Regression Analysis
This course will teach you how multiple linear regression models are derived, assumptions in the models, how to test whether data meets assumptions, and develop strategies for building and understanding useful models.
Overview
Regression is perhaps the most widely used statistical technique. It estimates relationships between independent variables (predictors) and a dependent variable (outcome). Regression models can be used to help understand and explain relationships among variables; they can also be used to predict outcomes.
In this course you will learn how to derive multiple linear regression models, how to use software to implement them, and what assumptions underlie the models. You will also learn how to test whether your data meets those assumptions, what can be done when those assumptions are not met, and strategies to build and understand useful models.
- Intermediate
- 4 Weeks
- Expert Instructor
- Tuiton-Back Guarantee
- 100% Online
- TA Support
Learning Outcomes
After completing this course you should be able to calculate both simple and multiple regression models. You will learn how to assess the model’s “fit”, test model assumptions, and transform predictor and response variables to improve outcomes. You will also learn to identify critical aspects of the data that can influence results of your model and how to exercise caution with respect to extrapolation from regression results.
- Calculate a simple linear regression model
- Assess the model with standard error, R-squared, and slope
- Review and check model assumptions
- Extend the model to multiple linear regression
- Assess parameter estimates globally, in subsets, and individually
- Test model assumptions
- Deal with qualitative predictors
- Transform predictors and response variables to improve model fit
- Handle interactions among predictors
- Identify influential points
- Deal with autocorrelation, multicollinearity, and missing data
- Exercise appropriate caution with respect to extrapolation
Who Should Take This Course
Scientists, business analysts, engineers and researchers who need to model relationships in data in which a single response variable depends on multiple predictor variables. If you were introduced to regression in an introductory statistics course and now find you need a more solid grounding in the subject, this course is for you. If you are planning to learn additional topics in statistics, a good knowledge of regression is often essential.
Our Instructors
Dr. Iain Pardoe
Dr. Iain Pardoe teaches online and writes courses for Thompson Rivers University Open Learning. He also does statistical consulting and was formerly an Associate Professor of Decision Sciences at the University of Oregon Lundquist College of Business. His research specialty is in the area of multivariate modeling. He has numerous journal publications (including a noted paper in the Journal of the Royal Statistical Society on predicting Academy Award winners).
Course Syllabus
Week 1
Foundations and Simple Linear Regression
- Brief review of univariate statistical ideas: confidence intervals
hypothesis testing
prediction - confidence intervals
- hypothesis testing
- prediction
- Simple linear regression model and least squares estimation
- Model evaluation: regression standard error
R-squared
testing the slope - regression standard error
- R-squared
- testing the slope
- Checking model assumptions
- Estimation and prediction
Week 2
Multiple Linear Regression
- Multiple linear regression model and least squares estimation
- Model evaluation: regression standard error
R-squared
testing the regression parameters globally
testing the regression parameters in subsets
testing the regression parameters individually - regression standard error
- R-squared
- testing the regression parameters globally
- testing the regression parameters in subsets
- testing the regression parameters individually
- Checking model assumptions
- Estimation and prediction
Week 3
Model Building I
- Predictor transformations
- Response transformations
- Predictor interactions
- Qualitative predictors and the use of indicator variables
Week 4
Model Building II
- Influential points (outliers and leverage)
- Autocorrelation
- Multicollinearity
- Excluding important predictors
- Overfitting
- Extrapolation
- Missing data
- Model building guidelines
- Model interpretation using graphics
Class Dates
2024
Instructors: Dr. Iain Pardoe
Instructors: Dr. Iain Pardoe
Instructors: Dr. Iain Pardoe
2025
Instructors: Dr. Iain Pardoe
Instructors: Dr. Iain Pardoe
Instructors: Dr. Iain Pardoe
Prerequisites
Introductory Statistics for Credit
- Skill: Intermediate
- Credit Options: ACE, CAP, CEU
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Additional Information
Time Requirements
About 15 hours per week, at times of your choosing.
Homework
Homework in this course consists of short answer questions to test concepts and guided data analysis problems using software.
Course Text
The required text for this course is Applied Regression Modeling, Third Edition by Iain Pardoe.
Software
You will need software that is capable of doing regression analysis, which all statistical software does. If you are undecided about which package to choose, consider the following:
1. If you are likely to take additional statistical modeling courses and intend to apply these methods to your research, you should choose a standard package with power and flexibility (R, SAS, JMP, SPSS, Minitab, Stata).
2. If your plans include applications of data science and data analytics in business, you should probably choose R (if your company already uses SAS or SPSS, that’s also fine).
3. If you want to work as a manager or analyst in business, but not as a data scientist, you could use an Excel add-in like XLStat or XLMiner (the latter does not cover all the procedures in the course).
4. If you have no immediate plans for further coursework and a short learning curve is your main consideration, consider Statcrunch, JMP or Minitab.
The instructor is most familiar with R and Minitab. There will be some supplementary materials in the course to provide assistance with R, SPSS, Minitab, SAS, JMP, EViews, Stata, and Statistica. Our teaching assistants can offer some help with R, Minitab, SAS, JMP, Stata, Excel, and StatCrunch.
Course Fee & Information
Enrollment
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Transfers and Withdrawals
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