*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: Mon, 14 Dec 2009 05:22:36 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Dec/14/t12607934198ldmykhpotumy15.htm/, Retrieved Mon, 14 Dec 2009 13:23:52 +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/2009/Dec/14/t12607934198ldmykhpotumy15.htm/}, year = {2009}, } @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 = {2009}, 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 «

87 0 96.3 0 107.1 0 115.2 0 106.1 1 89.5 1 91.3 1 97.6 1 100.7 1 104.6 1 94.7 1 101.8 1 102.5 1 105.3 1 110.3 1 109.8 1 117.3 1 118.8 1 131.3 1 125.9 1 133.1 1 147 1 145.8 1 164.4 1 149.8 1 137.7 1 151.7 1 156.8 1 180 1 180.4 1 170.4 1 191.6 1 199.5 1 218.2 1 217.5 1 205 1 194 1 199.3 1 219.3 1 211.1 1 215.2 1 240.2 1 242.2 1 240.7 1 255.4 1 253 1 218.2 1 203.7 1 205.6 1 215.6 1

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 3 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Y[t] = + 97.0073660714286 -41.5479166666667X[t] -10.3769915674603M1[t] -11.0925099206349M2[t] + 1.96768601190472M3[t] -0.68283234126981M4[t] + 12.3536284722222M5[t] + 11.1531101190475M6[t] + 8.95259176587297M7[t] + 10.3270734126984M8[t] + 14.7765550595238M9[t] + 19.5260367063492M10[t] + 4.10051835317459M11[t] + 3.7755183531746t + 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) 97.0073660714286 10.771543 9.0059 0 0 X -41.5479166666667 9.180043 -4.5259 6.3e-05 3.2e-05 M1 -10.3769915674603 9.676227 -1.0724 0.290668 0.145334 M2 -11.0925099206349 9.678689 -1.1461 0.259325 0.129663 M3 1.96768601190472 10.263234 0.1917 0.849037 0.424519 M4 -0.68283234126981 10.258875 -0.0666 0.9473 0.47365 M5 12.3536284722222 10.119179 1.2208 0.230093 0.115046 M6 11.1531101190475 10.102518 1.104 0.276921 0.13846 M7 8.95259176587297 10.088398 0.8874 0.380746 0.190373 M8 10.3270734126984 10.076831 1.0248 0.312279 0.15614 M9 14.7765550595238 10.067825 1.4677 0.150869 0.075434 M10 19.5260367063492 10.061387 1.9407 0.060158 0.030079 M11 4.10051835317459 10.057522 0.4077 0.685904 0.342952 t 3.7755183531746 0.160989 23.4521 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.972759442191093 R-squared 0.946260932371926 Adjusted R-squared 0.926855157950677 F-TEST (value) 48.7618227353908 F-TEST (DF numerator) 13 F-TEST (DF denominator) 36 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 14.2216622199358 Sum Squared Residuals 7281.2043467262 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 87 90.4058928571427 -3.40589285714275 2 96.3 93.4658928571429 2.83410714285714 3 107.1 110.301607142857 -3.20160714285718 4 115.2 111.426607142857 3.77339285714281 5 106.1 86.6906696428571 19.4093303571429 6 89.5 89.2656696428572 0.23433035714275 7 91.3 90.8406696428572 0.459330357142813 8 97.6 95.990669642857 1.60933035714288 9 100.7 104.215669642857 -3.51566964285716 10 104.6 112.740669642857 -8.1406696428571 11 94.7 101.090669642857 -6.39066964285716 12 101.8 100.765669642857 1.03433035714284 13 102.5 94.1641964285715 8.33580357142852 14 105.3 97.2241964285714 8.07580357142862 15 110.3 114.059910714286 -3.75991071428571 16 109.8 115.184910714286 -5.38491071428571 17 117.3 131.996889880952 -14.6968898809524 18 118.8 134.571889880952 -15.7718898809524 19 131.3 136.146889880952 -4.84688988095235 20 125.9 141.296889880952 -15.3968898809524 21 133.1 149.521889880952 -16.4218898809524 22 147 158.046889880952 -11.0468898809524 23 145.8 146.396889880952 -0.596889880952355 24 164.4 146.071889880952 18.3281101190476 25 149.8 139.470416666667 10.3295833333333 26 137.7 142.530416666667 -4.83041666666668 27 151.7 159.366130952381 -7.66613095238094 28 156.8 160.491130952381 -3.69113095238093 29 180 177.303110119048 2.69688988095239 30 180.4 179.878110119048 0.521889880952436 31 170.4 181.453110119048 -11.0531101190476 32 191.6 186.603110119048 4.99688988095237 33 199.5 194.828110119048 4.67188988095238 34 218.2 203.353110119048 14.8468898809524 35 217.5 191.703110119048 25.7968898809524 36 205 191.378110119048 