Data Science Statistics

Regression Analysis: Beyond the Basics

Model real-world relationships with rigor, diagnostics, and practical statistical judgment

Regression Analysis: Beyond the Basics logo
Quick Course Facts
19
Self-paced, Online, Lessons
19
Videos and/or Narrated Presentations
6.5
Approximate Hours of Course Media
About the Regression Analysis: Beyond the Basics Course

Regression Analysis: Beyond the Basics is a practical Data Science course for learners who want to move past simple fitted lines and build models they can defend. You will learn how to model real-world relationships with rigor, diagnostics, and practical statistical judgment while improving both prediction and interpretation.

Build Stronger Regression Models For Data Science

  • Move from basic regression formulas to a structured modeling mindset for real-world Data Science problems.
  • Diagnose residuals, outliers, leverage, heteroskedasticity, and other issues that can weaken your conclusions.
  • Design better model forms using transformations, polynomial terms, interactions, and categorical predictors.
  • Compare, validate, regularize, and communicate regression results with appropriate caution and clarity.

This course teaches advanced regression analysis techniques for building reliable, interpretable, and practical statistical models.

In Regression Analysis: Beyond the Basics, you will develop the judgment needed to choose, refine, and explain regression models in applied Data Science settings. The course begins with multiple regression structure, interpretation, assumptions, and estimators, then shows what can go wrong when those assumptions are ignored.

You will practice model diagnostics and repair strategies, including residual analysis, influential observation detection, robust standard errors, and approaches for handling unstable or misleading results. You will also learn how transformations, curved relationships, interaction effects, contrasts, and reference groups can help your models better represent the relationships in your data.

The course then expands into model reliability and selection, covering multicollinearity, AIC, BIC, adjusted R-squared, cross-validation, predictive performance, and regularization with ridge, lasso, and elastic net. You will also go beyond ordinary least squares with logistic regression, count models, robust regression, and quantile regression.

By the end of this course, you will be able to model real-world relationships with rigor, diagnostics, and practical statistical judgment. You will leave with a stronger Data Science workflow for building regression models, reviewing their limitations, and communicating results without overclaiming.

Course Lessons

Full lesson breakdown

Lessons are organized by topic area and each includes descriptive copy for search visibility and student clarity.

Foundations and Modeling Mindset

3 lessons

This lesson reframes regression as a disciplined modeling activity rather than a mechanical equation-fitting exercise. Students move from the familiar idea of drawing a line through data to thinking c…

Lesson 2: Multiple Regression Structure and Interpretation

20 min
This lesson establishes the structure and interpretation of multiple regression models. Students learn how a regression equation represents conditional relationships, what it means to hold other predi…

Lesson 3: Assumptions, Estimators, and What Can Go Wrong

21 min
This lesson establishes the modeling mindset needed for regression beyond fitting a line and reading coefficients. Students learn what ordinary least squares is estimating, why assumptions matter, and…

Model Diagnostics and Repair

3 lessons

Lesson 4: Residual Diagnostics in Practice

22 min
Residual diagnostics are where regression stops being a formula and starts becoming statistical judgment. In this lesson, Professor Victor Zane shows how to read residual patterns in practice, disting…

Lesson 5: Outliers, Leverage, and Influential Observations

20 min
This lesson teaches how to distinguish ordinary large residuals from observations that can materially change a regression model. Students learn the practical difference between outliers, high-leverage…

Lesson 6: Heteroskedasticity and Robust Standard Errors

19 min
This lesson explains how heteroskedasticity weakens ordinary least squares inference even when coefficient estimates remain unbiased under the usual exogeneity condition. You will learn to recognize n…

Model Form and Feature Design

4 lessons

Lesson 7: Transforming Predictors and Outcomes

21 min
This lesson shows how transformations help regression models represent real-world relationships more accurately without abandoning interpretability. Students learn when to transform predictors, when t…

Lesson 8: Polynomial Terms and Curved Relationships

18 min
Polynomial terms let a regression model represent curved relationships while still using the familiar linear regression framework. In this lesson, you will learn when polynomial features are useful, h…

Lesson 9: Interaction Effects and Conditional Interpretation

23 min
This lesson shows how interaction terms let a regression model represent relationships that change across groups or across levels of another predictor. Instead of treating one coefficient as a univers…

Lesson 10: Categorical Predictors, Contrasts, and Reference Groups

19 min
This lesson explains how categorical predictors enter regression models, why reference groups shape coefficient interpretation, and how contrast choices affect the questions a model answers. Students …

Model Reliability and Selection

4 lessons

Lesson 11: Multicollinearity, Variance Inflation, and Stability

20 min
This lesson examines multicollinearity as a reliability problem in multiple regression: predictors may jointly explain the outcome well while individual coefficient estimates become unstable, imprecis…

Lesson 12: Model Comparison with AIC, BIC, and Adjusted R-Squared

18 min
This lesson explains how to compare regression models using adjusted R-squared, AIC, and BIC without treating any single statistic as an automatic decision rule. Students learn what each criterion rew…

Lesson 13: Cross-Validation and Predictive Performance

21 min
This lesson explains how cross-validation estimates predictive performance and supports model selection in regression. It focuses on practical choices: train/test splits, k-fold cross-validation, repe…

Lesson 14: Regularization with Ridge, Lasso, and Elastic Net

23 min
This lesson introduces regularization as a practical response to unstable regression estimates, multicollinearity, and overfitting. Students learn how ridge, lasso, and elastic net modify ordinary lea…

Beyond Ordinary Least Squares

3 lessons

Lesson 15: Logistic Regression for Binary Outcomes

22 min
This lesson introduces logistic regression as the standard regression framework for binary outcomes, such as default versus no default, churn versus retention, or treatment success versus failure. It …

Lesson 16: Poisson and Negative Binomial Regression for Counts

21 min
This lesson shows how to model count outcomes when ordinary least squares is a poor fit. Students learn why counts require special treatment, how Poisson regression links predictors to expected event …

Lesson 17: Robust and Quantile Regression

20 min
This lesson extends regression practice beyond ordinary least squares by focusing on models that remain useful when the data contain outliers, heavy-tailed errors, skewed outcomes, or relationships th…

Application and Communication

2 lessons

Lesson 18: Communicating Regression Results Without Overclaiming

18 min
This lesson focuses on translating regression output into claims that are useful, honest, and appropriately limited. Students learn how to describe coefficients, uncertainty, model fit, assumptions, a…

Lesson 19: Applied Regression Workflow and Final Model Review

24 min
In this lesson, Professor Victor Zane brings the course together with an applied regression workflow for moving from a messy analytical question to a defensible final model. The focus is not on adding…
About Your Instructor
Professor Victor Zane

Professor Victor Zane

Professor Victor Zane guides this AI-built Virversity course with a clear, practical teaching style.