1. Stat 251 (2009, Summer)
Lab 2
TA: Yu, Chi Wai

2. Review 1) Basic commands in R;
2) Basic operations for a scalar and a vector;
Algebraic manipulations with a scalar and a vector;
Algebraic manipulations with vectors;
3) Summary/Descriptive statistics;
mean, median, sd, var, quantile, IQR, etc.
4) Graphic;
Scatterplot, histogram and boxplot.

3. Histogram Adv: Disadv: Detect outliers;
Show the skewness/ symmetry of the distribution;
Show the modality of the distribution.
Disadv:
Depends on the choice of bandwidth.

5. Boxplot Adv: Disadv: Detect outliers;
Show the skewness/ symmetry of the distribution;
Show lower (1st), mid (2nd) and upper (3rd) quartiles.
Disadv:
Cannot show the modality of the distribution.

6. x = c(rep(-2,5), rep(0, 3), rep(2, 5), rep(-1, 10), rep(1,10))-1 1 -2 2

7. Skewness/Symmetry of a distribution
Symmetric:

9. Skewness/Symmetry of a distribution
Asymmetric:
Left skewed
Heavy tail on the left

12. Skewness/Symmetry of a distribution
Asymmetric:
Right skewed
Heavy tail on the right

15. Outliers x = c(rep(0,10), rep(2, 5), rep(-2, 5)) hist(x)
An unusual point(s) far away from the majority of data
x = c(rep(0,10), rep(2, 5), rep(-2, 5))
human mistake
measurement error
hist(x)
 Skew the distribution of data

16. x[4] = -10

17. Boxplot to show potential outliers
Some small-valued observations are far away from the majority of the data.
Left skewed

18. x[4] = 10

19. Boxplot to show potential outliers
Some large-valued observations are far away from the majority of the data.
Right skewed

20. Lab 2 Matrix manipulation Read external data in R Data transformation
More techniques for Graphics

21. Matrix Scalar: 0 dimension e.g. x=1.3, 5, 200,… Vector: 1 dimension
e.g. x = c(4,0.35,0.9, 1.1, 5)
x[5]: the 5th element of x

22. x[1,2]: the element in the 1st row AND 2nd column
Matrix: 2 dimensions
e.g.
1st 2nd 3rd column
The (1,2)th element of x
1st row
x[1,2]: the element in the 1st row AND 2nd column
2nd row
3rd row
x[,1]
x[3,]
The 1st column vector
The 3rd row vector

23. Create a Matrix Use matrix() ?matrix Or help(matrix)
x = matrix(c(3,5,6,3,4,9,2,1,7), ncol=3, nrow=3, byrow=T)
The matrix is filled by rows.

24. Matrix Manipulation x[-i,]: drop the ith row vector of x.
x[-c(i,j),]: drop the ith and jth row vectors of x.
x[,-i]: drop the ith column vector of x.
x[,-c(i,j)]: drop the ith and jth column vectors of x.

25. Drop the (i,j)th element of x?
Matrix Manipulation
x[-i,-j] ?!?!?
Drop the (i,j)th element of x?

26. x[-1,-3] Remove the data in the 1st row and the 3rd column. x[-1,]
AND x[,-3]
1st 2nd
3rd column
Remove the data in the 1st row and the 3rd column.
1st row
2nd row
3rd row

27. Read External Data 1) Save data set into Z: drive; 2) Open R;
3) Change the directory by clicking on [File] at the top right and then choosing the option for [Change dir].

28. Read External Data Two ways to read a data in R:
i) read.table(): read a table of data, i.e. the data set has multiple columns and rows of data.
ii) scan(): read a single column of numerical data and it will ONLY read that type of dataset.

29. Read External Data rain = rain = Caution!!
Head(er) or not in the 1st row?!?!
With Header:
There is no option for a header if we use scan().
rain =
read.table(“rain.txt", head=T)
Without Header:
read.table(“rain.txt", head=F)
rain =

30. sep=“ ” (default setting)
Separation
? read.table( )
read.table(file, header = FALSE, sep = “ ", …..)
sep: the field separator character that separates values on each line of the file.
Separated by a single space.
sep=“ ” (default setting)

31. sep=“,” Separation ? read.table( )
read.table(file, header = FALSE, sep = “ ", …..)
sep: the field separator character that separate values on each line of the file.
25,28,14
26,29,28
27,22,30
28,31,27
29,25,33
30,20,11
Separated by commas.
sep=“,”

32. sep=“\t” Separation ? read.table( )
read.table(file, header = FALSE, sep = “ ", …..)
sep: the field separator character that separate values on each line of the file.
Separated by tabs.
sep=“\t”

33. Data manipulation Back to our data set The column Volume is our focus
Is the annual rainfall volume in Sydney, Australia over 49 years
3 methods to focus our attention on Volume

34. Data Manipulation Option A Option B Option C Function attach()
Specify a column by “$”
Option C
Manipulate the dataset as if it’s a matrix

35. Option A : attach() attach(“rain”)
Attach the columns in rain to pseudo-variables

36. Option A : attach() Now type > attach(rain)
4 pseudo-variables will be created, namely
ID, Year, Volume, and State
> Volume
We get the data in the column Volume in vector
form

37. Option A : attach() Can only attach ONE data set at a time
To attach another data set
Detach the previous data set by
> detach(“rain”)
Then attach the new data set
> attach(“MyNewDataset”)

38. Option B : $ The variable rain belongs to the class dataframe
Similar to a matrix but a dataframe can store different types of data in different columns
e.g. some columns contains numerical values, others contains letters, strings, etc.

