本文基于R语言进行基本数据统计分析，包括基本作图，线性拟合，逻辑回归，bootstrap采样和Anova方差分析的实现及应用。

不多说，直接上代码，代码中有注释。

1. 基本作图（盒图，qq图）

#basic plot

boxplot(x)

qqplot(x,y)

2. 线性拟合

#linear regression

n = 10

x1 = rnorm(n)#variable 1

x2 = rnorm(n)#variable 2

y = rnorm(n)*3

mod = lm(y~x1+x2)

model.matrix(mod) #erect the matrix of mod

plot(mod) #plot residual and fitted of the solution, Q-Q plot and cook distance

summary(mod) #get the statistic information of the model

hatvalues(mod) #very important, for abnormal sample detection

3. 逻辑回归

#logistic regression

x <- c(0, 1, 2, 3, 4, 5)

y <- c(0, 9, 21, 47, 60, 63) # the number of successes

n <- 70 #the number of trails

z <- n - y #the number of failures

b <- cbind(y, z) # column bind

fitx <- glm(b~x,family = binomial) # a particular type of generalized linear model

print(fitx)

plot(x,y,xlim=c(0,5),ylim=c(0,65)) #plot the points (x,y)

beta0 <- fitx$coef[1]

beta1 <- fitx$coef[2]

fn <- function(x) n*exp(beta0+beta1*x)/(1+exp(beta0+beta1*x))

par(new=T)

curve(fn,0,5,ylim=c(0,60)) # plot the logistic regression curve

3. Bootstrap采样

# bootstrap

# Application: 随机采样，获取最大eigenvalue占所有eigenvalue和之比，并画图显示distribution

dat = matrix(rnorm(100*5),100,5)

no.samples = 200 #sample 200 times

# theta = matrix(rep(0,no.samples*5),no.samples,5)

theta =rep(0,no.samples*5)

for (i in 1:no.samples)

{

j = sample(1:100,100,replace = TRUE)#get 100 samples each time

datrnd = dat[j,]#select one row each time

lambda = princomp(datrnd)$sdev^2#get eigenvalues

# theta[i,] = lambda

theta[i] = lambda[1]/sum(lambda)#plot the ratio of the biggest eigenvalue

}

# hist(theta[1,]) #plot the histogram of the first(biggest) eigenvalue

hist(theta)#plot the percentage distribution of the biggest eigenvalue

sd(theta)#standard deviation of theta

#上面注释掉的语句，可以全部去掉注释并将其下一条语句注释掉，完成画最大eigenvalue分布的功能

4. ANOVA方差分析

#Application：判断一个自变量是否有影响 (假设我们喂3种维他命给3头猪，想看喂维他命有没有用)

#

y = rnorm(9)#weight gain by pig(Yij, i is the treatment, j is the pig_id), 一般由用户自行输入

#y = matrix(c(1,10,1,2,10,2,1,9,1),9,1)

Treatment <- factor(c(1,2,3,1,2,3,1,2,3)) #each {1,2,3} is a group

mod = lm(y~Treatment) #linear regression

print(anova(mod))

#解释：Df（degree of freedom）

#Sum Sq: deviance (within groups, and residuals) 总偏差和

# Mean Sq: variance (within groups, and residuals) 平均方差和

# compare the contribution given by Treatment and Residual

#F value: Mean Sq(Treatment)/Mean Sq(Residuals)

#Pr(>F): p-value. 根据p-value决定是否接受Hypothesis H0：多个样本总体均数相等(检验水准为0.05)

qqnorm(mod$residual) #plot the residual approximated by mod

#如果qqnorm of residual像一条直线，说明residual符合正态分布，也就是说Treatment带来的contribution很小，也就是说Treatment无法带来收益（多喂维他命少喂维他命没区别）

如下面两图分别是

（左）用 y = matrix(c(1,10,1,2,10,2,1,9,1),9,1)和

（右）y = rnorm(9)

的结果。可见如果给定猪吃维他命2后体重特别突出的数据结果后，qq图种residual不在是一条直线，换句话说residual不再符合正态分布，i.e., 维他命对猪的体重有影响。

R不但数据分析好用，而且作图能力极好，推荐你用。

下面是R数据分析的一些代码，包括数据导入、方差分析、卡方测验、线性模型及其误差分析。希望可以帮到你：

1.1导入数据

install.packages('xslx')

library(xlsx)

Sys.setlocale("LC_ALL", "zh_cn.utf-8")

a=read.xlsx2('d:/1.xlsx',1,header=F)

head(a)显示前六行

class(a$y)/str(a)查看列/全集数据类型

a$y=as.numeric(a$y)转换数据类型

1.2方差分析(F test)

with(a,tapply(liqi,tan,shapiro.test))正态性检验

library(car)leveneTest(liqi~tan,a)方差齐性检验

q=aov(liqi~tan*chong,a)方差分析(正态型)

summary(q)

TukeyHSD(q)多重比较

1.3卡方测验(Pearson Chisq)

a1=summarySE(a,measurevar='y', groupvars=c('x1','x2'))卡方检验(逻辑型/计数型)

aa=a1$y

aaa=matrix(a2,ncol=2)

aaa= as.table(rbind(c(56,44), c(36,64), c(48,52),c(58,42)))

dimnames(aaa)= list(group=c("不添加抗性","不添加敏感","添加抗性","添加敏感"),effect=c("存活","死亡"))

aaa=xtabs(data=a,~x+y)

chisq.test(a)误差分析(卡方测验，Pearson法)

install.packages("rcompanion")

library(rcompanion)

pairwiseNominalIndependence(a)多重比较

1.4线性模型及其误差分析(Wald Chisq)

q=lm(data=a,y~x1*x2)一般线性模型(正态性)

summary(q)

q=glm(data=a,y~x1*x2,family = gaussian(link='identity'))广义线性模型(正态性)

summary(q)

q=glm(data=a,y~x1*x2,family = binomial(link='logit'))广义线性模型(逻辑型，二项分布)

summary(q)

q=glm(data=a,y~x1*x2,family = poisson(link='log'))广义线性模型(计数型，泊松分布)

summary(q)

install.packages('lmerTest')一般线性混合效应模型(正态性)

library(lmerTest)

install packages(‘lme4’)

library(lme4)

q=lmer(data=a,y~x1*(1|x2))

q=lmer(data=a,y~x1*(1|x2),family = gaussian(link='identity'))广义线性混合效应模型(正态性)

q=glmer(data=a,y~x1*(1|x2),family = binomial(link='logit'))广义线性混合效应模型(逻辑型，二项分布)

q=glmer(data=a,y~x1*(1|x2),family = poisson(link='log'))广义线性混合效应模型(计数型，泊松分布)

summary(q)

install.packages('car')

install.packages('openxlsx')

library(car)

install.packages('nlme')

library(nlme)

Anova(q,test='Chisq')线性模型的误差分析(似然比卡方测验,Wald法)

lsmeans(q,pairwise~chuli,adjust = "tukey")线性模型的多重比较(tukey法)