SHWWS7model3

*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: Fri, 20 Nov 2009 02:41:55 -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/Nov/20/t12587101935m1tohhs72pitcj.htm/, Retrieved Fri, 20 Nov 2009 10:43:26 +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/Nov/20/t12587101935m1tohhs72pitcj.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 «

161 0 149 0 139 0 135 0 130 0 127 0 122 0 117 0 112 0 113 0 149 0 157 0 157 0 147 0 137 0 132 0 125 0 123 0 117 0 114 0 111 0 112 0 144 0 150 0 149 0 134 0 123 0 116 0 117 0 111 0 105 0 102 0 95 0 93 0 124 0 130 0 124 0 115 0 106 0 105 0 105 1 101 1 95 1 93 1 84 1 87 1 116 1 120 1 117 1 109 1 105 1 107 1 109 1 109 1 108 1 107 1 99 1 103 1 131 1 137 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 4 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Y[t] = + 161.73125 + 3.70312500000001X[t] -3.91874999999995M1[t] -14.040625M2[t] -22.1625000000000M3[t] -24.4843750000000M4[t] -26.3468750000000M5[t] -28.66875M6[t] -32.790625M7[t] -34.9125000000001M8[t] -40.634375M9[t] -38.55625M10[t] -6.67812500000001M11[t] -0.678125t + 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) 161.73125 4.49667 35.9669 0 0 X 3.70312500000001 3.894231 0.9509 0.346612 0.173306 M1 -3.91874999999995 5.134656 -0.7632 0.449243 0.224621 M2 -14.040625 5.124802 -2.7397 0.008722 0.004361 M3 -22.1625000000000 5.117124 -4.331 8e-05 4e-05 M4 -24.4843750000000 5.111633 -4.7899 1.8e-05 9e-06 M5 -26.3468750000000 5.141215 -5.1246 6e-06 3e-06 M6 -28.66875 5.126993 -5.5917 1e-06 1e-06 M7 -32.790625 5.114928 -6.4108 0 0 M8 -34.9125000000001 5.105036 -6.8388 0 0 M9 -40.634375 5.097328 -7.9717 0 0 M10 -38.55625 5.091816 -7.5722 0 0 M11 -6.67812500000001 5.088506 -1.3124 0.195898 0.097949 t -0.678125 0.105988 -6.3982 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.922606451501705 R-squared 0.851202664352567 Adjusted R-squared 0.809151243408728 F-TEST (value) 20.2419477213234 F-TEST (DF numerator) 13 F-TEST (DF denominator) 46 p-value 8.77076189453874e-15 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 8.0438886132106 Sum Squared Residuals 2976.390625 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 161 157.134375000000 3.86562500000017 2 149 146.334375 2.665625 3 139 137.534375 1.46562499999998 4 135 134.534375 0.465624999999968 5 130 131.99375 -1.99374999999998 6 127 128.99375 -1.99374999999997 7 122 124.19375 -2.19375000000008 8 117 121.39375 -4.39375000000006 9 112 114.99375 -2.99375000000002 10 113 116.39375 -3.39374999999994 11 149 147.59375 1.40624999999998 12 157 153.59375 3.40625000000001 13 157 148.996875 8.00312499999996 14 147 138.196875 8.803125 15 137 129.396875 7.603125 16 132 126.396875 5.603125 17 125 123.85625 1.14374999999999 18 123 120.85625 2.14374999999999 19 117 116.05625 0.94375000000002 20 114 113.25625 0.743750000000013 21 111 106.85625 4.14375000000001 22 112 108.25625 3.74374999999999 23 144 139.45625 4.54375 24 150 145.45625 4.54374999999999 25 149 140.859375 8.14062499999996 26 134 130.059375 3.940625 27 123 121.259375 1.74062500000001 28 116 118.259375 -2.25937499999999 29 117 115.71875 1.28124999999999 30 111 112.71875 -1.71875000000000 31 105 107.91875 -2.91874999999997 32 102 105.11875 -3.11874999999999 33 95 98.71875 -3.71874999999999 34 93 100.11875 -7.11875 35 124 131.31875 -7.31874999999998 36 130 137.31875 -7.31875 37 124 132.721875 -8.72187500000004 38 115 121.921875 -6.921875 39 106 113.121875 -7.12187499999998 40 105 110.121875 -5.12187499999999 41 105 111.284375 -6.28437500000001 42 101 108.284375 -7.28437500000001 43 95 103.484375 -8.48437499999998 44 93 100.684375 -7.68437499999999 45 84 94.284375 -10.284375 46 87 95.684375 -8.68437500000002 47 116 126.884375 -10.884375 48 120 132.884375 -12.884375 49 117 128.2875 -11.2875000000000 50 109 117.4875 -8.4875 51 105 108.6875 -3.68749999999999 52 107 105.6875 1.31250000000001 53 109 103.146875 5.853125 54 109 100.146875 8.853125 55 108 95.346875 12.6531250000000 56 107 92.546875 14.4531250000000 57 99 86.146875 12.853125 58 103 87.546875 15.4531250000000 59 131 118.746875 