R语言讲义(包括各种回归)

R语言讲义,免费(没有权力和铜臭)资源公开,可改变代码(不是黑盒子,也不是吝啬鬼,透明是防止“腐败”的最好方式)容易学习。可编程以实行复杂的课题可扩展:通过数千个网上提供的适用于不同领域、不同目的、不同方法的软件包来实现你的目标。也可以把你的方法贡献出来功能强大(绘图功能,优秀的内在帮助系统,R社区的支持，不断更新，不断修正)没有任何一个商业软件有如此多和如此新的算法,世界应用统计学家大都把自己的方法首先以R来实现，并尽量放到R网站上一年多，R网站的软件包数量增加了两倍，从近1000个到近3000多个。大都都有关于计算、演示和输入输出方法的函数和例子数据除非得到巨额资助(或者永远使用盗版软件),没有理由在公立学校教授商业软件绝大多数美国统计研究生都会的语言(Berkeley统计和应用数学本科都开设R语言课)我的很大一部分数据分析知识的来源就是R.我都能学会,并且到处宣传和普及,相信你们会做得更好!,点击CRAN得到一批镜像网站,下载R(/),点击镜像网站比如Berkeley,Packages（每个都有大量数据和可以读写修改的函数/程序）,baseTheRBasePackagebootBootstrapR(S-Plus)Functions(Canty)classFunctionsforClassificationclusterClusterAnalysisExtendedRousseeuwetal.concordConcordanceandreliabilitydatasetsTheRDatasetsPackageexactRankTestsExactDistributionsforRankandPermutationTestsforeignReadDataStoredbyMinitab,S,SAS,SPSS,Stata,Systat,dBase,.graphicsTheRGraphicsPackagegrDevicesTheRGraphicsDevicesandSupportforColoursandFontsgridTheGridGraphicsPackageKernSmoothFunctionsforkernelsmoothingforWandsample(1:10,3)#随机种子!z=sample(1:200000,10000)z1:10#向量下标y=c(1,3,7,3,4,2)zy,一些基本运算例子,z=sample(x,20,rep=T)z(z1=unique(z);length(z1)z=sample(x,100,rep=T)xz=setdiff(x,z)sort(union(xz,z)sort(union(xz,z)=xsetequal(union(xz,z),x)intersect(1:10,7:50)sample(1:100,20,prob=1:100),一些基本运算例子,pi*102#能够用?”*”来看基本算术运算方法*(pi,(10,2)pi*(1:10)2x-pi*102xprint(x)(x=pi*102)pi(1:5)print(x,digits=12)class(x)typeof(x),一些基本运算例子,class(cars)typeof(cars)names(cars)summary(cars)str(cars)s(cars)class(distspeed)plot(distspeed,cars),一些基本运算例子,head(cars)#cars1:6,tail(cars)ncol(cars);nrow(cars)dim(cars)lm(distspeed,data=cars)cars$qspeed=cut(cars$speed,breaks=quantile(cars$speed),include.lowest=TRUE)names(cars)cars3table(cars3)is.factor(cars$qspeed)plot(distqspeed,data=cars)(a=lm(distqspeed,data=cars)summary(a),一些基本运算例子,x-round(runif(20,0,20),digits=2)summary(x)min(x);max(x)median(x)#medianmean(x)#meanvar(x)#variancesd(x)#standarddeviationsqrt(var(x)rank(x)#rankorder(x)xorder(x)sort(x)sort(x,decreasing=T)#sort(x,dec=T)sum(x);length(x)round(x),一些基本运算例子,fivenum(x)#quantilesquantile(x)#quantiles(differentconvention)有多种定义quantile(x,c(0,.33,.66,1)mad(x)#normalizedmeandeviationtothemedian(“medianaveragedistance“)可用?mad查看cummax(x)cummin(x)cumprod(x)cor(x,sin(x/20)#correlation,一些基本运算例子,#直方图x-rnorm(200)hist(x,col=lightblue)rug(x)#茎叶图stem(x)#散点图N-500 