應用多變量分析(1)
Wade
2016年9月23日
黃老師前面在LDS甚麼是多變量，舉了回歸和雙變數常態分配的例子：
以年齡和疾病發生機率為例： 沒受過統計訓練的人寫的線性多變量回歸模型：\(y = β_0 + β_{1}x_{i1} + β_{2}x_{i2} + ... + ε_i\)
受過統計訓練的人則會寫成非線性多變量回歸模型：\(y = β_0 + β_{1}x_{i1} + β_{2}x^{2}_{i2} + ... + ε_i\)
順便幫我們複習了常態分配的方程式： \(f(x) = \frac{1}{δ\sqrt{2π}}e^{-\frac{1}{2}(\frac{x-μ}{δ})}\)
然後說他最喜歡的數學是線性代數，但是說沒念過的人還是放棄好了… 但我個人認為，放棄之前可以先看看別的老師怎麼說：http://ocw.aca.ntu.edu.tw/ntu-ocw/ocw/cou/102S207
然後提到SEM(Structural Equation Modeling)，說直接學SEM會有95%的機率會失敗，建議先學EFA(Exploratory Factor Analysis)然後CFA(Confirmatory Factor Analysis)，之後學SEM才會成功。
PCA(Principal Components Analysis)也提到了，用來做影像處理，把一張圖轉換為一維向量後，再用特徵空間的方式找出人臉。
很多統計方法都是用距離來計算的。
R中的盒形圖上下的橫線代表最大值區間(Q3+1.5ΔQ)和最小值區間(Q1-1.5ΔQ)
ΔQ = Q3 - Q1 = 四分位間距(interquartile range)
!–上面雜七雜八寫了一些，沒寫到的就是我忘了，大家幫忙補充–!
以下是Lia分享的黃老師上課用到的R Code:
data(USArrests)
View(USArrests)
?USArrests#標準多變量資料範本## starting httpd help server ...## donedotchart(USArrests$Murder)#$為抽取資料中其中一項變數
dotchart(USArrests$Murder,labels = row.names.default(USArrests),cex = 0.5)#labels為增加表列的名稱,cex為字體大小
data2 <- USArrests[order(USArrests$Murder),c(1,3)]#小括號為參數,中括號為排序或整理資料,C(1,3)為取第一個及第三個變數,order = 重新排序資料
dotchart(data2$Murder,labels = row.names(data2),cex = 0.5,
main = "Murder arrests by state, 1973",
xlab = "Murder per 100,000 population",
col=c("darkblue","dodgerblue"))#main=主標題 xlab=下標題 col= 彩色變數 c(x,y)為向量函數 "xxx"="字串" 
V1 <- 1:10
V2 <- rep(3,2)
v3 <- c(V1,V2)
colors()#叫出彩色指令庫## [1] "white" "aliceblue" "antiquewhite"
## [4] "antiquewhite1" "antiquewhite2" "antiquewhite3"
## [7] "antiquewhite4" "aquamarine" "aquamarine1"
## [10] "aquamarine2" "aquamarine3" "aquamarine4"
## [13] "azure" "azure1" "azure2"
## [16] "azure3" "azure4" "beige"
## [19] "bisque" "bisque1" "bisque2"
## [22] "bisque3" "bisque4" "black"
## [25] "blanchedalmond" "blue" "blue1"
## [28] "blue2" "blue3" "blue4"
## [31] "blueviolet" "brown" "brown1"
## [34] "brown2" "brown3" "brown4"
## [37] "burlywood" "burlywood1" "burlywood2"
## [40] "burlywood3" "burlywood4" "cadetblue"
## [43] "cadetblue1" "cadetblue2" "cadetblue3"
## [46] "cadetblue4" "chartreuse" "chartreuse1"
## [49] "chartreuse2" "chartreuse3" "chartreuse4"
## [52] "chocolate" "chocolate1" "chocolate2"
## [55] "chocolate3" "chocolate4" "coral"
## [58] "coral1" "coral2" "coral3"
## [61] "coral4" "cornflowerblue" "cornsilk"
## [64] "cornsilk1" "cornsilk2" "cornsilk3"
## [67] "cornsilk4" "cyan" "cyan1"
## [70] "cyan2" "cyan3" "cyan4"
## [73] "darkblue" "darkcyan" "darkgoldenrod"
## [76] "darkgoldenrod1" "darkgoldenrod2" "darkgoldenrod3"
## [79] "darkgoldenrod4" "darkgray" "darkgreen"
## [82] "darkgrey" "darkkhaki" "darkmagenta"
## [85] "darkolivegreen" "darkolivegreen1" "darkolivegreen2"
## [88] "darkolivegreen3" "darkolivegreen4" "darkorange"
## [91] "darkorange1" "darkorange2" "darkorange3"
## [94] "darkorange4" "darkorchid" "darkorchid1"
## [97] "darkorchid2" "darkorchid3" "darkorchid4"
## [100] "darkred" "darksalmon" "darkseagreen"
## [103] "darkseagreen1" "darkseagreen2" "darkseagreen3"
## [106] "darkseagreen4" "darkslateblue" "darkslategray"
## [109] "darkslategray1" "darkslategray2" "darkslategray3"
## [112] "darkslategray4" "darkslategrey" "darkturquoise"
## [115] "darkviolet" "deeppink" "deeppink1"
## [118] "deeppink2" "deeppink3" "deeppink4"
## [121] "deepskyblue" "deepskyblue1" "deepskyblue2"
## [124] "deepskyblue3" "deepskyblue4" "dimgray"
## [127] "dimgrey" "dodgerblue" "dodgerblue1"
## [130] "dodgerblue2" "dodgerblue3" "dodgerblue4"
## [133] "firebrick" "firebrick1" "firebrick2"
## [136] "firebrick3" "firebrick4" "floralwhite"
## [139] "forestgreen" "gainsboro" "ghostwhite"
## [142] "gold" "gold1" "gold2"
## [145] "gold3" "gold4" "goldenrod"
## [148] "goldenrod1" "goldenrod2" "goldenrod3"
## [151] "goldenrod4" "gray" "gray0"
## [154] "gray1" "gray2" "gray3"
## [157] "gray4" "gray5" "gray6"
## [160] "gray7" "gray8" "gray9"
## [163] "gray10" "gray11" "gray12"
## [166] "gray13" "gray14" "gray15"
## [169] "gray16" "gray17" "gray18"
## [172] "gray19" "gray20" "gray21"
## [175] "gray22" "gray23" "gray24"
## [178] "gray25" "gray26" "gray27"
## [181] "gray28" "gray29" "gray30"
## [184] "gray31" "gray32" "gray33"
## [187] "gray34" "gray35" "gray36"
## [190] "gray37" "gray38" "gray39"
## [193] "gray40" "gray41" "gray42"
## [196] "gray43" "gray44" "gray45"
## [199] "gray46" "gray47" "gray48"
## [202] "gray49" "gray50" "gray51"
## [205] "gray52" "gray53" "gray54"
## [208] "gray55" "gray56" "gray57"
## [211] "gray58" "gray59" "gray60"
## [214] "gray61" "gray62" "gray63"
## [217] "gray64" "gray65" "gray66"
## [220] "gray67" "gray68" "gray69"
## [223] "gray70" "gray71" "gray72"
## [226] "gray73" "gray74" "gray75"
## [229] "gray76" "gray77" "gray78"
## [232] "gray79" "gray80" "gray81"
## [235] "gray82" "gray83" "gray84"
## [238] "gray85" "gray86" "gray87"
## [241] "gray88" "gray89" "gray90"
## [244] "gray91" "gray92" "gray93"
## [247] "gray94" "gray95" "gray96"
## [250] "gray97" "gray98" "gray99"
## [253] "gray100" "green" "green1"
## [256] "green2" "green3" "green4"
## [259] "greenyellow" "grey" "grey0"
## [262] "grey1" "grey2" "grey3"
## [265] "grey4" "grey5" "grey6"
## [268] "grey7" "grey8" "grey9"
## [271] "grey10" "grey11" "grey12"
## [274] "grey13" "grey14" "grey15"
## [277] "grey16" "grey17" "grey18"
## [280] "grey19" "grey20" "grey21"
## [283] "grey22" "grey23" "grey24"
## [286] "grey25" "grey26" "grey27"
## [289] "grey28" "grey29" "grey30"
