Regression Analysis

Topics:

1. Introduction-Overview
2. A. Simple linear regression models
   • 1. model and assumptions
   • 2. normal equations and least square estimators
   • Exercise 1
   • 3. Gauss-Markov theorem
   • 4. indicator variables - comparison between two means
   • 5. the normal model and statistical inference
     • 5.1 maximum likelihood estimators
     • 5.2 the normal model and statistical inference
       • Cochran's theorem
       • inferences concerning the intercept
       • confidence interval for E(y|x)
       • prediction interval
       • confidence band for line
       • choice of x values in experiments
       • analysis of variance for regression
       • choice of x values in experiments
       • descriptive measures of association
       • Exercise 2
       • Exercise 3
     • 6. matrix representation
     • Exercise 4
3. B. Multiple Regression
   • 1. general linear model
   • 2. matrix representation
   • 3. estimators
     • matrix representation
     • expectation
     • least squares estimators
     • weighted least squares estimators
     • Exercise 5
     • Exercise 6
   • 4. inferences and matrix representation
     • variance-covariance matrix
     • tests of combinations of coefficients
     • distributions of residuals
   • 5. indicator variables; polynomial regression and interaction
   • Exercise 7
   • 6. selection of dependent variables
     • criteria for selection
     • all possible regressions
     • stepwise regression
     • Cp criterion
   • C. Correlation
     • 1. Distiction between regression and correlation
     • 2. Bivariate normal distribution
     • 3. Total and partial correlation
     • 4. Multiple correlation
     • 5. Tests and estimation

   Literature

   • Neter, J., Wasserman, W., Kutner, M.H. Applied Linear Statistical Models
   • Draper, N.R. and Smith, H. Applied Regression Analysis
   • Faraggi, D. and Goldenshluger, A. Applied Regression (in Hebrew)