R语言自主练习题

1、 1， 某工厂生产一批滚珠，其直径服从正态分布N（，2），现从某天的产品中随机抽出六件，测得直径为：15.1,14.8,15.2,14.9,14.6,15.1,。若2 =0.06，求的置信区间。（置信度为0.95） 解： x<-c(15.1,14.8,15.2,14.9,14.6,15.1) sigema<-sqrt(0.06) alpha<-0.05 xbar<-mean(x) n<-length(x) t1<-xbar-qnorm(1-alpha/2)*sigema/sqrt(n) t2<-xbar+qnorm(1-alpha/2)*sigema/

2、sqrt(n) list(t1,t2), 2，某某自动包装机包装洗衣粉，其重量N（，2），其中，未知。今随机抽取十二袋测得其重量，经计算得样本均值为xbar=1000.25，修正样本标准差s*=2.6329，试求总体标准差的置信水平为0.95的置信区间。解： alpha<-0.05 Xbar<-1000.25 Sdx<-2.6329 T1<-sqrt(11)*Sdx/sqrt(qchisq(1-alpha/2,11) T2<-sqrt(11)*Sdx/sqrt(qchisq(alpha/2,11) list(T1,T2)使用t.text函数进行方差未知的均值假设检

3、验t检验 t.test():调用格式：(数统P138，例6-3)x <- c(11.6,11.5,11.3,11.2,11.4,11.7,11.5,11.6,11.4,11.3) <- 0.05solution <- t.test(x,mu=11.4,alternative="two.sided",conf.level = 1-)#x是一个服从正态分布的总体，mu是均值#alternative是指备择假设，“two.sided”(缺省)指双侧(H1:0),less表示单边检验(H1:<1),greater表示单边检验(H1:>1)#conf.l

4、evel指置信度即1-solutionif(solution$p.value>) print("接受H0")else print("拒绝H0，接受H1")#如果p-value>，则可以认为接受H0，否则拒绝H0，接受H1例题：水泥厂用自动包装机包装水泥，每袋额定重量是50kg，某日开工后随机抽查了9袋，称得重量如下：49.6,49.3,50.1,50.0,49.2,49.9,49.8,51.0,50.2 设每袋重量服从正态分布，问包装机工作是否正常（=0.05）？x <- c(49.6,49.3,50.1,50.0,49.2,49.9,

5、49.8,51.0,50.2) <- 0.05solution <- t.test(x,mu=50,alternative="two.sided",conf.level = 1-)solutionif(solution$p.value>) print("接受H0")else print("拒绝H0，接受H1")p-value>，接受H0认为包装机工作正常。 例题：一公司称某种类型的电池平均寿命是21.5小时，有一个实验检测了该公司所制造的6套电池，得如下的寿命小时数： 19,18,22,20,16,25 这些结

6、果是否表明这种类型的电池与该公司宣称的寿命不同？（=0.05）x <- c(19,18,22,20,16,25 ) <- 0.05solution <- t.test(x,mu=21.5,alternative="two.sided",conf.level = 1-)solutionif(solution$p.value>) print("接受H0")else print("拒绝H0，接受H1")p-value>，接受H0认为这种类型的电池与该公司宣称的寿命相同例题：据长期的经验和资料分析，某砖瓦厂所生产

7、的砖的“抗断强度”X服从正态分布，方差2=1.21 ，今从该厂所生产的一批砖中，随便抽取6块，测得抗断度如下：32.56, 29.66, 31,64， 30.00, 31.87, 31.03现在问：这一批砖的平均抗断强度可否认为是32.50？install.packages("BSDA")library("BSDA")x<-c(32.56,29.66,31.64,30.00,31.87,31.03) <- 0.05solution <- z.test(x,alternative="two.sided",sigma.x

8、 =0.11 conf.level = 1-)solutionif(solution$p.value>) print("接受H0")else print("拒绝H0，接受H1")例2：片剂车间生产的一种药片，片重服从N（，0.0004），今抽取8片，测得每片的重量如下：0.59,0.57,0.63,0.62,0.60,0.58,0.64,0.62。问：如果药片的标准重为0.5，那么这批药片是否合格？（0.05）install.packages("BSDA")library("BSDA")x<-c(0.5