## [292] "grey31" "grey32" "grey33"
## [295] "grey34" "grey35" "grey36"
## [298] "grey37" "grey38" "grey39"
## [301] "grey40" "grey41" "grey42"
## [304] "grey43" "grey44" "grey45"
## [307] "grey46" "grey47" "grey48"
## [310] "grey49" "grey50" "grey51"
## [313] "grey52" "grey53" "grey54"
## [316] "grey55" "grey56" "grey57"
## [319] "grey58" "grey59" "grey60"
## [322] "grey61" "grey62" "grey63"
## [325] "grey64" "grey65" "grey66"
## [328] "grey67" "grey68" "grey69"
## [331] "grey70" "grey71" "grey72"
## [334] "grey73" "grey74" "grey75"
## [337] "grey76" "grey77" "grey78"
## [340] "grey79" "grey80" "grey81"
## [343] "grey82" "grey83" "grey84"
## [346] "grey85" "grey86" "grey87"
## [349] "grey88" "grey89" "grey90"
## [352] "grey91" "grey92" "grey93"
## [355] "grey94" "grey95" "grey96"
## [358] "grey97" "grey98" "grey99"
## [361] "grey100" "honeydew" "honeydew1"
## [364] "honeydew2" "honeydew3" "honeydew4"
## [367] "hotpink" "hotpink1" "hotpink2"
## [370] "hotpink3" "hotpink4" "indianred"
## [373] "indianred1" "indianred2" "indianred3"
## [376] "indianred4" "ivory" "ivory1"
## [379] "ivory2" "ivory3" "ivory4"
## [382] "khaki" "khaki1" "khaki2"
## [385] "khaki3" "khaki4" "lavender"
## [388] "lavenderblush" "lavenderblush1" "lavenderblush2"
## [391] "lavenderblush3" "lavenderblush4" "lawngreen"
## [394] "lemonchiffon" "lemonchiffon1" "lemonchiffon2"
## [397] "lemonchiffon3" "lemonchiffon4" "lightblue"
## [400] "lightblue1" "lightblue2" "lightblue3"
## [403] "lightblue4" "lightcoral" "lightcyan"
## [406] "lightcyan1" "lightcyan2" "lightcyan3"
## [409] "lightcyan4" "lightgoldenrod" "lightgoldenrod1"
## [412] "lightgoldenrod2" "lightgoldenrod3" "lightgoldenrod4"
## [415] "lightgoldenrodyellow" "lightgray" "lightgreen"
## [418] "lightgrey" "lightpink" "lightpink1"
## [421] "lightpink2" "lightpink3" "lightpink4"
## [424] "lightsalmon" "lightsalmon1" "lightsalmon2"
## [427] "lightsalmon3" "lightsalmon4" "lightseagreen"
## [430] "lightskyblue" "lightskyblue1" "lightskyblue2"
## [433] "lightskyblue3" "lightskyblue4" "lightslateblue"
## [436] "lightslategray" "lightslategrey" "lightsteelblue"
## [439] "lightsteelblue1" "lightsteelblue2" "lightsteelblue3"
## [442] "lightsteelblue4" "lightyellow" "lightyellow1"
## [445] "lightyellow2" "lightyellow3" "lightyellow4"
## [448] "limegreen" "linen" "magenta"
## [451] "magenta1" "magenta2" "magenta3"
## [454] "magenta4" "maroon" "maroon1"
## [457] "maroon2" "maroon3" "maroon4"
## [460] "mediumaquamarine" "mediumblue" "mediumorchid"
## [463] "mediumorchid1" "mediumorchid2" "mediumorchid3"
## [466] "mediumorchid4" "mediumpurple" "mediumpurple1"
## [469] "mediumpurple2" "mediumpurple3" "mediumpurple4"
## [472] "mediumseagreen" "mediumslateblue" "mediumspringgreen"
## [475] "mediumturquoise" "mediumvioletred" "midnightblue"
## [478] "mintcream" "mistyrose" "mistyrose1"
## [481] "mistyrose2" "mistyrose3" "mistyrose4"
## [484] "moccasin" "navajowhite" "navajowhite1"
## [487] "navajowhite2" "navajowhite3" "navajowhite4"
## [490] "navy" "navyblue" "oldlace"
## [493] "olivedrab" "olivedrab1" "olivedrab2"
## [496] "olivedrab3" "olivedrab4" "orange"
## [499] "orange1" "orange2" "orange3"
## [502] "orange4" "orangered" "orangered1"
## [505] "orangered2" "orangered3" "orangered4"
## [508] "orchid" "orchid1" "orchid2"
## [511] "orchid3" "orchid4" "palegoldenrod"
## [514] "palegreen" "palegreen1" "palegreen2"
## [517] "palegreen3" "palegreen4" "paleturquoise"
## [520] "paleturquoise1" "paleturquoise2" "paleturquoise3"
## [523] "paleturquoise4" "palevioletred" "palevioletred1"
## [526] "palevioletred2" "palevioletred3" "palevioletred4"
## [529] "papayawhip" "peachpuff" "peachpuff1"
## [532] "peachpuff2" "peachpuff3" "peachpuff4"
## [535] "peru" "pink" "pink1"
## [538] "pink2" "pink3" "pink4"
## [541] "plum" "plum1" "plum2"
## [544] "plum3" "plum4" "powderblue"
## [547] "purple" "purple1" "purple2"
## [550] "purple3" "purple4" "red"
## [553] "red1" "red2" "red3"
## [556] "red4" "rosybrown" "rosybrown1"
## [559] "rosybrown2" "rosybrown3" "rosybrown4"
## [562] "royalblue" "royalblue1" "royalblue2"
## [565] "royalblue3" "royalblue4" "saddlebrown"
## [568] "salmon" "salmon1" "salmon2"
## [571] "salmon3" "salmon4" "sandybrown"
## [574] "seagreen" "seagreen1" "seagreen2"
## [577] "seagreen3" "seagreen4" "seashell"
## [580] "seashell1" "seashell2" "seashell3"
## [583] "seashell4" "sienna" "sienna1"
## [586] "sienna2" "sienna3" "sienna4"
## [589] "skyblue" "skyblue1" "skyblue2"
## [592] "skyblue3" "skyblue4" "slateblue"
## [595] "slateblue1" "slateblue2" "slateblue3"
## [598] "slateblue4" "slategray" "slategray1"
## [601] "slategray2" "slategray3" "slategray4"
## [604] "slategrey" "snow" "snow1"
## [607] "snow2" "snow3" "snow4"
## [610] "springgreen" "springgreen1" "springgreen2"
## [613] "springgreen3" "springgreen4" "steelblue"
## [616] "steelblue1" "steelblue2" "steelblue3"
## [619] "steelblue4" "tan" "tan1"
## [622] "tan2" "tan3" "tan4"
## [625] "thistle" "thistle1" "thistle2"
## [628] "thistle3" "thistle4" "tomato"
## [631] "tomato1" "tomato2" "tomato3"
## [634] "tomato4" "turquoise" "turquoise1"
## [637] "turquoise2" "turquoise3" "turquoise4"
## [640] "violet" "violetred" "violetred1"
## [643] "violetred2" "violetred3" "violetred4"
## [646] "wheat" "wheat1" "wheat2"
## [649] "wheat3" "wheat4" "whitesmoke"
## [652] "yellow" "yellow1" "yellow2"
## [655] "yellow3" "yellow4" "yellowgreen"name1 <- c("Handsome","Cute","Jone")
demo(colors)# show example of colors##
