R软件期末考试复习提纲

#期末考试专项复习#一、矩阵与数据框#1.生成特定的矩阵与数据框#矩阵#方法一a=array(1:10,dim=c(2,5))rownames(a)=1:2colnames(a)=c("one","two","three","four","five")adimnames(a)=list(1:2,c("one","two","three","four","five"))nrow=nrow(a)ncol=ncol(a)dim(a)#方法二a=matrix(1:10,nrow=2,byrow=F)rownames(a)=1:2colnames(a)=c("one","two","three","four","five")a=matrix(1:10,nrow=2,byrow=F,dimnames=list(1:2,c("one","two","three","four","five")))#数据框的生成df=data.frame(Name=c("Alice","Becka","James","Jeffrey","John"),Sex=c("F","F","M","M","M"),Age=c(13,13,12,13,12),Height=c(56.5,65.3,57.3,62.5,59.0),Weight=c(84.0,98.0,83.0,84.0,99.5));dfLst=list(Name=c("Alice","Becka","James","Jeffrey","John"), Sex=c("F","F","M","M","M"),Age=c(13,13,12,13,12),Height=c(56.5,65.3,57.3,62.5,59.0),Weight=c(84.0,98.0,83.0,84.0,99.5))LstLst[["Name"]]Lst["Name"]Lst[1]Lst[[1]]Lst$Namedf=as.data.frame(Lst)dfx=array(1:6,dim=c(2,3))as.data.frame(x)#数据框的引用df[1:2,3:5]df[["Height"]]df$Weightnames(df)#此属性一定非空rownames(df)=c("one","two","three","four","five") dfattach(df)r=Height/Weightrdf$r=rnames(df)detach()r=Height/Weight#2.矩阵的运算a=diag(1:3)a[2][1]=1a#1转置运算t(a)#2行列式det(a)#3向量积x=1:5y=2*1:5x%*%yt(x)%*%ycrossprod(x,y)#4向量的外积x%*%t(y)tcrossprod(x,y)outer(x,y)x%o%y#矩阵的乘法a=array(1:9,dim=c(3,3)) b=array(9:1,dim=c(3,3)) x=1:3a*ba%*%bx%*%a%*%xcrossprod(a,b)#t(a)%*%b tcrossprod(a,b)#a%*%t(b) #矩阵的逆solve(a)b=1:3solve(a,b)#ax=b的解#矩阵的特征值与特征向量sm=eigen(a)sme=diag(1:3)svde=svd(e)svdeattach(svde)u%*%diag(d)%*%t(v)#与矩阵运算有关的函数#取维数a=diag(1:4)nrow(a)ncol(a)#矩阵的合并x1=rbind(c(1,2),c(3,4))x2=x1+10x3=cbind(x1,x2)x3x4=rbind(x1,x2)x4cbind(1,x1)#矩阵的拉直a=matrix(1:6,ncol=2,dimnames=list(c("one","two","three"),c("first","second")),byrow=T)as.vector(a)#apply函数apply(a,1,mean)apply(a,2,sum)tapply(1:5,factor(c("f","f","m","m","m")),mean) #第二题#产生随机数x=rnorm(100,0,1)x#画随机数的直方图hist(x,freq=F)#核密度曲线density(x)lines(density(x),col="blue")#添加正态分布分布函数y=seq(-4,3,0.2)lines(y,dnorm(y,mean(x),sd(x)),col="red")#画随机数的经验分布函数z=rnorm(50,0,1)plot(ecdf(z),do.p=F,verticals=T)d=seq(-3,2,0.2)lines(d,pnorm(d,mean(z),sd(z)),col="red")y=rpois(100,2)plot(ecdf(y),col="red",verticals=T,do.p=F)x=0:8lines(x,ppois(x,mean(y)),col="blue")w=c(75,64,47.4,66.9,62.2,62.2,58.7,63.5,66.6,64.0,57.0,69.0 ,56.9,50.0,72.0)hist(w,freq=F)lines(density(w),col="blue")x=44:76lines(x,dnorm(x,mean(w),sd(w)),col="red")plot(ecdf(w),do.p=F,verticals=T)lines(x,pnorm(x,mean(w),sd(w)),col="red")#编写函数求随机数的各种描述统计量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(x^2)R=max(x)-min(x)#样本极差R1=quantile(x,3/4)-quantile(x,1/4)#四分位差sm=s/sqrt(n)#样本标准误g1=n/(n-1)/(n-2)*sum((x-m)^3)/s^3g2=n*(n+1)/(n-1)/(n-2)/(n-3)*sum((x-m)^4)/s^4-3*(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,s=1) }x=rnorm(100)data_outline(x)#第三题#r,p,q,drnorm(100,0,1)pnorm(1:5,0,1)dnorm(-3:3,0,1)qnorm(seq(0,1,0.25),0,1) rbeta(100,2,2)rbinom(100,100,0.5) pbinom(1:100,100,0.5) dbinom(1:5,100,0.5) qbinom(seq(0,1,0.1),100,0.5) rchisq(100,1）qchisq(seq(0,1,0.2),10) pchisq(1:10,10)dchisq(1:10,10)rexp(100,0.5)rpois(100,2)ppois(1:1000,2)dpois(1:100,2)runif(100,0,1)qunif(c(0,0.2,0.8),0,1)punif(seq(0,1,0.2),0,1)dunif(seq(0,1,0.01),0,1)rt(100,2)qt(0.8,2)pt(-3:3,2)dt(-3:3,2)rf(100,1,2)qf(0.8,1,2)#四置信区间#1#（1）sigma已知interval_estimate1=function(x,side=0,sigma=1,alpha=0.05){ xb=mean(x);n=length(x)if(side<0){tmp=sigma/sqrt(n)*qnorm(1-alpha)a=-Inf;b=xb+tmp}else if(side>0){tmp=sigma/sqrt(n)*qnorm(1-alpha)a=xb-tmp;b=Inf}else{tmp=sigma/sqrt(n)*qnorm(1-alpha/2)a=xb-tmp;b=xb+tmp}data.frame(mean=xb,a=a,b=b)}x=rnorm(100,0,4)interval_estimate1(x,sigma=4,side=0)interval_estimate1(x,sigma=4,side=-1)interval_estimate1(x,sigma=4,side=1)#（2）sigma未知interval_estimate2=function(x,side=0,alpha=0.05){ xb=mean(x);n=length(x)if(side<0){tmp=sd(x)/sqrt(n)*qt(1-alpha,n-1)a=-Inf;b=xb+tmp}else if(side>0){tmp=sd(x)/sqrt(n)*qt(1-alpha,n-1)a=xb-tmp;b=Inf}else{tmp=sd(x)/sqrt(n)*qt(1-alpha/2,n-1)a=xb-tmp;b=xb+tmp}data.frame(mean=xb,a=a,b=b)}x=rnorm(100,0,1)interval_estimate2(x,side=-1)interval_estimate2(x,side=0)interval_estimate2(x,side=1)t.test(x,side=-1)t.test(x,side=0)t.test(x,side=1)#两个总体sigma1=sigma2但未知interval_estimate3=function(x,y,alpha=0.05){xb=mean(x);yb=mean(y)n1=length(x);n2=length(y)sw=((n1-1)*var(x)+(n2-1)*var(y))/(n1+n1-2)tmp=sqrt((1/n1+1/n2)*sw)*qt(1-alpha/2,n1+n2-2) a=xb-yb-tmp;b=xb-yb+tmpdata.frame(mean=xb-yb,a=a,b=b)}x=rnorm(100,0,1)y=rnorm(100,1,1)interval_estimate3(x,y)-0.03643479 - 0.98699097#第五题假设检验#（1）sigam已知，双侧，检验mu=mu0 mean.test1=function(x,mu=0,sigma=1){ xb=mean(x);n=length(x)z=(xb-mu)/sigma*sqrt(n)p=pnorm(z)if(p<=1/2)P=2*pelseP=2*(1-p)data.frame(mean=xb,Z=z,p_value=P)}x=rnorm(100,0,2)mean.test1(x,mu=0,sigma=2)#(2)sigma未知，双侧，检验mu=mu0 mean.test2=function(x,mu=0){xb=mean(x);n=length(x)z=(xb-mu)/sd(x)*sqrt(n)p=pt(z,n-1)if(p<=1/2)elseP=2*(1-p)data.frame(mean=xb,Z=z,p_value=P)}x=rnorm(100)mean.test2(x,mu=0)t.test(x,mu=0,alt="two.side")#两个总体sigma1=sigma2但未知，检验mu1=mu2 