Paper - Central tendency - Regression Model

*The author of this computation has been verified*

R Software Module: rwasp_centraltendency.wasp (opens new window with default values)

Title produced by software: Central Tendency

Date of computation: Sun, 28 Dec 2008 07:22:10 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Dec/28/t1230474149oiq93bovr1gfz4g.htm/, Retrieved Sun, 28 Dec 2008 15:22:31 +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/2008/Dec/28/t1230474149oiq93bovr1gfz4g.htm/}, year = {2008}, } @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 = {2008}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Original text written by user:

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User-defined keywords:

Paper - Central tendency - Regression Model

Dataseries X:

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2.61072861587664 -1.64151512748939 -5.53397130675664 -11.8684507675144 4.92307208512571 6.26712823161773 -2.76872599233773 -3.56312607919330 3.84610531691476 3.92414528449639 -2.60085355983359 -4.52415672464345 0.712363410392165 -3.83027221556495 1.64369314986718 5.1373157082981 -4.77891279135298 -0.543348509239105 10.7317442356705 -7.66239213978311 -6.30680235597392 -7.34729981849825 0.617800822224108 2.85035364935883 1.77740032934145 -3.90118201853709 4.6323076169406 -1.74030963922678 -3.27944132766354 1.09665938498306 7.05463838922537 2.50775091630909 -4.16477564673257 -3.97156359496111 -4.61876313016936 -1.80864980481552 -0.236907168104795 -3.15041173459177 3.37110805438328 -2.30793345402054 2.737897737493 -1.58208769004317 -2.47767476900079 0.167763916859109 1.76974633325578 0.440544884754961 -2.45008188331654 4.47063460393658 -6.94943202424074 8.91682112964061 -0.296516314946182 2.40580572796091 -1.75212202583747 5.39306701500983 6.30609401440519 7.82784320522538 -2.60554495964265 1.29269020570918 1.09083902934299 0.640809564220057 -0.654553416503333 3.45822878067978 1.27021269162882 -1.88415061828193 0.908614567669563

Output produced by software:

Summary of computational transaction Raw Input view raw input (R code) Raw Output view raw output of R engine Computing time 1 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 1.55255249094911e-16 0.537515194322155 2.88838810018569e-16 Geometric Mean NaN Harmonic Mean 17.7114426437233 Quadratic Mean 4.30012155457724 Winsorized Mean ( 1 / 21 ) 0.0367867003338678 0.510472415622624 0.0720640316852361 Winsorized Mean ( 2 / 21 ) 0.0129748356221642 0.499560019125999 0.0259725260737722 Winsorized Mean ( 3 / 21 ) -0.00434841153518202 0.486992820863125 -0.00892910808720977 Winsorized Mean ( 4 / 21 ) -0.0108662396307734 0.468351164513666 -0.0232010518049141 Winsorized Mean ( 5 / 21 ) 0.045584934709982 0.455779154888889 0.100015400487314 Winsorized Mean ( 6 / 21 ) 0.0346000699834368 0.426400975745078 0.0811444437315788 Winsorized Mean ( 7 / 21 ) 0.0243045081573326 0.418046647692537 0.0581382682805483 Winsorized Mean ( 8 / 21 ) 0.00957992752391973 0.411050392150245 0.0233059685791958 Winsorized Mean ( 9 / 21 ) 0.0190806888705647 0.395210801579582 0.0482797757407006 Winsorized Mean ( 10 / 21 ) 0.0239328486809402 0.385838873855737 0.0620280907462127 Winsorized Mean ( 11 / 21 ) -0.0566392309064118 0.367742406656605 -0.154018763898777 Winsorized Mean ( 12 / 21 ) -0.0579555689881637 0.363182418028971 -0.159577022760889 Winsorized Mean ( 13 / 21 ) -0.0821016489608297 0.341793355162389 -0.240208440921335 Winsorized Mean ( 14 / 21 ) -0.0397647819875122 0.329193457290517 -0.120794569596866 Winsorized Mean ( 15 / 21 ) -0.130162815515054 0.305703541480945 -0.425781182921517 Winsorized Mean ( 16 / 21 ) -0.0638908572656482 0.287313638772335 -0.222373213950608 Winsorized Mean ( 17 / 21 ) -0.0544723574450599 0.276049189235856 -0.197328445686970 Winsorized Mean ( 18 / 21 ) -0.0816901019935648 0.271585874209845 -0.300789215312597 Winsorized Mean ( 19 / 21 ) -0.0754833566519066 0.261971653146981 -0.288135589271394 Winsorized Mean ( 20 / 21 ) -0.260348745247356 0.233167674088974 -1.11657306813469 Winsorized Mean ( 21 / 21 ) -0.216896697594788 0.226141308294060 -0.95912020334095 Trimmed Mean ( 1 / 21 ) 0.0180429608229192 0.492094955862672 0.0366656081472910 Trimmed Mean ( 2 / 21 ) -0.00192987636087854 0.469759068713365 -0.00410822587451973 Trimmed Mean ( 3 / 21 ) -0.0101400990634021 0.449820254153892 -0.0225425577656024 Trimmed Mean ( 4 / 21 ) -0.0123416177144798 0.431503892800614 -0.0286014052721016 Trimmed Mean ( 5 / 21 ) -0.0127775248755749 0.416330575666395 -0.0306908154778753 Trimmed Mean ( 6 / 21 ) -0.0270928451512776 0.401765810286526 -0.0674344218886018 Trimmed Mean ( 7 / 21 ) -0.04019754934656 0.392525841715543 -0.102407396086015 Trimmed Mean ( 8 / 21 ) -0.0524209713225164 0.383058504902947 -0.136848472626389 Trimmed Mean ( 9 / 21 ) -0.0631392118145864 0.372729381759244 -0.169396926844286 Trimmed Mean ( 10 / 21 ) -0.076334998344302 0.363402906183281 -0.210056103144653 Trimmed Mean ( 11 / 21 ) -0.0914917659178852 0.35345509795911 -0.258849756153381 Trimmed Mean ( 12 / 21 ) -0.0965148585470332 0.344808517998376 -0.279908568115733 Trimmed Mean ( 13 / 21 ) -0.101870315430210 0.334173767792281 -0.304842346253615 Trimmed Mean ( 14 / 21 ) -0.104541756844991 0.325174013939378 -0.321494806975813 Trimmed Mean ( 15 / 21 ) -0.113134620856697 0.315802949414137 -0.358244345300065 Trimmed Mean ( 16 / 21 ) -0.110898595295499 0.308762511117435 -0.359171179474309 Trimmed Mean ( 17 / 21 ) -0.117058883545378 0.303194718960027 -0.386084836658422 Trimmed Mean ( 18 / 21 ) -0.125310656763473 0.29747869634133 -0.421242456366321 Trimmed Mean ( 19 / 21 ) -0.131144681578378 0.289400937980273 -0.453159144865375 Trimmed Mean ( 20 / 21 ) -0.138761494463053 0.279436237840012 -0.496576591266947 Trimmed Mean ( 21 / 21 ) -0.121580687287011 0.273428312868993 -0.444652881814997 Median 0.167763916859109 Midrange -0.568353265921949 Midmean - Weighted Average at Xnp -0.199923480695139 Midmean - Weighted Average at X(n+1)p -0.110898595295499 Midmean - Empirical Distribution Function -0.110898595295499 Midmean - Empirical Distribution Function - Averaging -0.110898595295499 Midmean - Empirical Distribution Function - Interpolation -0.110898595295499 Midmean - Closest Observation -0.200296040568918 Midmean - True Basic - Statistics Graphics Toolkit -0.110898595295499 Midmean - MS Excel (old versions) -0.110898595295499 Number of observations 65

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/28/t1230474149oiq93bovr1gfz4g/1cfxn1230474128.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/28/t1230474149oiq93bovr1gfz4g/1cfxn1230474128.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/28/t1230474149oiq93bovr1gfz4g/2j6391230474128.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/28/t1230474149oiq93bovr1gfz4g/2j6391230474128.ps (open in new window)

Parameters (Session):

Parameters (R input):

R code (references can be found in the software module):