x-rnorm(N)y0);(1:10)x0diff(x)diff(x,lag=2)x=matrix(1:20,4,5);xx=matrix(1:20,4,5,byrow=T);xt(x)x=matrix(sample(1:100,20),4,5)2*xx+5y=matrix(sample(1:100,20),5,4)x+t(y)(z=x%*%y)z1=solve(z)#solve(a,b)可以解ax=b方程z1%*%zround(z1%*%z,14),矩阵,nrow(x);ncol(x);dim(x)#行列数目x=matrix(rnorm(24),4,6)xc(2,1),#第2和第1行x,c(1,3)#第1和第3列x2,1#第2,1元素xx,10,1#第1列大于0的元素sum(x,10)#第1列大于0的元素的个数sum(x,10apply(x,2,sum),矩阵/高维数组,#上下三角阵x=matrix(rnorm(24),4,6)diag(x)diag(1:5)diag(5)xlower.tri(x)=0#xupper.tri(x)=0;diag(x)=0 x=array(runif(24),c(4,3,2);xis.matrix(x)#可由dim(x)得到维数(4,3,2)is.matrix(x1,)x=array(1:24,c(4,3,2)xc(1,3),x=array(1:24,c(4,3,2)apply(x,1,mean)apply(x,1:2,sum)apply(x,c(1,3),prod),矩阵/高维数组/scale,#矩阵与向量之间的运算x=matrix(1:20,5,4)sweep(x,1,1:5,*)x*1:5sweep(x,2,1:4,+)(x=matrix(sample(1:100,24),6,4);(x1=scale(x)(x2=scale(x,scale=F);(x3=scale(x,center=F)round(apply(x1,2,mean),14)apply(x1,2,sd)round(apply(x2,2,mean),14);apply(x2,2,sd)round(apply(x3,2,mean),14);apply(x3,2,sd),Data.frame,x=matrix(1:6,2,3)z=data.frame(x);zz$X2attributes(z)names(z)=c(TOYOTA,GM,HUNDA)s(z)=c(2001,2002)Zattach(x)GMdetach(x)GMsapply(z,is.numeric)#apply(z,2,is.numeric),缺失值问题等,airqualitycomplete.cases(airquality)#哪一行没有缺失值which(complete.cases(airquality)=F)sum(complete.cases(airquality)na.omit(airquality)#append,cbind,vbindx=1:10;x12=3(x1=append(x,77,after=5)cbind(1:3,4:6);rbind(1:3,4:6)#去掉矩阵重复的行(x=rbind(1:5,runif(5),runif(5),1:5,7:11)x!duplicated(x),unique(x),List,#list可以是任何对象的集合(包括lists)z=list(1:3,Tom=c(1:2,a=list(R,letters1:5),w=hi!)z1;z2z$Tz$T$a2z$T3z$T$wattributes(airquality)#属性!airquality$Ozoneattributes(matrix(1:6,2,3),CategoricaldataAsurveyaskspeopleiftheysmokeornot.ThedataisYes,No,No,Yes,Yesx=c(Yes,No,No,Yes,Yes)table(x);xfactor(x),Barplot:Suppose,agroupof25peoplearesurveyedastotheirbeer-drinkingpreference.Thecategorieswere(1)Domesticcan,(2)Domesticbottle,(3)Microbrewand(4)import.Therawdatais3411343313212123231111431beer=scan()3411343313212123231111431barplot(beer)#thisisntcorrectbarplot(table(beer)#Yes,callwithsummarizeddatabarplot(table(beer)/length(beer)#dividebynforproportiontable(beer)/length(beer),Table/categoricaldata,library(MASS)quineattach(quine)table(Age)table(Sex,Age);tab=xtabs(Sex+Age,quine);unclass(tab)tapply(Days,Age,mean)tapply(Days,list(Sex,Age),mean)#apply,sapply,tapply,lapply,smokes=c(Y,N,N,Y,N,Y,Y,Y,N,Y)amount=c(1,2,2,3,3,1,2,1,3,2)(tmp=table(smokes,amount)#storethetableoptions(digits=3)#onlyprint3decimalplacesprop.table(tmp,1)#therowssumto1nowprop.table(tmp,2)#thecolumnssumto1now#上两行等价于下面两行sweep(tmp,1,margin.table(tmp,1),/)sweep(tmp,2,margin.table(tmp,2),/)prop.table(tmp)#amount#allthenumberssumto1options(digits=7)#restorethenumberofdigits,array/matrixtabledata.frame,#Startwithacontingencytable.ftable(Titanic,row.vars=1:3)ftable(Titanic,row.vars=1:2)data.frame(Titanic)#把array变成data.framea=xtabs(FreqSurvived+Sex,w)biplot(corresp(a,nf=2)#应用之一#Startwithadataframe.str(mtcars)x-ftable(mtcarsc(cyl,vs,am,gear)x#为array，其维的次序为(cyl,vs,am,gear)ftable(x,row.vars=c(2,4)#从x（array）确定表的行变量#Startwithexpressions,usetable()sdnntochangelabelsftable(mtcars$cyl,mtcars$vs,mtcars$am,mtcars$gear,row.vars=c(2,4),dnn=c(Cylinders,V/S,Transmission,Gears)ftable(vscarb,mtcars)#vs是列，carb是行#或ftable(mtcars$vsmtcars$carb)ftable(carbvs,mtcars)#vs是行，carb是列ftable(mtcars,c(8,11)#和上面ftable(carbvs,mtcars)等价ftable(breakswool+tension,warpbreaks)#as.data.frame(DF-as.data.frame(UCBAdmissions)#等价于data.frame(UCBAdmissions)xtabs(FreqAdmit+Gender+Dept,DF)#:把方阵变成原来的列联表(a=xtabs(FreqAdmit+Gender,data=DF)#如无频数(权)，左边为空,写函数,ss=function(n=100)z=2;for(iin2:n)if(any(i%2:(i-1)=0)=F)z=c(z,i);return(z)fix(ss)ss()t1=Sys.time()ss(10000)Sys.time()-t1system.time(ss(10000)#函数可以不写return,这时最后一个值为return的值.为了输出多个值最好使用list,#几个图一起:par(mfrow=c(2,4)#par(mfcol=c(2,4)layout(matrix(c(1,1,1,2,3,4,2,3,4),nr=3,byrow=T)hist(rnorm(100),col=Red,10)hist(rnorm(100),col=Blue,8)hist(rnorm(100),col=Green)hist(rnorm(100),col=Brown)#par(mar=c(bottom,left,top,right)设置边缘#缺省值c(5,4,4,2)+0.1(英寸)spring=data.frame(compression=c(41,39,43,53,42,48,47,46),distance=c(120,114,132,157,122,144,137,141)attach(spring)#(Hookeslaw:f=.5ks)par(mfcol=c(2,2)plot(distancecompression)plot(distancecompression,type=l)plot(compression,distance,type=o)plot(compression,distance,type=b),关于画图,关于画图,par(mfrow=c(2,2)#准备画2x2的4个图plot(compression,distance,main=HookesLaw)#只有标题plot(compression,distance,main=HookesLaw,xlab=x,ylab=y)#标题+x,y标记identify(compression,distance)#标出点号码plot(compression,distance,main=HookesLaw)#只有标题text(46,120,expression(f=frac(1,2)*k*s)#在指定位写入文字plot(compression,distance,main=HookesLaw)#只有标题的图text(locator(2),c(Iamhere!,youarethere!)#在点击的两个位置写入文字par(mfrow=c(1,1)plot(1:10,sin(1:10),type=l,lty=2,col=4,main=paste(strwrap(Thetitleistoolong,andIhatetomakeitshorter,!