Multivariate Analysis

Multivariate analysis deal with multi-dimensional data such as

$$Y=B_0+B_1{X}_1+B_2{X}_2+\cdots +B_n{X}_n+\epsilon$$

Dimensional reduction:

• PCA
• Factor anaylsis
• Feature selection

Some distances:

• Euclidian
• Manhattan
• Statistical

Also interested in cluster analysis.

• k-means
• hierarchical
• CART
• Classification
  • outputs binary
  • discrimination rule

More over it deals with canonical analysis and panel analysis.

Data Organization

Data is structured in the following form

$$\left[\begin{array}{ccccc}{v}_{1,1}& v_{1,2}& v_{1,3}& \dots & v_{1,p}\\ \dots & & & & \\ v_{n,1}& v_{n,2}& v_{n,3}& \dots & v_{n,p}\end{array}\right]$$

Here we have $n$ observations and $p$ variables.