geomean <- function(x) { return(exp(mean(log(x)))) } harmean <- function(x) { return(1/mean(1/x)) } quamean <- function(x) { return(sqrt(mean(x*x))) } winmean <- function(x) { x <-sort(x[!is.na(x)]) n<-length(x) denom <- 3 nodenom <- n/denom if (nodenom>40) denom <- n/40 sqrtn = sqrt(n) roundnodenom = floor(nodenom) win <- array(NA,dim=c(roundnodenom,2)) for (j in 1:roundnodenom) { win[j,1] <- (j*x[j+1]+sum(x[(j+1):(n-j)])+j*x[n-j])/n win[j,2] <- sd(c(rep(x[j+1],j),x[(j+1):(n-j)],rep(x[n-j],j)))/sqrtn } return(win) } trimean <- function(x) { x <-sort(x[!is.na(x)]) n<-length(x) denom <- 3 nodenom <- n/denom if (nodenom>40) denom <- n/40 sqrtn = sqrt(n) roundnodenom = floor(nodenom) tri <- array(NA,dim=c(roundnodenom,2)) for (j in 1:roundnodenom) { tri[j,1] <- mean(x,trim=j/n) tri[j,2] <- sd(x[(j+1):(n-j)]) / sqrt(n-j*2) } return(tri) } midrange <- function(x) { return((max(x)+min(x))/2) } q1 <- function(data,n,p,i,f) { np <- n*p; i <<- floor(np) f <<- np - i qvalue <- (1-f)*data[i] + f*data[i+1] } q2 <- function(data,n,p,i,f) { np <- (n+1)*p i <<- floor(np) f <<- np - i qvalue <- (1-f)*data[i] + f*data[i+1] } q3 <- function(data,n,p,i,f) { np <- n*p i <<- floor(np) f <<- np - i if (f==0) { qvalue <- data[i] } else { qvalue <- data[i+1] } } q4 <- function(data,n,p,i,f) { np <- n*p i <<- floor(np) f <<- np - i if (f==0) { qvalue <- (data[i]+data[i+1])/2 } else { qvalue <- data[i+1] } } q5 <- function(data,n,p,i,f) { np <- (n-1)*p i <<- floor(np) f <<- np - i if (f==0) { qvalue <- data[i+1] } else { qvalue <- data[i+1] + f*(data[i+2]-data[i+1]) } } q6 <- function(data,n,p,i,f) { np <- n*p+0.5 i <<- floor(np) f <<- np - i qvalue <- data[i] } q7 <- function(data,n,p,i,f) { np <- (n+1)*p i <<- floor(np) f <<- np - i if (f==0) { qvalue <- data[i] } else { qvalue <- f*data[i] + (1-f)*data[i+1] } } q8 <- function(data,n,p,i,f) { np <- (n+1)*p i <<- floor(np) f <<- np - i if (f==0) { qvalue <- data[i] } else { if (f == 0.5) { qvalue <- (data[i]+data[i+1])/2 } else { if (f < 0.5) { qvalue <- data[i] } else { qvalue <- data[i+1] } } } } midmean <- function(x,def) { x <-sort(x[!is.na(x)]) n<-length(x) if (def==1) { qvalue1 <- q1(x,n,0.25,i,f) qvalue3 <- q1(x,n,0.75,i,f) } if (def==2) { qvalue1 <- q2(x,n,0.25,i,f) qvalue3 <- q2(x,n,0.75,i,f) } if (def==3) { qvalue1 <- q3(x,n,0.25,i,f) qvalue3 <- q3(x,n,0.75,i,f) } if (def==4) { qvalue1 <- q4(x,n,0.25,i,f) qvalue3 <- q4(x,n,0.75,i,f) } if (def==5) { qvalue1 <- q5(x,n,0.25,i,f) qvalue3 <- q5(x,n,0.75,i,f) } if (def==6) { qvalue1 <- q6(x,n,0.25,i,f) qvalue3 <- q6(x,n,0.75,i,f) } if (def==7) { qvalue1 <- q7(x,n,0.25,i,f) qvalue3 <- q7(x,n,0.75,i,f) } if (def==8) { qvalue1 <- q8(x,n,0.25,i,f) qvalue3 <- q8(x,n,0.75,i,f) } midm <- 0 myn <- 0 roundno4 <- round(n/4) round3no4 <- round(3*n/4) for (i in 1:n) { if ((x[i]>=qvalue1) & (x[i]<=qvalue3)){ midm = midm + x[i] myn = myn + 1 } } midm = midm / myn return(midm) } (arm <- mean(x)) sqrtn <- sqrt(length(x)) (armse <- sd(x) / sqrtn) (armose <- arm / armse) (geo <- geomean(x)) (har <- harmean(x)) (qua <- quamean(x)) (win <- winmean(x)) (tri <- trimean(x)) (midr <- midrange(x)) midm <- array(NA,dim=8) for (j in 1:8) midm[j] <- midmean(x,j) midm bitmap(file='test1.png') lb <- win[,1] - 2*win[,2] ub <- win[,1] + 2*win[,2] if ((ylimmin == '') | (ylimmax == '')) plot(win[,1],type='b',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(win[,1],type='l',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(ylimmin,ylimmax)) lines(ub,lty=3) lines(lb,lty=3) grid() dev.off() bitmap(file='test2.png') lb <- tri[,1] - 2*tri[,2] ub <- tri[,1] + 2*tri[,2] if ((ylimmin == '') | (ylimmax == '')) plot(tri[,1],type='b',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(tri[,1],type='l',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(ylimmin,ylimmax)) lines(ub,lty=3) lines(lb,lty=3) grid() dev.off() load(file='createtable') a<-table.start() a<-table.row.start(a) a<-table.element(a,'Central Tendency - Ungrouped Data',4,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Measure',header=TRUE) a<-table.element(a,'Value',header=TRUE) a<-table.element(a,'S.E.',header=TRUE) a<-table.element(a,'Value/S.E.',header=TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,hyperlink('http://www.xycoon.com/arithmetic_mean.htm', 'Arithmetic Mean', 'click to view the definition of the Arithmetic Mean'),header=TRUE) a<-table.element(a,arm) a<-table.element(a,hyperlink('http://www.xycoon.com/arithmetic_mean_standard_error.htm', armse, 'click to view the definition of the Standard Error of the Arithmetic Mean')) a<-table.element(a,armose) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,hyperlink('http://www.xycoon.com/geometric_mean.htm', 'Geometric Mean', 'click to view the