##
## demo(colors)
## ---- ~~~~~~
##
## > ### ----------- Show (almost) all named colors ---------------------
## >
## > ## 1) with traditional 'graphics' package:
## > showCols1 <- function(bg = "gray", cex = 0.75, srt = 30) {
## + m <- ceiling(sqrt(n <- length(cl <- colors())))
## + length(cl) <- m*m; cm <- matrix(cl, m)
## + ##
## + require("graphics")
## + op <- par(mar=rep(0,4), ann=FALSE, bg = bg); on.exit(par(op))
## + plot(1:m,1:m, type="n", axes=FALSE)
## + text(col(cm), rev(row(cm)), cm, col = cl, cex=cex, srt=srt)
## + }
##
## > showCols1()##
## > ## 2) with 'grid' package:
## > showCols2 <- function(bg = "grey", cex = 0.75, rot = 30) {
## + m <- ceiling(sqrt(n <- length(cl <- colors())))
## + length(cl) <- m*m; cm <- matrix(cl, m)
## + ##
## + require("grid")
## + grid.newpage(); vp <- viewport(w = .92, h = .92)
## + grid.rect(gp=gpar(fill=bg))
## + grid.text(cm, x = col(cm)/m, y = rev(row(cm))/m, rot = rot,
## + vp=vp, gp=gpar(cex = cex, col = cm))
## + }
##
## > showCols2()## Loading required package: grid
##
## > showCols2(bg = "gray33")
##
## > ###
## >
## > ##' @title Comparing Colors
## > ##' @param col
## > ##' @param nrow
## > ##' @param ncol
## > ##' @param txt.col
## > ##' @return the grid layout, invisibly
## > ##' @author Marius Hofert, originally
## > plotCol <- function(col, nrow=1, ncol=ceiling(length(col) / nrow),
## + txt.col="black") {
## + stopifnot(nrow >= 1, ncol >= 1)
## + if(length(col) > nrow*ncol)
## + warning("some colors will not be shown")
## + require(grid)
## + grid.newpage()
## + gl <- grid.layout(nrow, ncol)
## + pushViewport(viewport(layout=gl))
## + ic <- 1
## + for(i in 1:nrow) {
## + for(j in 1:ncol) {
## + pushViewport(viewport(layout.pos.row=i, layout.pos.col=j))
## + grid.rect(gp= gpar(fill=col[ic]))
## + grid.text(col[ic], gp=gpar(col=txt.col))
## + upViewport()
## + ic <- ic+1
## + }
## + }
## + upViewport()
## + invisible(gl)
## + }
##
## > ## A Chocolate Bar of colors:
## > plotCol(c("#CC8C3C", paste0("chocolate", 2:4),
## + paste0("darkorange", c("",1:2)), paste0("darkgoldenrod", 1:2),
## + "orange", "orange1", "sandybrown", "tan1", "tan2"),
## + nrow=2)
##
## > ##' Find close R colors() to a given color {original by Marius Hofert)
## > ##' using Euclidean norm in (HSV / RGB / ...) color space
## > nearRcolor <- function(rgb, cSpace = c("hsv", "rgb255", "Luv", "Lab"),
## + dist = switch(cSpace, "hsv" = 0.10, "rgb255" = 30,
## + "Luv" = 15, "Lab" = 12))
## + {
## + if(is.character(rgb)) rgb <- col2rgb(rgb)
## + stopifnot(length(rgb <- as.vector(rgb)) == 3)
## + Rcol <- col2rgb(.cc <- colors())
## + uniqC <- !duplicated(t(Rcol)) # gray9 == grey9 (etc)
## + Rcol <- Rcol[, uniqC] ; .cc <- .cc[uniqC]
## + cSpace <- match.arg(cSpace)
## + convRGB2 <- function(Rgb, to)
## + t(convertColor(t(Rgb), from="sRGB", to=to, scale.in=255))
## + ## the transformation, rgb{0..255} --> cSpace :
## + TransF <- switch(cSpace,
## + "rgb255" = identity,
## + "hsv" = rgb2hsv,
## + "Luv" = function(RGB) convRGB2(RGB, "Luv"),
## + "Lab" = function(RGB) convRGB2(RGB, "Lab"))
## + d <- sqrt(colSums((TransF(Rcol) - as.vector(TransF(rgb)))^2))
## + iS <- sort.list(d[near <- d <= dist])# sorted: closest first
## + setNames(.cc[near][iS], format(d[near][iS], digits=3))
## + }
##
## > nearRcolor(col2rgb("tan2"), "rgb")
## 0.0 21.1 25.8 29.5
## "tan2" "tan1" "sandybrown" "sienna1"
##
## > nearRcolor(col2rgb("tan2"), "hsv")
## 0.0000 0.0410 0.0618 0.0638 0.0667
## "tan2" "sienna2" "coral2" "tomato2" "tan1"
## 0.0766 0.0778 0.0900 0.0912 0.0918
## "coral" "sienna1" "sandybrown" "coral1" "tomato"
##
## > nearRcolor(col2rgb("tan2"), "Luv")
## 0.00 7.42 7.48 12.41 13.69
## "tan2" "tan1" "sandybrown" "orange3" "orange2"
##
## > nearRcolor(col2rgb("tan2"), "Lab")
## 0.00 5.56 8.08 11.31
## "tan2" "tan1" "sandybrown" "peru"
##
## > nearRcolor("#334455")
## 0.0867
## "darkslategray"
##
## > ## Now, consider choosing a color by looking in the
## > ## neighborhood of one you know :
## >
## > plotCol(nearRcolor("deepskyblue", "rgb", dist=50))
##
## > plotCol(nearRcolor("deepskyblue", dist=.1))
##
## > plotCol(nearRcolor("tomato", "rgb", dist= 50), nrow=3)
##
## > plotCol(nearRcolor("tomato", "hsv", dist=.12), nrow=3)
##
## > plotCol(nearRcolor("tomato", "Luv", dist= 25), nrow=3)
##
## > plotCol(nearRcolor("tomato", "Lab", dist= 18), nrow=3)
dotchart(data2$Murder,labels = row.names(data2),cex = 0.5,
main = "Murder arrests by state, 1973",
xlab = "Murder per 100,000 population",
col=c("darkblue","dodgerblue"),pch=13)
data(mtcars)
View(mtcars)
data3 <- mtcars[order(mtcars$mpg),c(1,3)]
dotchart(data3$mpg,labels = row.names(mtcars),cex = 0.5,main = "X",xlab = "Y",col=c("green","red"),pch=13)
V4 <- c(1,2,3,4)
V5 <- c(3,5)
V4+V5## [1] 4 7 6 9##Box Plot##
data("MathAchieve",package="nlme")
View(MathAchieve)
par(mfrow=c(1,2))#一個視窗畫一個一列兩行的圖
boxplot(MathAchieve$MathAch,col = "red",main="Math Achievement Scores",ylab="Scores")
boxplot(MathAchieve$SES,col = "blue",main="secio-economic status",ylab="Scores")
library(nlme)
boxplot(MathAchieve$MathAch,col = "red")
boxplot(MathAchieve$SES,col = "blue")
par(mfrow=c(1,1))#一個視窗畫一個一列兩行的圖以下是YuLien分享的簡單的常態分配隨機取點的Code:
n1 <- rnorm(1000,0,1) #從標準常態分配中隨機取1000個點
n1## [1] 1.539123e-01 1.111998e+00 2.313382e-01 4.170520e-01
