Course Topics

Introduction to Linear Models


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


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

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
Determinants of Plasma Carotene and Retinol

Model Building Strategies


- Data Collection and Preparation
- Reduction of Covariates
- Model Refinement
- Model Validation
Determinants of Wages from the Current Population Survey
This sample write-up is an example of the type of scientific writing that is expected.

Single Factor Analysis of Variance


- Definitions
- Regression versus ANOVA

Analysis of Covariance

Two Factor Analysis of Variance


- Why two factor ANOVA?



- Concepts
- Parametrization
- Interaction between qualitative and quantitative covariates,
- Interaction between 2 qualitative covariates
- Testing specific hypotheses

Experimental Studies


- Clinical Trials
- Randomization
- Sample size and Power

Complex Data Sets

These data sets are more complex than the ones used for weekly assignments. They were used for the two projects given at midterm and for the final take-home exam. Students were required to assimilate all the material covered in the course and to make various decisions affecting the course of the analysis, such as which covariates to drop, which to transform, which hypotheses to test. Decisions made early in the analysis could lead to very different final models. The students needed to remain aware of their aims and to determine whether the final model achieved these aims and led to a meaningful interpretation.

Syllabus |  Data Sources | Examples |

©Copyright 1997, Therese A. Stukel, Dartmouth College