R basic
数学运算
## 四则运算
5 + (2.3 -1.125) * 3.2/1.1 + 1.23E3
## [1] 1238.418
#1.23E = 1.23 * 10^3
2^10
## [1] 1024
## 平方根
sqrt(6.25)
## [1] 2.5
## 指数
exp(1)
## [1] 2.718282
## 对数
log10(1000)
## [1] 3
## 取整(四舍五入)
round(1.1234,2)
## [1] 1.12
## 向下取整
floor(1.1234)
## [1] 1
## 向上取整
ceiling(1.1234)
## [1] 2
## 三角函数 pi表示圆周率。sin正弦, cos余弦, tan正切, 自变量以弧度为单位。 pi/6是30度。
pi
## [1] 3.141593
sin(pi/6)
## [1] 0.5
cos(pi/6)
## [1] 0.8660254
sqrt(3)/2
## [1] 0.8660254
tan(pi/6)
## [1] 0.5773503
## 反三角函数 asin反正弦, acos反余弦, atan反正切， 结果以弧度为单位。
pi/6
## [1] 0.5235988
asin(0.5)
## [1] 0.5235988
acos(sqrt(3)/2)
## [1] 0.5235988
atan(sqrt(3)/3)
## [1] 0.5235988
分布函数和分位数函数
## dnorm(x)表示标准正态分布密度 . pnorm(x)表示标准正态分布函数。 qnorm(y)表示标准正态分布分位数函数 。求自由度为10的t检验的双侧临界值。 其中qt(y,df)表示自由度为df的t分布的分位数函数。
dnorm(1.98)
## [1] 0.05618314
pnorm(1.98)
## [1] 0.9761482
qnorm(0.975)
## [1] 1.959964
qt(1-0.05/2,10)
## [1] 2.228139
数据输出
## 需要用print()函数显示一个表达式的结果
print(sin(pi/2))
## [1] 1
## 用cat()函数显示多项内容， 包括数值和文本， 文本包在两个单撇号或两个双撇号中
## cat()函数最后一项一般是"\n", 表示换行。 忽略此项将不换行。
cat("sin(pi/2)=", sin(pi/2),"\n")
## sin(pi/2)= 1
函数运行记录
sink("tmpres_20200819.txt", split=TRUE)
print(sin(pi/6))
## [1] 0.5
print(cos(pi/6))
## [1] 0.8660254
cat("t(10)的双侧0.05分位数（临界值）=", qt(1 - 0.05/2, 10), "\n")
## t(10)的双侧0.05分位数（临界值）= 2.228139
sink()
向量计算与变量赋值
## 向量生成
x1 <- 1:10
x2 <- c(3,4,5,6,7)
x3<- x2 *2
x3 - x2
## [1] 3 4 5 6 7
## R的许多函数都可以用向量作为自变量， 结果是自变量的每个元素各自的函数值。
sqrt(x3)
## [1] 2.449490 2.828427 3.162278 3.464102 3.741657
## 某人存入10000元1年期定期存款，年利率3%, 约定到期自动转存（包括利息）。
10000 * (1 + 3/100)^20
## [1] 18061.11
R 绘图
## 用curve()函数制作函数的曲线图， curve()函数第二、第三自变量是绘图区间：
curve(x^5, -2, 2)
image.png
## 类似的用sin函数曲线图用如下程序制作，用abline()函数添加参考线
curve(sin(x),0,2*pi)
abline(h=0)
image.png
## 条形图
barplot(c("男"=10,"女"=8),main="男女人数")
image.png
## 散点图
plot(1:10,pnorm(1:10))
image.png
demo("graphics")
