Paper statistiek: Multiple Regression Analysis

*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: Sat, 12 Dec 2009 02:54:28 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Dec/12/t1260611916mj3y7wvgze2uadh.htm/, Retrieved Sat, 12 Dec 2009 10:58:38 +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/Dec/12/t1260611916mj3y7wvgze2uadh.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:

ETP(36)

Dataseries X:

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-0.00109905175307049 -0.00105653160489032 -0.00101401145671809 -0.000971491308545764 -0.00199549144043077 -0.00195297129225846 0.00808954885591388 -0.000616542148499051 -0.000574022000326703 0.000535018427903076 0.000577538576075424 0.000620058724247772 0.000662578872420121 0.000705099020592469 0.000747619168764818 0.000790139316937166 0.000832659465109514 0.000875179613281863 0.000917699761454211 -0.000106300370430871 -6.37802222585223e-05 -2.12600740861740e-05 -0.00104526020597126 -0.00100274005779891 -0.00096021990962656 -0.00091769976145421 -0.000875179613281862 -0.000832659465109514 -0.000790139316937166 -0.000747619168764817 -0.000705099020592469 -0.00066257887242012 0.000446461555809658 0.000488981703982006 0.000531501852154354 0.000574022000326703 0.000616542148499051 -0.00723182407229876 0.00174417579581617 0.00178669594398852 0.00182921609216086 0.00187173624033321 -0.00671508336792435 -0.000320722958884853 -0.00392636254984536 0.00246799785919413 -0.002 etc...

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 'Gwilym Jenkins' @ 72.249.127.135 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean -1.41158040659929e-19 0.000413718580166721 -3.41193379816408e-16 Geometric Mean NaN Harmonic Mean -0.00548115773834646 Quadratic Mean 0.00317783271286185 Winsorized Mean ( 1 / 20 ) -3.27579852593772e-05 0.000391303228778187 -0.08371509062591 Winsorized Mean ( 2 / 20 ) -5.25542831342105e-05 0.000373581048590676 -0.140677058786761 Winsorized Mean ( 3 / 20 ) -4.8136133521284e-05 0.000347654839558478 -0.138459552533245 Winsorized Mean ( 4 / 20 ) -0.000140418536093773 0.000280783859373634 -0.500094757608274 Winsorized Mean ( 5 / 20 ) -0.000140418536093774 0.000270516139241878 -0.519076371884123 Winsorized Mean ( 6 / 20 ) -0.000149254835319604 0.000245825894795742 -0.607156684789538 Winsorized Mean ( 7 / 20 ) 1.22393691822510e-05 0.000190796957635756 0.0641486600935052 Winsorized Mean ( 8 / 20 ) -3.94394371468010e-05 0.000168971872821163 -0.233408297418488 Winsorized Mean ( 9 / 20 ) -3.9439437146807e-05 0.000166506985407306 -0.236863558909141 Winsorized Mean ( 10 / 20 ) 9.57937946891314e-05 0.000140708887801607 0.680794199895859 Winsorized Mean ( 11 / 20 ) 9.5793794690565e-05 0.000138013295099428 0.694091062904865 Winsorized Mean ( 12 / 20 ) -6.72471323980147e-05 0.000107650838945678 -0.624678200900489 Winsorized Mean ( 13 / 20 ) -6.96892688305033e-05 0.000105198712876972 -0.662453626329096 Winsorized Mean ( 14 / 20 ) -7.69806436562428e-05 0.000103303224440437 -0.745191101954697 Winsorized Mean ( 15 / 20 ) -7.97984933860433e-05 0.000100549891331386 -0.793620881429387 Winsorized Mean ( 16 / 20 ) -8.81314931868816e-05 9.84511277913474e-05 -0.895180128090186 Winsorized Mean ( 17 / 20 ) -8.81314931868814e-05 9.49343577760933e-05 -0.92834138505201 Winsorized Mean ( 18 / 20 ) -8.81314931868814e-05 9.12644876723447e-05 -0.965671264197403 Winsorized Mean ( 19 / 20 ) -8.81314931868817e-05 8.74456038156795e-05 -1.00784361181436 Winsorized Mean ( 20 / 20 ) -7.8309607510667e-05 8.57070769759752e-05 -0.913688930642428 Trimmed Mean ( 1 / 20 ) -4.86759292961681e-05 0.000358217578884251 -0.135883697968648 Trimmed Mean ( 2 / 20 ) -6.57308693355869e-05 0.000315395423805386 -0.208407809290682 Trimmed Mean ( 3 / 20 ) -7.30511950030183e-05 0.000272509935302693 -0.268068006114625 Trimmed Mean ( 4 / 20 ) -8.26339109575315e-05 0.000230372784267249 -0.358696498027606 Trimmed Mean ( 5 / 20 ) -6.5298523416659e-05 0.000208095624801573 -0.313790948170696 Trimmed Mean ( 6 / 20 ) -4.65185202473802e-05 0.000182838357803884 -0.25442429480403 Trimmed Mean ( 7 / 20 ) -2.41845387099402e-05 0.000158807442211217 -0.152288446770487 Trimmed Mean ( 8 / 20 ) -3.12801051824450e-05 0.000147637318285394 -0.211871263618986 Trimmed Mean ( 9 / 20 ) -2.98230816173814e-05 0.000140017870438581 -0.212994823617627 Trimmed Mean ( 10 / 20 ) -2.82203556958105e-05 0.000130593292426119 -0.216093454507058 Trimmed Mean ( 11 / 20 ) -4.78015373355381e-05 0.000125514637332077 -0.380844325025364 Trimmed Mean ( 12 / 20 ) -6.95584058243416e-05 0.000119204563684613 -0.583521332357515 Trimmed Mean ( 13 / 20 ) -6.9898298975272e-05 0.000119332593920982 -0.585743564927086 Trimmed Mean ( 14 / 20 ) -6.99284475538444e-05 0.000119614041280736 -0.584617381079211 Trimmed Mean ( 15 / 20 ) -6.89209909677875e-05 0.000119905258726722 -0.574795398464268 Trimmed Mean ( 16 / 20 ) -6.73670620508939e-05 0.000120380461844186 -0.559617906584294 Trimmed Mean ( 17 / 20 ) -6.4372192175511e-05 0.000120855402888038 -0.532638100053715 Trimmed Mean ( 18 / 20 ) -6.08781773208977e-05 0.000121683329077225 -0.500300063965723 Trimmed Mean ( 19 / 20 ) -5.67488870381729e-05 0.000122972910184271 -0.461474701648815 Trimmed Mean ( 20 / 20 ) -5.17937386989031e-05 0.000124878074110482 -0.414754464046909 Median -4.25201481723481e-05 Midrange 0.00141160194958887 Midmean - Weighted Average at Xnp -9.90441866720172e-05 Midmean - Weighted Average at X(n+1)p -6.89209909677874e-05 Midmean - Empirical Distribution Function -9.90441866720172e-05 Midmean - Empirical Distribution Function - Averaging -6.89209909677874e-05 Midmean - Empirical Distribution Function - Interpolation -6.89209909677874e-05 Midmean - Closest Observation -9.90441866720172e-05 Midmean - True Basic - Statistics Graphics Toolkit -6.89209909677874e-05 Midmean - MS Excel (old versions) -6.99284475538444e-05 Number of observations 60

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/12/t1260611916mj3y7wvgze2uadh/1mqsd1260611666.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/12/t1260611916mj3y7wvgze2uadh/1mqsd1260611666.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/12/t1260611916mj3y7wvgze2uadh/2a6vq1260611666.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/12/t1260611916mj3y7wvgze2uadh/2a6vq1260611666.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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