12.253125 60 137 124.746875 12.253125 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.00235999754142147 0.00471999508284294 0.997640002458579 18 0.000264928712250751 0.000529857424501501 0.99973507128775 19 4.75498500139823e-05 9.50997000279646e-05 0.999952450149986 20 4.8299956388852e-06 9.6599912777704e-06 0.999995170004361 21 2.14177406416343e-06 4.28354812832686e-06 0.999997858225936 22 6.71133508482571e-07 1.34226701696514e-06 0.999999328866491 23 2.16464806705663e-07 4.32929613411326e-07 0.999999783535193 24 4.19736007423164e-07 8.39472014846329e-07 0.999999580263993 25 6.41118728715735e-06 1.28223745743147e-05 0.999993588812713 26 0.000702097625081705 0.00140419525016341 0.999297902374918 27 0.0277905704973603 0.0555811409947205 0.97220942950264 28 0.388348184478839 0.776696368957677 0.611651815521161 29 0.507273360250059 0.985453279499881 0.492726639749941 30 0.572916305231527 0.854167389536945 0.427083694768473 31 0.5786358838364 0.8427282323272 0.4213641161636 32 0.528154763712839 0.943690472574321 0.471845236287161 33 0.602587769205207 0.794824461589586 0.397412230794793 34 0.645631234640811 0.708737530718378 0.354368765359189 35 0.739445575522662 0.521108848954676 0.260554424477338 36 0.825087619153324 0.349824761693353 0.174912380846677 37 0.90319656551168 0.193606868976642 0.0968034344883208 38 0.919179513812177 0.161640972375647 0.0808204861878233 39 0.881976667666389 0.236046664667222 0.118023332333611 40 0.798943426061765 0.40211314787647 0.201056573938235 41 0.943909276186814 0.112181447626371 0.0560907238131857 42 0.993296251828141 0.0134074963437176 0.00670374817185878 43 0.988308432792182 0.0233831344156364 0.0116915672078182 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 10 0.370370370370370 NOK 5% type I error level 12 0.444444444444444 NOK 10% type I error level 13 0.481481481481481 NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Nov/20/t12587101935m1tohhs72pitcj/10jxgl1258710109.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/20/t12587101935m1tohhs72pitcj/10jxgl1258710109.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/20/t12587101935m1tohhs72pitcj/1hcep1258710109.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/20/t12587101935m1tohhs72pitcj/1hcep1258710109.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/20/t12587101935m1tohhs72pitcj/2hcbm1258710109.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/20/t12587101935m1tohhs72pitcj/2hcbm1258710109.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/20/t12587101935m1tohhs72pitcj/3gmmp1258710109.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/20/t12587101935m1tohhs72pitcj/3gmmp1258710109.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/20/t12587101935m1tohhs72pitcj/4a17f1258710109.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/20/t12587101935m1tohhs72pitcj/4a17f1258710109.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/20/t12587101935m1tohhs72pitcj/56ip11258710109.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/20/t12587101935m1tohhs72pitcj/56ip11258710109.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/20/t12587101935m1tohhs72pitcj/6n9ix1258710109.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/20/t12587101935m1tohhs72pitcj/6n9ix1258710109.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/20/t12587101935m1tohhs72pitcj/7b31a1258710109.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/20/t12587101935m1tohhs72pitcj/7b31a1258710109.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/20/t12587101935m1tohhs72pitcj/8n0zz1258710109.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/20/t12587101935m1tohhs72pitcj/8n0zz1258710109.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/20/t12587101935m1tohhs72pitcj/9tedl1258710109.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/20/t12587101935m1tohhs72pitcj/9tedl1258710109.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

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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.

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