R语言讲义(包括各种回归).ppt

R语言讲义 吴喜之 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 http www r project org 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 graphicsTheRGraphicsPackagegrDevicesTheRGraphicsDevicesandSupportforColoursandFontsgridTheGridGraphicsPackageKernSmoothFunctionsforkernelsmoothingforWand Jones 1995 latticeLatticeGraphicsInterfacetoolsToolsforPackageDevelopmentutilsTheRUtilsPackage Packages 继续 MASSMainPackageofVenablesandRipley sMASSmethodsFormalMethodsandClassesmgcvGAMswithGCVsmoothnessestimationandGAMMsbyREML PQLmulttestResampling basedmultiplehypothesistestingnlmeLinearandnonlinearmixedeffectsmodelsnnetFeed forwardNeuralNetworksandMultinomialLog LinearModelsnortestTestsforNormalityoutliersTestsforoutliersplsPartialLeastSquaresRegression PLSR andPrincipalComponentRegression PCR pls pcrPLSandPCRfunctionsrpartRecursivePartitioningSAGxStatisticalAnalysisoftheGeneChipsmaStatisticalMicroarrayAnalysisspatialFunctionsforKrigingandPointPatternAnalysissplinesRegressionSplineFunctionsandClassesstatsTheRStatsPackagestats4StatisticalFunctionsusingS4ClassessurvivalSurvivalanalysis includingpenalisedlikelihood tcltkTcl TkInterfacetoolsToolsforPackageDevelopmentutilsTheRUtilsPackage Packages 网上 网上还有许多 所有这些Packages可以自由下载 Base中的package包含常用的函数和数据而其他的packages包含各个方向统计学家自己发展的方法和数据 希望你是下一个加盟这些packages的作者之一 安装Packages 关机时是否保存 如果是 你的运算结果 赋值的变量及函数等 保存在一个文件 名字为 RData 中 下次开机时还会重新载入 如果你不要则删去该文件即可 其实 除非是做一个需要多次才完成的大课题 一般你都不想保存 你所用的代码可以以程序脚本形式 R 注意 一定要自己敲入 R 没有默认 保存 几个有用的函数 函数 f x 名字 变元 getwd setwd dir f 2010stat 或setwd f 2010stat getwd x rnorm 100 ls rnorm 或help rnorm apropos norm identical 1 10 1 10 identical 1 10 as numeric 1 10 identical 1 10 as integer 1 10 赋值和运算 z rnorm 1000000 4 0 1 median z 赋值 可以用 y w简单数学运算有 mod 整数除法 等等常用的数学函数有 abs sign log log2 log10 logb expm1 log1p x sqrt exp sin cos tan acos asin atan cosh sinh tanh 赋值和运算 round floor ceilinggamma lgamma digammaandtrigamma sum prod cumsum cumprodmax min cummax cummin pmax pmin rangemean length var duplicated uniqueunion intersect setdiff 从高到低的运算次序 一些基本运算例子 x 1 100 x 1 100 sample x 20 set seed 0 sample 1 10 3 随机种子 z sample 1 200000 10000 z 1 10 向量下标y c 1 3 7 3 4 2 z y 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 10 2 能够用 来看基本算术运算方法 pi 10 2 pi 1 10 2x pi 10 2xprint x x pi 10 2 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 row names cars class dist speed plot dist speed cars 一些基本运算例子 head cars cars 1 6 tail cars ncol cars nrow cars dim cars lm dist speed data cars cars qspeed cut cars speed breaks quantile cars speed include lowest TRUE names cars cars 3 table cars 3 is factor cars qspeed plot dist qspeed data cars a lm dist qspeed data cars summaryu 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 x order 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 y x rnorm N plot y x a lm y x abline a col red 或者abline lm y x col red print HelloWorld paste x的最小值 min x cat end document n file RESULT tex append TRUE demo graphics 演示画图 一些基本运算例子 复数运算x 2 3i z complex real rnorm 10 imaginary rnorm 10 complex re rnorm 3 im rnorm 3 Re z Im z Mod z Arg z choose 3 2 factorial 6 解方程f function x x 3 2 x 1uniroot f c 0 2 迭代 如果知道根为极值f function x x 2 2 x 1optimize f c 2 2 分布和产生随机数 正态分布 pnorm 1 2 2 1 dnorm 1 2 2 1 qnorm 7 2 1 rnorm 10 0 1 rnorm 10 t分布 pt 1 2 1 dt 1 2 2 qt 7 1 rt 10 1 此外还有指数分布 F分布 卡方 分布 Beta分布 二项分布 Cauchy分布 Gamma分布 几何分布 超几何分布 对数正态分布 Logistic分布 负二项分布 Poisson分布 均匀分布 Weibull分布 Willcoxon分布等变元可以是向量 a factor letters 1 10 a 3 w 不行a as character a a 3 w a factor a a 可能遇到的问题 输入输出数据 x scan 1 52 63 72 18 912 1 2 4 等价于x c 1 5 2 6 3 7 2 1 8 9 