definition of the Geometric Mean'),header=TRUE) a<-table.element(a,geo) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,hyperlink('http://www.xycoon.com/harmonic_mean.htm', 'Harmonic Mean', 'click to view the definition of the Harmonic Mean'),header=TRUE) a<-table.element(a,har) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,hyperlink('http://www.xycoon.com/quadratic_mean.htm', 'Quadratic Mean', 'click to view the definition of the Quadratic Mean'),header=TRUE) a<-table.element(a,qua) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) for (j in 1:length(win[,1])) { a<-table.row.start(a) mylabel <- paste('Winsorized Mean (',j) mylabel <- paste(mylabel,'/') mylabel <- paste(mylabel,length(win[,1])) mylabel <- paste(mylabel,')') a<-table.element(a,hyperlink('http://www.xycoon.com/winsorized_mean.htm', mylabel, 'click to view the definition of the Winsorized Mean'),header=TRUE) a<-table.element(a,win[j,1]) a<-table.element(a,win[j,2]) a<-table.element(a,win[j,1]/win[j,2]) a<-table.row.end(a) } for (j in 1:length(tri[,1])) { a<-table.row.start(a) mylabel <- paste('Trimmed Mean (',j) mylabel <- paste(mylabel,'/') mylabel <- paste(mylabel,length(tri[,1])) mylabel <- paste(mylabel,')') a<-table.element(a,hyperlink('http://www.xycoon.com/arithmetic_mean.htm', mylabel, 'click to view the definition of the Trimmed Mean'),header=TRUE) a<-table.element(a,tri[j,1]) a<-table.element(a,tri[j,2]) a<-table.element(a,tri[j,1]/tri[j,2]) a<-table.row.end(a) } a<-table.row.start(a) a<-table.element(a,hyperlink('http://www.xycoon.com/median_1.htm', 'Median', 'click to view the definition of the Median'),header=TRUE) a<-table.element(a,median(x)) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,hyperlink('http://www.xycoon.com/midrange.htm', 'Midrange', 'click to view the definition of the Midrange'),header=TRUE) a<-table.element(a,midr) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) a<-table.row.start(a) mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean') mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_1.htm','Weighted Average at Xnp',''),sep=' - ') a<-table.element(a,mylabel,header=TRUE) a<-table.element(a,midm[1]) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) a<-table.row.start(a) mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean') mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_2.htm','Weighted Average at X(n+1)p',''),sep=' - ') a<-table.element(a,mylabel,header=TRUE) a<-table.element(a,midm[2]) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) a<-table.row.start(a) mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean') mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_3.htm','Empirical Distribution Function',''),sep=' - ') a<-table.element(a,mylabel,header=TRUE) a<-table.element(a,midm[3]) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) a<-table.row.start(a) mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean') mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_4.htm','Empirical Distribution Function - Averaging',''),sep=' - ') a<-table.element(a,mylabel,header=TRUE) a<-table.element(a,midm[4]) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) a<-table.row.start(a) mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean') mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_5.htm','Empirical Distribution Function - Interpolation',''),sep=' - ') a<-table.element(a,mylabel,header=TRUE) a<-table.element(a,midm[5]) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) a<-table.row.start(a) mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean') mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_6.htm','Closest Observation',''),sep=' - ') a<-table.element(a,mylabel,header=TRUE) a<-table.element(a,midm[6]) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) a<-table.row.start(a) mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean') mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_7.htm','True Basic - Statistics Graphics Toolkit',''),sep=' - ') a<-table.element(a,mylabel,header=TRUE) a<-table.element(a,midm[7]) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) a<-table.row.start(a) mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean') mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_8.htm','MS Excel (old versions)',''),sep=' - ') a<-table.element(a,mylabel,header=TRUE) a<-table.element(a,midm[8]) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Number of observations',header=TRUE) a<-table.element(a,length(x)) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable.tab')

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Software written by Ed van Stee & Patrick Wessa

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