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1、第二章答案：Ex2.1x-c(1,2,3)y-c(4,5,6)e-c(1,1,1)z=2*x+y+ez1=crossprod(x,y)#z1为x1与x2的内积 或者 x%*%yz2=tcrossprod(x,y)#z1为x1与x2的外积 或者 x%o%yz;z1;z2要点：基本的列表赋值方法，内积和外积概念。内积为标量，外积为矩阵。Ex2.2A-matrix(1:20,c(4,5);AB-matrix(1:20,nrow=4,byrow=TRUE);BC=A+B;C#不存在AB这种写法E=A*B;EF-A1:3,1:3;FH-matrix(c(1,2,4,5),nrow=1);H#H起过渡作用
2、，不规则的数组下标G-B,H;G要点：矩阵赋值方法。默认是byrow=FALSE,数据按列放置。 取出部分数据的方法。可以用数组作为数组的下标取出数组元素。 Ex2.3x-c(rep(1,times=5),rep(2,times=3),rep(3,times=4),rep(4,times=2);x #或者省略times=，如下面的形式x-c(rep(1,5),rep(2,3),rep(3,4),rep(4,2);x要点：rep（）的使用方法。rep（a,b）即将a重复b次 Ex2.4n - 5; H-array(0,dim=c(n,n)for (i in 1:n)for (j in 1:n)H
3、i,j-1/(i+j-1);HG - solve(H);G #求H的逆矩阵ev - eigen(H);ev #求H的特征值和特征向量要点：数组初始化；for循环的使用待解决：如何将很长的命令（如for循环）用几行打出来再执行？每次想换行的时候一按回车就执行了还没打完的命令.Ex2.5StudentData-data.frame(name=c(zhangsan,lisi,wangwu,zhaoliu,dingyi),sex=c(F,M,F,M,F),age=c(14,15,16,14,15),height=c(156,165,157,162,159),weight=c(42,49,41.5,52
4、,45.5);StudentData要点：数据框的使用待解决：SSH登陆linux服务器中文显示乱码。此处用英文代替。Ex2.6write.table(StudentData,file=studentdata.txt)#把数据框StudentData在工作目录里输出，输出的文件名为studentdata.txt.StudentData_a-read.table(studentdata.txt);StudentData_a#以数据框的形式读取文档studentdata.txt，存入数据框StudentData_a中。write.csv(StudentData_a,studentdata.csv)
5、#把数据框StudentData_a在工作目录里输出，输出的文件名为studentdata.csv,可用Excel打开.要点：读写文件。read.table(file) write.table(Rdata,file) read.csv(file) write.csv(Rdata,file) 外部文件，不论是待读入或是要写出的，命令中都得加双引号。Ex2.7Fun-function(n)if(n = 0) list(fail=please input a integer above 0!)elserepeat if(n=1) break else if(n%2=0)n-n/2 else n- 3
6、*n+1list(sucess!)在linux下新建一个R文件，输入上述代码，保存为2.7.R然后在当前目录下进入R环境，输入source(2.7.R)，即打开了这个程序脚本。然后就可以执行函数了。输入Fun(67)，显示sucess!输入Fun(-1)，显示$fail1 please input a integer above 0!待解决：source(*.R)是可以理解为载入这个R文件吧？如何在R环境下关闭R文件呢？OK,自己写的第一个R程序Ex3.1新建txt文件如下：3.1.txt74.3 79.5 75.0 73.5 75.8 74.0 73.5 67.2 75.8 73.5 78.
