STAT 462: Applied Regression Analysis

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course overview

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.

1. 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.

2. 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.

3. 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.

4. 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.

5. 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.

6. 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.

7. 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.

8. 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.

 course topics

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

prerequisites

  • STAT 200, STAT 240, STAT 250, STAT 301 or STAT 401

textbook

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 http://www.iainpardoe.com/arm2e/.

software

Students will use their choice of  statistical software programs R or Minitab in this course. See the Statistical Software page for more information.

assessment plan

Participation: The class will have discussion boards and you will be expected to follow the discussion boards and also participate in any discussions. You are also expected to keep up with all class communications and check Canvas on a regular basis.

Quizzes: 12 online quizzes based on material in the textbook and the online notes to be submitted online by the end of each lesson.

Assignments: 12 written assignments consisting of problems specially prepared for the course and selected from the textbook to be submitted online by the end of each lesson.

Midterm Exams: 2 midterm exams to be submitted online by the end of each midterm exam period. Midterm exams have to be completed within a 3-hour time period at a time of your choice during the exam period.

Final Exam: The final exam will be comprehensive and is proctored (please see your course syllabus you receive upon enrollment for details).

academic integrity

All Penn State policies regarding ethics and honorable behavior apply to this course. Academic integrity is the pursuit of scholarly activity free from fraud and deception and is an educational objective of this institution. All University policies regarding academic integrity apply to this course. Academic dishonesty includes, but is not limited to, cheating, plagiarizing, fabricating of information or citations, facilitating acts of academic dishonesty by others, having unauthorized possession of examinations, submitting work of another person or work previously used without informing the instructor, or tampering with the academic work of other students.

For any material or ideas obtained from other sources, such as the text or things you see on the web, in the library, etc., a source reference must be given. Direct quotes from any source must be identified as such.

All exam answers must be your own, and you must not provide any assistance to other students during exams. Any instances of academic dishonesty WILL be pursued under the University and Eberly College of Science regulations concerning academic integrity. For more information on academic integrity, see Penn State's statement on plagiarism and academic dishonesty.

The Eberly College of Science Code of Mutual Respect and Cooperation embodies the values that we hope our faculty, staff, and students possess and will endorse to make The Eberly College of Science a place where every individual feels respected and valued, as well as challenged and rewarded.

disabilities

Penn State welcomes students with disabilities into the University's educational programs. If you have a disability-related need for reasonable academic adjustments in this course, contact the Office for Disability Services (ODS) at 814-863-1807 (V/TTY). For further information regarding ODS, please visit the Office for Disability Services Web site at http://equity.psu.edu/ods/.

In order to receive consideration for course accommodations, you must contact ODS and provide documentation (see the documentation guidelines at http://equity.psu.edu/ods/guidelines/documentation-guidelines). If the documentation supports the need for academic adjustments, ODS will provide a letter identifying appropriate academic adjustments. Please share this letter and discuss the adjustments with your instructor as early in the course as possible. You must contact ODS and request academic adjustment letters at the beginning of each semester.

course author

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.