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- March 2022 (Revised January 2025)
- Technical Note
Linear Regression
This note provides an overview of linear regression for an introductory data science course. It begins with a discussion of correlation, and explains why correlation does not necessarily imply causation. The note then describes the method of least squares, and how to... View Details
Keywords: Data Science; Linear Regression; Mathematical Modeling; Mathematical Methods; Analytics and Data Science
Bojinov, Iavor I., Michael Parzen, and Paul Hamilton. "Linear Regression." Harvard Business School Technical Note 622-100, March 2022. (Revised January 2025.)
- June 2021
- Technical Note
Introduction to Linear Regression
By: Michael Parzen and Paul Hamilton
This technical note introduces (from an applied point of view) the theory and application of simple and multiple linear regression. The motivation for the model is introduced, as well as how to interpret the summary output with regard to prediction and statistical... View Details
- May 2020
- Article
Scalable Holistic Linear Regression
By: Dimitris Bertsimas and Michael Lingzhi Li
We propose a new scalable algorithm for holistic linear regression building on Bertsimas & King (2016). Specifically, we develop new theory to model significance and multicollinearity as lazy constraints rather than checking the conditions iteratively. The resulting... View Details
Bertsimas, Dimitris, and Michael Lingzhi Li. "Scalable Holistic Linear Regression." Operations Research Letters 48, no. 3 (May 2020): 203–208.
- 2023
- Working Paper
PRIMO: Private Regression in Multiple Outcomes
By: Seth Neel
We introduce a new differentially private regression setting we call Private Regression in Multiple Outcomes (PRIMO), inspired the common situation where a data analyst wants to perform a set of l regressions while preserving privacy, where the covariates... View Details
Neel, Seth. "PRIMO: Private Regression in Multiple Outcomes." Working Paper, March 2023.
- 2024
- Working Paper
Anytime-Valid Inference in Linear Models and Regression-Adjusted Causal Inference
By: Michael Lindon, Dae Woong Ham, Martin Tingley and Iavor I. Bojinov
Linear regression adjustment is commonly used to analyze randomized controlled experiments due to its efficiency and robustness against model misspecification. Current testing and interval estimation procedures leverage the asymptotic distribution of such estimators to... View Details
Lindon, Michael, Dae Woong Ham, Martin Tingley, and Iavor I. Bojinov. "Anytime-Valid Inference in Linear Models and Regression-Adjusted Causal Inference." Harvard Business School Working Paper, No. 24-060, March 2024.
- 2013
- Other Teaching and Training Material
Operations Management Reading: Forecasting
By: Steven C. Wheelwright and Ann B. Winslow
This reading provides an introduction to forecasting methods. It includes a brief summary of methods based on judgment and a longer section on quantitative analysis. It also provides sample data so students can develop an understanding of concepts such as correlation,... View Details
Wheelwright, Steven C., and Ann B. Winslow. "Operations Management Reading: Forecasting." Core Curriculum Readings Series. Boston: Harvard Business Publishing 8042, 2013.
- 2022
- Working Paper
Machine Learning Models for Prediction of Scope 3 Carbon Emissions
By: George Serafeim and Gladys Vélez Caicedo
For most organizations, the vast amount of carbon emissions occur in their supply chain and in the post-sale processing, usage, and end of life treatment of a product, collectively labelled scope 3 emissions. In this paper, we train machine learning algorithms on 15... View Details
Keywords: Carbon Emissions; Climate Change; Environment; Carbon Accounting; Machine Learning; Artificial Intelligence; Digital; Data Science; Environmental Sustainability; Environmental Management; Environmental Accounting
Serafeim, George, and Gladys Vélez Caicedo. "Machine Learning Models for Prediction of Scope 3 Carbon Emissions." Harvard Business School Working Paper, No. 22-080, June 2022.
- September 2009
- Article
A Detailed Analysis of the Reduction Mammaplasty Learning Curve: A Statistical Process Model for Approaching Surgical Performance Improvement
By: Matthew Carty MD, Rodney Chan, Robert S. Huckman, Daniel C. Snow and Dennis Orgill
Background: The increased focus on quality and efficiency improvement within academic surgery has met with variable success among plastic surgeons. Traditional surgical performance metrics, such as morbidity and mortality, are insufficient to improve the... View Details
Keywords: Experience and Expertise; Health Care and Treatment; Medical Specialties; Outcome or Result; Performance Efficiency; Performance Improvement
Carty, Matthew, MD, Rodney Chan, Robert S. Huckman, Daniel C. Snow, and Dennis Orgill. "A Detailed Analysis of the Reduction Mammaplasty Learning Curve: A Statistical Process Model for Approaching Surgical Performance Improvement." Plastic and Reconstructive Surgery 124, no. 3 (September 2009): 706–714.
- 2009
- Article
Modeling Expert Opinions on Food Healthfulness: A Nutrition Metric
By: Jolie M. Martin, John Beshears, Katherine L. Milkman, Max H. Bazerman and Lisa Sutherland
Research over the last several decades indicates the failure of existing nutritional labels to substantially improve the healthiness of consumers' food and beverage choices. The difficulty for policy-makers is to encapsulate a wide body of scientific knowledge in a... View Details
Keywords: Judgments; Food; Nutrition; Labels; Knowledge Use and Leverage; Demand and Consumers; Measurement and Metrics; Mathematical Methods
Martin, Jolie M., John Beshears, Katherine L. Milkman, Max H. Bazerman, and Lisa Sutherland. "Modeling Expert Opinions on Food Healthfulness: A Nutrition Metric." Journal of the American Dietetic Association 109, no. 6 (June 2009): 1088–1091.