12 1 2 4 setwd f 2010stat 或setwd f 2010stat x rnorm 20 write x f 2010stat test txt y scan f 2010stat test txt yy iris y 1 5 str y write table y f 2010stat test txt row names F w read table f 2010stat test txt header T str w write csv y f 2010stat test csv v read csv f 2010stat test csv str v data read table clipboard write table clipboard 序列和向量 z seq 1 10 length 100 z seq 1 10 len 100 z seq 10 1 1 z 10 1x rep 1 3 3 x rep 3 5 1 3 x rep c 1 10 c 4 5 w c 1 3 x z w 3 x rep 0 10 z 1 3 x zx zrev x z c nocat has nine tails z 1 nocat z 1 5z 7 8 zz NULLz c 1 3 5 1 3 zrnorm 10 c 2 5 z c 1 3 去掉第1 3元素z sample 1 100 10 zwhich z max z 给出下标 向量 矩阵 x sample 1 100 12 xall x 0 all x 0 any x 0 1 10 x 0 diff 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 x c 2 1 第2和第1行x c 1 3 第1和第3列x 2 1 第 2 1 元素x x 1 0 1 第1列大于0的元素sum x 1 0 第1列大于0的元素的个数sum x 1 0apply 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 x lower tri x 0 x upper 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 x 1 x array 1 24 c 4 3 2 x c 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 row names 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 x 12 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 letters 1 5 w hi z 1 z 2 z Tz T a2z T 3 z 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 thisisn tcorrectbarplot 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 matrix table data frame Startwithacontingencytable ftable Titanic row vars 1 3 ftable Titanic row vars 1 2 data frame Titanic 把array变成data framea xtabs Freq Survived Sex w biplot corresp a nf 2 应用之一 Startwithadataframe str mtcars x ftable mtcars c 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 s dnn tochangelabelsftable mtcars cyl mtcars vs mtcars am mtcars gear row vars c 2 4 dnn c Cylinders V S Transmission Gears ftable vs carb mtcars vs是列 carb是行 或ftable mtcars vs mtcars carb ftable carb vs mtcars vs是行 carb是列ftable mtcars c 8 11 和上面ftable carb vs mtcars 等价ftable breaks wool tension warpbreaks as data frame DF as data frame UCBAdmissions 等价于data frame UCBAdmissions xtabs Freq Admit Gender Dept DF 把方阵变成原来的列联表 a xtabs Freq Admit 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 Hooke slaw f 5ks par mfcol c 2 2 plot distance compression plot distance compression 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 Hooke sLaw 只有标题plot compression distance main Hooke sLaw xlab x ylab y 标题 x y标记identify compression distance 标出点号码plot compression distance main Hooke sLaw 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 Hooke sLaw 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 width 50 collapse n legend 1 2 1 0 Justasine lty 2 col 4 关于画图 library MASS 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 brain body log xy par mfrow c 1 1 par cex 0 7 mex 0 7 character cex margin mex expansionplot log body log brain text x log body y log brain labels row names Animals adj 1 5 adj 0impliesleftadjustedtextplot log body log brain identify log body log brain row names Animals 关于画图 符号颜色大小形状等 plot 1 1 xlim c 1 7 5 ylim c 0 5 type n Donotplotpointspoints 1 7 rep 4 5 7 cex seq 1 4 l 7 col 1 7 pch 0 6 text 1 7 rep 3 5 7 labels paste 0 6 letters 1 7 cex seq 1 4 l 7 col 1 7 points 1 7 rep 2 7 pch 0 6 7 Plotsymbols7to13text 1 7 0 25 rep 2 7 paste 0 6 7 Labelwithsymbolnumberpoints 1 7 rep 1 7 pch 0 6 14 Plotsymbols14to20text 1 7 0 25 rep 1 7 paste 0 6 14 Labelswithsymbolnumber 调色板par mfrow c 2 4 palette 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 h plotting is bar plotbarplot 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 iris 1 4 main Anderson sIrisData 