13.6218898809524 37 194 184.776636904762 9.22336309523808 38 199.3 187.836636904762 11.4633630952381 39 219.3 204.672351190476 14.6276488095239 40 211.1 205.797351190476 5.30264880952383 41 215.2 222.609330357143 -7.40933035714284 42 240.2 225.184330357143 15.0156696428572 43 242.2 226.759330357143 15.4406696428571 44 240.7 231.909330357143 8.79066964285713 45 255.4 240.134330357143 15.2656696428572 46 253 248.659330357143 4.34066964285711 47 218.2 237.009330357143 -18.8093303571429 48 203.7 236.684330357143 -32.9843303571429 49 205.6 230.082857142857 -24.4828571428572 50 215.6 233.142857142857 -17.5428571428572 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.0531603014845088 0.106320602969018 0.946839698515491 18 0.0413083500769449 0.0826167001538898 0.958691649923055 19 0.0391166476542541 0.0782332953085081 0.960883352345746 20 0.0170517819634329 0.0341035639268659 0.982948218036567 21 0.00940215987967969 0.0188043197593594 0.99059784012032 22 0.00992089948272068 0.0198417989654414 0.99007910051728 23 0.0142074908956239 0.0284149817912479 0.985792509104376 24 0.0356561797563818 0.0713123595127636 0.964343820243618 25 0.0264183059498499 0.0528366118996999 0.97358169405015 26 0.0141163857476742 0.0282327714953484 0.985883614252326 27 0.0107841265227166 0.0215682530454332 0.989215873477283 28 0.0059990589999283 0.0119981179998566 0.994000941000072 29 0.00291562946381056 0.00583125892762113 0.99708437053619 30 0.00374012451079740 0.00748024902159481 0.996259875489203 31 0.0132675441072830 0.0265350882145659 0.986732455892717 32 0.0248800843184148 0.0497601686368297 0.975119915681585 33 0.229579017214600 0.459158034429201 0.7704209827854 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 2 0.117647058823529 NOK 5% type I error level 11 0.647058823529412 NOK 10% type I error level 15 0.88235294117647 NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/14/t12607934198ldmykhpotumy15/10ixns1260793351.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/14/t12607934198ldmykhpotumy15/10ixns1260793351.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/14/t12607934198ldmykhpotumy15/1rzx61260793351.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/14/t12607934198ldmykhpotumy15/1rzx61260793351.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/14/t12607934198ldmykhpotumy15/257ot1260793351.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/14/t12607934198ldmykhpotumy15/257ot1260793351.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/14/t12607934198ldmykhpotumy15/3ngkk1260793351.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/14/t12607934198ldmykhpotumy15/3ngkk1260793351.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/14/t12607934198ldmykhpotumy15/4bqfe1260793351.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/14/t12607934198ldmykhpotumy15/4bqfe1260793351.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/14/t12607934198ldmykhpotumy15/5vwta1260793351.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/14/t12607934198ldmykhpotumy15/5vwta1260793351.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/14/t12607934198ldmykhpotumy15/68f5f1260793351.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/14/t12607934198ldmykhpotumy15/68f5f1260793351.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/14/t12607934198ldmykhpotumy15/70sr21260793351.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/14/t12607934198ldmykhpotumy15/70sr21260793351.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/14/t12607934198ldmykhpotumy15/852mv1260793351.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/14/t12607934198ldmykhpotumy15/852mv1260793351.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/14/t12607934198ldmykhpotumy15/9xbnk1260793351.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/14/t12607934198ldmykhpotumy15/9xbnk1260793351.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') }

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