#$%data(Animals);attach(Animals)par(mfrow=c(2,2)plot(body,brain)plot(sqrt(body),sqrt(brain)plot(body)0.1,(brain)0.1)plot(log(body),log(brain)#或者plot(brainbody,log=xy)par(mfrow=c(1,1)par(cex=0.7,mex=0.7)#character(cex)barplot(rnorm(15,10,3),col=1:15)palette(rainbow(15);barplot(rnorm(15,10,3),col=1:15)palette(heat.colors(15);barplot(rnorm(15,10,3),col=1:15)palette(terrain.colors(15);barplot(rnorm(15,10,3),col=1:15)palette(topo.colors(15);barplot(rnorm(15,10,3),col=1:15)palette(cm.colors(15);barplot(rnorm(15,10,3),col=1:15)palette(gray(seq(0,0.9,l=15);barplot(rnorm(15,10,3),col=1:15)palette(grey(seq(0,0.5,l=15);barplot(rnorm(15,10,3),col=1:15)palette(default)par(mfrow=c(1,1),关于画图,#matplotsines=outer(1:20,1:4,function(x,y)sin(x/20*pi*y)matplot(sines,pch=1:4,type=o,col=rainbow(ncol(sines)#legendx-seq(-pi,pi,len=65)plot(x,sin(x),type=l,ylim=c(-1.2,1.8),col=3,lty=2)points(x,cos(x),pch=3,col=4)lines(x,tan(x),type=b,lty=1,pch=4,col=6)title(legend(.,lty=c(2,-1,1),pch=c(-1,3,4),merge=TRUE),cex.main=1.1)legend(-1,1.9,c(sin,cos,tan),col=c(3,4,6),lty=c(2,-1,1),pch=c(-1,3,4),merge=TRUE,bg=gray90),关于画图,#barplotandtablepar(mfrow=c(2,2)tN=table(Ni=rpois(100,lambda=5);tNr=barplot(tN,col=gray)lines(r,tN,type=h,col=red,lwd=2)#-type=hplotting*is*barplotbarplot(tN,space=1.5,axisnames=FALSE,sub=barplot(.,space=0,axisnames=FALSE)#如space=1.5则有稀牙缝barplot(tN,space=0,axisnames=FALSE,sub=barplot(.,space=0,axisnames=FALSE)pie(tN)#pieplotpar(mfrow=c(1,1)#加gridplot(1:3)grid(10,5,lwd=2)dev.set;dev.off;dev.list,关于画图(pairs/三维),#pairs#data(iris)pairs(iris1:4,main=AndersonsIrisData-3species,pch=21,bg=c(red,green3,blue)unclass(iris$Species)#iris为150 x5数据,这里是4个数量变量的点图(最后一个是分类变量(iris$Species)#stars#data(mtcars)stars(mtcars,1:7,key.loc=c(14,1.5),main=MotorTrendCars:fullstars(),flip.labels=FALSE)#mtcars为32x11数据,这里只选前7个数量变量的点图#perspx-seq(-10,10,length=30)y-xf-function(x,y)r-sqrt(x2+y2);10*sin(r)/rz-outer(x,y,f)zis.na(z)-1persp(x,y,z,theta=30,phi=30,expand=0.5,col=lightblue),data(volcano)par(mfrow=c(2,2)z-2*volcano#Exaggeratethereliefx-10*(1:nrow(z)#10meterspacing(StoN)y-10*(1:ncol(z)#10meterspacing(EtoW)#Dontdrawthegridlines:border=NA#par(bg=slategray)persp(x,y,z,theta=135,phi=30,col=green3,scale=FALSE,ltheta=-120,shade=0.75,border=NA,box=FALSE)par(bg=white)#contourrx-range(x-10*1:nrow(volcano)ry-range(y-10*1:ncol(volcano)ry-ry+c(-1,1)*(diff(rx)-diff(ry)/2tcol-terrain.colors(12)opar-par(pty=s,bg=lightcyan);par(opar)plot(x=0,y=0,type=n,xlim=rx,ylim=ry,xlab=,ylab=)u-par(usr)rect(u1,u3,u2,u4,col=tcol8,border=“red”)#rect画矩形contour(x,y,volcano,col=tcol2,lty=solid,add=TRUE,vfont=c(sansserif,plain)title