9、9,0.57,0.63,0.62,0.60,0.58,0.64,0.62) <- 0.05solution <- z.test(x,alternative="two.sided",sigma.x = 0.02,conf.level = 1-)solutionif(solution$p.value>) print("接受H0")else print("拒绝H0，接受H1")一、 练习题（题目、数据、代码、结果及解释）1. 使用t.text函数完成下面的例题（P144例6-10）用10只家兔试验某批注射液对体温的影响，测

10、定每只兔子注射前后的体温，如下注射前：(37.8,38.2,38.0,37.6,37.9,38.1,38.2,37.5,38.5,37.9)注射后：(37.9,39.0,38.9,38.4,37.9,39.0,39.5,38.6,38.8,39.0)已知家兔体温服从正态分布，问注射前后体温有无显著差异？（=0.01）（配对）2. 使用t.text函数完成下面的例题有甲、乙两台机床加工相同的产品，假定两台机床加工的产品均服从正态分布，且总体方差相等，从这两台机床加工的产品中随机地抽取若干件，测得产品直径(mm)为甲：(20.5,19.8,19.7,20.4,20.1,20.0,19.0,19.9

11、);乙：(19.7,20.8,20.5,19.8,19.4,20.6,19.2)试比较甲乙两台机床加工的产品直径有无显著应差异？.（=0.05）1. 答案代码x <- c(37.8,38.2,38.0,37.6,37.9,38.1,38.2,37.5,38.5,37.9)y <- c(37.9,39.0,38.9,38.4,37.9,39.0,39.5,38.6,38.8,39.0) <- 0.01solution <- t.test(x,y,mu = 0,alternative="two.sided",paired = TRUE,var.equal

12、 = FALSE,conf.level=1-)if(solution$p.value>) print("接受H0")else print("拒绝H0，接受H1")输出结果：拒绝H0，接受H1（即：注射前后体温差异显著）2答案代码x <- c(20.5,19.8,19.7,20.4,20.1,20.0,19.0,19.9)y <- c(19.7,20.8,20.5,19.8,19.4,20.6,19.2) <- 0.05solution <- t.test(x,y,mu = 0,alternative="two.si

13、ded",paired =FALSE,var.equal = FALSE,conf.level=1-)if(solution$p.value>) print("接受H0")else print("拒绝H0，接受H1")输入结果：接受H0(即：甲乙两台机床加工的产品直径无显著性差异)”1：根据经验，在人的身高相等的情况下，血压的收缩Y与体重X1（千克）和年龄X2（岁数）有关，现收集了13个男子的数据，试建立Y关于X1、X2的线性回归方程。第一步、录入数据，建立多元线性数据模型X1<-c(76.0,91.5,85.5,82.5,79.0

14、,80.5,74.5,79.0,85.0,76.5,82.0,95.0,92.5)X2<-c(50,20,20,30,30,50,60,50,40,55,40,40,20)Y<-c(120,141,124,126,117,125,123,125,132,123,132,155,147)blood<-data.frame(X1,X2,Y)lm.sol<-lm(Y1+X1+X2,data=blood)summary(lm.sol)得出Call:lm(formula=YX1+X2,data=blood)Residuals:Min1QMedian3QMaxCoefficient

15、s:EstimateStd.ErrortvaluePr(>|t|)(Intercept)-62.9633616.99976-3.7040.004083*X12.136560.1753412.1852.53e-07*X20.400220.083214.8100.000713*-Signif.codes:0*0.001*0.01*0.05.0.11Residualstandarderror:2.854on10degreesoffreedomMultipleR-squared:0.9461,AdjustedR-squared:0.9354F-statistic:87.84on2and10DF,

16、p-value:4.531e-07在我们的输入中，关键是lm.sol<-lm(YX1+X2+1,data=blood)的调用，这里可以看到，lm使用了参数Y1+X1+X2,即表示我们使用的是模型y=d+cx2+bx+e从计算结果可以得到，回归系数与回归方程检验都是显著的，因此，回归方程为：Y=-62.96+2.13X1+0.40X22: 一元线性回归：x<-c(0.10, 0.11, 0.12, 0.13, 0.14, 0.15,0.16, 0.17, 0.18, 0.20, 0.21, 0.23)y<-c(42.0, 43.5, 45.0, 45.5, 45.0, 47.5

