Science Experiment MR

*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: Wed, 15 Dec 2010 19:03:30 +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/15/t12924398151re7ki30sx0emcl.htm/, Retrieved Wed, 15 Dec 2010 20:03:45 +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/15/t12924398151re7ki30sx0emcl.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:

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6.3 0.301029996 0.653212514 0 0.819543936 1.62324929 3 1 3 2.1 0.255272505 1.838849091 3.406028945 3.663040975 2.79518459 3 5 4 9.1 -0.15490196 1.431363764 1.02325246 2.254064453 2.255272505 4 4 4 15.8 0.591064607 1.278753601 -1.638272164 -0.522878745 1.544068044 1 1 1 5.2 0 1.482873584 2.204119983 2.227886705 2.593286067 4 5 4 10.9 0.556302501 1.447158031 0.51851394 1.408239965 1.799340549 1 2 1 8.3 0.146128036 1.698970004 1.717337583 2.643452676 2.361727836 1 1 1 11 0.176091259 0.84509804 -0.37161107 0.806179974 2.049218023 5 4 4 3.2 -0.15490196 1.477121255 2.667452953 2.626340367 2.44870632 5 5 5 6.3 0.322219295 0.544068044 -1.124938737 0.079181246 1.62324929 1 1 1 6.6 0.612783857 0.77815125 -0.105130343 0.544068044 1.62324929 2 2 2 9.5 0.079181246 1.017033339 -0.698970004 0.698970004 2.079181246 2 2 2 3.3 -0.301029996 1.301029996 1.441852176 2.06069784 2.170261715 5 5 5 11 0.531478917 0.591064607 -0.920818754 0 1.204119983 3 1 2 4.7 0.176091259 1.612783857 1.929418926 2.511883361 2.491361694 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 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation SWS[t] = + 7.19519299579455 + 3.36679474202788PS[t] + 3.43730615240639L[t] -1.65097896744842Wb[t] -0.880440616381254Wbr[t] -0.315657209275309Tg[t] + 1.33733451027365P[t] + 0.314979429813487S[t] -1.8837396565904D[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) 7.19519299579455 4.516729 1.593 0.121641 0.060821 PS 3.36679474202788 2.745137 1.2265 0.229566 0.114783 L 3.43730615240639 1.782017 1.9289 0.063254 0.031627 Wb -1.65097896744842 1.157343 -1.4265 0.164042 0.082021 Wbr -0.880440616381254 1.620254 -0.5434 0.590872 0.295436 Tg -0.315657209275309 1.911325 -0.1652 0.869933 0.434967 P 1.33733451027365 0.993734 1.3458 0.188461 0.09423 S 0.314979429813487 0.626066 0.5031 0.618562 0.309281 D -1.8837396565904 1.344971 -1.4006 0.171599 0.085799 Multiple Linear Regression - Regression Statistics Multiple R 0.827535230258193 R-squared 0.684814557318481 Adjusted R-squared 0.600765105936743 F-TEST (value) 8.14775761245805 F-TEST (DF numerator) 8 F-TEST (DF denominator) 30 p-value 8.60521098511313e-06 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 2.50737645315805 Sum Squared Residuals 188.608100335543 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 6.3 7.89580447858142 -1.59580447858142 2 2.1 2.69658009911775 -0.596580099117745 3 9.1 6.28217128635656 2.81782871364344 4 15.8 16.0269484710272 -0.226948471027212 5 5.2 5.26249293291376 -0.0624929329137551 6 10.9 11.4621261596098 -0.562126159609779 7 8.3 7.38744267930867 0.912557320691332 8 11 10.3614264823333 0.638573517666651 9 3.2 3.10466202956652 0.0953379704334817 10 6.3 11.1938874110275 -4.89388741102751 11 6.6 10.6523611499443 -4.05236114994431 12 9.5 10.3770581634728 -0.877058163472793 13 3.3 4.616748165744 -1.31674816574400 14 11 12.7159103188329 -1.71591031883285 15 4.7 7.54681065752132 -2.84681065752132 16 10.4 14.2719906123763 -3.87199061237634 17 7.4 8.73478335079519 -1.33478335079519 18 2.1 3.66476364640126 -1.56476364640126 19 17.9 16.0172259551301 1.88277404486992 20 6.1 8.30425895410857 -2.20425895410858 21 11.9 11.9797381420859 -0.0797381420859159 22 13.8 11.7977816522966 2.00221834770342 23 14.3 10.2852261457175 4.01477385428248 24 15.2 10.1020748797700 5.09792512022995 25 10 6.43296801568258 3.56703198431742 26 11.9 9.44092968369552 2.45907031630448 27 6.5 