## [5] -1.809983e+00 -8.007749e-01 2.395713e-01 -7.327806e-01
## [9] -1.803306e-01 9.680131e-01 3.251851e-01 2.837830e-02
## [13] -2.341106e-01 -1.084194e+00 -2.942679e-01 7.633681e-01
## [17] 3.422082e-01 -8.567561e-01 2.262577e+00 2.935191e+00
## [21] -1.752134e-01 -1.777010e+00 4.395186e-02 -7.086983e-02
## [25] -7.859787e-01 1.128198e+00 2.919786e-01 9.588936e-01
## [29] -6.618248e-01 -3.258219e-01 1.527460e+00 -4.584533e-02
## [33] 9.570674e-01 -5.657843e-01 2.651358e-01 -2.414969e-01
## [37] 3.748234e-01 1.565428e+00 9.146691e-01 8.655394e-01
## [41] 1.401906e+00 3.438233e-01 -5.694540e-01 6.488149e-01
## [45] -1.565991e+00 2.550725e-01 -3.044795e-01 5.691777e-01
## [49] 1.214950e+00 2.148283e+00 -3.760253e-01 1.293406e+00
## [53] -1.171351e+00 -5.848580e-01 -7.788385e-01 8.157812e-01
## [57] -5.319831e-01 -1.979726e-02 -1.155866e+00 -3.238620e-01
## [61] 1.079343e+00 9.352136e-01 -1.465121e+00 5.216918e-01
## [65] 2.214862e-01 -1.029923e+00 1.102108e+00 -6.080228e-01
## [69] -2.886582e-01 1.750306e+00 5.476367e-01 -1.393368e-01
## [73] 2.062814e-01 -4.721294e-01 4.091768e-01 1.126042e+00
## [77] 8.088947e-01 -9.898829e-01 3.309085e-01 9.680690e-01
## [81] -1.017824e+00 2.660339e-01 3.552154e-01 -1.636531e-01
## [85] -1.986268e-01 -1.837618e+00 1.986225e+00 -5.461366e-01
## [89] -2.515950e-01 -9.163893e-01 -5.044316e-01 -1.033618e+00
## [93] 3.031989e-01 -1.866087e+00 1.722252e+00 3.280471e-01
## [97] 1.588786e+00 -8.241103e-01 1.543194e+00 6.422330e-01
## [101] -4.802583e-01 -7.695930e-02 2.031273e+00 -2.933530e-01
## [105] -5.728836e-01 -1.806912e+00 -1.104015e+00 1.014540e+00
## [109] -5.654166e-02 -2.829149e-01 2.130956e-01 3.375557e-01
## [113] 1.646287e-01 2.065140e-02 9.275517e-01 -7.039200e-01
## [117] 1.539181e+00 5.710610e-01 -9.743513e-01 1.813279e+00
## [121] 2.994932e-01 -2.590925e+00 -1.149609e+00 -6.390442e-01
## [125] -6.104864e-01 2.529489e-02 -1.132329e+00 -2.531883e+00
## [129] 1.629701e+00 -5.095368e-01 1.755404e+00 2.578501e-02
## [133] 6.264166e-01 -6.113754e-01 -1.476378e+00 -4.725413e-01
## [137] -6.750510e-01 -7.437122e-02 5.112644e-01 8.586736e-01
## [141] -5.547213e-02 3.315375e-02 3.518976e-01 5.108769e-01
## [145] -3.689947e-01 1.116757e+00 4.359950e-01 1.902915e+00
## [149] -8.916054e-01 -2.257618e-01 -6.746209e-01 -7.535520e-01
## [153] 1.037429e+00 5.863542e-01 1.103480e+00 5.579115e-02
## [157] 2.227252e+00 1.097697e+00 1.843284e-02 -1.235150e+00
## [161] 1.687275e+00 -8.724267e-01 2.099299e-01 -8.375932e-01
## [165] 3.642258e-01 -1.458193e+00 -1.055470e+00 -2.553862e+00
## [169] -1.864291e-02 -2.277929e+00 1.697990e+00 7.025516e-02
## [173] -2.850767e-01 1.843729e+00 3.808892e-01 -5.699153e-01
## [177] 1.905383e+00 3.946355e-01 -3.802663e-01 5.754282e-01
## [181] -6.751072e-01 9.169487e-02 -8.805471e-01 -7.650840e-01
## [185] -2.096107e+00 6.881515e-01 7.317776e-01 -4.073976e-01
## [189] -4.368877e-01 -1.298823e-01 1.434476e+00 -4.489754e-01
## [193] 6.405105e-01 -1.125632e-01 5.204474e-01 1.177253e+00
## [197] -1.122313e+00 9.326376e-01 1.920765e+00 1.735486e+00
## [201] 1.667038e+00 -5.070555e-02 -1.493494e-01 2.051852e-01
## [205] 1.008992e-01 -3.325261e-01 -5.135804e-01 1.526548e+00
## [209] 4.436664e-03 3.927130e-01 -7.375377e-01 9.269076e-01
## [213] 3.848826e-02 -1.439535e-01 7.487277e-01 9.185820e-01
## [217] 2.600365e-01 -8.903053e-02 -1.194690e+00 5.025926e-01
## [221] 4.821733e-01 8.832208e-01 2.691907e-01 -1.530660e+00
## [225] -7.327098e-01 8.052622e-01 1.546527e+00 -8.152020e-02
## [229] 7.330390e-02 1.074029e+00 -1.909714e-01 1.026543e+00
## [233] 2.729816e-01 1.374425e+00 9.544608e-01 -6.385171e-02
## [237] -4.437383e-01 -1.497485e-01 -1.444921e+00 1.443894e+00
## [241] 2.500368e-01 -2.175619e+00 -3.393749e-01 -7.351067e-01
## [245] 1.770089e-01 2.891007e-01 -9.512881e-01 3.584046e-01
## [249] -4.880203e-01 8.485963e-01 -8.352882e-01 2.693204e+00
## [253] 1.492378e-01 9.558845e-02 -4.994135e-01 3.793130e-02
## [257] 1.722840e+00 8.327222e-01 2.772465e-01 -1.176525e+00
## [261] 1.001572e+00 1.498121e+00 1.184642e-01 6.290745e-01
## [265] -1.462698e+00 1.655478e+00 2.304894e+00 1.076500e+00
## [269] -1.896858e+00 -2.042874e-01 6.559374e-01 2.438465e+00
## [273] 1.007196e+00 9.065797e-01 -5.256108e-01 2.510837e-01
## [277] 5.604225e-02 3.043629e-01 -1.179781e+00 -3.131878e-01
## [281] -1.719428e+00 -1.551364e-01 2.593561e-01 -4.470455e-01
## [285] -7.584745e-01 9.573721e-01 -1.600214e-01 -1.616269e+00
## [289] -9.440260e-02 1.819800e+00 -9.281368e-01 -1.382926e+00
## [293] -1.641214e+00 8.603717e-01 -2.354126e-02 -5.028225e-01
## [297] -1.458967e+00 3.144247e-01 1.262048e+00 2.452521e-01
## [301] 1.316227e+00 -1.048436e+00 -1.846419e+00 -8.925099e-01
## [305] -9.827377e-01 1.348855e-01 1.484166e+00 -1.926110e-01
## [309] 7.535119e-02 2.669739e-01 1.206507e+00 -5.329390e-01
## [313] 4.897114e-01 -6.106237e-02 -4.258260e-01 -5.473666e-01
## [317] 3.399151e-01 1.402106e+00 1.234383e-01 1.571495e+00
## [321] -5.760557e-01 1.584460e-03 -9.600731e-01 1.624184e-01
## [325] 5.091670e-01 -1.550160e+00 7.344062e-01 -6.347621e-01
## [329] -6.029364e-02 5.053494e-01 5.089791e-01 -5.942060e-01
## [333] 2.465613e+00 2.179900e-01 1.251945e+00 -9.397731e-01
## [337] 4.207362e-01 9.290286e-01 -4.397362e-01 1.239661e-01
## [341] 1.593953e-01 -1.119240e+00 8.525109e-01 5.347096e-01
## [345] 1.797821e+00 1.811160e-01 -1.601210e+00 -5.406815e-01
## [349] 5.480063e-01 1.664064e-01 -8.310323e-02 5.884152e-02
## [353] -1.127933e+00 6.742900e-01 1.635035e+00 -7.350854e-01
## [357] -4.741045e-01 3.359328e-01 -6.203464e-01 1.874158e+00
## [361] -1.098179e+00 2.079177e+00 8.935325e-01 -1.880821e-03
## [365] 2.280061e-01 6.792598e-01 -8.151278e-01 8.132111e-01
## [369] -4.609006e-01 -1.390982e+00 8.930657e-01 -4.491529e-02
## [373] 2.601861e-01 7.918064e-01 2.117447e+00 7.515106e-02
## [377] -1.144466e+00 9.620133e-01 7.812221e-01 9.171236e-01
## [381] 4.005511e-01 -2.333277e-01 -2.663230e-01 -1.256028e+00
## [385] -1.181843e+00 1.096267e-02 2.258602e-01 -4.524781e-01
## [389] -3.574582e-02 4.540249e-01 -5.647632e-01 -1.735213e+00
## [393] 8.786556e-01 -3.842387e-02 -9.248367e-01 7.218601e-01
## [397] 9.252130e-02 -1.163557e+00 -1.127015e+00 1.144931e-01
## [401] -9.795363e-01 1.705888e+00 5.512063e-01 -8.808366e-01
## [405] -1.508906e+00 -1.309961e+00 -2.289886e-01 -9.480685e-02
## [409] -2.932455e-01 -1.851808e+00 5.596356e-06 2.089941e+00
## [413] 5.007767e-02 -1.404256e-02 1.011793e+00 1.391057e-01
## [417] 5.197019e-01 -9.317173e-01 5.544281e-01 -9.373820e-02
## [421] 2.063858e-01 -2.044022e-01 -4.987478e-01 5.947833e-01
## [425] 1.286142e+00 6.188335e-01 7.107065e-01 -7.103263e-01
## [429] 1.586796e+00 -3.572347e-01 6.662730e-01 1.823280e+00
## [433] 1.594556e-01 -5.087700e-01 -1.202116e-01 -3.647788e-01
## [437] -2.264271e+00 1.174463e+00 -8.580209e-01 3.332050e-01
## [441] -3.648647e-01 6.654102e-01 5.671176e-01 -1.948461e+00
## [445] 8.322039e-01 -7.889433e-01 7.418770e-01 4.299521e-02
## [449] 1.271659e+00 -1.922382e+00 9.922539e-01 -1.093865e+00
## [453] -3.096923e-01 8.731361e-02 1.798389e-01 1.835886e+00
## [457] -9.311811e-01 6.769979e-01 -2.618644e-01 4.784595e-01
## [461] 1.771211e-01 1.447970e+00 -5.432306e-01 -1.539785e+00
## [465] 2.546657e-01 4.634321e-01 -1.109325e+00 -2.191261e-01
## [469] 1.209571e+00 -7.924640e-01 -4.025223e-01 1.006454e+00
## [473] -2.238465e-01 4.241431e-01 -1.570750e+00 -1.097593e+00
## [477] 2.240634e+00 5.002185e-01 5.586675e-01 9.779512e-01
## [481] 2.449637e-01 -1.246307e-01 -7.282859e-01 1.028726e+00
## [485] 5.098369e-01 -2.538246e-01 1.575436e-01 7.402133e-02
## [489] 1.777575e+00 1.696950e+00 6.846289e-02 6.911213e-01
## [493] 8.411605e-02 5.022666e-02 5.017399e-01 -8.001612e-02
## [497] -4.983521e-02 -2.704647e-01 1.157168e+00 2.928245e-01
## [501] -1.173983e+00 -1.407039e+00 1.094345e-01 -1.080459e+00
## [505] 2.595877e-01 1.362751e+00 -2.501720e-01 2.234458e-01
## [509] 6.752163e-01 7.403804e-01 -3.478861e-01 2.208879e-01
## [513] -1.786618e-02 -3.442812e-01 -1.806592e-01 -2.820139e-01
## [517] -4.990641e-01 1.587636e+00 4.349865e-01 1.345199e+00
## [521] -1.893770e-01 -1.670014e+00 1.464600e-02 -7.126146e-01
## [525] -7.032827e-01 5.430892e-01 -6.054057e-01 -2.537447e-01
## [529] -4.876256e-01 -1.264713e+00 -4.891869e-01 -1.394489e+00
## [533] 6.991587e-01 -7.396353e-02 -5.571421e-01 -2.521164e+00
## [537] 2.112115e+00 2.700223e-01 -4.999432e-01 7.851473e-01
## [541] -4.431126e-01 -9.587916e-01 1.548021e+00 -1.153395e+00
## [545] -1.162288e-01 -1.279464e-01 9.818250e-01 -8.877406e-01
## [549] 6.919640e-01 -7.153760e-01 -5.997800e-01 4.957260e-02
## [553] 1.512771e-01 -2.833628e-01 -3.164939e-01 -1.604553e+00
## [557] -2.327754e-02 8.976210e-01 1.579876e+00 -1.525210e+00
## [561] -2.732724e-01 6.194822e-02 -2.330804e-01 5.591313e-01
## [565] 1.628522e+00 -3.107453e-01 1.424729e+00 -9.556990e-01
## [569] 2.671682e+00 4.857247e-01 -1.136812e+00 5.845687e-01
## [573] 2.912216e+00 -7.318538e-01 -1.775614e+00 8.113045e-01
## [577] 1.188868e-01 -7.202253e-01 -1.596234e-01 -3.205412e-01
## [581] -1.508979e+00 5.284698e-01 8.773712e-01 2.306885e-01
## [585] 2.071061e+00 2.200400e+00 -1.532191e+00 1.342393e-01
## [589] 7.642520e-02 -1.858482e+00 -1.058236e+00 -1.737826e+00
## [593] 1.886073e+00 1.295315e+00 1.241789e+00 -1.489098e+00
## [597] 2.519338e-01 3.223380e-01 2.689115e-01 2.901010e-01
## [601] -1.120480e-01 2.088471e+00 -7.273539e-01 6.429305e-01
## [605] 6.404030e-02 1.314801e+00 -1.502712e-01 -6.422100e-01
## [609] -1.731207e+00 5.042453e-01 -1.802695e-01 -2.367691e+00
## [613] 1.142632e+00 -7.925873e-01 -9.525673e-01 -2.137059e+00
## [617] -4.246546e-01 -3.764766e-01 -5.175721e-01 -1.754673e-01
## [621] -2.307118e-01 7.084790e-01 -1.871459e-01 1.244915e+00
## [625] -6.396312e-01 1.333444e+00 7.960923e-01 -2.424560e-01
## [629] -9.136538e-02 -2.817474e+00 -1.297657e+00 -7.598231e-01
## [633] 8.889932e-02 1.188588e+00 -1.322320e+00 -1.647937e-01
## [637] -6.057185e-01 -6.975671e-01 8.691563e-01 -2.147924e-01
## [641] -1.720785e+00 -8.173661e-01 2.632794e-01 -2.642529e-01
## [645] 1.362451e+00 -1.680832e+00 -2.260392e-01 6.733783e-01
## [649] 1.634582e-01 1.184765e+00 1.238002e+00 -1.625959e+00
## [653] 2.146950e+00 -1.369414e+00 5.355861e-01 2.729754e-01
## [657] 5.937415e-01 8.648389e-02 2.031912e-01 -2.784608e-01
## [661] 1.113248e+00 -2.201260e-01 6.566426e-01 8.642663e-01
## [665] 1.860195e+00 -3.937546e-02 5.277626e-01 7.713349e-01
## [669] -4.091798e-01 -2.784175e-01 -5.508211e-01 9.977731e-01
## [673] -1.852643e-01 -1.655952e+00 -4.728656e-01 -5.147818e-01
## [677] 6.262106e-01 1.667990e-01 1.954032e+00 3.806645e-01
## [681] -5.511060e-01 1.485946e-01 -1.332705e+00 -4.996345e-01
## [685] 2.827850e-01 -3.306439e-02 -1.990206e+00 