Stat 430/Math 468 – Notes #1
Chapter 1
Aspects of Multivariate Analysis
Introduction
We will analyze the data which include simultaneous measurement on many variables,
and the methodology is called multivariate analysis.
We will try to provide explanations
based on algebraic concepts and minimize the requirement on calculus of many variables.
Many multivariate methods are based on the underlining multivariate normal distribution
probability model.
Other methods are ad hoc in nature and are justified by logical or
commonsense arguments.
Statistical software packages are inevitably used to implement
these techniques.
Different multivariate techniques will be provided in this course.
However, the choice of
methods and the types of analyses employed are largely determined by the objectives of
the investigation.
The objects of investigation scientific investigation to which multivariate methods could
apply include the following:
1.
Data reduction or structure simplification.
2.
Sorting and grouping.
3.
Investigation of the dependence among the variables.
4.
Prediction.
5.
Hypothesis construction and testing
The Organization of Data
Multivariate data arise whenever an investigator selects a number
of
variables
or
characters
to record.
The values of these variables are all recorded for each distinct
item
,
individual
, or
experimental unit
.
1
p
≥
Notation:
jk
x
: measurement of the kth variable on the jth item/individual/experimental unit.
The n measurements on p variables can be displayed in a matrix (data array/matrix)
Variable1 Variable2
... Variable p
11
12
1
21
22
2
12
...
item 1
...
item 2
...
item n
p
p
nn
n
p
xx
x
x
x
⎛⎞
⎜⎟
=
⎝⎠
X
MM
M
M
M
1
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View Full DocumentExample:
A selection of four receipts from a bookstore was collected.
The information
on each receipt includes, among other things, # of books sold and total amount of each
sale.
Here are the data
Variable 1 (dollar sales):
42
52
48
58
Variable 2 ( # of books):
4
5
4
3
Use the notation above, list the data in an array.
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 Spring '10
 Hua
 Statistics, Variance, Pearson productmoment correlation coefficient, Covariance matrix, bookstore receipt data

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