##
##
## demo(graphics)
## ---- ~~~~~~~~
##
## > # Copyright (C) 1997-2009 The R Core Team
## >
## > require(datasets)
##
## > require(grDevices); require(graphics)
##
## > ## Here is some code which illustrates some of the differences between
## > ## R and S graphics capabilities. Note that colors are generally specified
## > ## by a character string name (taken from the X11 rgb.txt file) and that line
## > ## textures are given similarly. The parameter "bg" sets the background
## > ## parameter for the plot and there is also an "fg" parameter which sets
## > ## the foreground color.
## >
## >
## > x <- stats::rnorm(50)
##
## > opar <- par(bg = "white")
##
## > plot(x, ann = FALSE, type = "n")
image.png
##
## > abline(h = 0, col = gray(.90))
##
## > lines(x, col = "green4", lty = "dotted")
##
## > points(x, bg = "limegreen", pch = 21)
##
## > title(main = "Simple Use of Color In a Plot",
## + xlab = "Just a Whisper of a Label",
## + col.main = "blue", col.lab = gray(.8),
## + cex.main = 1.2, cex.lab = 1.0, font.main = 4, font.lab = 3)
##
## > ## A little color wheel. This code just plots equally spaced hues in
## > ## a pie chart. If you have a cheap SVGA monitor (like me) you will
## > ## probably find that numerically equispaced does not mean visually
## > ## equispaced. On my display at home, these colors tend to cluster at
## > ## the RGB primaries. On the other hand on the SGI Indy at work the
## > ## effect is near perfect.
## >
## > par(bg = "gray")
##
## > pie(rep(1,24), col = rainbow(24), radius = 0.9)
image.png
##
## > title(main = "A Sample Color Wheel", cex.main = 1.4, font.main = 3)
##
## > title(xlab = "(Use this as a test of monitor linearity)",
## + cex.lab = 0.8, font.lab = 3)
##
## > ## We have already confessed to having these. This is just showing off X11
## > ## color names (and the example (from the postscript manual) is pretty "cute".
## >
## > pie.sales <- c(0.12, 0.3, 0.26, 0.16, 0.04, 0.12)
##
## > names(pie.sales) <- c("Blueberry", "Cherry",
## + "Apple", "Boston Cream", "Other", "Vanilla Cream")
##
## > pie(pie.sales,
## + col = c("purple","violetred1","green3","cornsilk","cyan","white"))
image.png
##
## > title(main = "January Pie Sales", cex.main = 1.8, font.main = 1)
##
## > title(xlab = "(Don't try this at home kids)", cex.lab = 0.8, font.lab = 3)
##
## > ## Boxplots: I couldn't resist the capability for filling the "box".
## > ## The use of color seems like a useful addition, it focuses attention
## > ## on the central bulk of the data.
## >
## > par(bg="cornsilk")
##
## > n <- 10
##
## > g <- gl(n, 100, n*100)
##
## > x <- rnorm(n*100) + sqrt(as.numeric(g))
##
## > boxplot(split(x,g), col="lavender", notch=TRUE)
image.png
##
## > title(main="Notched Boxplots", xlab="Group", font.main=4, font.lab=1)
##
## > ## An example showing how to fill between curves.
## >
## > par(bg="white")
##
## > n <- 100
##
## > x <- c(0,cumsum(rnorm(n)))
##
## > y <- c(0,cumsum(rnorm(n)))
##
## > xx <- c(0:n, n:0)
##
## > yy <- c(x, rev(y))
##
## > plot(xx, yy, type="n", xlab="Time", ylab="Distance")
image.png
