GRA 6020 Multivariate Statistics Ulf H Olsson Professor

GRA 6020 Multivariate Statistics Ulf H. Olsson Professor of Statistics

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

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

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