This course aims to provide students with a comprehensive applied understanding of the common statistical tools employed for linear regression. An emphasis will be placed on exploring and understanding the discussed methods and to see them employed in a variety of applications.
- The first objective is to provide a thorough foundation for simple linear regression as a tool for exploring the linear relationship between two variables. Students will learn how to estimate and interpret the model.
- Once students understand the model, they will explore how to evaluate the model. Students will learn about estimating residual error, assessing the proportion of variation explained by the model, understanding the sampling distribution of the parameter estimates, and carrying out hypothesis tests.
- Students will also list the assumptions underlying the simple linear regression model and use graphical and numerical methods to check the assumptions. They will also use the model to estimate means and predict individual responses, and construct intervals for the estimates and predictions.
- Students will then move onto multiple linear regression where more than one predictor is included in the model. They will learn how estimation, evaluation, checking assumptions, estimating means, and predicting individual responses generalize to this setting.
- Students will learn about using variable transformations and interactions to incorporate nonlinear and nonadditive relationships in the model. They will also learn how to construct and fit a regression model with categorical predictors.
- Students will learn how to identify and diagnose potential problems with a linear regression model. They will learn procedures to identify outliers or violations of fundamental modeling assumptions. Students will also learn how to fix these issues.
- By adding transformations and interactions to the regression toolbox, datasets with multiple predictors offer a myriad of potential models. Students will use strategies for building models and selecting variables in such circumstances.
- Multiple linear regression can be generalized to handle a response variable that is categorical or a count variable. Students will learn the basics of such models, specifically logistic and Poisson regression, including model fitting and inference.
This undergraduate level course covers the following topics:
- Statistical Inference Foundations
- Simple Linear Regression (SLR) Model
- SLR Evaluation
- SLR Model Assumptions, Estimation & Prediction
- Multiple Linear Regression (MLR) Model & Evaluation
- MLR Model Assumptions, Estimation & Prediction
- Transformation & Interactions
- Categorical Predictors
- Influential Points
- Regression Pitfalls
- Model Building
- Logistic & Poisson Regression
Dr. Iain Pardoe is the primary author of these course materials and has taught online for the Department of Statistics for many years. He is also the primary course author for STAT 501: Regression Methods.
Students will use their choice of statistical software programs R or Minitab in this course. See the Statistical Software page for more information.
Pardoe, I. (2012). Applied Regression Modeling, 2nd Edition, Wiley. ISBN: 978-1-118-09728-1 (or E-Text: 978-1-119-09428-9 or E-Book: 978-1-118-34504-7). See https://www.iainpardoe.com/arm2e/.
- STAT 200, STAT 240, STAT 250, STAT 301 or STAT 401