Yt / Xt = c + et

*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: Wed, 28 Oct 2009 15:34:04 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Oct/28/t1256765697q0iboelkoer1j0s.htm/, Retrieved Wed, 28 Oct 2009 22:34:57 +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/Oct/28/t1256765697q0iboelkoer1j0s.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:

SHWS3

Dataseries X:

» Textbox « » Textfile « » CSV «

0,874485563 0,894815147 0,892411256 0,900121586 0,906755235 0,910994657 0,911280136 0,909133373 0,904285745 0,885407186 0,876697559 0,876891448 0,879117576 0,862191652 0,871510016 0,875215328 0,883313093 0,887365664 0,88896251 0,891731309 0,889529695 0,871587153 0,861408317 0,86226747 0,870116571 0,889652426 0,89663202 0,898790085 0,894552676 0,905523406 0,913761746 0,920488714 0,919339327 0,899479828 0,878813701 0,867623842 0,892203067 0,900966942 0,911833088 0,912316884 0,922796715 0,92798179 0,923041866 0,929510651 0,928583559 0,89396483 0,871127942 0,859666401 0,887346077 0,906724018 0,913663934 0,92495686 0,926075244 0,933403677 0,927753559 0,936510006 0,925148583 0,904674545 0,884073526 0,870558829 0,911405438 0,93879943 0,963458958 0,982290995 1,001576337 1,01534672 1,037109345 1,043382387 1,043967412 1,02941477 0,996086572 0,983931523

