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 15:10:23 +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/t1290524951ru4djac155agwsf.htm/, Retrieved Tue, 23 Nov 2010 16:09:29 +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/t1290524951ru4djac155agwsf.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 67 53,5 315 6166 54 65 4 684 62 76,5 17 449 73 70 8 643 68 71 56 1551 68 60,5 15 616 60 51,5 503 36660 50 78 26 403 74 76 26 346 73 57,5 44 2471 57 61 24 7427 59 64,5 23 2992 64 78,5 38 233 75 79 18 609 76 61 96 7615 59 70 90 370 67 70 49 1066 67 72 66 600 68 64,5 21 4873 63 54,5 592 3485 53 56,5 73 2364 56 64,5 14 1016 62 64,5 88 1062 62 73 39 480 69 72 6 559 69 69 32 259 64 64 11 1340 61 78,5 26 275 75 53 23 12550 52 75 32 965 72 52,5 NA 25229 50 68,5 11 4883 66 70 5 1189 68 70,5 3 226 66 76 3 611 73 75,5 13 404 72 74,5 56 576 71 65 29 3096 63 54 NA 23193 52

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 5 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Yt[t] = -6.07613317665566 + 0.000351314085121308X1t[t] + 9.30390784089718e-06X2t[t] + 1.13154878529155X4t[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) -6.07613317665566 2.006939 -3.0276 0.004679 0.002339 X1t 0.000351314085121308 0.001606 0.2187 0.828184 0.414092 X2t 9.30390784089718e-06 3.4e-05 0.2757 0.784452 0.392226 X4t 1.13154878529155 0.029538 38.308 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.993295841481829 R-squared 0.986636628705095 Adjusted R-squared 0.985457507708486 F-TEST (value) 836.7560509416 F-TEST (DF numerator) 3 F-TEST (DF denominator) 34 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.940888746055703 Sum Squared Residuals 30.0992355034453 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 70.5 69.7424831401196 0.757516859880394 2 53.5 55.1955330616482 -1.69553306164825 3 65 64.0876606407241 0.912339359275858 4 76.5 76.5370779436952 -0.0370779436951658 5 70 70.8779771485924 -0.877977148592454 6 71 70.9032881729978 0.0967118270021877 7 60.5 61.8277948593442 -1.32779485934420 8 51.5 51.0190983341852 0.480901665814824 9 78 77.6713605759921 0.328639424007873 10 76 76.5392814679536 -0.539281467953644 11 57.5 58.4605953609829 -0.960595360982923 12 61 60.7627768171231 0.237223182876914 13 64.5 66.3789065982213 -1.87890659822134 14 78.5 78.8055434659722 -0.305543465972182 15 79 79.9335642389095 -0.933564238909482 16 61 60.7898205659259 0.210179434074092 17 70 69.7726961514403 0.227303848559715 18 70 69.7647677938076 0.235232206192423 19 72 70.8979532974923 1.10204670250767 20 64.5 65.2641558354083 -0.764155835408272 21 54.5 54.1363545010139 0.363645498986137 22 56.5 57.3382391660209 -0.838239166020916 23 64.5 64.0942626789785 0.405737321021466 24 64.5 64.1206879010382 0.379312098961809 25 73 72.0189001335447 0.981099866455301 26 72 72.0080417774551 -0.00804177745512728 27 69 66.3566408448583 2.64335915514174 28 64 62.964674417572 1.03532558242793 29 78.5 78.80171846108 -0.301718461080044 30 53 52.889247925866 0.110752074133976 31 75 75.4155996861263 -0.415599686126337 32 52.5 52.6553820895101 -0.155382089510121 33 68.5 69.3820031400182 -0.88200314001822 34 70 68.1092432780141 1.89075672198591 35 70.5 71.0336667795737 -0.533666779573694 36 76 75.9037052262103 0.0962947737897103 37 75.5 75.2888632187276 0.211136781272411 38 74.5 74.750433303856 -0.250433303855969 39 65 NA NA 40 54 NA NA Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 7 0.723923655479075 0.55215268904185 0.276076344520925 8 0.644282360229007 0.711435279541987 0.355717639770993 9 0.503938831106383 0.992122337787233 0.496061168893617 10 0.417883081985796 0.835766163971591 0.582116918014204 11 0.396169059124384 0.792338118248768 0.603830940875616 12 0.28635921699209 0.57271843398418 0.71364078300791 13 0.678009897267288 0.643980205465423 0.321990102732712 14 0.576366475035925 0.84726704992815 0.423633524964075 15 0.562239742354077 0.875520515291845 0.437760257645923 16 0.489038440258569 0.978076880517138 0.510961559741431 17 0.455154655383144 0.910309310766287 0.544845344616856 18 0.381628901129223 0.763257802258447 0.618371098870776 19 0.470848894319822 0.941697788639643 0.529151105680178 20 0.427676416151010 0.855352832302019 0.57232358384899 21 0.410179160310692 0.820358320621384 0.589820839689308 22 0.588297206513198 0.823405586973605 0.411702793486802 23 0.588915936880092 0.822168126239815 0.411084063119908 24 0.66885588290104 0.66228823419792 0.33114411709896 25 0.623441690058323 0.753116619883353 0.376558309941677 26 0.515338476602909 0.969323046794183 0.484661523397091 27 0.834901465502765 0.33019706899447 0.165098534497235 28 0.760017725856118 0.479964548287764 0.239982274143882 29 0.648071700852789 0.703856598294422 0.351928299147211 30 0.532950006106734 0.934099987786531 0.467049993893265 31 0.365334299712512 0.730668599425025 0.634665700287488 32 0.564239718199508 0.871520563600985 0.435760281800492 33 0.935328455671135 0.129343088657729 0.0646715443288645 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 0 0 OK 10% type I error level 0 0 OK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/23/t1290524951ru4djac155agwsf/10dxg21290525016.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290524951ru4djac155agwsf/10dxg21290525016.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290524951ru4djac155agwsf/1oej81290525016.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290524951ru4djac155agwsf/1oej81290525016.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290524951ru4djac155agwsf/2oej81290525016.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290524951ru4djac155agwsf/2oej81290525016.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290524951ru4djac155agwsf/3hn0b1290525016.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290524951ru4djac155agwsf/3hn0b1290525016.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290524951ru4djac155agwsf/4hn0b1290525016.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290524951ru4djac155agwsf/4hn0b1290525016.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290524951ru4djac155agwsf/5hn0b1290525016.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290524951ru4djac155agwsf/5hn0b1290525016.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290524951ru4djac155agwsf/6sxzw1290525016.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290524951ru4djac155agwsf/6sxzw1290525016.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290524951ru4djac155agwsf/7k6hh1290525016.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290524951ru4djac155agwsf/7k6hh1290525016.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290524951ru4djac155agwsf/8k6hh1290525016.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290524951ru4djac155agwsf/8k6hh1290525016.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290524951ru4djac155agwsf/9k6hh1290525016.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290524951ru4djac155agwsf/9k6hh1290525016.ps (open in new window)

Parameters (Session):

par1 = 1 ; 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