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: Fri, 11 Dec 2009 05:41:52 -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/11/t1260535428osbcunkxj9howln.htm/, Retrieved Fri, 11 Dec 2009 13:43:50 +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/11/t1260535428osbcunkxj9howln.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:

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User-defined keywords:

ETP(34)

Dataseries X:

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-0.000126798975092287 -8.5611140368076e-05 -0.00111064771810136 -0.00261336816931995 -0.00259377249402379 -0.00209649294524237 0.00862669144214783 0.000600055658846702 -0.000405385243590406 2.22254744285334e-05 0.00197215231896213 0.00344439529001038 0.000525133433912763 0.000566321268629165 -0.000458715309104021 -0.00196143576032256 -0.000747630401313108 -0.00025035085253165 0.000472833534858542 0.00122269135263744 0.000217250450200341 -0.000549348515494088 0.000206368645326135 0.00167861161637438 -0.00124065023972324 -0.00119946240500683 -0.00222449898274002 -0.00372721943395856 -0.00251341407494911 -0.00201613452616765 -0.00129295013877746 0.000651117362714818 0.000839886143991086 7.32871782966574e-05 0.00202321402283025 0.00349545699387849 0.000576195137780881 -0.00590794877347171 0.00187280496508174 0.000370084513863197 0.00158388987287265 0.00208116942165411 -0.00713096070028606 0.00113249937358561 -0.00355354895647211 0.00199924465021286 -0.0009256456165875 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 -6.17656425137836e-19 0.000374206208472698 -1.65057770596262e-15 Geometric Mean NaN Harmonic Mean 0.00116545263675230 Quadratic Mean 0.0028743324270361 Winsorized Mean ( 1 / 20 ) 8.80432224007272e-06 0.000363695591182027 0.0242079432732695 Winsorized Mean ( 2 / 20 ) -2.05871061983296e-05 0.000344683866924717 -0.0597275015567413 Winsorized Mean ( 3 / 20 ) -5.05140841812956e-05 0.000288611885148789 -0.17502426885592 Winsorized Mean ( 4 / 20 ) -9.4155045338687e-05 0.00027455990366433 -0.342930792450301 Winsorized Mean ( 5 / 20 ) -9.40089547183236e-05 0.000272670108378343 -0.344771765696743 Winsorized Mean ( 6 / 20 ) -0.000120522764538140 0.000255351682377934 -0.471987352563276 Winsorized Mean ( 7 / 20 ) -0.000176278861929592 0.000238260715010424 -0.739857017225351 Winsorized Mean ( 8 / 20 ) -0.000133611872168725 0.000219662651529466 -0.608259397937762 Winsorized Mean ( 9 / 20 ) -0.000139365830697880 0.000217625559051336 -0.640392752144546 Winsorized Mean ( 10 / 20 ) -0.000129967656288332 0.000214411025679689 -0.606161254423978 Winsorized Mean ( 11 / 20 ) -8.19668167792994e-05 0.000203854547091120 -0.402084809727896 Winsorized Mean ( 12 / 20 ) -6.65846640994635e-05 0.000197600925361003 -0.336965345571221 Winsorized Mean ( 13 / 20 ) -5.96282905860234e-05 0.000192808463249888 -0.309261790592370 Winsorized Mean ( 14 / 20 ) -9.217702658722e-05 0.00018303945641487 -0.503591020169417 Winsorized Mean ( 15 / 20 ) -1.18507192430023e-05 0.000161720953468658 -0.0732788113650282 Winsorized Mean ( 16 / 20 ) -4.08480183279916e-05 0.000135304086550473 -0.301897890665364 Winsorized Mean ( 17 / 20 ) -5.15841076606478e-05 0.000128972672210059 -0.399961532755035 Winsorized Mean ( 18 / 20 ) -0.000127011726124082 0.000113841793750241 -1.11568626898777 Winsorized Mean ( 19 / 20 ) -0.000158663856008168 0.000100969588916933 -1.57140241641173 Winsorized Mean ( 20 / 20 ) -0.000114017056792932 8.894889230205e-05 -1.28182660674128 Trimmed Mean ( 1 / 20 ) -2.57884610665829e-05 0.000334721053752302 -0.0770446339645748 Trimmed Mean ( 2 / 20 ) -6.2852157466571e-05 0.000297389111521397 -0.211346532309233 Trimmed Mean ( 3 / 20 ) -8.63327415044829e-05 0.000263173142517333 -0.32804541025229 Trimmed Mean ( 4 / 20 ) -0.000100109148167247 0.000250166442604552 -0.400170171206751 Trimmed Mean ( 5 / 20 ) -0.000101895379015815 0.000239684060440941 -0.4251237183998 Trimmed Mean ( 6 / 20 ) -0.000103866985090188 0.000227008786108275 -0.457546101500439 Trimmed Mean ( 7 / 20 ) -0.000100246163471068 0.000216650841724208 -0.462708396022203 Trimmed Mean ( 8 / 20 ) -8.54345988362911e-05 0.000208530095425964 -0.40969913077426 Trimmed Mean ( 9 / 20 ) -7.68315143126421e-05 0.000203319595394122 -0.377885437769581 Trimmed Mean ( 10 / 20 ) -6.64091282484357e-05 0.000196827376300329 -0.337397822887733 Trimmed Mean ( 11 / 20 ) -5.63735711895047e-05 0.000188912812350989 -0.298410523288203 Trimmed Mean ( 12 / 20 ) -5.24958067062024e-05 0.000181180373208302 -0.289743341271564 Trimmed Mean ( 13 / 20 ) -5.04239159130758e-05 0.000172245812897376 -0.292743928371243 Trimmed Mean ( 14 / 20 ) -4.90963618737084e-05 0.000161036548456678 -0.304877137173095 Trimmed Mean ( 15 / 20 ) -4.29419812003496e-05 0.000148099666093220 -0.289953261429504 Trimmed Mean ( 16 / 20 ) -4.73835900513992e-05 0.000136943263886870 -0.346008914250381 Trimmed Mean ( 17 / 20 ) -4.83262205884291e-05 0.000130165955601204 -0.371266206783658 Trimmed Mean ( 18 / 20 ) -4.7847119548397e-05 0.000121859633844046 -0.392641254852538 Trimmed Mean ( 19 / 20 ) -3.58524821884447e-05 0.000114714212529553 -0.312537404022264 Trimmed Mean ( 20 / 20 ) -1.64612126379621e-05 0.000108154216933095 -0.152201302036565 Median 4.77563263625954e-05 Midrange 0.000747865370930885 Midmean - Weighted Average at Xnp -0.000104828877301066 Midmean - Weighted Average at X(n+1)p -4.29419812003495e-05 Midmean - Empirical Distribution Function -0.000104828877301066 Midmean - Empirical Distribution Function - Averaging -4.29419812003495e-05 Midmean - Empirical Distribution Function - Interpolation -4.29419812003495e-05 Midmean - Closest Observation -0.000104828877301066 Midmean - True Basic - Statistics Graphics Toolkit -4.29419812003495e-05 Midmean - MS Excel (old versions) -4.90963618737085e-05 Number of observations 60

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/11/t1260535428osbcunkxj9howln/1pzhq1260535310.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/11/t1260535428osbcunkxj9howln/1pzhq1260535310.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/11/t1260535428osbcunkxj9howln/24dob1260535310.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/11/t1260535428osbcunkxj9howln/24dob1260535310.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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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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