17、,49.0, 53.0, 50.0, 55.0, 55.0, 60.0)lm.sol<-lm(y 1+x)lm()函数返回拟合结果的对象，可以用summary()函数查看其内容。summary(lm.sol)Residuals:  Min       1Q   Median    3Q     Max-2.0431  -0.7056  0.1694  0.6633  2.2653Coefficient

18、s:            Estimate Std. Error      t value   Pr(>|t|)   (Intercept)   28.493      1.580   18.04    5.88e-09 *x   

19、         130.835      9.683   13.51 9.50e-08 *y=-28.49+130.84x1、 删除异常点，重新拟定模型，数据如下（提示：residuals()函数绘图观察）x <- c(194.5,194.3,197.9,198.4,199.4,199.9,200.9,201.1, 201.4,201.3,203.6,204.6,209.5,208.6,210.7,211.9,212.2)y <-

20、c(131.79,131.79,135.02,135.55,136.46,136.83,137.82,138.00, 138.06,138.05,140.04,142.44,145.47,144.34,146.30,147.54,147.80)答案x <- c(194.5,194.3,197.9,198.4,199.4,199.9,200.9,201.1, 201.4,201.3,203.6,204.6,209.5,208.6,210.7,211.9,212.2)y <- c(131.79,131.79,135.02,135.55,136.46,136.83,137.82,138.

21、00, 138.06,138.05,140.04,142.44,145.47,144.34,146.30,147.54,147.80)plot(x,y) #查看x和y之间的关系lm.sol=lm(xy) #拟合模型summary(lm.sol)lm.res <- residuals(lm.sol) #残差plot(lm.res) #奇异点，可以看到第12位有明显问题lm.up<- lm(xy,subset = -12) summary(lm.up)一、玫瑰图的绘制，主要是先绘制一个直方图，接着将（ ）坐标转化为（ ）坐标答案：直角、极 2、 以下哪列代码是将直方图转化为玫瑰图的关键

22、（ ）A、 theme(axis.text.y = element_blank() B、 coord_polar() + theme_bw()C、 theme(axis.ticks = element_blank()D、 theme(panel.border = element_blank()答案：B前言R语言定义：R是用于统计分析、绘图的语言和操作环境。R是属于GNU系统的一个自由、免费、源代码开放的软件，它是一个用于统计计算和统计制图的优秀工具。今天由我们组为大家讲解一下R语言的绘图方面。 发展历史：R是统计领域广泛使用的诞生于1980年左右的S语言的一个分支。可以认为R是S语言的一种实现

23、。而S语言是由AT&T贝尔实验室开发的一种用来进行数据探索、统计分析和作图的解释型语言。最初S语言的实现版本主要是S-PLUS。S-PLUS是一个商业软件，它基于S语言，并由MathSoft公司的统计科学部进一步完善。后来Auckland大学的Robert Gentleman和Ross Ihaka及其他志愿人员开发了一个R系统。由"R开发核心团队"负责开发。 R是基于S语言的一个GNU项目，所以也可以当作S语言的一种实现，通常用S语言编写的代码都可以不作修改的在R环境下运行。 R的语法是来自Scheme。R的使用与S-PLUS有很多类似之处，这两种语言有一定的兼容性

24、。S-PLUS的使用手册，只要稍加修改就可作为R的使用手册。所以有人说:R，是S-PLUS的一个"克隆"。但是请不要忘了:R是免费的。(R is free）R语言源代码托管在github，具体地址可以看参考资料。R语言的下载可以通过cran的镜像来查找，具体地址可以看参考资料。R语言有域名为.cn的下载地址，其中一个由Datagurn，另一个由中国科学技术大学提供的。R语言Windows版，其中由两个下载地点是Datagurn和USTC提供的。具体地址可以看参考资料。目录崔迎-颜色成金-坐标轴 于志藩-图例周义-玫瑰图 郑湘丽-三维图 R语言：颜色绘图是R语言的主要功能之一

25、，而颜色是传递信息的重要图形要素。将从区别 使用条件 函数定义 颜色调法 例题来向大家说明1、 R预设调色板这一系列函数有5个，即：rainbowheat.colorsterrain.colorstopo.colorscm.colors定义 rainbow(n, s = 1, v = 1, start = 0, end = max(1, n - 1)/n, alpha = 1)heat.colors(n, alpha = 1)terrain.colors(n, alpha = 1)topo.colors(n, alpha = 1)cm.colors(n, alpha = 1)使用条件nthe

