Multiple Regression PS

*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 10:10:50 +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/t12923213709hz7ryn37rhp1tk.htm/, Retrieved Tue, 14 Dec 2010 11:09:40 +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/2010/Dec/14/t12923213709hz7ryn37rhp1tk.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 «

0,301030 1,623249 3,000000 0,255273 2,795185 4,000000 -0,154902 2,255273 4,000000 0,591065 1,544068 1,000000 0,000000 2,593286 4,000000 0,556303 1,799341 1,000000 0,146128 2,361728 1,000000 0,176091 2,049218 4,000000 -0,154902 2,448706 5,000000 0,322219 1,623249 1,000000 0,612784 1,623249 2,000000 0,079181 2,079181 2,000000 -0,301030 2,170262 5,000000 0,531479 1,204120 2,000000 0,176091 2,491362 1,000000 0,531479 1,447158 3,000000 -0,096910 1,832509 4,000000 -0,096910 2,526339 5,000000 0,301030 1,698970 1,000000 0,278754 2,426511 1,000000 0,113943 1,278754 3,000000 0,748188 1,079181 1,000000 0,491362 2,079181 1,000000 0,255273 2,146128 2,000000 -0,045757 2,230449 4,000000 0,255273 1,230449 2,000000 0,278754 2,060698 4,000000 -0,045757 1,491362 5,000000 0,414973 1,322219 3,000000 0,380211 1,716003 1,000000 0,079181 2,214844 2,000000 -0,045757 2,352183 2,000000 -0,301030 2,352183 3,000000 -0,221849 2,178977 5,000000 0,361728 1,778151 2,000000 -0,301030 2,301030 3,000000 0,414 etc...