7.413732e-02
## [689] 5.203844e-01 1.186523e+00 9.886011e-01 -6.883002e-01
## [693] -1.095268e+00 -7.793460e-01 1.068109e+00 -3.090142e-01
## [697] 1.723590e-01 -1.534678e-01 3.119327e-01 -1.132824e+00
## [701] -6.253733e-01 5.876037e-01 -1.478716e+00 -1.471885e+00
## [705] 6.107924e-01 -9.110657e-01 -4.535410e-01 -5.086643e-01
## [709] -1.516763e+00 -7.968262e-01 1.514776e+00 -1.399434e+00
## [713] 7.603271e-01 1.457992e+00 1.095568e+00 3.573263e-03
## [717] -8.304702e-01 4.947640e-01 -9.396056e-01 -2.079131e-01
## [721] -3.835348e-01 -1.414606e+00 2.288501e-01 -2.669374e+00
## [725] -7.141212e-01 4.905095e-01 5.191050e-01 1.001167e+00
## [729] -1.383351e-01 6.048060e-01 4.032323e-02 1.152710e+00
## [733] 1.794755e+00 -4.644539e-01 4.601365e-01 2.799019e-01
## [737] 2.258824e-01 -1.636724e+00 -1.142866e-01 -1.378561e+00
## [741] 7.941793e-01 -7.277720e-01 -3.469572e-02 -4.907120e-02
## [745] 1.317081e+00 -9.955029e-01 -2.751887e-01 -3.520818e-01
## [749] 9.308301e-01 1.164930e+00 -1.951224e+00 1.064213e+00
## [753] 3.911812e-01 -1.791874e+00 -1.102699e+00 -1.416747e+00
## [757] 8.350873e-01 -5.237235e-01 1.517998e+00 9.299236e-01
## [761] -1.166420e+00 2.438315e+00 -1.316254e-01 -1.066033e+00
## [765] 1.073295e-01 2.144509e+00 2.790002e+00 -5.710262e-01
## [769] -7.411949e-01 5.063559e-01 -2.499660e-01 5.258738e-01
## [773] 7.313331e-01 8.456467e-01 2.331478e-01 1.426300e+00
## [777] 1.100335e+00 -1.454935e-01 -4.059422e-01 -8.579608e-01
## [781] 1.871921e+00 3.128322e-01 2.389799e-01 -1.709268e+00
## [785] 2.786199e-01 2.183948e-01 -1.181705e-01 -4.939789e-01
## [789] 5.727909e-01 3.500345e-01 2.202151e+00 -6.733718e-01
## [793] 1.912994e+00 9.942654e-01 6.930482e-02 -7.072527e-01
## [797] 1.477618e+00 1.728964e+00 1.802539e-01 7.872456e-01
## [801] -3.238205e-01 -8.879992e-01 5.188665e-01 5.189872e-01
## [805] -1.006545e+00 -9.113449e-01 1.043152e-01 5.467160e-01
## [809] -4.882417e-01 1.072515e+00 1.895505e-01 -1.888618e-01
## [813] -3.572132e-01 5.661453e-01 8.515777e-01 3.231975e-01
## [817] -8.841505e-01 8.971051e-01 9.967052e-01 -1.976281e+00
## [821] 1.542899e+00 -2.411513e+00 -5.564187e-01 -8.380053e-01
## [825] -3.420956e-01 3.787139e-01 3.251104e-01 1.093408e+00
## [829] -1.292192e+00 -1.154907e+00 -1.987644e-01 -1.325463e-01
## [833] -1.284182e+00 1.672910e+00 -1.123415e-01 -7.615004e-01
## [837] 1.302582e+00 -1.447623e+00 -1.746402e+00 -1.752726e+00
## [841] -5.546305e-01 2.202872e+00 -3.743067e-01 -3.515524e-02
## [845] -5.491512e-01 5.513624e-01 -2.703568e-01 6.498377e-01
## [849] 8.289361e-01 3.087670e-01 1.365433e+00 3.197749e-01
## [853] -7.212832e-02 -5.855587e-01 5.052263e-01 1.081109e+00
## [857] -1.723189e+00 9.392488e-03 -3.003167e-01 -4.328780e-01
## [861] 1.307833e+00 -4.343172e-01 3.162700e-01 2.118406e+00
## [865] -7.102587e-01 5.542593e-01 -2.578211e-01 9.505513e-01
## [869] 4.426431e-01 -2.767944e-01 1.817403e+00 5.320060e-01
## [873] -6.836070e-01 -1.236702e+00 5.624683e-01 8.858404e-01
## [877] -8.490337e-01 -3.420275e-01 9.915708e-01 -7.296866e-01
## [881] 3.296589e-01 -1.027047e+00 -1.531748e+00 -9.051196e-01
## [885] -4.520458e-02 9.367131e-01 -3.211098e-01 2.896258e-01
## [889] -1.765617e+00 7.182761e-01 -1.422344e+00 -6.267121e-01
## [893] -1.016365e+00 8.406876e-01 1.381836e+00 -4.797902e-01
## [897] 1.398453e-01 -4.423427e-01 -4.400663e-01 -1.683973e+00
## [901] -1.035644e+00 -6.283251e-01 1.682920e+00 -1.114070e+00
## [905] -1.386926e+00 2.304719e-01 -7.417627e-01 -5.527721e-01
## [909] -6.258051e-01 4.103489e-02 -3.209386e-01 -2.228039e+00
## [913] 6.294171e-01 1.227646e+00 -1.554447e-01 1.561200e+00
## [917] -4.006508e-01 -3.822833e-01 -4.644311e-01 1.136524e+00
## [921] 4.501260e-01 -1.996381e+00 -1.126025e-02 9.595071e-01
## [925] 2.376206e-01 -8.405509e-01 -1.442824e+00 4.606851e-01
## [929] 1.545133e-01 -2.174768e+00 -7.868751e-01 1.052711e+00
## [933] -6.182762e-01 -1.468428e+00 -9.133345e-01 5.200543e-01
## [937] -1.606602e+00 3.859740e-01 -1.250452e+00 3.612210e-01
## [941] 1.678808e+00 1.081980e-01 9.262983e-01 2.773787e-01
## [945] 4.193827e-02 -1.429381e+00 1.227116e+00 -9.392877e-01
## [949] 3.634149e-01 -7.518713e-01 1.275339e+00 -6.175160e-01
## [953] 3.671827e-02 -1.061427e+00 -2.190800e-01 -2.090433e-01
## [957] -1.691758e+00 -1.468891e+00 -1.729659e+00 -3.432666e-01
## [961] 1.367694e+00 -5.025048e-01 1.150992e-01 1.217724e-01
## [965] -1.414196e+00 -6.014491e-01 -1.605153e+00 -2.920556e-01
## [969] -9.840739e-01 7.943245e-01 -3.265819e-01 2.112809e+00
## [973] -1.007785e+00 -2.852091e-01 -3.276157e-01 -8.517682e-02
## [977] 1.917352e-01 3.222842e-01 2.437535e-01 -9.854208e-01
## [981] 6.759349e-01 -1.732894e+00 7.528873e-01 1.318630e+00
## [985] -2.522047e+00 6.890013e-01 -9.276314e-01 2.566581e-01
## [989] 7.030819e-01 1.834903e-01 1.135429e+00 -4.790528e-01
## [993] 5.240944e-02 1.518640e-01 3.051210e-01 1.040201e+00
## [997] 3.617890e-02 -8.097128e-01 -1.659831e+00 9.997208e-01boxplot(n1,col="blue") #畫出這1000個點的盒型圖
n2 <- rnorm(1000,10,2) #從平均數10，標準差2的常態分配中隨機取1000個點
n2## [1] 12.503052 10.716534 9.545057 8.525313 12.012465 11.448333