(ATopographicMapofMaungaWhau,font=4)abline(h=200*0:4,v=200*0:4,col=lightgray,lty=2,lwd=0.1);par(opar)#imagex-10*(1:nrow(volcano)y-10*(1:ncol(volcano)image(x,y,volcano,col=terrain.colors(100),axes=FALSE)contour(x,y,volcano,levels=seq(90,200,by=5),add=TRUE,col=peru)axis(1,at=seq(100,800,by=100)axis(2,at=seq(100,600,by=100)box()title(main=MaungaWhauVolcano,font.main=4)par(mfrow=c(1,1),关于画图(三维),多窗口操作,x11()plot(1:10)x11()plot(rnorm(10)dev.set(dev.prev()abline(0,1)#throughthe1:10pointsdev.set(dev.next()abline(h=0,col=gray)#fortheresidualplotdev.set(dev.prev()dev.off();dev.off()#-closethetwoXdevices#dev.list(),画图杂项,#模拟布朗运动n=100;x=cumsum(rnorm(100);y=cumsum(rnorm(100);plot(x,y,type=l)x=0;y=0;plot(100,ylim=c(-15,15),xlim=c(-15,15)#慢动作for(iin1:200)x1=x+rnorm(1);y1=y+rnorm(1);segments(x,y,x1,y1);x=x1;y=y1Sys.sleep(.05)#散点大小同因变量值成比例x=1:10;y=runif(10)symbols(x,y,circle=y/2,inches=F,bg=x)#数据框的每一列都做Q-Q图table=data.frame(x1=rnorm(100),x2=rnorm(100,1,1)par(ask=TRUE)#waitforchanging等待页面改变的确认results=apply(table,2,qqnorm)par(ask=FALSE)#在一个图上添加一个小图x=rnorm(100)hist(x)op=par(fig=c(.02,.5,.5,.98),new=TRUE)boxplot(x)#数学符号x=1:10;plot(x,type=n)text(3,2,expression(paste(Temperature(,degree,C)in2003)text(4,4,expression(bar(x)=sum(frac(xi,n),i=1,n)text(6,6,expression(hat(beta)=(Xt*X).1*Xt*y)text(8,8,expression(zi=sqrt(xi2+yi2),改变大小写字母,x=c(I,am,A,BIG,Cat)tolower(x)toupper(x),R统计模型讲义,#基础x=rnorm(20,10)t.test(x,m=9,alt=greater)t.test(x1:10,m=9,alt=greater)$p.valuet.test(x,con=.90)$confx=rnorm(30,10);y=rnorm(30,10.1)t.test(x,y,alt=less)library(TeachingDemos)ci.examp()run.ci.examp()vis.boxcox()vis.boxcoxu(),回归,#相关x=rnorm(20);y=rnorm(20);cor(x,y)cor(x,y,method=kendall);cor(x,y,method=spearman)cor.test(x,y);cor.test(x,y,method=kendall);cor.test(x,y,method=spearman)cor.test(x,y,method=kendall)$p.value#相关吗?x=rnorm(3);y=rnorm(3);cor(x,y);cor.test(x,y)$p.valuelibrary(TeachingDemos)put.points.demo(),相关,基本原理,#基本原理set.seed(100)x1=rnorm(100);x2=rnorm(100);eps=rnorm(100)y=5+2*x1-3*x2+epsa=lm(yx1+x2)(lm(y0+x1+x2)#不要截距:等价于(lm(y-1+x1+x2)summary(a);anova(a)names(a)shapiro.test(a$res)qqnorm(a$res);qqline(a$res)#数学原理x=cbind(1,x1,x2)dim(x)b=solve(t(x)%*%x)%*%t(x)%*%yba$coe,63,例1：cross.txt,例1:cross.txt,w=read.table(cross.txt,header=T)head(w)plot(yx,w);summary(w)a=lm(yx+z,w)summary(a)anova(a)qqnorm(a$res);qqline(a$res)shapiro.test(a$res)a1=lm(yx*z,w)summary(a1);anova(a1)qqnorm(a1$res);qqline(a1$res)shapiro.test(a1$res)anova(a,a1)library(party)#更简单的方法wt=mob(yx|z,data=w)coef(wt);plot(wt)plot(yx,w);abline(coef(wt)1,col=2);abline(coef(wt)2,col=4),65,回归方程,66,PoisonExperimentThedatagivethesurvivaltimes(in10hourunits)ina3x4factorialexperiment,thefactorsbeing(a)threepoisonsand(b)fourtreatments.Eachcombinationofthetwofactorsisusedforfouranimals,theallocationtoanimalsbeingcompletelyrandomized.Box,G.E.P.,andCox,D.R.(1964).Ananalysisoftransformations(withDiscussion).J.R.Statist.Soc.B,26,211-252./data/general/poison.html,67,例2：poison.txt：3种毒药，4种处理，用于动物实验，48个观测值,回归,setwd(f:/2010stat)w=read.table(poison.txt,head=T)head(w);tail(w)str(w);summary(w)dim(w)w$Poison=factor(w$Poison)w$Treatment=factor(w$Treatment)pairs(w)#直接回归a=lm(TimePoison*Treatment,w)anova(a)a=lm(Time.,w)anova(a)qqnorm(a$res);qqline(a$res)shapiro.test(a$res)#变换a=lm(1/TimePoison+Treatment,w)anova(a)qqnorm(a$res);qqline(a$res)shapiro.test(a$res)summary(a),逐步回归(step或stepAICMASS),library(MASS)quine.hi-aov(log(Days+2.5).4,quine)quine.nxt-update(quine.hi,.-Eth:Sex:Age:Lrn)quine.stp-stepAIC(quine.nxt,scope=list(upper=Eth*Sex*Age*Lrn,lower=1),trace=FALSE)quine.stp$anovacpus1-cpusattach(cpus)for(vinnames(cpus)2:7)cpus1v-cut(cpusv,unique(quantile(cpusv),include.lowest=TRUE)detach()cpus0-cpus1,2:8#excludesnames,authorspredictionscpus.samp-sample(1:209,100)cpus.lm-lm(log10(perf).,data=cpus1cpus.samp,2:8)cpus.lm2-stepAIC(cpus.lm,trace=FALSE)cpus.lm2$anova,example(birthwt)birthwt.glm-glm(low.,family=binomial,data=bwt)birthwt.step-stepAIC(birthwt.glm,trace=FALSE)birthwt.step$anovabirthwt.step2-stepAIC(birthwt.glm,.2+I(scale(age)2)+I(scale(lwt)2),trace=FALSE)birthwt.step2$anovaquine.nb-glm.nb(Days.4,data=quine)quine.nb2-stepAIC(quine.nb)quine.nb2$anova,71,变换并拟合主效应,72,结果解释,异方差时的考虑,Box-Cox变换加权最小二乘(如:lm中weights=1/x2)异常值处理不一定是一个模型等等(要做探索分析),多项式回归,#多项式回归y-cars$dist;x-cars$speedo=order(x)plot(yx)do.it-function(model,col)r-lm(model);yp-predict(r)lines(ypoxo,col=col,lwd=3)do.it(yx,col=red)do.it(yx+I(x2),col=blue)do.it(y-1+I(x2),col=green)legend(par(usr)1,par(usr)4,c(affinefunction,degree-2polynomial,degree2monomial),lwd=3,col=c(red,blue,green),)n-100 x-runif(n,min=-4,max=4)+sign(x)*.2y-1/x+rnorm(n)#双曲线plot(yx)lm(1/yx)n-100 