Math 416 / Math 516 Syllabus

Linear Statistical Modeling Methods with SAS

Course Description

Linear models are used in regression, analysis of variance, analysis of covariance, and extensions such as logistic regression, generalized linear models and mixed models. This course covers these topics, especially the first three with illustrative examples and problems using real data. The course is intended for advanced undergraduate students, graduate students and working professionals, who engage in applied research. The combination of theory, applications, and SAS computer software, should enable students to more correctly analyze their own data and to interpret the output from a linear models computer package.

Course Content

• Review of elementary statistical analysis using SAS/Analyst. Designing simple experiments and studies within Error Rates, Power and Sample Size trade-off relationships.
• Introduction to the SAS Data Step, and procedures PRINT, MEAN and TTEST.
• Introduction to Interactive data exploration, straight-line regression and correlation analysis using SAS /Insight and SAS/Graph along with SAS procedures CORR and REG.
• Multiple regression analysis: General considerations of assumptions and the determination of the best estimating equation. SAS procedures REG and GLMMOD.
• Testing hypotheses in multiple regression: Full and reduced models paradigm, partial and sequential sums of squares, and their corresponding F tests.
• Correlations: Multiple, partial, and multiple-partial correlation. Their representation and interpretation in terms of the regression model.
• Confounding and Interaction in regression.
• Regression diagnostics and robustness using SAS/Insight and the procedure REG:
• Residual analysis: plots and cutoffs
• Influence diagnostics: Cooks D, dffits, covratio, dfbetas
• Outliers and leverage: the hat matrix diagonal using standardized, studentized and studentized deleted residuals, with predicted values, time and non-modeled regressors. Partial leverage plots and residual normal quantile plots
• Colliniarity diagnostics: tolerance, variance inflation, condition indices, condition number
• Polynomial regression, lack of fit tests and orthogonal polynomials.
• Regression using nominal and indicator (dummy) variables in regression: Comparing straight-line models.
• Analysis of covariance and other methods for adjusting continuous data using SAS procedure GLM.
• Analysis of Variance using SAS/Insight and SAS procedures ANOVA, GLM, MULTTEST
• One-way analysis of variance, multiple comparisons and multiple testing techniques.
• Two-way balanced ANOVA and randomized block experiments.
• Unbalanced ANOVA with multiple factors: Over-parameterization and interpretation using effects, cell means, and reference cell comparisons.
• Cell means, least square means, contrasts and non-standard test of hypotheses.
• Introduction to the Analysis of data involving repeated measures, random effects, random regression coefficients, multiple error terms, or multiple experimental units, using SAS procedures GLM, VARCOMP, MIXED)
• The generalized linear model: Logit analysis and Poisson regression using SAS/Insight and the SAS procedure GENMOD.
• Introduction to logistic regression analysis using SAS procedures LOGISTIC and GENMOD