## [7] 8.819914 9.087817 10.703583 11.122346 10.835099 10.507674
## [13] 10.874848 11.111168 7.364150 9.082381 9.563788 12.654573
## [19] 7.227902 9.962606 10.995101 8.982487 11.200596 8.634886
## [25] 9.721437 10.492097 12.517171 10.797675 7.684423 13.471051
## [31] 8.209623 6.681106 10.995387 12.269428 10.204647 8.505906
## [37] 14.175878 8.686266 10.322895 6.507746 6.415918 8.994723
## [43] 9.153579 10.722280 8.415600 9.871850 11.268131 8.853520
## [49] 6.217102 10.747363 9.503064 10.386618 11.045030 12.227654
## [55] 6.172885 7.022145 7.427765 9.244364 7.419168 10.099120
## [61] 6.489441 12.553855 10.040121 9.832236 8.743970 10.031160
## [67] 10.913451 8.207492 8.882830 5.199575 11.735405 11.962563
## [73] 10.338390 8.451566 9.848477 10.063998 9.956069 6.219835
## [79] 11.932422 11.304792 8.717339 5.121950 9.920010 11.064053
## [85] 12.887785 8.846895 13.145648 13.294067 8.733050 6.994921
## [91] 8.408516 6.570890 9.478247 9.143945 8.749615 9.759621
## [97] 9.463018 9.310115 10.793395 7.964112 15.095053 7.066650
## [103] 11.237510 13.764491 7.108991 9.663017 10.057214 9.968000
## [109] 10.432158 7.088311 12.623898 9.450180 10.093562 12.898751
## [115] 7.895413 6.246086 8.932498 10.808937 10.101531 9.381088
## [121] 12.217563 8.790932 9.648245 11.213661 9.473273 8.362113
## [127] 9.777069 11.214938 9.642356 14.095502 11.246665 8.305257
## [133] 9.138809 12.421707 9.497526 11.542632 9.204074 8.552753
## [139] 7.776508 11.331108 9.135733 8.813759 12.298388 6.144770
## [145] 10.996907 6.784431 10.640095 12.661857 9.417248 11.527951
## [151] 8.075102 9.594112 11.000373 9.443557 11.634566 10.849470
## [157] 6.597283 8.891286 9.275952 6.850264 9.476001 10.506468
## [163] 9.269477 2.366735 8.780582 9.226120 10.950579 9.950099
## [169] 9.085928 9.414284 7.389247 10.760720 12.699421 6.611817
## [175] 9.920782 8.432389 11.923767 15.919722 8.779769 14.958868
## [181] 11.790015 9.253494 7.602842 11.854873 7.687617 12.099074
## [187] 10.896919 11.361763 10.103179 14.992523 6.584738 10.172735
## [193] 9.708576 9.110260 11.868001 9.143820 5.009267 10.648537
## [199] 8.074497 10.226700 5.776703 7.969324 9.914282 11.679465
## [205] 11.752539 11.718298 7.079498 9.520850 6.724280 11.200190
## [211] 14.017541 11.657720 7.829387 7.868227 11.958827 10.051176
## [217] 13.940727 5.552692 13.690136 8.400118 11.508927 7.791084
## [223] 11.085182 6.050852 12.045365 13.425970 10.264170 12.960058
## [229] 8.621780 3.167258 8.290105 6.217900 10.924562 3.804054
## [235] 8.514094 9.479599 10.569918 9.838405 13.133274 6.294591
## [241] 11.435683 12.526420 9.695481 10.365049 11.217484 14.691543
## [247] 8.755394 12.132104 11.279200 10.417579 7.493334 10.887129
## [253] 7.245822 10.338817 7.079103 9.607539 10.985740 13.674416
## [259] 12.030277 14.098874 5.744304 11.460750 12.578230 10.253743
## [265] 11.882929 9.845326 8.056166 8.729761 10.152195 4.997775
## [271] 12.509969 12.786232 6.641456 9.903537 11.857875 7.548089
## [277] 12.451217 7.753360 14.602899 7.847823 10.121622 8.976844
## [283] 12.988455 9.643468 10.660618 8.232832 9.203299 11.052748
## [289] 10.827320 7.817171 14.710321 10.343169 7.600911 13.353695
## [295] 7.730682 8.801983 8.238874 10.979789 8.717679 9.547537
## [301] 13.485067 11.987796 9.048575 9.093221 9.708300 13.160537
## [307] 8.501214 10.408256 10.341040 11.842985 10.787215 10.455666
## [313] 10.961303 9.897071 12.063068 10.388570 5.232640 10.212632
## [319] 9.168063 11.527305 11.064398 8.130666 8.765552 9.560698
## [325] 9.471941 10.801253 8.343439 9.092798 8.993657 6.577245
## [331] 10.170606 10.413236 10.055404 10.568247 8.760656 10.140012
## [337] 6.723026 8.680347 8.266096 9.452164 8.276825 14.123675
## [343] 9.000090 6.476632 9.587959 9.415127 10.881459 12.835478
## [349] 10.800449 9.953130 11.110803 9.441150 13.570628 9.575759
## [355] 11.406098 10.351505 7.393762 6.673977 10.063727 9.360981
## [361] 10.460610 10.506465 11.229436 11.243813 12.661992 9.737340
## [367] 7.126114 11.047932 10.055418 10.241012 10.083342 8.385904
## [373] 10.343019 9.540179 7.566899 9.628558 12.321279 10.089569
## [379] 8.183011 10.551692 11.128033 10.955370 11.341588 9.201615
## [385] 11.814777 11.743223 10.039169 9.078289 8.451699 6.823201
## [391] 10.597537 11.220009 11.470236 9.982190 10.041207 10.247816
## [397] 8.843197 10.053110 13.680848 7.403075 10.137422 10.271766
## [403] 11.418725 10.240026 14.141965 9.001700 11.611678 9.816600
## [409] 12.729715 11.555154 11.366069 8.218536 10.924162 5.373726
## [415] 10.467843 7.916491 10.415842 8.585230 11.520175 10.659782
## [421] 8.320220 11.278641 10.837631 8.516253 10.378213 12.512152
## [427] 9.967889 8.173929 6.671710 15.218623 13.449489 11.393140
## [433] 9.468915 10.642329 10.808465 7.251845 5.699700 12.237461
## [439] 10.747032 11.154415 8.612458 10.465620 10.589732 11.120992
## [445] 9.319715 12.197231 10.658949 7.588036 11.823393 9.111767
## [451] 10.936205 9.554333 9.861938 14.050767 8.930462 12.321263
## [457] 6.881655 10.201169 11.051868 10.408040 8.716869 10.019200
## [463] 10.566364 7.771325 10.104785 9.173017 10.257459 10.761947
## [469] 12.215325 7.764318 8.602626 11.422243 7.408047 11.794063
## [475] 8.529538 8.121229 12.470456 6.922619 11.231363 11.869179
## [481] 11.391027 8.827929 12.773579 8.511997 10.465581 6.767905
## [487] 9.633702 6.359778 7.223402 11.380517 12.214352 7.106422
## [493] 6.764721 7.747446 10.057217 9.100802 12.338215 7.240901
## [499] 10.366435 10.170919 12.867823 12.733670 9.380408 9.761651
## [505] 12.477015 6.908273 8.466669 7.318234 6.436416 11.612151
## [511] 6.875457 13.087651 10.061175 9.078395 12.833525 10.837058
## [517] 5.870572 8.643784 6.040841 