under no legal theory shall we be liable to you or any other person for any direct, indirect, special, incidental, exemplary, or consequential damages arising from your access to, or use of, this web site.

Privacy Policy

We may request personal information to be submitted to our servers in order to be able to:

• personalize online software applications according to your needs
• enforce strict security rules with respect to the data that you upload (e.g. statistical data)
• manage user sessions of online applications
• alert you about important changes or upgrades in resources or applications

We NEVER allow other companies to directly offer registered users information about their products and services. Banner references and hyperlinks of third parties NEVER contain any personal data of the visitor.

We do NOT sell, nor transmit by any means, personal information, nor statistical data series uploaded by you to third parties.

We carefully protect your data from loss, misuse, alteration, and destruction. However, at any time, and under any circumstance you are solely responsible for managing your passwords, and keeping them secret.

We store a unique ANONYMOUS USER ID in the form of a small 'Cookie' on your computer. This allows us to track your progress when using this website which is necessary to create state-dependent features. The cookie is used for NO OTHER PURPOSE. At any time you may opt to disallow cookies from this website - this will not affect other features of this website.

We examine cookies that are used by third-parties (banner and online ads) very closely: abuse from third-parties automatically results in termination of the advertising contract without refund. We have very good reason to believe that the cookies that are produced by third parties (banner ads) do NOT cause any privacy or security risk.

FreeStatistics.org is safe. There is no need to download any software to use the applications and services contained in this website. Hence, your system's security is not compromised by their use, and your personal data - other than data you submit in the account application form, and the user-agent information that is transmitted by your browser - is never transmitted to our servers.

As a general rule, we do not log on-line behavior of individuals (other than normal logging of webserver 'hits'). However, in cases of abuse, hacking, unauthorized access, Denial of Service attacks, illegal copying, hotlinking, non-compliance with international webstandards (such as robots.txt), or any other harmful behavior, our system engineers are empowered to log, track, identify, publish, and ban misbehaving individuals - even if this leads to ban entire blocks of IP addresses, or disclosing user's identity.

FreeStatistics.org is powered by