26、number of colors ( 1) to be in the palette.颜色数量s, vthe saturation and value to be used to complete the HSV color descriptions.描述颜色的变量，在所有的情况下，H(Hue) 代表色相，S(Saturation) 代表饱和度。v明度startthe (corrected) hue in 0,1 at which the rainbow begins.endthe (corrected) hue in 0,1 at which the rainbow ends.alphath

27、e alpha transparency, a number in 0,1, see argument alpha in hsv.透明度数值均在0或1在R环境里面输入问号（?）和上面任一函数名就可以获得这5个函数的用法说明。这些函数最少需要一个参数，n，表示要得到颜色的数量。n在系统允许范围内没有限制。下面用彩虹色调色板函数rainbow产生的颜色绘一个色盘： setwd("D:/"); n=1000 png("rainbow.disc.png", bg = "transparent") par(mar = c(0,0,0,0) pi

28、e(rep(1,times=n),labels="",col=rainbow(n),border=rainbow(n) dev.off()运行后回在D盘根目录下得到一个文件，图形如下：之后再这个文件下进行的。改变n值，改变颜色的个数例题 给出函数barplot(rep(1,times=n),col= ,border= ,axes=FALSE, main=); box()rainbowheat.colorsterrain.colors地带topo.colorscm.colors毕竟颜色一般应用在画图。来得到下图 n <- 10 barplot（柱形图）(rep（菱纹分布

29、）(1,times=n),col=rainbow(n),border（边界）=rainbow(n),axes（轴线）=FALSE, main（要点）="Rainbow colors"); box()框的意思 barplot(rep(1,times=n),col=rainbow(n),border=rainbow(n),axes=FALSE, main="Rainbow colors"); box() barplot(rep(1,times=n),col=heat.colors(n),border=heat.colors(n),axes=FALSE, ma

30、in="heat.colors"); box() barplot(rep(1,times=n),col=terrain.colors(n),border=terrain.colors(n),axes=FALSE, main="terrain.colors"); box() barplot(rep(1,times=n),col=topo.colors(n),border=topo.colors(n),axes=FALSE, main="topo.colors"); box() barplot(rep(1,times=n),col=cm.

31、colors(n),border=cm.colors(n),axes=FALSE, main="cm.colors"); box()  "Whatever", "is" , "worth" , "doing" ,"is" , "worth" , "doing" , "well"1）将各元素第一个"t"或"r"替换为"k" 2）将所有&qu

32、ot;t"或"r"替换为"k" 1）>sub("tr","k",c("Whatever", "is" , "worth" , "doing" ,"is" , "worth" , "doing" , "well" ) #将各元素第一个"t"或"r"替换为"k" 1 "Whak

33、ever" "is" "wokth" "doing" "is" "wokth" "doing" "well" 2）>gsub("tr","k",c("Whatever", "is" , "worth" , "doing" ,"is" , "worth" , "doing&q

34、uot; , "well" ) #将所有"t"或"r"替换为"k" 1 "Whakevek" "is" "wokkh" "doing" "is" "wokkh" "doing" "well"1.将A到F的小写形式、大写形式、和字母表中的顺序(16),用-依次连接在一起。x <- c("a","b","c

35、","d","e","f")y <- c("A","B","C","D","E","F")z=1:6paste(x,y,z,sep="-")1 "a-A-1" "b-B-2" "c-C-3" "d-D-4" "e-E-5" "f-F-6"一、提取出 0123456

36、789 中所有包含相连三位数的子字符串代码substring(0123456789,1:8,3:9)结果1 "123" "234" "345" "456" "567" "678" "789" ""二、依次提取所有小于1500的四位数中，偶数的百、十、个位数，奇数的十、个位数字代码x=1000:1499substring(x,2:3,4)结果1 "000" "01" "002"

37、"03" "004" "05" "006" "07" "008" "09" "010" "11" "012" "13" "014" "15" "016" "17" "018" 20 "19" "020" "21" &qu

38、ot;022" "23" "024" "25" "026" "27" "028" "29" "030" "31" "032" "33" "034" "35" "036" "37" 39 "038" "39" "040" "

39、;41" "042" "43" "044" "45" "046" "47" "048" "49" "050" "51" "052" "53" "054" "55" "056" 58 "57" "058" "59" "06

40、0" "61" "062" "63" "064" "65" "066" "67" "068" "69" "070" "71" "072" "73" "074" "75" 77 "076" "77" "078" "79&q