39. rain ID Year Volume State 1 2 3 4 5 1937 1938 1939 1940 1941 387.93104
State 2 1

40. rain ID Year Volume State 1 2 3 4 5 1937 1938 1939 1940 1941 387.93104
State 2 1

41. Option B : $ To bring up a specific column, we go by rain$Volume
Name of the column
dataframe

42. Option B : $ volume = rain$Volume
We can store the column in a new variable
volume = rain$Volume

43. Option B : $ Function : names() > names(rain)
returns the name of the columns in a dataframe
> names(rain)
[1] “ID” “Year” “Volume” “State”

44. Data Manipulation rain = read.table(“rain.txt", head=T)
rain: 4 columns of data, ID, Year, Volume, State, and 49 rows of data.
Not include the 3rd, 5th-10th rows
v = rain[,3]
v[-c(3,5:10)] OR rain[-c(3,5:10), 3]
Keep the first 10 rows of volume data
rain[1:10,3]
v[1:10] OR

45. Data Transformation Square root; Square; Natural logarithm;
Removing outliers may make
the data distribution symmetric.
Symmetrically distributed
Make analysis easier
Common transformations of data
Square root;
Square;
Natural logarithm;
Exponential, etc.

46. WARNING!
Please don’t think that we can always deal with an outlier by simply removing it

47. Multiple Graphs par(mfrow=c(r,c))
How to place multiple plots on one display.
par(mfrow=c(r,c))
Bring up a display with r number of rows
and c number of columns.

48. par(mfrow=c(2,2)) hist(v^2) hist(sqrt(v)) hist(log(v)) hist(exp(v))
Find a better function for transforming the data.
par(mfrow=c(2,2))
hist(v^2)
hist(sqrt(v))
hist(log(v))
hist(exp(v))

50. hist(v)

51. Sorting sv = sort(v, decreasing = T) sv1=sv[-1]
Remove the largest observations of v
Sort a vector into ascending (or descending) order by using sort()
descending
sv = sort(v, decreasing = T)
sv1=sv[-1]

53. par(mfrow=c(2,2))
hist(sv1^2)
hist(sqrt(sv1))
hist(log(sv1))
hist(exp(sv1))

55. Sorting sv2 = sort(v, decreasing = F) sv2[-(1:3)] or sv2[-c(1:3)]
Remove the first three smallest observations of v
ascending
sv2 = sort(v, decreasing = F)
sv2[-(1:3)] or sv2[-c(1:3)]

56. Side by side Boxplot boxplot(rain[,3]~rain[,4])
Get a boxplot of the volumn data BY State
Volumn: rain[,3 ], the 3rd column vector of the dataset rain
State: rain[,4], the 4th column vector of the dataset rain
boxplot(rain[,3]~rain[,4])

57. Summary statistics
How to find the summary statistics of volume data by state (=1 or 2)?
What is the sample mean of the volume data for state=1 ?
What is the sample variance of the volume data for state=2 ?

58. v1 = rain[s==1, 3] OR v1= v[s==1]
What is the sample mean of the volume data for state = 1?
s = rain[,4]
v1 = rain[s==1, 3] OR v1= v[s==1]
mean(v1), mean(rain[s==1, 2]) or mean(v[s==1])

59. OR by(v, s, mean): get the sample means of v by s.
by(v, s, median): get the sample medians of v by s.
by(v, s, var): get the sample variances of v by s.

60. More Graphics
x = seq(-3.14,3.14, by=0.2)
plot(x, cos(x))

61. x = seq(-3.14,3.14, by=0.2)
plot(x, cos(x), )
type = “ l ”

62. type: the type of plot. Possible types are "p" for points,
"l" for lines,
"b" for both,
"c" for the lines part alone of "b",
"o" for both ‘overplotted’,
"h" for ‘histogram’ like (or ‘high-density’) vertical lines,
"s" for stair steps,
"n" for no plotting.

63. x = seq(-3.14,3.14, by=0.2)
plot(x, cos(x),
type = “l”, )
lty = 2

64. lty: the line type. Line types can either be specified as an integer
0=blank, 1=solid (default), 2=dashed, 3=dotted, 4=dotdash, 5=longdash, or 6=twodash… Or
as one of the character strings
"blank", "solid", "dashed", "dotted", "dotdash", "longdash", or "twodash“…

65. x = seq(-3.14,3.14, by=0.2)
plot(x, cos(x), xlab="variable x", ylab="function of x",
main = “Stat 305”,
type="l", lty=2, )
col = 2

66. col: the colors for lines and points.
“col” can either be specified
as an integer
col=1 (black), col=2 (red), col=3 (green), col=4 (blue), etc. Or
as one of the character strings
col= “black”, col = “red”, col = “green”, col =“blue”, col=“white”, col=“brown”, etc

67. Use abline() abline(a=2, b=3) Add a line on the existing picture
A line : y = a + bx
Vertical line: abline(v=10)
abline(a=2, b=3)
Horizontal line: abline(h=-5)

68. abline(v=0, lty=2, col=3) x = seq(-3.14,3.14, by=0.2)
plot(x, cos(x), xlab="variable x", ylab="function of x",
main = “Stat 305”,
type="l", lty=2, col=2, )
abline(v=0, lty=2, col=3)

69. Exercise for students Click “summary of R commands“
Go to our course website by
Stat251  Mike  Lab materials
Click “summary of R commands“

70. matrix(0, ncol=10, nrow=5)