##
## > polygon(xx, yy, col="gray")
##
## > title("Distance Between Brownian Motions")
##
## > ## Colored plot margins, axis labels and titles. You do need to be
## > ## careful with these kinds of effects. It's easy to go completely
## > ## over the top and you can end up with your lunch all over the keyboard.
## > ## On the other hand, my market research clients love it.
## >
## > x <- c(0.00, 0.40, 0.86, 0.85, 0.69, 0.48, 0.54, 1.09, 1.11, 1.73, 2.05, 2.02)
##
## > par(bg="lightgray")
##
## > plot(x, type="n", axes=FALSE, ann=FALSE)
image.png
##
## > usr <- par("usr")
##
## > rect(usr[1], usr[3], usr[2], usr[4], col="cornsilk", border="black")
##
## > lines(x, col="blue")
##
## > points(x, pch=21, bg="lightcyan", cex=1.25)
##
## > axis(2, col.axis="blue", las=1)
##
## > axis(1, at=1:12, lab=month.abb, col.axis="blue")
##
## > box()
##
## > title(main= "The Level of Interest in R", font.main=4, col.main="red")
##
## > title(xlab= "1996", col.lab="red")
##
## > ## A filled histogram, showing how to change the font used for the
## > ## main title without changing the other annotation.
## >
## > par(bg="cornsilk")
##
## > x <- rnorm(1000)
##
## > hist(x, xlim=range(-4, 4, x), col="lavender", main="")
image.png
##
## > title(main="1000 Normal Random Variates", font.main=3)
##
## > ## A scatterplot matrix
## > ## The good old Iris data (yet again)
## >
## > pairs(iris[1:4], main="Edgar Anderson's Iris Data", font.main=4, pch=19)
image.png
##
## > pairs(iris[1:4], main="Edgar Anderson's Iris Data", pch=21,
## + bg = c("red", "green3", "blue")[unclass(iris$Species)])
image.png
##
## > ## Contour plotting
## > ## This produces a topographic map of one of Auckland's many volcanic "peaks".
## >
## > x <- 10*1:nrow(volcano)
##
## > y <- 10*1:ncol(volcano)
##
## > lev <- pretty(range(volcano), 10)
##
## > par(bg = "lightcyan")
##
## > pin <- par("pin")
##
## > xdelta <- diff(range(x))
##
## > ydelta <- diff(range(y))
##
## > xscale <- pin[1]/xdelta
##
## > yscale <- pin[2]/ydelta
##
## > scale <- min(xscale, yscale)
##
## > xadd <- 0.5*(pin[1]/scale - xdelta)
##
## > yadd <- 0.5*(pin[2]/scale - ydelta)
##
## > plot(numeric(0), numeric(0),
## + xlim = range(x)+c(-1,1)*xadd, ylim = range(y)+c(-1,1)*yadd,
## + type = "n", ann = FALSE)
image.png
##
## > usr <- par("usr")
##
## > rect(usr[1], usr[3], usr[2], usr[4], col="green3")
##
## > contour(x, y, volcano, levels = lev, col="yellow", lty="solid", add=TRUE)
##
## > box()
##
## > title("A Topographic Map of Maunga Whau", font= 4)
##
## > title(xlab = "Meters North", ylab = "Meters West", font= 3)
##
## > mtext("10 Meter Contour Spacing", side=3, line=0.35, outer=FALSE,
## + at = mean(par("usr")[1:2]), cex=0.7, font=3)
##
## > ## Conditioning plots
## >
## > par(bg="cornsilk")
##
## > coplot(lat ~ long | depth, data = quakes, pch = 21, bg = "green3")
image.png
##
## > par(opar)
demo("image")
##
##
## demo(image)
## ---- ~~~~~
##
## > # Copyright (C) 1997-2009 The R Core Team
## >
## > require(datasets)
##
## > require(grDevices); require(graphics)
##
## > x <- 10*(1:nrow(volcano)); x.at <- seq(100, 800, by=100)
##
## > y <- 10*(1:ncol(volcano)); y.at <- seq(100, 600, by=100)
##
## > # Using Terrain Colors
## >
## > image(x, y, volcano, col=terrain.colors(100),axes=FALSE)
image.png
