paper: multiple regressie

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

Title produced by software: Central Tendency

Date of computation: Mon, 07 Jan 2008 13:27:43 -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/Jan/07/t1199737712c4rny8wdt725cxg.htm/, Retrieved Mon, 07 Jan 2008 21:28:34 +0100

User-defined keywords:

central tendency van de residu's Tinne Van der Eycken

Dataseries X:

» Textbox « » Textfile « » CSV «

-5.97140410767898 -3.6691753651635 3.22573243778312 8.46994742622872 2.36104613837392 2.27810301334516 -1.89643356409454 -5.57048190071753 1.59306810529995 -1.15395525058041 -6.72929075561101 5.66399576285171 0.880403851972294 0.0619490573441767 8.08456537817682 -6.2448790022095 -2.24567792980042 2.59166701507407 0.601813487319091 4.8272769098794 5.09668174354169 -3.33658622020570 5.34417316066118 1.99609666699276 0.415333303125725 -0.900878021038933 -3.09016502696032 -1.53443811684522 5.61627406480226 -0.498380340378351 -0.443356334553083 -2.97096557941350 0.937268288719855 0.471804866159551 -0.0743614606905861 -6.83970786794111 -0.673055658412168 2.52156302681157 -8.65114003996448 -3.54390202061101 -4.50157864426839 -3.61584164436451 -1.48647635742622 1.68874294472572 -6.24526584517324 3.14185515887046 0.155104567902546 -4.48946146647238 1.49426292301859 1.98654130204668 0.431007250964857 2.85327171343702 -1.23006362910736 -0.75554804367637 3.22445276875476 2.02542762552591 -1.38175229238826 0.876881445756102 1.30437448773787 3.669076904569 3.85445968797453

Text written by user:

Output produced by software:

Summary of compuational transaction Raw Input view raw input (R code) Raw Output view raw output of R engine Computing time 2 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean -2.37138121070518e-16 0.477685409874949 -4.96431576448185e-16 Geometric Mean NaN Harmonic Mean 4.48362555709723 Quadratic Mean 3.70013527434388 Winsorized Mean ( 1 / 20 ) 0.0233778708847780 0.467722447476899 0.0499823581504127 Winsorized Mean ( 2 / 20 ) -0.0523648341314519 0.446904400178921 -0.117172339566331 Winsorized Mean ( 3 / 20 ) -0.0309072990959607 0.440641049419652 -0.0701416700433772 Winsorized Mean ( 4 / 20 ) -0.0487246145829994 0.43689382057979 -0.111525071511285 Winsorized Mean ( 5 / 20 ) -0.0465948213525871 0.427534222061207 -0.108985009733131 Winsorized Mean ( 6 / 20 ) -0.0336586862739812 0.413320729707582 -0.0814347886635016 Winsorized Mean ( 7 / 20 ) -0.0226324200148026 0.366197335079752 -0.0618038905440796 Winsorized Mean ( 8 / 20 ) -0.0453557781275266 0.361646245525345 -0.125414762875916 Winsorized Mean ( 9 / 20 ) 0.0102585613922602 0.326874770874253 0.0313837662197754 Winsorized Mean ( 10 / 20 ) 0.0187920125021998 0.325205865987343 0.0577849739737817 Winsorized Mean ( 11 / 20 ) 0.0168700805769735 0.320361633653287 0.0526594910401511 Winsorized Mean ( 12 / 20 ) 0.000883002866521472 0.30378781007351 0.00290664350984921 Winsorized Mean ( 13 / 20 ) -0.00235282609296044 0.285661361014884 -0.00823641700999192 Winsorized Mean ( 14 / 20 ) 0.00891498423458836 0.278327923351213 0.0320305060564794 Winsorized Mean ( 15 / 20 ) 0.147793040261333 0.241630367191252 0.611649280590441 Winsorized Mean ( 16 / 20 ) 0.217642546012709 0.223503272213111 0.97377789531952 Winsorized Mean ( 17 / 20 ) 0.248108792083384 0.197225261372578 1.25799702511071 Winsorized Mean ( 18 / 20 ) 0.253606405459537 0.193801857563423 1.30858604065001 Winsorized Mean ( 19 / 20 ) 0.283249115324221 0.188512763006335 1.50254609187762 Winsorized Mean ( 20 / 20 ) 0.235344297606168 0.166749335126690 1.41136573304693 Trimmed Mean ( 1 / 20 ) 0.00307106124975840 0.448573384487309 0.006846285035989 Trimmed Mean ( 2 / 20 ) -0.0186607876578941 0.424945514959282 -0.04391336536328 Trimmed Mean ( 3 / 20 ) 2.96381138061212e-05 0.409920262988187 7.23021438122352e-05 Trimmed Mean ( 4 / 20 ) 0.0118985259741569 0.394312543227904 0.0301753676835987 Trimmed Mean ( 5 / 20 ) 0.0300260336897772 0.37621034340895 0.0798118239325976 Trimmed Mean ( 6 / 20 ) 0.0491030629044067 0.356670086369253 0.137670819003227 Trimmed Mean ( 7 / 20 ) 0.0670054270883842 0.336481032503691 0.199135822277439 Trimmed Mean ( 8 / 20 ) 0.0843638673210648 0.325320508384076 0.259325388799234 Trimmed Mean ( 9 / 20 ) 0.107366478868635 0.31195929947357 0.344168226591787 Trimmed Mean ( 10 / 20 ) 0.123419549237358 0.304198626823363 0.405720270752646 Trimmed Mean ( 11 / 20 ) 0.139784369085678 0.294061137450601 0.475358186727955 Trimmed Mean ( 12 / 20 ) 0.15820641232654 0.281508301468018 0.561995548626881 Trimmed Mean ( 13 / 20 ) 0.181055764652876 0.268925150815994 0.673257090694204 Trimmed Mean ( 14 / 20 ) 0.207134841658694 0.256593544197622 0.807248842937232 Trimmed Mean ( 15 / 20 ) 0.234995236365769 0.241069165088683 0.974804207246167 Trimmed Mean ( 16 / 20 ) 0.247223590302253 0.231104038344476 1.06975019594314 Trimmed Mean ( 17 / 20 ) 0.25140054331536 0.222162262816776 1.13160777230063 Trimmed Mean ( 18 / 20 ) 0.251873006433361 0.217223251007166 1.15951218511619 Trimmed Mean ( 19 / 20 ) 0.251617602229021 0.209683500803529 1.19998760639152 Trimmed Mean ( 20 / 20 ) 0.246781706743289 0.198620478714748 1.24247866252356 Median 0.415333303125725 Midrange -0.0905963068678801 Midmean - Weighted Average at Xnp 0.164126872965497 Midmean - Weighted Average at X(n+1)p 0.234995236365769 Midmean - Empirical Distribution Function 0.234995236365769 Midmean - Empirical Distribution Function - Averaging 0.234995236365769 Midmean - Empirical Distribution Function - Interpolation 0.234995236365769 Midmean - Closest Observation 0.134808960872667 Midmean - True Basic - Statistics Graphics Toolkit 0.234995236365769 Midmean - MS Excel (old versions) 0.234995236365769 Number of observations 61

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jan/07/t1199737712c4rny8wdt725cxg/184w91199737661.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jan/07/t1199737712c4rny8wdt725cxg/184w91199737661.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jan/07/t1199737712c4rny8wdt725cxg/2xoil1199737661.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jan/07/t1199737712c4rny8wdt725cxg/2xoil1199737661.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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