RAUndergraduate courses
Regression Analysis
How multiple linear regression models are derived, what they assume, how to test whether your data meets those assumptions, and how to build a model worth trusting.
- Intermediate
- 4 weeks
- Approx. 15 hours per week
- 3 semester hours
About this course
Regression is the most widely applied statistical technique there is: it describes the relationship between one or more predictor variables and a response variable, and it is used both to explain that relationship and to forecast the response. This course covers how simple and multiple linear regression models are derived and how to fit them in software, the assumptions they rest on, how to check whether your data meets those assumptions, and what to do when it does not. It goes on to model building — transformations, interactions, qualitative predictors — and to the problems that show up in real data: influential points, autocorrelation, multicollinearity, missing data and overfitting.
Who this course is for
Scientists, business analysts, engineers and researchers who need to model relationships in data where a single response variable depends on multiple predictor variables. It also suits anyone who wants a firmer footing in regression after an introductory statistics course, or who is heading toward further statistical study that will assume it.
What you will learn
11 outcomes
By the end of this course, you will be able to:
- Compute simple and multiple linear regression models
- Evaluate model fit using the regression standard error, R-squared and tests of the slope
- Check and verify model assumptions
- Assess regression parameters globally, in subsets and individually
- Incorporate qualitative predictors using indicator variables
- Transform predictor and response variables for a better fit
- Handle interactions between predictors
- Identify influential data points — outliers and high-leverage observations
- Deal with autocorrelation, multicollinearity and missing data
- Recognize overfitting and the limits of extrapolation
- Interpret and communicate a model using graphics
Week by week
4-Week curriculum overview
This curriculum is identical across all start dates. Expand a week to explore the topics covered.
- Weeks
- 4
- Your week
- Approx. 15 hours
- Level
- Intermediate
Foundations and simple linear regressionWeek 1
- Brief review of univariate statistical concepts — confidence intervals, hypothesis testing, prediction
- The simple linear regression model and least squares estimation
- Model evaluation — regression standard error, R-squared, testing the slope
- Checking model assumptions
- Estimation and prediction
Multiple linear regressionWeek 2
- The multiple linear regression model and least squares estimation
- Model evaluation — regression standard error and R-squared
- Testing regression parameters globally, in subsets and individually
- Checking model assumptions
- Estimation and prediction
Model building IWeek 3
- Predictor transformations
- Response transformations
- Predictor interactions
- Qualitative predictors and indicator variables
Model building IIWeek 4
- Influential points — outliers and leverage
- Autocorrelation
- Multicollinearity
- Excluding important predictors
- Overfitting
- Extrapolation
- Missing data
- Model building guidelines
- Model interpretation using graphics
Instructors
Expert-Led Guidance
Each cohort is led by dedicated instructors and assistant teachers who actively lead weekly discussions, provide personalized feedback and grade your assignments.
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.
Before you start
What you need to know first
An introductory statistics course
Course Format & Schedule
This is a 4-week, 100% online, asynchronous course.
- No mandatory live sessions: Log in and complete your work at times that fit your schedule.
- Weekly Releases: At the start of each week, you will receive new lecture materials and answer keys for the previous week's exercises.
- Interactive Community: Work through exercises, submit assignments, and engage with your instructor and peers via a private discussion board.
Homework
Short-answer questions testing the concepts, and guided data analysis problems using software.
Texts
The required text for this course is Applied Regression Modeling, Third Edition by Iain Pardoe.
Software
Any statistical software that can fit a regression will do, and you should use whichever one you expect to keep using. A full package — R, SAS, JMP, SPSS, Minitab or Stata — is the better choice if you intend to study further; R, SAS and SPSS are the usual ones in business and data science work; and if you want something simpler, an Excel add-in such as XLStat or XLMiner, StatCrunch, JMP or Minitab is enough for the course. Supplementary course materials are provided for R, SPSS, Minitab, SAS, JMP, EViews, Stata and Statistica.
FAQ
How is this different from the regression in a predictive analytics course?This course
The purpose differs, and so does the emphasis. A predictive course judges a regression by how well it does on records it has not seen. Here the model itself is the object of study: where the coefficients come from, what the model assumes, how to test whether your data meets those assumptions, and what to do about influential points, multicollinearity and autocorrelation when it does not.
Is there a money-back or satisfaction guarantee?Every course
We handle cancellation and refund requests on an individual basis. If a course is not meeting your expectations or your circumstances change, please reach out to our team (support@learnstatistics.org) so we can work with you on a solution.
Can I transfer to a later start date or withdraw after the course begins?Every course
Yes. If you need to defer your enrollment to a future start date, withdraw mid-course, or transfer your seat to a colleague, please contact us directly. We address these requests flexibly on a case-by-case basis.
Who teaches the course?Every course
Each cohort is led by dedicated instructors and assistant teachers who actively lead weekly discussions, provide personalized feedback and grade your assignments.
Something not answered here? Ask us before you book — and the terms set out what a purchase covers.
Credit, and where it counts
This course carries a verified figure of 3 semester hours. A credit recommendation from the American Council on Education says what a course is worth; the institution receiving it decides whether to award it.
Anyone can take this subject: there is no application, and you do not have to be studying at a university. It also counts toward a degree at Thomas Edison State University, which decides what to award for it. The full position — including the limits each university publishes is on its own page, and worth reading before you buy.