1 Set-up

Install R and RStudio:

• Download R

• Download RStudio Desktop

• For Windows users, install Rtools for using some R packages (e.g., ggplot2).

R creates an interactive environment for you to play with data and statistical models. If you have no exposure to computer-based statistical computing before, I dare say that learning R will be the most valuable experience for you in this course.

After installing R and RStudio on your PC/Mac, you can play with the following scripts in RStudio. You can run R Scripts line by line using the shortcut Ctrl-Enter/Command-Enter (or maybe Shift-Enter depending on your local machine).

2 Use R as a calculator

# In R, comments start with # symbol
# This line will not be run

num = 3
num + 2

[1] 5

## vector
x = c(2, 7, 5) # Here "c" is short for combine
x

[1] 2 7 5

## a vector (sequence) from 1 to 5
y = seq(1, 5)
y

[1] 1 2 3 4 5

## a sequence from 1 to 5 with step=2
seq(1, 5, 2) # seq(from=1, to=5, by=2)

[1] 1 3 5

?seq

x + y

Warning in x + y: longer object length is not a multiple of shorter object
length

[1]  3  9  8  6 12

options(warn = -1) # hide warnings
x / y

[1] 2.000000 3.500000 1.666667 0.500000 1.400000

## extracting sub-vector (also called subsetting)
x[1]

[1] 2

c(x[1], x[3])

[1] 2 5

x[1:3] # same as x as length(x) == 3

[1] 2 7 5

length(x)

[1] 3

x[-1]

[1] 7 5

## matrix
z = matrix(seq(1,12), nrow= 3)
z

     [,1] [,2] [,3] [,4]
[1,]    1    4    7   10
[2,]    2    5    8   11
[3,]    3    6    9   12

dim(z)

[1] 3 4

length(z)

[1] 12

ls()

[1] "num" "x"   "y"   "z"  

rm(x)
ls()

[1] "num" "y"   "z"  

3 Generate random data

set.seed(2020)
x = runif(20)
x

 [1] 0.646902839 0.394225758 0.618501814 0.476891136 0.136097186 0.067384386
 [7] 0.129152617 0.393117930 0.002582699 0.620205954 0.764414018 0.743835758
[13] 0.826165695 0.422729083 0.409287665 0.539692614 0.960722398 0.653557334
[19] 0.546715299 0.266063566

e = runif(20)
y = 0.5 + x * 2 + e
plot(x,y)

4 Linear model

Basic R provides lm() for fitting linear models. Here we simply regress y on x.

First, we create a dataframe for our generated data:

my_data = data.frame(y = y, x = x)

my_lm = lm(y ~ x, data = my_data)
summary(my_lm)

Call:
lm(formula = y ~ x, data = my_data)

Residuals:
     Min       1Q   Median       3Q      Max 
-0.56217 -0.30050  0.00473  0.40064  0.44601 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)    0.946      0.176   5.374 4.16e-05 ***
x              2.132      0.323   6.602 3.36e-06 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.3703 on 18 degrees of freedom
Multiple R-squared:  0.7077,    Adjusted R-squared:  0.6915 
F-statistic: 43.59 on 1 and 18 DF,  p-value: 3.362e-06

my_lm["coefficients"]

$coefficients
(Intercept)           x 
  0.9459971   2.1324126 

# To know other options besides coefficients, run
# str(my_lm)
# Also, try running: 
# my_lm$coefficients

#create scatterplot
plot(y ~ x, data=my_data)

#add fitted regression line to scatterplot
abline(my_lm)

5 Loading packages

• Base R is powerful enough for many routine statistical tasks. You can also use third-party R packages to make your work easier.

• ggplot2 is a package for plotting, which provides a more sophisticated layout than the base plot() function:

# install ggplot2. You only need to do it once.
install.packages("ggplot2")

library(ggplot2)
#create scatterplot with fitted regression line
ggplot(my_data, aes(x = x, y = y)) +
  geom_point() +
  stat_smooth(method = "lm", se=FALSE)

`geom_smooth()` using formula = 'y ~ x'

6 Further readings

You should have a basic understanding about using R now. For further knowledge, I recommend the following materials:

• Hands-On Programming with R

• R for Data Science

7 Review questions

1. How do you create a vector $(3,4,5)$ in R?

2. Given a vector x, how to get its length?

3. How to create a vector $(2, 5, 8, 11)$ in R?

4. Given x=c(1,2,3) and y=c(1,5), what’s x-y?

5. Given a vector x, how do you get its third element? What if length(x) == 2?

6. How do you generate a sequence $\{x_i\}_{i=1}^{20}$ where each $x_i \sim N(0,1)$?

7. what’s a seed? Why do we use set.seed(2020)?

8. Given a data set data with two variables x and y, how do you fit the linear model $y = \beta_0 + \beta_1 x$?

9. Explain the output of summary(my_lm) in our example:

   Call:
   lm(formula = y ~ x, data = my_data)
   
   Residuals:
        Min       1Q   Median       3Q      Max 
   -0.56217 -0.30050  0.00473  0.40064  0.44601 
   
   Coefficients:
               Estimate Std. Error t value Pr(>|t|)    
   (Intercept)    0.946      0.176   5.374 4.16e-05 ***
   x              2.132      0.323   6.602 3.36e-06 ***
   ---
   Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
   
   Residual standard error: 0.3703 on 18 degrees of freedom
   Multiple R-squared:  0.7077,    Adjusted R-squared:  0.6915 
   F-statistic: 43.59 on 1 and 18 DF,  p-value: 3.362e-06