1. GRA 6020 Multivariate Statistics Ulf H. Olsson Professor of Statistics

2. 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

3. 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.

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

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

6. Ulf H. Olsson Univariate Normal Distribution

7. Ulf H. Olsson Bivariate normal distribution

8. Ulf H. Olsson Standard Normal density functions

9. Ulf H. Olsson Regression Analysis/OLS-Regression

10. Ulf H. Olsson Factor Analysis

11. Ulf H. Olsson Structure Equation Modeling

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

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

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