GRA 6020 Multivariate Statistics Ulf H. Olsson Professor of Statistics

Ulf H. Olsson Multivariate Statistics 1) Examining relationships with respect to a single variable Univariate Analysis Univariate Distributions 2) Examining relationships with respect to two or more variables simultaneously Multivariate Analysis Multivariate Distributions

Ulf H. Olsson Statistical Models Statistical models are mathematical representations of population behavior; they describe salient features of the hypothesized process of interest among individuals in the target population. When you use a particular statistical model to analyze a particular set of data, you implicitly declare that this population model gave rise to these sample data.

Ulf H. Olsson True Process Theoretical Domain Empirical Domain Making Sense

Ulf H. Olsson Relationships (Stochastic) Loyalty Branch Loan Savings Satisfaction

Ulf H. Olsson Univariate Normal Distribution

Ulf H. Olsson Bivariate normal distribution

Ulf H. Olsson Standard Normal density functions

Ulf H. Olsson Regression Analysis/OLS-Regression

Ulf H. Olsson Factor Analysis

Ulf H. Olsson Structure Equation Modeling

Ulf H. Olsson Regression Models All variables, both ys and xs, are directly observed

Ulf H. Olsson Factor Models Observed variables are ”linked” to latent variables (factors)

Ulf H. Olsson Structural Equation Models Regression models where all variables are latent (factors)