1. Stat 251 (2009, Summer)
Lab 1
TA: Yu, Chi Wai

2. Set up lab accounts
Introduction to R

3. Lab account User name: Password:
Select any one of the Window 2000 server
Press Ctrl+\ and return to the ezConnect Manager if you are in a Unix login page.
User name:
the first eight (8) letters of the full name that you used to register at UBC.
Password:
a capital “S” followed by the next seven (7) digits of your student ID number.

4. Lab account (cont’) CHANGE YOUR PASSWORD:
Type in simultaneously, Ctl+Alt+Del, which will bring you back to a similar login page as before.
At the bottom right of the window, there will be an option for changing your password there.

5. Introduction to R Open R by double-clicking your desktop Icon :
R is a free statistical programming language.
Download at:
Open R by double-clicking your desktop Icon :

6. Basic commands in R: 1. Basic operations: 2+3 # addition
2*3 # multiplication
2/3 # division
2^3 # power
log(5) # natural logarithms
sqrt(2) # square root
exp(0.2) # exponential function
abs(-7) # absolute value

7. c(……): stands for concatenation
Basic commands in R:
2. Basic Vector Manipulation:
Create a column vector y = OR
c(……): stands for concatenation
y = OR
y = c(“a”,”b”,”c”)
c(0,1,3)
<-
Use t() to convert a column vector to a row vector
For example: t(y)

8. 2. Basic Vector Manipulation:
Two fast ways to create a vector with sequences:
a) Use Colon : to create a vector of consecutive integers
x = 10:16
Step size = 1
Output: 10, 11, 12, 13, 14, 15, 16
How to create a sequence of odd numbers, or a vector of (2, 5, 8, 11)’ ?

9. 2. Basic Vector Manipulation:
b) Use seq(from, to, by=) to create a sequence with a chosen step size.
x = seq(11,20, by=2)
Step size = 2
Output: 11, 13, 15, 17, 19
x = seq(11,10, by=-0.2)
Output:

10. 2. Basic Vector Manipulation:
Additionally,
rep(x, B)
replicates the values in x B times
For example:
rep(1, 5)  (1,1,1,1,1)
rep(c(1,2),3)  (1,2,1,2,1,2)
rep(“Mike”, 3)  (“Mike”, “Mike”, “Mike”)

11. 2. Basic Vector Manipulation:
Add extra elements to an existing vector:
For example, y = c(2,5,9),
add 19 to y to create a new vector called z.
In general, stick several vectors together to make a new one.
For example, y =c(2,5,9) and x = c(1,3,10), then z=
c(y,19)
u1= c(y,x)
add 19 and 23 to y to create another vector w.
Output:
w= c(y,19,23)
u2 = c(x,y)
Output:

12. 2. Basic Vector Manipulation:
Delete elements in a vector:
x = seq(11,20, by=2)
drop the 2nd element of x to create a new vector w.
Drop the 2nd and 4th elements of x.
x[i]
: the ith element of x.
x[-c(2,4)]  (11,15,19)
For example: x[2] = 13; x[c(3,5)] = (15,19)
x[-i]
: drop the ith element of x.
For example: w= x[-2]  w = (11,15,17,19)

13. 3. Algebraic manipulation
a) Sum of a vector and a scalar
x = c(11,8,3)
x + 7 ?
Each element of x will be added to 7 to form a new vector.
x+7  (18, 15, 10)

14. 3. Algebraic manipulation
b) Multiplication of a vector by a scalar
x = c(11,8,3)
x*7 ?
Each element of x will be multiplied by 7 to form a new vector.
x*7  (77, 56, 21)
c) Division of a vector by a scalar
x/7  (11/7, 8/7, 3/7)

15. 3. Algebraic manipulation
d) Vector Sum (sum elementwisely)
x = c(11,8,3), and y = c(2,6,3)
x + y  (11+2, 8+6, 3+3)
e) Vector Subtraction
x - y  (11-2, 8-6, 3-3)

16. 3. Algebraic manipulation
f1) Vector Multiplication (elementwisely)
x = c(11,8,3), and y = c(2,6,3)
x * y  (11*2, 8*6, 3*3)
f2) Vector Multiplication (usual),i.e. xTy
t(x)%*%y  11*2+8*6+3*3
t(x)%*%y = sum(x*y)

17. 3. Algebraic manipulation
g) Vector Division (elementwisely)
x = c(11,8,3), and y = c(2,6,3)
x/y  (11/2, 8/6, 3/3)

18. 4. Summary statistics a) Measure the location of data: i) Sample mean:
x = c(0.18, -0.07, 0.09, -0.25, -0.76, -0.58)
a) Measure the location of data:
i) Sample mean:
mean(x)
ii) Sample median/ the 0.5th sample quantile (Q(0.5)):
median(x) or quantile(x, 0.5)

19. 4. Summary statistics b) Measure the dispersion of data:
x = c(0.18, -0.07, 0.09, -0.25, -0.76, -0.58)
b) Measure the dispersion of data:
i) Sample standard deviation and sample variance:
sd(x) and var(x)
ii) Sample IQR, i.e. Q(0.75)-Q(0.25):
quantile(x, 0.75)- quantile(x, 0.25)

20. 4. Summary statistics c) Other measures: max(x): a maximum of x
x = c(0.18, -0.07, 0.09, -0.25, -0.76, -0.58)
c) Other measures:
max(x): a maximum of x
min(x): a minimum of x
range(x): a range of x
summary(x): a summary of x

21. 5. Graphics a) Histogram: hist(x) x = rnorm(20)
Generate 20 data randomly from the standard normal distribution.
x = rnorm(20)
a) Histogram:
hist(x)

22. 5. Graphics b) Boxplot: boxplot(x)
The distribution is skewed to the left;
The distribution has a heavy tail on the left;
Some small-valued observations are far away from the majority of the data.

23. 5. Graphics c) Scatterplot: plot(x,y) x = rnorm(20)