# Regression Analysis II - Linear Models

**Course content**

The goal is to develop an applied and intuitive (not purely theoretical or mathematical) understanding of the topics and procedures, so that participants can use them in their own research and also understand the work of others. Whenever possible presentations will be in “Words,” “Picture,” and “Math” languages in order to appeal to a variety of learning styles.

Advanced regression topics will be covered only after the foundations have been established. The ordinary least squares multiple regression topics that will be covered include:

- Various F‑tests (e.g., group significance test; Chow test; relative importance of

variables and groups of variables; comparison of overall model performance). - Categorical independent variables (e.g., new tests for “Intervalness” and

“Collapsing”). - Dichotomous dependent variables: Logit and Probit analysis.
- Outliers, influence, and leverage.
- Advanced diagnostic plots and graphical techniques.
- Matrix algebra: A quick primer.
*(Optional)* - Regression models… now from a matrix perspective.
- Heteroskedasticity: Definition, consequences, detection, and correction.
- Autocorrelation: Definition, consequences, detection, and correction.
- Generalized Least Squares (GLS) and Weighted Least Squares (WLS).

**Structure**

This course will utilize approximately 325 pages of “Lecture Transcripts.” These Lecture Transcripts are organized in nine Packets and will serve as the sole required textbook for this course. (They also will serve as an information resource after the course ends.) In addition, the Lecture Transcripts will significantly reduce the amount of notes participants have to write during class, which means they can concentrate much more on learning and understanding the material itself. These nine Packets will be provided at the beginning of the first class.

It is important to note that *this is a course on regression analysis, not on computer or software usage. *While in‑class examples are presented using SPSS, participants are free and encouraged to use the statistical software package of their choice to replicate these examples and to analyze their own datasets. Note that many statistical software packages can be used with the material in this course. Participants can, at their option, complete several formative data analysis projects; a detailed and comprehensive “Tutorial and Answer Key” will be provided for each.

**Prerequisites**

This course is a continuation of Tim McDaniel’s “Regression I – Introduction” course. While it is not necessary that participants have taken that specific course, they will need to be familiar with many of the topics that are covered in it.

Note: We will use matrix algebra in the second half of the course. We will not use calculus.

**Literature**

The aforementioned Lecture Transcript Packets that we will use in each class serve as the de facto required textbook for this course.

In addition, the course syllabus includes full bibliographic information pertaining to several supplemental (and optional) readings for each of the nine Packets of Lecture Transcripts.

- Some of these readings are from four traditional textbooks, each of which takes a somewhat (though at times only subtly) different pedagogical approach.
- The optional supplemental readings also include several “little green books” from the Sage Series on Quantitative Applications in the Social Sciences.
- Finally, I have included several articles from a number of journals across several academic disciplines.Some of these optional supplemental readings are older classics and others are more recently written and published.

**Examination part**

Decentral ‑ Written examination (100%)

**Supplementary aids**

Open Book

**Examination content**

The potential substantive content areas for the Final Examination are:

- Various F‑tests (e.g., group significance test; Chow test; relative importance of

variables and groups of variables; comparison of overall model performance). - Categorical independent variables (e.g., new tests for “Intervalness” and “Collapsing”).
- Dichotomous dependent variables: Logit and Probit analysis.
- Outliers, influence, and leverage.
- Advanced diagnostic plots and graphical techniques.
- Regression models… now from a matrix perspective.
- Heteroskedasticity: Definition, consequences, detection, and correction.
- Autocorrelation: Definition, consequences, detection, and correction.
- Generalized Least Squares (GLS) and Weighted Least Squares (WLS).

Since this final examination is the only artifact that will be formally graded in the course, it will determine the course grade. Note that class attendance, discussion participation, and studying the material outside of class are indirectly very important for earning a good score on the final examination.

The final examination will be written, open‑ook (i.e., class notes, Lecture Transcripts, and Tutorial and Answer Key documents are allowed), and open‑note. No other materials, including Laptops, cell phones, or other electronic devices, will be permitted.The written final exam will be two hours in length and administered during the last course meeting.

**Literature**

Literature relevant to the exam:

- Lecture Transcripts (nine Packets; approximately 325 pages).
- Class notes (taken by each participant individually).
- Assignment Tutorial and Answer Key documents (for each optional data analysis

project).

Supplementary/Voluntary literature not directly relevant to the exam:

- Optional supplemental readings listed in the course syllabus (and discussed earlier).
- Any other textbooks, articles, etc., the participant reads before or during the course.