7、8 75.6 73.5 75.0 75.872.0 79.5 76.5 73.5 79.5 68.8 75.0 78.8 72.0 68.8 76.5 73.5 72.7 75.0 70.478.0 78.8 74.3 64.3 76.5 74.3 74.7 70.4 72.7 76.5 70.4 72.0 75.8 75.8 70.476.5 65.0 77.2 73.5 72.7 80.5 72.0 65.0 80.3 71.2 77.6 76.5 68.8 73.5 77.280.5 72.0 74.3 69.7 81.2 67.3 81.6 67.3 72.7 84.3 69.7 74
8、.3 71.2 74.3 75.072.0 75.4 67.3 81.6 75.0 71.2 71.2 69.7 73.5 70.4 75.0 72.7 67.3 70.3 76.573.5 72.0 68.0 73.5 68.0 74.3 72.7 72.7 74.3 70.4编写一个函数（程序名为data_outline.R）描述样本的各种描述性统计量。data_outline-function(x)n-length(x)m-mean(x)v-var(x)s-sd(x)me-median(x)cv-100*s/mcss-sum(x-m)2)uss-sum(x2)R - max(x)-min
9、(x)R1 -quantile(x,3/4)-quantile(x,1/4)sm -s/sqrt(n)g1 -n/(n-1)*(n-2)*sum(x-m)3)/s3g2 -(n*(n+1)/(n-1)*(n-2)*(n-3)*sum(x-m)4)/s4-(3*(n-1)2)/(n-2)*(n-3)data.frame(N=n,Mean=m,Var=v,std_dev=s,Median=me,std_mean=sm,CV=cv,CSS=css,USS=uss,R=R,R1=R1,Skewness=g1,Kurtosis=g2,row.names=1)进入R，source(data_outline
10、.R) #将程序调入内存serumdata-scan(3.1.txt);serumdata #将数据读入向量serumdata。data_outline(serumdata)结果如下： N Mean Var std_dev Median std_mean CV CSS USS R1 100 73.696 15.41675 3.926417 73.5 0.3926417 5.327857 1526.258 544636.3 20 R1 Skewness Kurtosis1 4.6 0.03854249 0.07051809要点：read.table()用于读表格形式的文件。上述形式的数据由于第七
11、行缺几个数据，故用read.table()不能读入。 scan()可以直接读纯文本文件。scan()和matrix()连用还可以将数据存放成矩阵形式。 X-matrix(scan(3.1.txt,0),ncol=10,byrow=TRUE) #将上述数据放置成10*10的矩阵。scan()还可以从屏幕上直接输入数据。 Yhist(serumdata,freq=FALSE,col=purple,border=red,density=3,angle=60,main=paste(the histogram of serumdata),xlab=age,ylab=frequency)#直方图。col是
12、填充颜色。 默认空白。border是边框的颜色，默认前景色。density是在图上画条纹阴影，默认不画。angle是条纹阴影的倾斜角度（逆时针方向），默认45度。main, xlab, ylab是 标题，x和y坐标轴名称。lines(density(serumdata),col=blue)#密度估计曲线。x lines(x,dnorm(x,mean(serumdata),sd(serumdata),col=green) #正态分布的概率密度曲线 plot(ecdf(serumdata),verticals=TRUE,do.p=FALSE) #绘制经验分布图 lines(x,pnorm(x,me
13、an(serumdata),sd(serumdata),col=blue) #正态经验分布 qqnorm(serumdata,col=purple) #绘制QQ图 qqline(serumdata,col=red) #绘制QQ直线Ex3.3 stem(serumdata,scale=1) #作茎叶图。原始数据小数点后数值四舍五入。 The decimal point is at the | 64 | 300 66 | 23333 68 | 00888777 70 | 34444442222 72 | 0000000777777755555555555 74 | 0333333337000000
14、04688888 76 | 5555555226 78 | 0888555 80 | 355266 82 | 84 | 3boxplot(serumdata,col=lightblue,notch=T) #作箱线图。notch表示带有缺口。 fivenum(serumdata) #五数总结1 64.3 71.2 73.5 75.8 84.3Ex3.4 shapiro.test(serumdata) #正态性Shapori-Wilk检验方法 Shapiro-Wilk normality testdata: serumdataW = 0.9897, p-value = 0.6437结论：p值0.0
15、5，可认为来自正态分布的总体。 ks.test(serumdata,pnorm,mean(serumdata),sd(serumdata) #Kolmogrov-Smirnov检验，正态性 One-sample Kolmogorov-Smirnov testdata: serumdataD = 0.0701, p-value = 0.7097alternative hypothesis: two-sidedWarning message:In ks.test(serumdata, pnorm, mean(serumdata), sd(serumdata) : cannot compute co
16、rrect p-values with ties结论：p值0.05，可认为来自正态分布的总体。注意，这里的警告信息，是因为数据中有重复的数值，ks检验要求待检数据时连续的，不允许重复值。Ex3.5 y f plot(f,y,col=lightgreen) #plot()生成箱线图 x y z boxplot(x,y,z,names=c(1,2,3),col=c(5,6,7) #boxplot()生成箱线图结论：第2和第3组没有显著差异。第1组合其他两组有显著差异。Ex3.6数据太多，懒得录入。离散图应该用plot即可。Ex3.7 studata data.frame(studata) #转化为
