*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, 17 Dec 2010 12:00:00 +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/17/t1292587094wo7svy23w5bzvlx.htm/, Retrieved Fri, 17 Dec 2010 12:58:26 +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/2010/Dec/17/t1292587094wo7svy23w5bzvlx.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 «

461 463 462 456 455 456 472 472 471 465 459 465 468 467 463 460 462 461 476 476 471 453 443 442 444 438 427 424 416 406 431 434 418 412 404 409 412 406 398 397 385 390 413 413 401 397 397 409 419 424 428 430 424 433 456 459 446 441 439 454 460

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 7 seconds R Server 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation HPC[t] = + 466.011764705882 + 4.00392156862764M1[t] -4.59215686274512M2[t] -7.7529411764706M3[t] -9.1137254901961M4[t] -13.2745098039216M5[t] -11.6352941176471M6[t] + 9.60392156862745M7[t] + 11.6431372549020M8[t] + 3.08235294117648M9[t] -3.87843137254902M10[t] -8.2392156862745M11[t] -0.83921568627451t + 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) 466.011764705882 11.71066 39.7938 0 0 M1 4.00392156862764 13.657384 0.2932 0.770657 0.385328 M2 -4.59215686274512 14.33487 -0.3203 0.750094 0.375047 M3 -7.7529411764706 14.316564 -0.5415 0.590643 0.295321 M4 -9.1137254901961 14.300165 -0.6373 0.526947 0.263474 M5 -13.2745098039216 14.28568 -0.9292 0.357426 0.178713 M6 -11.6352941176471 14.273115 -0.8152 0.41899 0.209495 M7 9.60392156862745 14.262474 0.6734 0.503941 0.251971 M8 11.6431372549020 14.253761 0.8168 0.418052 0.209026 M9 3.08235294117648 14.246981 0.2164 0.829631 0.414815 M10 -3.87843137254902 14.242137 -0.2723 0.786543 0.393272 M11 -8.2392156862745 14.239229 -0.5786 0.565546 0.282773 t -0.83921568627451 0.166146 -5.0511 7e-06 3e-06 Multiple Linear Regression - Regression Statistics Multiple R 0.632982889193472 R-squared 0.400667338011716 Adjusted R-squared 0.250834172514645 F-TEST (value) 2.67408978968377 F-TEST (DF numerator) 12 F-TEST (DF denominator) 48 p-value 0.0078111502846312 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 22.5126652806640 Sum Squared Residuals 24327.3647058823 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 461 469.176470588234 -8.17647058823438 2 463 459.741176470588 3.2588235294117 3 462 455.741176470588 6.25882352941172 4 456 453.541176470588 2.45882352941174 5 455 448.541176470588 6.45882352941175 6 456 449.341176470588 6.65882352941173 7 472 469.741176470588 2.25882352941173 8 472 470.941176470588 1.05882352941173 9 471 461.541176470588 9.45882352941174 10 465 453.741176470588 11.2588235294117 11 459 448.541176470588 10.4588235294117 12 465 455.941176470588 9.05882352941173 13 468 459.105882352941 8.8941176470585 14 467 449.670588235294 17.3294117647059 15 463 445.670588235294 17.3294117647059 16 460 443.470588235294 16.5294117647058 17 462 438.470588235294 23.5294117647059 18 461 439.270588235294 21.7294117647059 19 476 459.670588235294 16.3294117647059 20 476 460.870588235294 15.1294117647059 21 471 451.470588235294 19.5294117647059 22 453 443.670588235294 9.32941176470586 23 443 438.470588235294 4.52941176470586 24 442 445.870588235294 -3.87058823529413 25 444 449.035294117647 -5.03529411764724 26 438 439.6 -1.59999999999999 27 427 435.6 -8.6 28 424 433.4 -9.4 29 416 428.4 -12.4000000000000 30 406 429.2 -23.2 31 431 449.6 -18.6 32 434 450.8 -16.8 33 418 441.4 -23.4 34 412 433.6 -21.6 35 404 428.4 -24.4 36 409 435.8 -26.8 37 412 438.964705882353 -26.9647058823531 38 406 429.529411764706 -23.5294117647059 39 398 425.529411764706 -27.5294117647059 40 397 423.329411764706 -26.3294117647059 41 385 418.329411764706 -33.3294117647059 42 390 419.129411764706 -29.1294117647059 43 413 439.529411764706 -26.5294117647059 44 413 440.729411764706 -27.7294117647059 45 401 431.329411764706 -30.3294117647059 46 397 423.529411764706 -26.5294117647058 47 397 418.329411764706 -21.3294117647059 48 409 425.729411764706 -16.7294117647059 49 419 428.894117647059 -9.89411764705896 50 424 419.458823529412 4.54117647058829 51 428 415.458823529412 12.5411764705883 52 430 413.258823529412 16.7411764705883 53 424 408.258823529412 15.7411764705883 54 433 409.058823529412 23.9411764705883 55 456 429.458823529412 26.5411764705883 56 459 430.658823529412 28.3411764705883 57 446 421.258823529412 24.7411764705883 58 441 413.458823529412 27.5411764705883 59 439 408.258823529412 30.7411764705883 60 454 415.658823529412 38.3411764705883 61 460 418.823529411765 41.1764705882352 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 16 0.000444189407039094 0.000888378814078189 0.999555810592961 17 5.49289896581173e-05 0.000109857979316235 0.999945071010342 18 4.09720977349934e-06 8.19441954699869e-06 0.999995902790227 19 2.98475209221193e-07 5.96950418442387e-07 0.99999970152479 20 2.21183336164477e-08 4.42366672328955e-08 0.999999977881666 21 1.72462664061682e-08 3.44925328123364e-08 0.999999982753734 22 6.63149324278127e-06 1.32629864855625e-05 0.999993368506757 23 6.9397182390108e-05 0.000138794364780216 0.99993060281761 24 0.000587158561266959 0.00117431712253392 0.999412841438733 25 0.00131169017005360 0.00262338034010720 0.998688309829946 26 0.00439168324424299 0.00878336648848599 0.995608316755757 27 0.0165157491186753 0.0330314982373505 0.983484250881325 28 0.0310524602449928 0.0621049204899857 0.968947539755007 29 0.088982014956112 0.177964029912224 0.911017985043888 30 0.189903483211499 0.379806966422999 0.8100965167885 31 0.238764142350838 0.477528284701676 0.761235857649162 32 0.309535735048503 0.619071470097006 0.690464264951497 33 0.48606546728387 0.97213093456774 0.51393453271613 34 0.680855442044422 0.638289115911157 0.319144557955578 35 0.851286182779829 0.297427634440342 0.148713817220171 36 0.948014782077367 0.103970435845266 0.0519852179226331 37 0.996627606931514 0.00674478613697154 0.00337239306848577 38 0.999909026007541 0.000181947984917148 9.09739924585739e-05 39 0.99998311325964 3.37734807212868e-05 1.68867403606434e-05 40 0.999999254780716 1.49043856807607e-06 7.45219284038036e-07 41 0.999999448827775 1.10234444987671e-06 5.51172224938354e-07 42 0.99999430893179 1.13821364208502e-05 5.69106821042508e-06 43 0.999945164068434 0.000109671863131805 5.48359315659024e-05 44 0.99974066293838 0.000518674123238078 0.000259337061619039 45 0.998269509811303 0.00346098037739302 0.00173049018869651 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 20 0.666666666666667 NOK 5% type I error level 21 0.7 NOK 10% type I error level 22 0.733333333333333 NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/17/t1292587094wo7svy23w5bzvlx/10ewky1292587192.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/17/t1292587094wo7svy23w5bzvlx/10ewky1292587192.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/17/t1292587094wo7svy23w5bzvlx/18dn41292587192.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/17/t1292587094wo7svy23w5bzvlx/18dn41292587192.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/17/t1292587094wo7svy23w5bzvlx/25pbv1292587192.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/17/t1292587094wo7svy23w5bzvlx/25pbv1292587192.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/17/t1292587094wo7svy23w5bzvlx/35pbv1292587192.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/17/t1292587094wo7svy23w5bzvlx/35pbv1292587192.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/17/t1292587094wo7svy23w5bzvlx/45pbv1292587192.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/17/t1292587094wo7svy23w5bzvlx/45pbv1292587192.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/17/t1292587094wo7svy23w5bzvlx/55pbv1292587192.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/17/t1292587094wo7svy23w5bzvlx/55pbv1292587192.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/17/t1292587094wo7svy23w5bzvlx/6yzsg1292587192.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/17/t1292587094wo7svy23w5bzvlx/6yzsg1292587192.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/17/t1292587094wo7svy23w5bzvlx/74n3v1292587192.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/17/t1292587094wo7svy23w5bzvlx/74n3v1292587192.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/17/t1292587094wo7svy23w5bzvlx/84n3v1292587192.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/17/t1292587094wo7svy23w5bzvlx/84n3v1292587192.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/17/t1292587094wo7svy23w5bzvlx/9ewky1292587192.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/17/t1292587094wo7svy23w5bzvlx/9ewky1292587192.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.

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