r语言数据分析论文

R语言基本数据分析本文基于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) (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 detection3. 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 curve3. 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) = 200 #sample 200 times # theta = matrix(rep(0,*5),) theta =rep(0,*5); for (i in 1:) { j = sample(1:100,100,replace = TRUE)#get 100 samples each time datrnd = dat[j,]; #select one row each time lambda = princomp(datrnd)$sdev^2; #get eigenvalues # theta[i,] = lambda; theta[i] = lambda[1]/sum(lambda); #plot the ratio of the biggest eigenvalue } # hist(theta[1,]) #plot the histogram of the first(biggest) eigenvalue hist(theta); #plot the percentage distribution of the biggest eigenvalue sd(theta)#standard deviation of theta #上面注释掉的语句，可以全部去掉注释并将其下一条语句注释掉，完成画最大eigenvalue分布的功能4. ANOVA方差分析 #Application：判断一个自变量是否有影响 (假设我们喂3种维他命给3头猪，想看喂维他命有没有用) # y = rnorm(9); #weight gain by pig(Yij, i is the treatment, j is the pig_id), 一般由用户自行输入 #y = matrix(c(1,10,1,2,10,2,1,9,1),9,1) Treatment <- factor(c(1,2,3,1,2,3,1,2,3)) #each {1,2,3} is a group mod = lm(y~Treatment) #linear regression print(anova(mod)) #解释：Df（degree of freedom） #Sum Sq: deviance (within groups, and residuals) 总偏差和 # Mean Sq: variance (within groups, and residuals) 平均方差和 # compare the contribution given by Treatment and Residual #F value: Mean Sq(Treatment)/Mean Sq(Residuals) #Pr(>F): p-value. 根据p-value决定是否接受Hypothesis H0：多个样本总体均数相等(检验水准为) qqnorm(mod$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，., 维他命对猪的体重有影响。