Advance Applied Linear Models

###Basic review:

  • Simple Linear Regression Examples
  • Assumptions for Linear Models
  • Ordinary Least Squares (OLS) estimators
  • R2
  • Residuals
  • Transformations

###Inference in Linear Regression

  • Inferences concerning intercept and slope
  • Confidence intervals for intercept and slope
  • Prediction intervals for E(Y)
  • Regression through the Origin
  • ANOVA Approach to regression
  • F-distribution

Regression Diagnostics

  • Outliers
  • Influential points
  • Graphical diagnostics
  • Remedies
  • Weighted Least Squares

Regression in Matrix Notation

Multiple Regression

  • Why multiple regression?
  • Examples
  • Assumptions
  • Visual representation
  • Estimation
  • Fundamental Equation of Regression Analysis
  • ANOVA approach to Multiple regression
  • Regression diagnostics
  • Marginal effects of covariates (Extra sums of squares)
  • Pooled tests of significance
  • Uncorrelated Predictors
  • Multicollinearity
  • Confounding

Qualitative Predictor Variables

  • Categorical Variable (2 levels)
  • Categorical Variable (3 levels)
  • Mixture of Continuous and Categorical Variables
  • Two Qualitative Predictors
  • Two Qualitative and One Continuous Predictor

Model Building Strategies

  • Data Collection and Preparation
  • Reduction of Covariates
  • Model Refinement
  • Model Validation

Single Factor Analysis of Variance

  • Definitions
  • Regression versus ANOVA

Two Factor Analysis of Variance

  • Why two factor ANOVA?
  • Interactions

Two Factor Analysis of Covariance

Case Studies

Books recommended: Neter J, Kutner M, Nachtsheim C, Wasserman W, Applied Linear Statistical Models, 4th ed, 1996. Chicago: Irwin. Bowerman, B. L.; R. T. O�Connell; and D.A. Dickey. Linear Statistical Models: An Applied Approach. 2nd . ed. Boston: Duxbury Press, 1990.