10.549063 9.278589 5.320789
## [523] 12.590369 10.488914 7.745647 9.947821 12.103383 8.741324
## [529] 8.495618 8.020349 9.571557 8.604555 9.434923 10.034535
## [535] 9.195649 8.229545 8.729917 12.090888 9.102035 9.502413
## [541] 9.045790 12.147372 7.596758 8.588865 6.762167 9.789555
## [547] 8.996841 10.384739 11.287074 10.937389 11.986257 8.330858
## [553] 8.978562 9.694571 10.033279 9.889012 9.112075 11.791119
## [559] 9.155620 10.635814 7.113286 10.389701 11.526090 6.945917
## [565] 10.923579 10.299409 11.920198 6.310212 10.337092 8.254168
## [571] 9.689197 11.441656 10.436366 12.151621 9.273815 11.446652
## [577] 10.118846 8.271199 9.765145 11.546247 10.531920 8.630988
## [583] 12.151549 9.047838 12.509306 10.252560 7.161832 9.842317
## [589] 11.452313 12.474908 7.737535 8.022904 12.579499 8.700878
## [595] 9.146234 11.660769 12.627131 8.559910 9.553079 12.293841
## [601] 12.151244 13.311447 12.607848 10.575066 12.437909 11.328517
## [607] 7.812120 9.805098 10.017278 12.122453 11.847622 11.370762
## [613] 10.893780 10.859467 8.754256 7.926141 10.476805 7.746161
## [619] 12.237555 8.313400 11.548428 6.429824 8.421050 12.096702
## [625] 11.940426 7.199582 9.219490 8.966183 9.414307 10.653278
## [631] 8.897892 6.091280 11.104467 10.784966 9.182322 12.490090
## [637] 8.115354 12.186364 5.656012 8.837560 8.009017 7.810303
## [643] 14.627401 9.050505 8.495080 8.948579 8.724752 9.060927
## [649] 11.022329 11.465622 10.215757 8.516648 8.214322 9.463934
## [655] 10.579965 7.490422 10.694420 8.534030 8.009512 13.076762
## [661] 8.848184 10.087722 7.016782 8.644249 11.911603 8.697546
## [667] 9.762436 10.290520 8.501370 11.536856 13.058135 6.492136
## [673] 13.912322 12.976486 12.177070 9.614330 5.311618 10.193392
## [679] 7.909131 9.273922 11.366480 6.418213 11.381299 10.815085
## [685] 6.920792 9.141023 6.823937 11.027351 12.884059 9.607894
## [691] 9.981544 12.865699 10.950327 10.133243 11.407761 9.718252
## [697] 11.475119 10.963528 12.426969 11.235829 8.226629 7.434765
## [703] 11.935733 7.596245 7.251504 11.545957 6.932292 8.676818
## [709] 8.943694 9.845949 11.597504 10.849533 4.831989 11.921087
## [715] 8.992689 8.888308 10.236872 9.576607 9.402455 9.378480
## [721] 7.907022 8.145634 12.440541 11.320843 9.160382 10.925341
## [727] 11.102343 12.647350 10.414794 10.719100 10.519619 9.318163
## [733] 11.685654 11.713847 8.648433 10.459505 7.504669 12.248062
## [739] 9.394200 10.706285 7.750317 11.203744 12.009124 9.425609
## [745] 11.666560 8.568609 12.341600 11.199541 10.140694 11.429299
## [751] 9.704917 8.162784 6.199492 10.027685 8.168899 11.991793
## [757] 9.636300 6.353169 9.374077 10.027891 9.366636 10.115856
## [763] 9.911957 10.052164 10.338506 10.424466 10.393646 7.085721
## [769] 12.187871 8.063818 14.312979 11.442533 10.101432 7.772971
## [775] 13.310598 10.133548 6.174484 8.477690 11.465437 11.092138
## [781] 10.288560 8.002043 7.669993 11.730197 7.272759 10.894651
## [787] 11.136982 9.331485 10.256720 9.391776 8.866971 8.490527
## [793] 9.174101 12.542767 10.753966 6.908122 10.324144 7.116835
## [799] 7.732575 12.528161 9.097347 9.239470 10.316186 10.639789
## [805] 9.445912 10.760491 8.983163 14.582371 6.208947 9.434480
## [811] 14.120271 8.815701 6.422320 11.237378 11.158284 5.780618
## [817] 9.076422 9.552516 11.393504 11.449568 9.694999 8.312101
## [823] 11.673172 10.256632 12.091593 10.433905 9.555254 12.565744
## [829] 9.528480 12.449632 15.988835 12.679276 7.737954 7.810784
## [835] 12.070282 10.383173 10.976270 10.485551 13.154251 12.272135
## [841] 14.529003 10.074703 13.069535 10.495947 9.729350 11.945380
## [847] 13.032937 12.799007 10.778742 11.883553 9.679958 6.318334
## [853] 8.536766 11.592583 7.443386 8.656187 9.844681 5.929712
## [859] 9.424512 7.576136 11.683780 5.910109 8.554296 12.402981
## [865] 7.367179 12.761268 10.856347 10.976455 11.213787 8.588869
## [871] 12.335509 9.673621 14.421098 7.701439 13.114308 8.690903
## [877] 8.336331 11.462064 10.757724 6.754925 10.762350 8.370277
## [883] 10.380685 10.674115 2.579962 9.048056 10.532440 8.260414
## [889] 8.408620 10.014655 12.106799 8.413426 11.544194 10.871643
## [895] 9.328471 14.124535 12.210289 11.875979 5.890628 11.748795
## [901] 11.853481 12.279648 9.370890 12.019518 11.759077 9.407606
## [907] 6.924401 6.065852 10.483765 7.842133 11.068360 9.947260
## [913] 12.110985 10.520425 12.771584 12.495212 10.769190 11.160136
## [919] 11.445106 13.525150 12.042165 9.704007 8.470795 9.510217
## [925] 13.854694 6.052561 8.558237 11.366007 11.381257 8.279817
## [931] 8.082813 9.657777 12.485699 11.117435 11.323528 8.704344
## [937] 10.977728 9.003432 9.365509 11.142029 10.825530 7.877593
## [943] 12.659543 8.862329 12.136987 6.539417 10.165011 8.791393
## [949] 8.993487 13.453797 10.751920 9.489786 6.654352 9.825537
## [955] 10.005705 9.642679 10.751665 7.469646 7.105550 12.792104
## [961] 10.499848 7.564194 9.251686 13.425160 8.782745 9.033734
## [967] 10.395618 9.896965 11.247417 11.713770 12.503329 9.435977
## [973] 9.436815 12.569230 13.659557 10.405785 10.623483 12.985818
## [979] 6.655386 5.488771 8.269300 10.739604 10.132951 9.589131
## [985] 8.098203 9.619237 14.336524 9.590008 6.885352 10.787594
## [991] 10.390811 11.292351 13.446769 8.439219 9.059206 12.014421
## [997] 10.413143 5.846810 8.810353 9.456623mean(n2)## [1] 9.936038sd(n2)## [1] 2.028621hist(n2,col="red") #畫出直方圖