##
## > contour(x, y, volcano, levels=seq(90, 200, by=5), add=TRUE, col="brown")
##
## > axis(1, at=x.at)
##
## > axis(2, at=y.at)
##
## > box()
##
## > title(main="Maunga Whau Volcano", sub = "col=terrain.colors(100)", font.main=4)
##
## > # Using Heat Colors
## >
## > image(x, y, volcano, col=heat.colors(100), axes=FALSE)
image.png
##
## > contour(x, y, volcano, levels=seq(90, 200, by=5), add=TRUE, col="brown")
##
## > axis(1, at=x.at)
##
## > axis(2, at=y.at)
##
## > box()
##
## > title(main="Maunga Whau Volcano", sub = "col=heat.colors(100)", font.main=4)
##
## > # Using Gray Scale
## >
## > image(x, y, volcano, col=gray(100:200/200), axes=FALSE)
image.png
##
## > contour(x, y, volcano, levels=seq(90, 200, by=5), add=TRUE, col="black")
##
## > axis(1, at=x.at)
##
## > axis(2, at=y.at)
##
## > box()
##
## > title(main="Maunga Whau Volcano \n col=gray(100:200/200)", font.main=4)
##
## > ## Filled Contours are even nicer sometimes :
## > example(filled.contour)
##
## flld.c> require("grDevices") # for colours
##
## flld.c> filled.contour(volcano, asp = 1) # simple
image.png
##
## flld.c> x <- 10*1:nrow(volcano)
##
## flld.c> y <- 10*1:ncol(volcano)
##
## flld.c> filled.contour(x, y, volcano, color = function(n) hcl.colors(n, "terrain"),
## flld.c+ plot.title = title(main = "The Topography of Maunga Whau",
## flld.c+ xlab = "Meters North", ylab = "Meters West"),
## flld.c+ plot.axes = { axis(1, seq(100, 800, by = 100))
## flld.c+ axis(2, seq(100, 600, by = 100)) },
## flld.c+ key.title = title(main = "Height\n(meters)"),
## flld.c+ key.axes = axis(4, seq(90, 190, by = 10))) # maybe also asp = 1
image.png
##
## flld.c> mtext(paste("filled.contour(.) from", R.version.string),
## flld.c+ side = 1, line = 4, adj = 1, cex = .66)
##
## flld.c> # Annotating a filled contour plot
## flld.c> a <- expand.grid(1:20, 1:20)
##
## flld.c> b <- matrix(a[,1] + a[,2], 20)
##
## flld.c> filled.contour(x = 1:20, y = 1:20, z = b,
## flld.c+ plot.axes = { axis(1); axis(2); points(10, 10) })
image.png
##
## flld.c> ## Persian Rug Art:
## flld.c> x <- y <- seq(-4*pi, 4*pi, len = 27)
##
## flld.c> r <- sqrt(outer(x^2, y^2, "+"))
##
## flld.c> filled.contour(cos(r^2)*exp(-r/(2*pi)), axes = FALSE)
image.png
##
## flld.c> ## rather, the key *should* be labeled:
## flld.c> filled.contour(cos(r^2)*exp(-r/(2*pi)), frame.plot = FALSE,
## flld.c+ plot.axes = {})
image.png
数据读写
## read csv file 程序中的选项header=TRUE指明第一行作为变量名行， 选项as.is=TRUE说明字符型列要原样读入而不是转换为因子(factor)。技巧：read.csv()的一个改进版本是readr扩展包的read_csv()函数， 此函数读入较大表格速度要快得多， 而且读入的转换设置更倾向于不做不必要的转换。 但是， 这两种输入方法的默认中文编码可能不一样。
tax.tab <- read.csv("taxsamp.csv",header = T,as.is = T)
### 分类统计变量频数
table(tax.tab$征收方式)
##
## 查帐征收 定期定额征收 定期定率征收
## 31 16 2
table(tax.tab[["申报渠道"]])
##
## 大厅申报 网上申报
## 18 31
## 交叉取频数
table(tax.tab[["征收方式"]],tax.tab[["申报渠道"]])
##
## 大厅申报 网上申报
## 查帐征收 9 22
## 定期定额征收 9 7
## 定期定率征收 0 2
## 制表
knitr::kable(table(tax.tab[["征收方式"]], tax.tab[["申报渠道"]]) )
| 大厅申报 | 网上申报 | |
|---|---|---|
| 查帐征收 | 9 | 22 |
| 定期定额征收 | 9 | 7 |
| 定期定率征收 | 0 | 2 |
## 数值变量统计 中位数是从小到大排序后排在中间的值。 四分之一和四分之三分位数类似。
## 如果数据中有缺失值， 可以删去缺失值后计算统计量， 这时在mean, sd等函数中加入na.rm=TRUE选项。
summary(tax.tab[["营业额"]])
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0 650 2130 247327 9421 6048000
mean(tax.tab[["营业额"]])
## [1] 247327.4
sd(tax.tab[["营业额"]], na.rm=T)
## [1] 1036453
source("ssq.r")
参考材料：https://www.math.pku.edu.cn/teachers/lidf/docs/Rbook/html/_Rbook/intro-example.html