- 19 Oct 2021
- HBS Seminar
Cynthia Rudin, Duke University
- March 2024
- Article
Investigation of Divergent Thinking among Surgeons and Surgeon Trainees in Canada (IDEAS): A Mixed-methods Study
By: Alex Thabane, Tyler McKechnie, Vikram Arora, Goran Calic, Jason W Busse, Ranil Sonnadara and Mohit Bhandari
Objective: To assess the creative potential of surgeons and surgeon trainees, as measured by divergent thinking. The secondary objectives were to identify factors associated with divergent thinking, assess confidence in creative problem-solving and the perceived effect... View Details
Thabane, Alex, Tyler McKechnie, Vikram Arora, Goran Calic, Jason W Busse, Ranil Sonnadara, and Mohit Bhandari. "Investigation of Divergent Thinking among Surgeons and Surgeon Trainees in Canada (IDEAS): A Mixed-methods Study." BMJ Open 14, no. 3 (March 2024).
- February 2022
- Article
Sugar-sweetened Beverage Purchases and Intake at Event Arenas with and without a Portion Size Cap
By: Sheri Volger, James Scott Parrott, Brian Elbel, Leslie K. John, Jason P. Block, Pamela Rothpletz-Puglia and Christina A. Roberto
This is the first real-world study to examine the association between a voluntary 16-ounce (oz.) portion-size cap on sugar-sweetened beverages (SSB) at a sporting arena on volume of SSBs and food calories purchased and consumed during basketball games. Cross-sectional... View Details
Keywords: Sugar-sweetened Beverages; Nutrition Policy; Obesity Prevention; Portion Sizes; Nutrition; Policy; Health; Behavior
Volger, Sheri, James Scott Parrott, Brian Elbel, Leslie K. John, Jason P. Block, Pamela Rothpletz-Puglia, and Christina A. Roberto. "Sugar-sweetened Beverage Purchases and Intake at Event Arenas with and without a Portion Size Cap." Art. 101661. Preventative Medicine Reports 25 (February 2022).
- February 2025
- Article
Variation in Batch Ordering of Imaging Tests in the Emergency Department and the Impact on Care Delivery
By: Jacob C. Jameson, Soroush Saghafian, Robert S. Huckman and Nicole Hodgson
Objectives: To examine heterogeneity in physician batch ordering practices and measure the impact of a physician's tendency to batch order imaging tests on patient outcomes and resource utilization.
Study Setting and Design: In this retrospective study, we used... View Details
Study Setting and Design: In this retrospective study, we used... View Details
Keywords: Health Care; Operations Management; Productivity; Health Care and Treatment; Operations; Outcome or Result; Resource Allocation; Health Industry; United States
Jameson, Jacob C., Soroush Saghafian, Robert S. Huckman, and Nicole Hodgson. "Variation in Batch Ordering of Imaging Tests in the Emergency Department and the Impact on Care Delivery." Health Services Research 60, no. 1 (February 2025).
- Article
Preventing Fairness Gerrymandering: Auditing and Learning for Subgroup Fairness
By: Michael J Kearns, Seth Neel, Aaron Leon Roth and Zhiwei Steven Wu
The most prevalent notions of fairness in machine learning are statistical definitions: they fix a small collection of pre-defined groups, and then ask for parity of some statistic of the classifier (like classification rate or false positive rate) across these groups.... View Details
Kearns, Michael J., Seth Neel, Aaron Leon Roth, and Zhiwei Steven Wu. "Preventing Fairness Gerrymandering: Auditing and Learning for Subgroup Fairness." Proceedings of the International Conference on Machine Learning (ICML) 35th (2018).
- Web
Online Business Analytics Course | HBS Online
results of a series of website A/B tests 8 hrs Module 4 Single Variable Linear Regression Analyze the relationship between two variables and develop forecasts for values outside the data set. Highlights... View Details
- Web
Business Fundamentals Course - CORe | HBS Online
uses data to recognize trends and inform business decisions in the movie industry. Show Hide Details Modules Describing and Summarizing Data Sampling and Estimation Hypothesis Testing Single Variable Linear View Details
- 01 Jun 2022
- News
A Sustainable Solution for Fashion
sell toothpicks; you can just follow a linear regression line. But if you are trying to sell a three-quarter-length floral print dress that’s only available for one season, you need more sophisticated models... View Details
Keywords: April White
- Web
Frequently Asked Questions | HBS Online
sampling and estimation, hypothesis testing, and regression analysis. The course is intended for individuals at all stages of their careers who would like to strengthen their analytical skills, including college students and recent... View Details
- 16 Aug 2011
- First Look
First Look: August 16
their collective interest levels to implement a regression discontinuity approach. We confirm the positive effects for venture operations, with qualitative support for a higher likelihood of successful exits. On the other hand, there is... View Details
Keywords: Sean Silverthorne
- 01 Sep 2015
- First Look
First Look -- September 1, 2015
inadequate in the study of bounded dependent variables and may produce predicted values that lie outside the unit interval. Established nonlinear approaches, such as logit and probit transformations or censored and truncated regressions... View Details
Keywords: Sean Silverthorne