5.72224181110631 0.777758188893687 28 7.5 8.11768636346933 -0.61768636346933 29 10.6 9.8282295932576 0.771770406742397 30 7.4 8.57552835820276 -1.17552835820276 31 8.4 8.28352818624708 0.116471813752919 32 5.7 7.98733730490201 -2.28733730490201 33 4.9 5.02211161876452 -0.122111618764523 34 3.2 4.22072100537454 -1.02072100537454 35 11 9.0294159061704 1.97058409382961 36 4.9 5.68237661528557 -0.782376615285571 37 13.2 11.4578087146267 1.74219128537329 38 9.7 6.63891893149884 3.06108106850116 39 12.8 10.9199240676769 1.88007593232306 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 12 0.0297158298932441 0.0594316597864883 0.970284170106756 13 0.0605689334568977 0.121137866913795 0.939431066543102 14 0.0247739769265243 0.0495479538530486 0.975226023073476 15 0.0151794925406772 0.0303589850813544 0.984820507459323 16 0.450376711488359 0.900753422976717 0.549623288511641 17 0.342066127106946 0.684132254213892 0.657933872893054 18 0.329419603682306 0.658839207364613 0.670580396317694 19 0.229275160535754 0.458550321071507 0.770724839464246 20 0.463631916408468 0.927263832816936 0.536368083591532 21 0.489587473093327 0.979174946186653 0.510412526906673 22 0.622229258918395 0.75554148216321 0.377770741081605 23 0.727030459285787 0.545939081428426 0.272969540714213 24 0.844470163623206 0.311059672753588 0.155529836376794 25 0.916201265418629 0.167597469162742 0.0837987345813711 26 0.884110697014314 0.231778605971371 0.115889302985686 27 0.8062656576367 0.3874686847266 0.1937343423633 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 2 0.125 NOK 10% type I error level 3 0.1875 NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/15/t12924398151re7ki30sx0emcl/105i531292439801.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/15/t12924398151re7ki30sx0emcl/105i531292439801.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/15/t12924398151re7ki30sx0emcl/1r98v1292439801.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/15/t12924398151re7ki30sx0emcl/1r98v1292439801.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/15/t12924398151re7ki30sx0emcl/2r98v1292439801.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/15/t12924398151re7ki30sx0emcl/2r98v1292439801.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/15/t12924398151re7ki30sx0emcl/3r98v1292439801.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/15/t12924398151re7ki30sx0emcl/3r98v1292439801.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/15/t12924398151re7ki30sx0emcl/4kipy1292439801.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/15/t12924398151re7ki30sx0emcl/4kipy1292439801.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/15/t12924398151re7ki30sx0emcl/5kipy1292439801.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/15/t12924398151re7ki30sx0emcl/5kipy1292439801.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/15/t12924398151re7ki30sx0emcl/6kipy1292439801.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/15/t12924398151re7ki30sx0emcl/6kipy1292439801.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/15/t12924398151re7ki30sx0emcl/7u9611292439801.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/15/t12924398151re7ki30sx0emcl/7u9611292439801.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/15/t12924398151re7ki30sx0emcl/85i531292439801.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/15/t12924398151re7ki30sx0emcl/85i531292439801.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/15/t12924398151re7ki30sx0emcl/95i531292439801.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/15/t12924398151re7ki30sx0emcl/95i531292439801.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

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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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