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 8 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation logPS[t] = + 1.07450734616664 -0.303538833951603LogGestationTime[t] -0.110510503182968danger[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) 1.07450734616664 0.128751 8.3456 0 0 LogGestationTime -0.303538833951603 0.068904 -4.4053 9.1e-05 4.5e-05 danger -0.110510503182968 0.022191 -4.98 1.6e-05 8e-06 Multiple Linear Regression - Regression Statistics Multiple R 0.809091592228325 R-squared 0.654629204614566 Adjusted R-squared 0.635441938204264 F-TEST (value) 34.1178983298573 F-TEST (DF numerator) 2 F-TEST (DF denominator) 36 p-value 4.88811024990099e-09 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.181764075869477 Sum Squared Residuals 1.18937445396066 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 0.30103 0.250256727944634 0.0507732720553663 2 0.255273 -0.215981862144241 0.471254862144242 3 -0.154902 -0.0520976032277633 -0.102804396772237 4 0.591065 0.49531224272169 0.0957527572783097 5 0 -0.154697675108247 0.154697675108247 6 0.556303 0.417826973962363 0.138476026037637 7 0.146128 0.247120679752823 -0.100992679752823 8 0.176091 0.0104480912021337 0.165642908797866 9 -0.154902 -0.221322533678492 0.0664205336784922 10 0.322219 0.471277734310569 -0.149058734310569 11 0.612784 0.3607672311276 0.252016768872400 12 0.079181 0.222374163486378 -0.143193163486378 13 -0.30103 -0.136803966597672 -0.164226033402328 14 0.531479 0.487989159062902 0.0434898409370984 15 0.176091 0.207771726552341 -0.0316807265523407 16 0.531479 0.303707184754004 0.227771815245996 17 -0.09691 0.0762276883689517 -0.173137688368952 18 -0.09691 -0.244887163974657 0.147977163974657 19 0.30103 0.448293470264919 -0.147263470264919 20 0.278754 0.227456523472936 0.051297476527064 21 0.113943 0.354824338546790 -0.240881338546790 22 0.748188 0.636423500620949 0.111764499379051 23 0.491362 0.332884666669346 0.158477333330654 24 0.255273 0.202053149169820 0.0532198508301798 25 -0.045757 -0.0445625552137491 -0.00119444478625089 26 0.255273 0.47999728510379 -0.22472428510379 27 0.278754 0.0069634653883694 0.271790534611631 28 -0.045757 0.069268547772071 -0.115025547772071 29 0.414973 0.341631023129083 0.0733419768709168 30 0.380211 0.443123293306222 -0.0629122933062215 31 0.079181 0.181195174656002 -0.102014174656002 32 -0.045757 0.139507454739923 -0.185264454739923 33 -0.30103 0.0289969515569544 -0.330026951556954 34 -0.221849 -0.139449307535560 -0.0823996924644396 35 0.361728 0.313748458670829 0.0479795413291709 36 -0.30103 0.0445238735300809 -0.345553873530081 37 0.414973 0.348774715337006 0.0661982846629935 38 -0.221849 -0.0724183140054877 -0.149430685994512 39 0.819544 0.616102486304391 0.203441513695609 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 6 0.597929708193841 0.804140583612318 0.402070291806159 7 0.805815945204428 0.388368109591145 0.194184054795572 8 0.720982889511788 0.558034220976424 0.279017110488212 9 0.649765918387215 0.70046816322557 0.350234081612785 10 0.613006410057831 0.773987179884338 0.386993589942169 11 0.690108525322084 0.619782949355833 0.309891474677916 12 0.691201280225957 0.617597439548087 0.308798719774043 13 0.737899544082571 0.524200911834857 0.262100455917429 14 0.651774401644713 0.696451196710573 0.348225598355287 15 0.566644452402687 0.866711095194626 0.433355547597313 16 0.594690479157793 0.810619041684414 0.405309520842207 17 0.610881366535095 0.77823726692981 0.389118633464905 18 0.61344209197828 0.77311581604344 0.38655790802172 19 0.589206361851363 0.821587276297273 0.410793638148637 20 0.50342891914205 0.9931421617159 0.49657108085795 21 0.59140132727073 0.81719734545854 0.40859867272927 22 0.526282106480342 0.947435787039317 0.473717893519658 23 0.534352967904985 0.93129406419003 0.465647032095015 24 0.482915389080512 0.965830778161025 0.517084610919488 25 0.41430288421975 0.8286057684395 0.58569711578025 26 0.602855475979316 0.794289048041369 0.397144524020684 27 0.960558804011821 0.0788823919763572 0.0394411959881786 28 0.9705527635969 0.0588944728062003 0.0294472364031002 29 0.961721904783826 0.0765561904323471 0.0382780952161736 30 0.932745861396603 0.134508277206794 0.067254138603397 31 0.91360537248153 0.172789255036940 0.0863946275184699 32 0.936354228945889 0.127291542108222 0.0636457710541112 33 0.880357589160963 0.239284821678075 0.119642410839038 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 3 0.107142857142857 NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/14/t12923213709hz7ryn37rhp1tk/101tvu1292321439.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t12923213709hz7ryn37rhp1tk/101tvu1292321439.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t12923213709hz7ryn37rhp1tk/15jx31292321439.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t12923213709hz7ryn37rhp1tk/15jx31292321439.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t12923213709hz7ryn37rhp1tk/25jx31292321439.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t12923213709hz7ryn37rhp1tk/25jx31292321439.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t12923213709hz7ryn37rhp1tk/35jx31292321439.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t12923213709hz7ryn37rhp1tk/35jx31292321439.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t12923213709hz7ryn37rhp1tk/4yswo1292321439.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t12923213709hz7ryn37rhp1tk/4yswo1292321439.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t12923213709hz7ryn37rhp1tk/5yswo1292321439.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t12923213709hz7ryn37rhp1tk/5yswo1292321439.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t12923213709hz7ryn37rhp1tk/6yswo1292321439.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t12923213709hz7ryn37rhp1tk/6yswo1292321439.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t12923213709hz7ryn37rhp1tk/7qjvq1292321439.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t12923213709hz7ryn37rhp1tk/7qjvq1292321439.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t12923213709hz7ryn37rhp1tk/81tvu1292321439.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t12923213709hz7ryn37rhp1tk/81tvu1292321439.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t12923213709hz7ryn37rhp1tk/91tvu1292321439.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t12923213709hz7ryn37rhp1tk/91tvu1292321439.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