17、数据框 V1 V2 V3 V4 V5 V61 1 alice f 13 56.5 84.02 2 becka f 13 65.3 98.03 3 gail f 14 64.3 90.04 4 karen f 12 56.3 77.05 5 kathy f 12 59.8 84.56 6 mary f 15 66.5 112.07 7 sandy f 11 51.3 50.58 8 sharon f 15 62.5 112.59 9 tammy f 14 62.8 102.510 10 alfred m 14 69.0 112.511 11 duke m 14 63.5 102.512 12 g
18、uido m 15 67.0 133.013 13 james m 12 57.3 83.014 14 jeffery m 13 62.5 84.015 15 john m 12 59.0 99.516 16 philip m 16 72.0 150.017 17 robert m 12 64.8 128.018 18 thomas m 11 57.5 85.019 19 william m 15 66.5 112.0 names(studata) attach(studata) #将数据框调入内存 plot(weightheight,col=red) #体重对于身高的散点图 coplot(w
19、eightheight|sex,col=blue) #不同性别，体重与身高的散点图 coplot(weightheight|age,col=blue) #不同年龄，体重与身高的散点图 coplot(weightheight|age+sex,col=blue) #不同年龄和性别，体重与身高的散点图Ex3.8 x y f z contour(x,y,z,levels=c(0,1,2,3,4,5,10,15,20,30,40,50,60,80,100),col=blue) #二维等值线 persp(x,y,z,theta=120,phi=0,expand=0.7,col=lightblue) #三位
20、网格曲面Ex3.9 attach(studata) cor.test(height,weight) #Pearson相关性检验 Pearsons product-moment correlationdata: height and weightt = 7.5549, df = 17, p-value = 7.887e-07alternative hypothesis: true correlation is not equal to 095 percent confidence interval: 0.7044314 0.9523101sample estimates: cor0.877785
21、2由此可见身高和体重是相关的。Ex3.10Ex3.11上述两题原始数据太多，网上找不到，懒得录入。略。Ex4.2指数分布，的极大似然估计是n/sum(Xi) x lamda x mean(x)1 1平均为1个。Ex4.4 obj-function(x)f x0nlm(obj,x0)$minimum1 48.98425$estimate1 11.4127791 -0.8968052$gradient11.411401e-08 -1.493206e-07$code1 1$iterations1 16Ex4.5 x t.test(x)#t.test()做单样本正态分布区间估计One Sample t
22、-testdata:xt = 35.947, df = 9, p-value = 4.938e-11alternative hypothesis: true mean is not equal to 095 percent confidence interval:63.1585 71.6415sample estimates:mean of x67.4平均脉搏点估计为 67.4 ，95%区间估计为 63.1585 71.6415 。 t.test(x,alternative=less,mu=72)#t.test()做单样本正态分布单侧区间估计One Sample t-testdata:xt =
23、 -2.4534, df = 9, p-value = 0.01828alternative hypothesis: true mean is less than 7295 percent confidence interval:-Inf 70.83705sample estimates:mean of x67.4p值小于0.05，拒绝原假设，平均脉搏低于常人。要点：t.test()函数的用法。本例为单样本；可做双边和单侧检验。Ex4.6 x y t.test(x,y,var.equal=TRUE)Two Sample t-testdata:x and yt = 4.6287, df = 18
24、, p-value = 0.0002087alternative hypothesis: true difference in means is not equal to 095 percent confidence interval:7.53626 20.06374sample estimates:mean of x mean of y140.6126.8期望差的95%置信区间为7.53626 20.06374 。要点：t.test()可做两正态样本均值差估计。此例认为两样本方差相等。ps：我怎么觉得这题应该用配对t检验？Ex4.7 x y t.test(x,y,var.equal=TRUE
25、)Two Sample t-testdata:x and yt = 1.198, df = 7, p-value = 0.2699alternative hypothesis: true difference in means is not equal to 095 percent confidence interval:-0.0019963510.006096351sample estimates:mean of x mean of y0.141250.13920期望差的95%的区间估计为-0.0019963510.006096351Ex4.8接Ex4.6 var.test(x,y)F te
26、st to compare two variancesdata:x and yF = 0.2353, num df = 9, denom df = 9, p-value = 0.04229alternative hypothesis: true ratio of variances is not equal to 195 percent confidence interval:0.05845276 0.94743902sample estimates:ratio of variances0.2353305要点：var.test可做两样本方差比的估计。基于此结果可认为方差不等。因此，在Ex4.6