mean.test3=function(x,y,mu=0){xb=mean(x);yb=mean(y)n1=length(x);n2=length(y)sw=((n1-1)*var(x)+(n2-1)*var(y))/(n1+n2-2)t=(xb-yb-mu)/sqrt(sw*(1/n1+1/n2))p=pt(t,n1+n2-1)if(p<=1/2)P=2*pelseP=2*(1-p)data.frame(mean=xb-yb,T=t,p_value=P)}x=rnorm(100,0,1)y=rnorm(100,2,1)mean.test3(x,y,mu=-2)t.test(x,y,var.equal=T,mu=-2)x=rnorm(100,0,1)y=rnorm(100,0,2)mean.test3(x,y)t.test(x,y,var.equal=T)#第六题调用R函数#k-s检验两组数是否同分布x=rnorm(100,0,1)y=rt(100,5)z=rnorm(100,0,1)ks.test(x,y),alt="l"ks.test(x,z)#检验一组数是否服从已知分布ks.test(x,"pnorm",0,2)ks.test(x,"pt",1)#符号检验两组数是否有差异x=rbinom(100,100,0.5)binom.test(sum(x>=50),100)y=rbinom(100,100,0.4)binom.test(sum(x<y),length(x)),alt="g"#wilcoxon符号秩和检验（精确或大样本近似）#wilcox.test(x,y,alt,mu,paired=F,exact=NULL,correct=T,conf.int=F, conf.level=0.95)r=runif(100,136,145)wilcox.test(r,mu=140,alt="l",exact=F,conf.int=T,correct=F)x=rnorm(100)y=rnorm(100)wilcox.test(x,y,paired=T,alt="g")wilcox.test(x-y,alt="g")binom.test(sum(x>y),length(x),alt="g")#第七题#相关性检验x=1:6y=6:1z=2:7cor.test(x,y,alt="g",method="spearman")cor.test(x,z,alt="g",method="spearman")#无节点x=c(2,3,1,4,5,8,6)y=1:7cor.test(x,y,alt="g",method="spearman",correct=T)n=length(x)r=rank(x)rR=rank(y)Rs=sum((r-R)^2)rho=1-6*s/n/(n^2-1)rho#有节点x=c(2,3,4,4,5,8,6)y=1:7cor.test(x,y,alt="g",method="spearman",correct=T)exact=F, n=length(x)r=rank(x)rR=rank(y)Rsxy=sum((r*R))sx=sum(r^2)sy=sum(y^2)t=n*((n+1)/2)^2rho=(sxy-t)/sqrt(sx-t)/sqrt(sy-t)rho#第八题回归x=c(seq(0.1,0.18,0.01),0.20,0.21,0.23)y=c(42,43.5,45,45.5,45,47.5,49,53,50,55,55,60)#散点图plot(x,y)#做回归lm.sol=lm(y~x)lm.sol=lm(y~1+x)#汇总统计量summary(lm.sol)#画回归线abline(lm.sol)#求回归系数的区间估计beta.int=function(lm.sol,alpha=0.05){A=summary(lm.sol)$coefficientsdf=lm.sol$df.residualleft=A[,1]-A[,2]*qt(1-alpha/2,df)right=A[,1]+A[,2]*qt(1-alpha/2,df)rowname=dimnames(A)[[1]]#列表的第一个元素colname=c("estimate","left","right")matrix(c(A[,1],left,right),ncol=3,dimnames=list(rowname,colname)) }beta.int(lm.sol)#对新的自变量求因变量的预测值及预测区间new=data.frame(x=c(0.16,0.19,1.20))lm.predict=predict(lm.sol,new)lm.predictlm.predict=predict(lm.sol,new,interval="confidence",level=0.95) lm.predict=predict(lm.sol,new,interval="prediction",level=0.95) #残差图resid=lm.sol$residualsplot(resid)y.res=resid(lm.sol)y.fit=predict(lm.sol)plot(y.res~y.fit)plot(y.res~x)plot(lm.sol,1)plot(lm.sol,2)plot(lm.sol,3)plot(lm.sol,4)。