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 2 seconds R Server 'RServer@AstonUniversity' @ vre.aston.ac.uk Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 0.913665354111111 0.00527983802679055 173.047989251765 Geometric Mean 0.912629352414542 Harmonic Mean 0.911638210247116 Quadratic Mean 0.914747847367684 Winsorized Mean ( 1 / 24 ) 0.913681422041667 0.00527358722362365 173.256150566492 Winsorized Mean ( 2 / 24 ) 0.913528930180555 0.00521127192532639 175.298649402821 Winsorized Mean ( 3 / 24 ) 0.913211481972222 0.00510588267738917 178.854771970433 Winsorized Mean ( 4 / 24 ) 0.912727499861111 0.00482272880861536 189.255406240261 Winsorized Mean ( 5 / 24 ) 0.911944329444444 0.00452298499090482 201.624442990250 Winsorized Mean ( 6 / 24 ) 0.911523703861111 0.00439226731877303 207.529195676493 Winsorized Mean ( 7 / 24 ) 0.910397293416667 0.00407407410942712 223.461151899537 Winsorized Mean ( 8 / 24 ) 0.910257465194444 0.00402215243945416 226.311030945902 Winsorized Mean ( 9 / 24 ) 0.907913102694445 0.00345508626454796 262.775813157079 Winsorized Mean ( 10 / 24 ) 0.904890725194444 0.00269148898823651 336.204505814211 Winsorized Mean ( 11 / 24 ) 0.904652443958333 0.00261269064694995 346.253179653864 Winsorized Mean ( 12 / 24 ) 0.904381760958333 0.00248666030395022 363.693327762407 Winsorized Mean ( 13 / 24 ) 0.903713861222222 0.00236936555077032 381.415970586898 Winsorized Mean ( 14 / 24 ) 0.90390736475 0.00228307615291695 395.916432132643 Winsorized Mean ( 15 / 24 ) 0.9038453035 0.00225428972972536 400.944604228009 Winsorized Mean ( 16 / 24 ) 0.904726922611111 0.00210765830223601 429.256925399761 Winsorized Mean ( 17 / 24 ) 0.904510200472222 0.00202176000025403 447.387523919046 Winsorized Mean ( 18 / 24 ) 0.904611950222222 0.00194009914351527 466.270990967582 Winsorized Mean ( 19 / 24 ) 0.905073008444444 0.00186253548190133 485.935982019799 Winsorized Mean ( 20 / 24 ) 0.9045465065 0.00178292470750699 507.338589617057 Winsorized Mean ( 21 / 24 ) 0.904940750875 0.00171017384467150 529.151322068561 Winsorized Mean ( 22 / 24 ) 0.904408834875 0.00158502325230982 570.596572357549 Winsorized Mean ( 23 / 24 ) 0.904080875319444 0.00152776111369666 591.7684821365 Winsorized Mean ( 24 / 24 ) 0.902914642652778 0.00118342178820395 762.969426161323 Trimmed Mean ( 1 / 24 ) 0.912575309757143 0.00503667604955409 181.186024429333 Trimmed Mean ( 2 / 24 ) 0.911404132044118 0.00474795193791702 191.957320537655 Trimmed Mean ( 3 / 24 ) 0.910245151242424 0.00443533708303021 205.225698566420 Trimmed Mean ( 4 / 24 ) 0.90913277721875 0.00410101113063698 221.685030412863 Trimmed Mean ( 5 / 24 ) 0.908089148064516 0.00380442814273388 238.692679686666 Trimmed Mean ( 6 / 24 ) 0.907163904533333 0.003545758089194 255.844838173815 Trimmed Mean ( 7 / 24 ) 0.906261877086207 0.00326357434458935 277.689974671081 Trimmed Mean ( 8 / 24 ) 0.905502310821429 0.00301040712620679 300.790648194615 Trimmed Mean ( 9 / 24 ) 0.904709785092593 0.00269759073584830 335.376961771814 Trimmed Mean ( 10 / 24 ) 0.904216967 0.00247655359926236 365.111002349928 Trimmed Mean ( 11 / 24 ) 0.90411994582 0.00240621515260939 375.743600832842 Trimmed Mean ( 12 / 24 ) 0.9040473324375 0.00233501131541232 387.170428884136 Trimmed Mean ( 13 / 24 ) 0.904003711326087 0.0022725463183605 397.793305255168 Trimmed Mean ( 14 / 24 ) 0.904040195954545 0.00221763888498665 407.658885346424 Trimmed Mean ( 15 / 24 ) 0.904056461 0.00216426808443848 417.719259226870 Trimmed Mean ( 16 / 24 ) 0.9040817999 0.00209877100553862 430.76724307423 Trimmed Mean ( 17 / 24 ) 0.904005403789474 0.00204494951498276 442.067345509552 Trimmed Mean ( 18 / 24 ) 0.903946015944444 0.00199108175698117 453.997437711944 Trimmed Mean ( 19 / 24 ) 0.903867670735294 0.0019351579946422 467.076938026662 Trimmed Mean ( 20 / 24 ) 0.903724933375 0.00187388073661544 482.274520313010 Trimmed Mean ( 21 / 24 ) 0.9036263446 0.00180748011865464 499.937086595782 Trimmed Mean ( 22 / 24 ) 0.903465396892857 0.00172861841450615 522.651725395953 Trimmed Mean ( 23 / 24 ) 0.903346642461539 0.00165234386735901 546.706203415989 Trimmed Mean ( 24 / 24 ) 0.903250872958333 0.00155289498231764 581.656121787619 Median 0.904480145 Midrange 0.9518169065 Midmean - Weighted Average at Xnp 0.903408921621621 Midmean - Weighted Average at X(n+1)p 0.903946015944444 Midmean - Empirical Distribution Function 0.903408921621621 Midmean - Empirical Distribution Function - Averaging 0.903946015944444 Midmean - Empirical Distribution Function - Interpolation 0.903946015944444 Midmean - Closest Observation 0.903408921621621 Midmean - True Basic - Statistics Graphics Toolkit 0.903946015944444 Midmean - MS Excel (old versions) 0.904005403789474 Number of observations 72

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Oct/28/t1256765697q0iboelkoer1j0s/16y9e1256765639.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/28/t1256765697q0iboelkoer1j0s/16y9e1256765639.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/28/t1256765697q0iboelkoer1j0s/2fovt1256765639.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/28/t1256765697q0iboelkoer1j0s/2fovt1256765639.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')

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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