notes1 - Stat 430/Math 468 Notes #1 Aspects of Multivariate...

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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 k-th variable on the j-th 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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Example: 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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notes1 - Stat 430/Math 468 Notes #1 Aspects of Multivariate...

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