SP

*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, 14 Dec 2010 18:22:33 +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/Dec/14/t1292350896y0gat3e713bbpuk.htm/, Retrieved Tue, 14 Dec 2010 19:21:39 +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/Dec/14/t1292350896y0gat3e713bbpuk.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 «

1 1 6.3 2.1 3.5 0.075 1.2 42 1 2 2 6.6 4.1 6 0.785 3.5 42 2 2 2 9.5 1.2 10.4 0.2 5 120 2 5 5 3.3 0.5 20 27.66 115 148 5 1 2 11 3.4 3.9 0.12 1 16 3 3 1 4.7 1.5 41 85 325 310 1 1 3 10.4 3.4 9 0.101 4 28 5 3 4 7.4 0.8 7.6 1.04 5.5 68 5 5 5 2.1 0.8 46 521 655 336 5 1 1 17.9 2 24 0.01 0.25 50 1 1 1 6.1 1.9 100 62 1320 267 1 1 3 11.9 1.3 3.2 0.023 0.4 19 4 1 1 13.8 5.6 5 1.7 6.3 12 2 1 1 14.3 3.1 6.5 3.5 10.8 120 2 2 2 15.2 1.8 12 0.48 15.5 140 2 4 4 10 0.9 20.2 10 115 170 4 1 2 11.9 1.8 13 1.62 11.4 17 2 4 4 6.5 1.9 27 192 180 115 4 5 5 7.5 0.9 18 2.5 12.1 31 5 1 3 10.6 2.6 4.7 0.28 1.9 21 3 1 1 7.4 2.4 9.8 4.235 50.4 52 1 3 2 8.4 1.2 29 6.8 179 164 2 2 2 5.7 0.9 7 0.75 12.3 225 2 2 3 4.9 0.5 6 3.6 21 225 3 5 5 3.2 0.6 20 55.5 175 151 5 1 2 11 2.3 4.5 0.9 2.6 60 2 1 3 4.9 0.5 7.5 2 12.3 200 3 2 2 13.2 2.6 2.3 0.104 2.5 46 3 3 4 9.7 0.6 24 4.19 58 210 4 1 1 12.8 6.6 3 3.5 3.9 14 2

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 'RServer@AstonUniversity' @ vre.aston.ac.uk 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 S[t] = -0.44848360563522 + 1.01946778957491D[t] -0.0701399164268452SWS[t] + 0.236237232406613PS[t] + 0.0731354251388876L[t] + 0.00206321954317301WB[t] -0.00542342168080034Wbr[t] + 0.00257997006234144Tg[t] -0.272489817386976`P `[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) -0.44848360563522 1.034829 -0.4334 0.669151 0.334576 D 1.01946778957491 0.43024 2.3695 0.027469 0.013735 SWS -0.0701399164268452 0.056213 -1.2478 0.225853 0.112927 PS 0.236237232406613 0.165002 1.4317 0.16694 0.08347 L 0.0731354251388876 0.029431 2.485 0.021461 0.010731 WB 0.00206321954317301 0.002053 1.0052 0.326253 0.163126 Wbr -0.00542342168080034 0.002222 -2.4413 0.023577 0.011788 Tg 0.00257997006234144 0.002667 0.9675 0.344304 0.172152 `P ` -0.272489817386976 0.348129 -0.7827 0.442526 0.221263 Multiple Linear Regression - Regression Statistics Multiple R 0.900009031117382 R-squared 0.810016256092849 Adjusted R-squared 0.737641496509172 F-TEST (value) 11.1919716314407 F-TEST (DF numerator) 8 F-TEST (DF denominator) 21 p-value 4.88135444098869e-06 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.7416523261178 Sum Squared Residuals 11.5510116295548 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 1 0.710690447170703 0.289309552829297 2 2 2.08093048810084 -0.0809304881008395 3 2 1.70612817600359 0.293871823996411 4 5 4.45098237857557 0.549017621424427 5 1 1.12598187454436 -0.125981874544365 6 3 2.53429737288629 0.465702627113708 7 1 2.03019482194413 -1.03019482194413 8 3 2.64047699447143 0.359523005528566 9 5 5.08179789513783 -0.0817978951378251 10 1 1.39837781055102 -0.398377810551017 11 1 1.29088913147572 -0.290889131475716 12 1 1.27333476719684 -0.273334767196844 13 1 0.746978887029197 0.253021112970803 14 1 0.488964149854557 0.511035850145443 15 2 1.56032084710727 0.439679152892726 16 4 3.36351182855728 0.636488171442723 17 1 1.57216977795725 -0.572169777957252 18 4 4.22364485357897 -0.22364485357897 19 5 4.30892176222187 0.691078237778132 20 1 2.05137307080173 -1.05137307080173 21 1 0.932711234425785 0.067288765574215 22 3 2.32706155092513 0.672938449074866 23 2 1.88556889225615 0.114431107743847 24 2 2.47972488655911 -0.47972488655911 25 5 4.22139473487986 0.778605265120141 26 1 1.28894251066482 -0.288942510664816 27 1 2.56881139006279 -1.56881139006279 28 2 0.734898550094146 1.26510144990585 29 3 3.99194378204456 -0.99194378204456 30 1 0.928975132921195 0.0710248670788049 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 12 0.0780588152283114 0.156117630456623 0.921941184771689 13 0.118727145662097 0.237454291324194 0.881272854337903 14 0.0483935325123255 0.096787065024651 0.951606467487675 15 0.0452520604065756 0.0905041208131513 0.954747939593424 16 0.0251135983029102 0.0502271966058204 0.97488640169709 17 0.0141974231908183 0.0283948463816366 0.985802576809182 18 0.0061956797615397 0.0123913595230794 0.99380432023846 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 0 0 OK 5% type I error level 2 0.285714285714286 NOK 10% type I error level 5 0.714285714285714 NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/14/t1292350896y0gat3e713bbpuk/10thhs1292350944.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t1292350896y0gat3e713bbpuk/10thhs1292350944.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t1292350896y0gat3e713bbpuk/1ng2g1292350944.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t1292350896y0gat3e713bbpuk/1ng2g1292350944.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t1292350896y0gat3e713bbpuk/2ng2g1292350944.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t1292350896y0gat3e713bbpuk/2ng2g1292350944.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t1292350896y0gat3e713bbpuk/3f71j1292350944.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t1292350896y0gat3e713bbpuk/3f71j1292350944.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t1292350896y0gat3e713bbpuk/4f71j1292350944.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t1292350896y0gat3e713bbpuk/4f71j1292350944.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t1292350896y0gat3e713bbpuk/5f71j1292350944.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t1292350896y0gat3e713bbpuk/5f71j1292350944.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t1292350896y0gat3e713bbpuk/6qgi41292350944.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t1292350896y0gat3e713bbpuk/6qgi41292350944.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t1292350896y0gat3e713bbpuk/717zp1292350944.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t1292350896y0gat3e713bbpuk/717zp1292350944.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t1292350896y0gat3e713bbpuk/817zp1292350944.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t1292350896y0gat3e713bbpuk/817zp1292350944.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t1292350896y0gat3e713bbpuk/917zp1292350944.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t1292350896y0gat3e713bbpuk/917zp1292350944.ps (open in new window)

Parameters (Session):

par1 = 5 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; 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