41、uot; "080" "81" "082" "83" "084" "85" "086" "87" "088" "89" "090" "91" "092" "93" "094" 96 "95" "096" "97" "098&quo

42、t; "99" "100" "01" "102" "03" "104" "05" "106" "07" "108" "09" "110" "11" "112" "13" 115 "114" "15" "116" "17"

43、 "118" "19" "120" "21" "122" "23" "124" "25" "126" "27" "128" "29" "130" "31" "132"134 "33" "134" "35" "136" &

44、quot;37" "138" "39" "140" "41" "142" "43" "144" "45" "146" "47" "148" "49" "150" "51" 153 "152" "53" "154" "55" &qu

45、ot;156" "57" "158" "59" "160" "61" "162" "63" "164" "65" "166" "67" "168" "69" "170"172 "71" "172" "73" "174" "

46、;75" "176" "77" "178" "79" "180" "81" "182" "83" "184" "85" "186" "87" "188" "89" 191 "190" "91" "192" "93" "1

47、94" "95" "196" "97" "198" "99" "200" "01" "202" "03" "204" "05" "206" "07" "208"210 "09" "210" "11" "212" "13&

48、quot; "214" "15" "216" "17" "218" "19" "220" "21" "222" "23" "224" "25" "226" "27" 229 "228" "29" "230" "31" "232&q

49、uot; "33" "234" "35" "236" "37" "238" "39" "240" "41" "242" "43" "244" "45" "246"248 "47" "248" "49" "250" "51"

50、; "252" "53" "254" "55" "256" "57" "258" "59" "260" "61" "262" "63" "264" "65" 267 "266" "67" "268" "69" "270"

51、 "71" "272" "73" "274" "75" "276" "77" "278" "79" "280" "81" "282" "83" "284"286 "85" "286" "87" "288" "89" &q

52、uot;290" "91" "292" "93" "294" "95" "296" "97" "298" "99" "300" "01" "302" "03" 305 "304" "05" "306" "07" "308" &qu

53、ot;09" "310" "11" "312" "13" "314" "15" "316" "17" "318" "19" "320" "21" "322"324 "23" "324" "25" "326" "27" "

54、328" "29" "330" "31" "332" "33" "334" "35" "336" "37" "338" "39" "340" "41" 343 "342" "43" "344" "45" "346" "4

55、7" "348" "49" "350" "51" "352" "53" "354" "55" "356" "57" "358" "59" "360"362 "61" "362" "63" "364" "65" "366&

56、quot; "67" "368" "69" "370" "71" "372" "73" "374" "75" "376" "77" "378" "79" 381 "380" "81" "382" "83" "384" "85&qu

57、ot; "386" "87" "388" "89" "390" "91" "392" "93" "394" "95" "396" "97" "398"400 "99" "400" "01" "402" "03" "404"

58、; "05" "406" "07" "408" "09" "410" "11" "412" "13" "414" "15" "416" "17" 419 "418" "19" "420" "21" "422" "23"

59、"424" "25" "426" "27" "428" "29" "430" "31" "432" "33" "434" "35" "436"438 "37" "438" "39" "440" "41" "442" &q

60、uot;43" "444" "45" "446" "47" "448" "49" "450" "51" "452" "53" "454" "55" 457 "456" "57" "458" "59" "460" "61" &quo

61、t;462" "63" "464" "65" "466" "67" "468" "69" "470" "71" "472" "73" "474"476 "75" "476" "77" "478" "79" "480" "

62、81" "482" "83" "484" "85" "486" "87" "488" "89" "490" "91" "492" "93" 495 "494" "95" "496" "97" "498" "99"第一题：俩向量V1

63、跟V2合并在一起v1 <- c(1, 2, 3)v2 <- c(4, 5, 6)c(v1,v2)1 1 2 3 4 5 6第二题：在向量V中在第3个向量后面加入10v<-c(1,2,3,3,3,4) append(v,10,after=3) 1 1 2 3 10 3 3 4如有°，请无视1、 利用mtcars中的hp", "disp", "mpg", "qsec", "wt"数据，运用TeachingDemos包中的faces2()函数，制作一张脸谱图，将图片保存到目标文件夹中。（which分别为14, 9, 11, 6, 5）答案：library(TeachingDemos)faces2(mtcars c("hp",