---
title: "Ordinary least squares (OLS): formula and papers"
description: "Ordinary least squares (OLS) was mentioned in 113 papers in the last 30 days (2026-09-27 to 2026-10-26), ranking #7 of the 104 equations and models mentioned."
url: https://scholar4ai.com/equations/ordinary-least-squares-ols
markdown_url: https://scholar4ai.com/equations/ordinary-least-squares-ols.md
license: CC BY-NC 4.0 (https://creativecommons.org/licenses/by-nc/4.0/)
data_url: https://scholar4ai.com/data/rankings.json
updated: 2026-10-26T12:13:05+09:00
window: 2026-09-27 to 2026-10-26
source: OpenAlex (CC0)
---

# Ordinary least squares (OLS)

$$
\hat\beta = (X^\top X)^{-1} X^\top y
$$

Linear regression coefficients that minimize the sum of squared residuals.

- area: Regression models
- 20 papers in the last 7 days
- Names searched for: ordinary least squares, OLS

Back to the ranking: https://scholar4ai.com/rankings/equations.md

## Key findings

- Ordinary least squares (OLS) was mentioned in 113 papers in the last 30 days (2026-09-27 to 2026-10-26), ranking #7 of the 104 equations and models mentioned.
- By journal category: Economics (41), Finance (41), Management (24), Accounting (4), AI (2) and Operations Research (1).
- Most of them appeared in International Review of Economics & Finance (19), Future Business Journal (6) and Empirical Economics (3).
- Often mentioned together with Instrumental variables (two-stage least squares) (37), Logistic regression (logit) (24) and Two-way fixed-effects panel regression (22).
- Datasets named in the same papers: OR-Library (18), World Development Indicators (World Bank) (15) and S&P 500 (12).

*Papers mentioning Ordinary least squares (OLS), newest first. Newest 50 of 113 papers; all of them are in /data/papers.json.*