27、中，计算期望差时应该采取方差不等的参数。 t.test(x,y)Welch Two Sample t-testdata:x and yt = 4.6287, df = 13.014, p-value = 0.0004712alternative hypothesis: true difference in means is not equal to 095 percent confidence interval:7.359713 20.240287sample estimates:mean of x mean of y140.6126.8期望差的95%置信区间为 7.359713 20.240
28、287 。要点：t.test(x,y，var.equal=TRUE)做方差相等的两正态样本的均值差估计t.test(x,y)做方差不等的两正态样本的均值差估计Ex4.9 x n tmp mean(x)1 1.904762 mean(x)-tmp;mean(x)+tmp1 1.4940411 2.315483平均呼唤次数为1.90.95的置信区间为1.49,2,32Ex4.10 x t.test(x,alternative=greater)One Sample t-testdata:xt = 23.9693, df = 9, p-value = 9.148e-10alternative hypo
29、thesis: true mean is greater than 095 percent confidence interval:920.8443Infsample estimates:mean of x997.1灯泡平均寿命置信度95%的单侧置信下限为 920.8443要点：t.test()做单侧置信区间估计Ex5.1 x t.test(x,mu=225)One Sample t-testdata:xt = -3.4783, df = 19, p-value = 0.002516alternative hypothesis: true mean is not equal to 22595
30、percent confidence interval:172.3827 211.9173sample estimates:mean of x192.15原假设：油漆工人的血小板计数与正常成年男子无差异。备择假设：油漆工人的血小板计数与正常成年男子有差异。p值小于0.05，拒绝原假设，认为油漆工人的血小板计数与正常成年男子有差异。上述检验是双边检验。也可采用单边检验。 备择假设：油漆工人的血小板计数小于正常成年男子。 t.test(x,mu=225,alternative=less)One Sample t-testdata:xt = -3.4783, df = 19, p-value = 0
31、.001258alternative hypothesis: true mean is less than 22595 percent confidence interval:-Inf 208.4806sample estimates:mean of x192.15同样可得出油漆工人的血小板计数小于正常成年男子的结论。Ex5.2 pnorm(1000,mean(x),sd(x)1 0.5087941 x1 1067919 1196785 1126936918 1156920948 pnorm(1000,mean(x),sd(x)1 0.5087941x A B t.test(A,B,paire
32、d=TRUE)Paired t-testdata:A and Bt = -0.6513, df = 7, p-value = 0.5357alternative hypothesis: true difference in means is not equal to 095 percent confidence interval:-15.628898.87889sample estimates:mean of the differences-3.375p值大于0.05，接受原假设，两种方法治疗无差异。Ex5.4（1）正态性W检验：xy shapiro.test(x)Shapiro-Wilk n
33、ormality testdata:xW = 0.9699, p-value = 0.7527 shapiro.test(y)Shapiro-Wilk normality testdata:yW = 0.971, p-value = 0.7754ks检验： ks.test(x,pnorm,mean(x),sd(x)One-sample Kolmogorov-Smirnov testdata:xD = 0.1065, p-value = 0.977alternative hypothesis: two-sidedWarning message:In ks.test(x, pnorm, mean(
34、x), sd(x) :cannot compute correct p-values with ties ks.test(y,pnorm,mean(y),sd(y)One-sample Kolmogorov-Smirnov testdata:yD = 0.1197, p-value = 0.9368alternative hypothesis: two-sidedWarning message:In ks.test(y, pnorm, mean(y), sd(y) :cannot compute correct p-values with tiespearson拟合优度检验，以x为例。 sor
35、t(x)1 -5.6 -1.6 -1.4 -0.7 -0.50.40.71.72.02.52.52.83.03.54.0164.54.65.86.07.1 x1 p p1 0.04894712 0.24990009 0.62002288 0.90075856 0.98828138 p chisq.test(x1,p=p)Chi-squared test for given probabilitiesdata:x1X-squared = 0.5639, df = 4, p-value = 0.967Warning message:In chisq.test(x1, p = p) : Chi-sq
36、uared approximation may be incorrectp值为0.967，接受原假设，x符合正态分布。（2）方差相同模型t检验： t.test(x,y,var.equal=TRUE)Two Sample t-testdata:x and yt = -0.6419, df = 38, p-value = 0.5248alternative hypothesis: true difference in means is not equal to 095 percent confidence interval:-2.3261791.206179sample estimates:mean of x mean of y2.0652.625方差不同模型t检验： t.test(x,y)Welch Two Sample t-testdata:x and yt = -0.6419,
