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    • News  (1)
    • Research  (21)
    • Events  (1)
  • Faculty Publications  (14)

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  • All HBS Web  (27)
    • News  (1)
    • Research  (21)
    • Events  (1)
  • Faculty Publications  (14)
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  • March 2022 (Revised January 2025)
  • Technical Note

Linear Regression

By: Iavor I. Bojinov, Michael Parzen and Paul Hamilton
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
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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
Keywords: Linear Regression; Regression; Analysis; Forecasting and Prediction; Risk and Uncertainty; Theory; Compensation and Benefits; Mathematical Methods; Analytics and Data Science
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Parzen, Michael, and Paul Hamilton. "Introduction to Linear Regression." Harvard Business School Technical Note 621-086, June 2021.
  • 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
Keywords: Mathematical Methods; Analytics and Data Science
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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
Keywords: Analytics and Data Science; Mathematical Methods
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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
Keywords: Mathematical Methods; Analytics and Data Science
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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
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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
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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
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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
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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.
  • 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
Keywords: Creativity; Cognition and Thinking; Surveys; Health Industry
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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
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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).
  • 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
Keywords: Machine Learning; Algorithms; Fairness; Mathematical Methods
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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).
  • 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
Keywords: Health Care; Operations Management; Productivity; Health Care and Treatment; Operations; Outcome or Result; Resource Allocation; Health Industry; United States
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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).
  • 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
  • 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
  • 26 Jan 2010
  • First Look

First Look: Jan. 26

between 1995 and 2007. Multiple linear regression analyses were conducted to determine the relative impact of key factors on operative time. Explanatory learning curve models were generated, and complication... View Details
Keywords: Martha Lagace
  • 18 Mar 2008
  • First Look

First Look: March 18, 2008

beverages, and after verifying the similarity of their responses, we generated a model that calculates the expected average healthiness rating that experts would give to any other product based on its nutrient content. Results—The form of the model is a View Details
Keywords: Martha Lagace
  • 19 Dec 2006
  • First Look

First Look: December 19, 2006

series models within the context of a single-stage stochastic inventory system with periodic review, constant leadtimes, infinite supply, full backlogging, linear holding and penalty costs and no ordering costs. Forecasting ARIMA time... View Details
Keywords: Sean Silverthorne
  • 10 Apr 2018
  • First Look

First Look at New Research, April 10, 2018

that occurred near the end of their time at university (2 or 3 years later). Linear regression models showed that students who made more friends in their first term reported better health and a healthier... View Details
Keywords: Sean Silverthorne
  • 01 Feb 2011
  • First Look

First Look: Feb. 1

transformations were homologically related to changes in the prevailing mode of governance in the American economy: business schools became essential sites for the development of tools and methods (e.g., input-output approaches, linear... View Details
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