x-rlnorm(n)3.14#alog-normaldistributionisaprobabilitydistributionofarandomvariablewhoselogarithmisnormallydistributed.y-x-.1*rlnorm(n)plot(yx)lm(log(y)log(x),多项式p,q正交,如,#关于正交多项式y-cars$dist;x-cars$speed#非正交:一项加一项(互相影响,显著的系数变成不显著)summary(lm(yx)summary(lm(yx+I(x2)summary(lm(yx+I(x2)+I(x3)summary(lm(yx+I(x2)+I(x3)+I(x4)summary(lm(yx+I(x2)+I(x3)+I(x4)+I(x5)#正交:不会改变开始显著的系数poly:ComputeOrthogonalPolynomialssummary(lm(ypoly(x,1)summary(lm(ypoly(x,2)summary(lm(ypoly(x,3)summary(lm(ypoly(x,4)summary(lm(ypoly(x,5),#对正交多项式点出系数的p-valuesn-5p-matrix(nrow=n,ncol=n+1)for(iin1:n)pi,1:(i+1)-summary(lm(ypoly(x,i)$coefficients,4matplot(p,type=l,lty=1,lwd=3)legend(par(usr)1,par(usr)4,as.character(1:n),lwd=3,lty=1,col=1:n)title(main=Evolutionofthep-values(orthonormalpolynomials)#对非正交多项式,点出系数的p-valuesp-matrix(nrow=n,ncol=n+1)p1,1:2-summary(lm(yx)$coefficients,4p2,1:3-summary(lm(yx+I(x2)$coefficients,4p3,1:4-summary(lm(yx+I(x2)+I(x3)$coefficients,4p4,1:5-summary(lm(yx+I(x2)+I(x3)+I(x4)$coefficients,4p5,1:6-summary(lm(yx+I(x2)+I(x3)+I(x4)+I(x5)$coefficients,4matplot(p,type=l,lty=1,lwd=3)legend(par(usr)1,par(usr)4,as.character(1:n),lwd=3,lty=1,col=1:n)title(main=Evolutionofthep-values(nonorthonormalpolynomials)“),#例子data(beavers)y-beaver1$tempx-1:length(y)plot(yx)for(iin1:10)r-lm(ypoly(x,i)lines(predict(r),type=l,col=i)summary(r),非参数回归,#非参数:样条plot(quakes$long,quakes$lat)lines(smooth.spline(quakes$long,quakes$lat),col=red,lwd=3)library(Design)#rcs:DesignSpecialTransformationFunctions#4-nodespliner3-lm(quakes$latrcs(quakes$long)plot(quakes$latquakes$long)o-order(quakes$long)lines(quakes$longo,predict(r)o,col=red,lwd=3)r-lm(quakes$latrcs(quakes$long,10)lines(quakes$longo,predict(r)o,col=blue,lwd=6,lty=3)title(main=Regressionwithrcs)legend(par(usr)1,par(usr)3,yjust=0,c(4knots,10knots),lwd=c(3,3),lty=c(1,3),col=c(red,blue)#更多的样条library(splines)data(quakes)x-quakes,2y-quakes,1o-order(x)x-xoy-yor1-lm(ybs(x,df=10)r2-lm(yns(x,df=6)plot(yx)lines(predict(r1)x,col=red,lwd=3)lines(predict(r2)x,col=green,lwd=3),#核光滑plot(cars$speed,cars$dist)lines(ksmooth(cars$speed,cars$dist,normal,bandwidth=2),col=red)lines(ksmooth(cars$speed,cars$dist,normal,bandwidth=5),col=green)lines(ksmooth(cars$speed,cars$dist,normal,bandwidth=10),col=blue)#加权局部最小二乘.WeightedLocalLeastSquares:loess#各种核函数curve(dnorm(x),xlim=c(-3,3),ylim=c(0,1.1)x-seq(-3,3,length=200)D.Epanechikov-function(t)ifelse(abs(t)1,3/4*(1-t2),0)lines(D.Epanechikov(x)x,col=red)D.tricube-function(t)#akatriweightkernelifelse(abs(t)1,(1-abs(t)3)3,0)lines(D.tricube(x)x,col=blue)legend(par(usr)1,par(usr)4,yjust=1,c(noyaugaussien,noyaudEpanechikov,noyautricub