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 x 2 y 2 10 sin r r z outer x y f z is 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 Don tdrawthegridlines 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 u 1 u 3 u 2 u 4 col tcol 8 border red rect画矩形contour x y volcano col tcol 2 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 x i n i 1 n text 6 6 expression hat beta X t X 1 X t y text 8 8 expression z i sqrt x i 2 y i 2 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 x 1 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 y x1 x2 lm y 0 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 例1 cross txt 63 例1 cross txt w read table cross txt header T head w plot y x w summary w a lm y x z w summary a anova a qqnorm a res qqline a res shapiro test a res a1 lm y x 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 y x z data w coef wt plot wt plot y x w abline coef wt 1 col 2 abline coef wt 2 col 4 回归方程 65 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 http www statsci org data general poison html 66 例2 poison txt 3种毒药 4种处理 用于动物实验 48个观测值 67 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 Time Poison 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 Time Poison Treatment w anova a qqnorm a res qqline a res shapiro test a res summary a 变换并拟合主效应 69 结果解释 70 多项式回归 多项式回归y cars dist x cars speedo order x plot y x do it function model col r lm model yp predict r lines yp o x o col col lwd 3 do it y x col red do it y x I x 2 col blue do it y 1 I x 2 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 y x lm 1 y x n 100 x rlnorm n 3 14 alog normaldistributionisaprobabilitydistributionofarandomvariablewhoselogarithmisnormallydistributed y x 1 rlnorm n plot y x 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 y x summary lm y x I x 2 summary lm y x I x 2 I x 3 summary lm y x I x 2 I x 3 I x 4 summary lm y x I x 2 I x 3 I x 4 I x 5 正交 不会改变开始显著的系数poly ComputeOrthogonalPolynomialssummary lm y poly x 1 summary lm y poly x 2 summary lm y poly x 3 summary lm y poly x 4 summary lm y poly 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 p i 1 i 1 summary lm y poly x i coefficients 4 matplot 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 p 1 1 2 summary lm y x coefficients 4 p 2 1 3 summary lm y x I x 2 coefficients 4 p 3 1 4 summary lm y x I x 2 I x 3 coefficients 4 p 4 1 5 summary lm y x I x 2 I x 3 I x 4 coefficients 4 p 5 1 6 summary lm y x I x 2 I x 3 I x 4 I x 5 coefficients 4 matplot 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 y x for iin1 10 r lm y poly 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 lat rcs quakes long plot quakes lat quakes long o order quakes long lines quakes long o predict r o col red lwd 3 r lm quakes lat rcs quakes long 10 lines quakes long o 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 2 y quakes 1 o order x x x o y y o r1 lm y bs x df 10 r2 lm y ns x df 6 plot y x 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 t 2 0 lines D Epanechikov x x col red D tricube function t aka triweightkernel ifelse 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 noyaud Epanechikov noyautricube lwd 1 lty 1 col c par fg red blue title main Differentskernels 局部多项式回归library KernSmooth data quakes x quakes long y quakes latplot y x bw dpill x y 2lines locpoly x y degree 0 bandwidth bw col red lines locpoly x y degree 1 bandwidth bw col green lines locpoly x y degree 2 bandwidth bw col blue legend par usr 1 par usr 3 yjust 0 c degree 0 degree 1 degree 2 lwd 1 lty 1 col c red green blue title main LocalPolyn