| Date | Title | Journal | Authors | Affiliations |
|---|---|---|---|---|
| 2026-10-24 | [Fiscal information and stated willingness to pay taxes: evidence from a survey experiment](https://doi.org/10.1007/s10797-026-10007-3) | [International Tax and Public Finance](https://scholar4ai.com/journals/international-tax-and-public-finance.md) | José María Durán-Cabré, Alejandro Esteller Moré, Riccardo Secomandi | Barcelona School of Economics; Universitat de Barcelona; University of Ferrara |
| 2026-10-24 | [Too much of a good thing? Knowledge transfer and scientists’ job satisfaction](https://doi.org/10.1007/s10961-026-10400-4) | [The Journal of Technology Transfer](https://scholar4ai.com/journals/the-journal-of-technology-transfer.md) | Christian Schröder, Ann-Christin Grözinger, Arndt Werner et al. | University of Siegen; University of Göttingen; ZHAW Zurich University of Applied Sciences |
| 2026-10-23 | [Dynamic prediction of loss given default in Norwegian retail credit card debt: advanced machine learning versus statistical models](https://doi.org/10.1007/s42521-026-00230-2) | [Digital Finance](https://scholar4ai.com/journals/digital-finance.md) | Cathy Ho, Isabel A. C. Sandersen, Espen Selliken et al. | Norwegian University of Science and Technology |
| 2026-10-23 | [Job insecurity and health: evidence from older European workers](https://doi.org/10.1007/s00181-026-02992-5) | [Empirical Economics](https://scholar4ai.com/journals/empirical-economics.md) | Eduard Suari‐Andreu, Tim Schwartz, Max van Lent et al. | Leiden University; Network for Studies on Pensions, Aging and Retirement; SEO Amsterdam Economics; … |
| 2026-10-23 | [Public support for regulatory research on the potential ecological effects of RF-EMF](https://doi.org/10.1016/j.techfore.2026.124938) | [Technological Forecasting and Social Change](https://scholar4ai.com/journals/technological-forecasting-and-social-change.md) | Laura Recuero Virto, Peter Bou Saba, Arno Thielens et al. | Centre Européen de Recherche en Economie Financière et Gestion des Entreprises; ICN Business School Nancy-Paris-Berlin; Université de Lorraine; … |
| 2026-10-23 | [Evaluating machine learning and econometric models for inflation forecasting: evidence from a Sub-Saharan African panel](https://doi.org/10.1186/s43093-026-01003-4) | [Future Business Journal](https://scholar4ai.com/journals/future-business-journal.md) | Baffour Osei, Abigail Boatemaa, Isaac Nyame et al. | University of Skills Training and Entrepreneurial Development; University of Bradford; Kwame Nkrumah University of Science and Technology; … |
| 2026-10-23 | [From pixels to profits: trading arbitrage portfolios based on image representations](https://doi.org/10.1007/s11408-026-00507-x) | [Financial markets and portfolio management](https://scholar4ai.com/journals/financial-markets-and-portfolio-management.md) | Niklas Paluszkiewicz | Universität Ulm |
| 2026-10-23 | [Managerial slack, information environment and stock price crash risk: Evidence from China](https://doi.org/10.1016/j.iref.2026.106011) | [International Review of Economics & Finance](https://scholar4ai.com/journals/international-review-of-economics-finance.md) | Chuyue Wu, Yuyang Ling, Yikai Han | Central University of Finance and Economics |
| 2026-10-23 | [The impact of LLM-based recommendations on decisions under uncertainty](https://doi.org/10.1017/eec.2026.10062) | [Experimental Economics](https://scholar4ai.com/journals/experimental-economics.md) | Marty Haoyuan Chen, Emel Filiz‐Ozbay, Erkut Yusuf Ozbay | University of Maryland, College Park |
| 2026-10-22 | [Do long-term yields help to estimate short-term risk premia?](https://doi.org/10.1016/j.jfineco.2026.104386) | [Journal of Financial Economics](https://scholar4ai.com/journals/journal-of-financial-economics.md) | Andrea Berardi, Roger Brown, Stephen M. Schaefer |  |
| 2026-10-22 | [Asymmetric decentralization and inequality](https://doi.org/10.1007/s00168-026-01586-4) | [The Annals of Regional Science](https://scholar4ai.com/journals/the-annals-of-regional-science.md) | Melissa Ziegler Rogers, Melissa Ziegler Rogers | Duke University; Claremont Graduate University |
| 2026-10-22 | [Asymmetric behavioural responses to updating caloric information](https://doi.org/10.1007/s11166-026-09511-y) | [Journal of Risk and Uncertainty](https://scholar4ai.com/journals/journal-of-risk-and-uncertainty.md) | Jan Michael Bauer, Jeffrey M. Brunstrom, Giulia Priolo et al. | Copenhagen Business School; University of Bristol; University of Cambridge |
| 2026-10-22 | [Business networks and the persistence of entrepreneurship: evidence from China](https://doi.org/10.1007/s11187-026-01292-7) | [Small Business Economics](https://scholar4ai.com/journals/small-business-economics.md) | Han Wang, Neil Lee | University of Southampton; London School of Economics and Political Science |
| 2026-10-21 | [Hot–cold reciprocation gaps](https://doi.org/10.1017/eec.2026.10059) | [Experimental Economics](https://scholar4ai.com/journals/experimental-economics.md) | Riccardo Ghidoni, Sigrid Suetens, Jierui Yang | University of Bologna; Tilburg University; Xiangtan University |
| 2026-10-21 | [When bargaining power matters: foreign direct investment and bilateral GDP disparities](https://doi.org/10.1007/s00181-026-02990-7) | [Empirical Economics](https://scholar4ai.com/journals/empirical-economics.md) | Xing Xu, Emin Gahramanov, Qinglai Meng et al. | Shanghai Institute of Technology; American University of Sharjah; Oregon State University; … |
| 2026-10-21 | [The gendered inequality impact of the cost-of-living crisis: a comparative analysis](https://doi.org/10.1007/s10888-026-09754-4) | [The Journal of Economic Inequality](https://scholar4ai.com/journals/the-journal-of-economic-inequality.md) | Denisa Maria Sologon, Karina Doorley, Iryna Kyzyma et al. | Luxembourg Institute of Socio-Economic Research; Trinity College Dublin; Ollscoil na Gaillimhe – University of Galway |
| 2026-10-21 | [Leveraging Machine Learning for Profit Forecasting and Cost Optimization Using Public Financial Data](https://doi.org/10.1007/s10614-026-11455-z) | [Computational Economics](https://scholar4ai.com/journals/computational-economics.md) | Bilal Ahmad, Abdu Salam, Mian Abdulbasit et al. | University of Peshawar; Abdul Wali Khan University Mardan; Yeungnam University; … |
| 2026-10-21 | [Buffering institutional erosion: organizational ties and SME exports under populism](https://doi.org/10.1057/s41267-026-00911-5) | [Journal of International Business Studies](https://scholar4ai.com/journals/journal-of-international-business-studies.md) | Xiaolong Shui, Luyang Chen, