TABLE OF CONTENTS Multivariate statistical methods deal with multivariate random variables. Unlike the univariate random variable, which is a single variable, multivariate random variables are expressed by X = ( X 1, X 2,..., X p) T, where p represents the number of variables. So X is a random vector. In a multivariate random vector, the variables X 1, X 2,..., X p may be correlated with each other. For example, if X 1 increases, the other random variables X 2, ..., X p may follow the change of X 1 in some ways.
Example 3.1 : Welding Technician Training Program Let us assume that there is a welding technician training program. In this program, three courses are offered. They are basic welding technology (BWT), advanced welding technology (AWT), and practical welding workshop (PWW). The training program will teach courses to students and each student will be given grades in these three courses. The lowest possible grade is 0 and the highest is 100. For each incoming student, his/her final grade in these three courses can be represented by
where <i class="emphasis">X</i><sub1</sub> = grade for BWT<i class="emphasis"> X</i><sub2</sub> = grade for AWT<i class="emphasis"> X</i><sub3</sub> = grade...
