R Cookbook

ISLR v2 Resources

R version 4.3.2 (2023-10-31 ucrt) -- "Eye Holes"

Basics

print(paste("Hello,", "world!"))
# Ask for help
?funcname
# packages
install.packages("some_packages")

# logical #issue
& | ! # elementwise
&& || # only examine the first element

if (condition) {
 expr1
} else {
 expr2
}

for(var in seq) {
    expr
    break
}

while(condition) {
    expr
}
while(condition) {
    break # stop the while loop

strsplit() #issue

Loading Data

## import data
data <- read.table(file = "./Resources/Datasets/Auto.data", header = TRUE, na.strings = "?", stringsAsFactors = TRUE)
# set stringsAsFactors to TRUE: treat variable containing strings as a quanlitative variable
# also using data <- na.omit(data)

data <. read.csv(file = "...") # read a csv file

## export data
write.table()

Literals

## vector
vec <- c(1, 2, 4, 3)
vec = c(1, 2, 4, 3)
length(x)

# name a vector
names(vector) <- vec_names

seq(0, 1, length=100)
seq(0, 10) # 0:10 note that this will include both the start and the end number

## matrix
mat <- matrix(data = vec, nrow = 2, ncol = 2, byrow = TRUE) 
# matrix(vec, 2, 2, byrow=TRUE)
# Note that by default byrow = FALSE
length(mat) # dim(mat)[1] * dim(mat)[2]
dim(mat)

# name a matrix
rownames(matrix) <- row_names_vec
colnames(matrix) <- col_names_vec
# alternatively, you can use `dimnames = list(row_names, col_names)`

# indexing the matrix
mat[1,1]
mat[1:2, ]
mat[1:2, 2]
mat[c(1,2), c(2,1)]
mat[-1, ] # ignore the first row
mat[-c(1,2), -c(2,2)] # ignorw the 1st,2nd row and the 2nd row

# matrix arithmetic
rowSums(matrix)
colSums(matrix)
matrix1 * matrix2 # elementwise
matrix1 %*% matrix2

## cached objects
ls() # check a list of all the objects: data & functions
rm() # delete objects
rm(list = ls()) # remove all objects

## combine matrices and vectors
big_matrix = cbind(mat1, mat2, ..., vec1, ...)
big_matrix = rbind(mat1, mat2, ..., vec2, ...)

Factor

R use term factor to describe the vector whose values represent categories or enumerated types.

vec <- c(1,3,5)
fac_vec <- factor(vec)
fac_vec <- as.factor(vec)

## factor with levels
fac_vec <- factor(vector, order = TRUE, levels = c("lev1", "lev2", ...))
# acsending
# alternatively levels(fac_vec) <- c("lev1", "lev2", ...)
# you can also use levels() to change the existing levels to another set of levels, e.g. levels(fac_vec) = new_levels

## Order factor
order(fac_vec)
fac_vec[order(fac_vec)]

List

my_list <- list(comp1, comp2, ...)
my_list <- list(name1 = comp1, name2 = comp2, ...)
# or equivalently names(my_list) <- name_list

# select components
my_list$name1
my_list[[1]]

Arithmetic

mat1 * mat2 # elementwise
mat1 %*% mat2 # matrix mulitplication
sqrt(vec_or_mat)
vec_or_mat^2

mean(vec_or_mat)
var(vec_or_mat)
sd(vec_or_mat) == sqrt(var(vec_or_mat)) # sd for standard deviation

cor(vec, vec + rnorm(length(vec), mean=1, sd=.2)) # correlation

# outer product
mat <- outer(vec1, vec2, function(x, y) cos(x) + sin(y))
dim(mat)

Random Variables

set.seed(1919)
vec <- rnorm(19, mean=1, sd=.2) # generate random normal variables
# by default rnorm() creates std normal random variables

Graphics

ggplot

# line: intercept a and slope b, lwd: line width
abline(a, b, lwd = 3, col = "red") 

## scatter
x <- rnorm(10)
y <- rnorm(10)
plot(x, y, xlab = "the x-axis label", ylab = "the y-axis label", main = "the title", col = "green", pch = "+")
# plot(y ~ x), pch option to create plotting symbols

## countour
z <- outer(x, y, function(x,y) cos(y) / (1 + x^2))
contour(x, y, z, nlevels=30, add=FALSE) 
# if add set TRUE, will do modifcation on the original figure

## heatmap
image(x, y, z) # the color depends on z

## 3d plot
persp(x, y, z, theta = 30, phi = 20)

## histogram
hist(vec, breaks = 15)

## output the R plot
pdf("Figure.pdf")
plot(x, y)
dev.off() # indicates that the creation is done

## plot a data frame's column
plot(data$property1, data$property2)
attach(data)
plot(property1, property2)

If the variable on x-axis is qualitative, plot() function will produce the boxplots.

fac_vec <- factor(vec)
plot(fac_vec, vec2, varwidth = TRUE)
# set varwidth to TRUE to indicate the group size by the box width

In some cases you want to see the relationship of each two variables of the data frame. You can use pairs to achieve it.

pairs(data)

# or select some properties
pairs(~ property1 + property2 + ..., data = data)

You can also use kind of a interactive mode. Clicking the point and you will see the values you offer. (❗Not working in VSCode)

attach(data)
plot(property1, property2)
identify(property1, property2, property_to_be_query)

# then clicking on the plotted dot

Genetic Functions

# index of the max / min variable
which.max(object)
which.min(object)
# repetition
rep(x, times)

Data Frame

## create data frame (by column)
df <- data.frame(vec1, vec2, ...)

## exploring the data frame
View(df) # Open a new window to see the data frame
head(df) # show the first lines of the data frame
tail(df)
dim(df)
names(df) # check the variable names

str(df) # this will give a overview of each variable in the data frame
summary(df) # produce a summary for each variable in the data frame, e.g. min, 1st Qu, Median, Mean, 3st Qu, Max
# note that summary can also be used to vector, matrix

df[1, ]
df[ , 2] # or df$2thColName or df[ , "2thColName"]
df[1, 2]

R Toy Dataset

mtcars # Motor Trend Car Road Tests

NaN

# missing values omit
df <- na.omit(df) # remove the rows containing missing values

# missing values are indicated as NaN
df.isna()
df.isna().any() # check the column
df.isna().sum() # check the number of NaN in each column
df.isna().sum().plot(kind="bar")
# removing missing values
df.dropna()
# replacing missing values
df.fillna(0)

Model

Linear Regression

Single-variable LM

# y: response, x: predictor, data: data set
lm.fit <- lm(y ~ x, data)
# check coefficients
lm.fit
# check residuals, coefficients (estimated, std error, t value, p value), RSE, multiple R^2 & adjusted R^2 #issue , F-statistic and corresponding p-value 
summary(lm.fit)

# check predicted values
predict(lm.fit)
# for a few given value, give confidence inteval, prediction inteval
predict(lm.fit, data.frame(predictor = (c(1,2,3))), interval = "confidence")
predict(lm.fit, data.frame(predictor = (c(1,2,3))), interval = "prediction")

# check statistics you can get from linear regression
names(lm.fit)
# e.g. plot residual by index
plot(lm.fit$residuals)
# acquire coefficients
lm.fit$coefficients # or coef(lm.fit)

# confidence interval
confint(lm.fit)

# R^2
summary(lm.fit)$r.sq

# residuals and studentized residuals
lm.fit$residuals
rstudent(lm.fit)
# RSE
summary(lm.fit)$sigma

# leverages
plot(hatvalues(lm.fit))
# tell which one has the largest leverage
which.max(hatvlaues(lm.fit))

# plot the scatter and regression line
plot(x, y)
abline(lm.fit, lwd = 3) # abline for a,b line, a + bx

Diagonostic plots.

par(mfrow=c(2,2))
plot(lm.fit) 
## four diagnostic plots
# residuals ~ fitted values
# standardized residuals ~ theoretical quantiles
# standardized residuals ~ fitted values
# standardized residuals ~ leverage

Multi-variable LM

lm.fit <- lm(y ~ x1 + x2 + ..., data)
# fit LM without some variables 
lm.fit1 <- update(lm.fit, ~ . -var_to_be_ignored)
# altenatively
lm.fit1 <- lm(y ~ . -var_to_be_ignored)

# VIF
library(car)
vif(lm.fit)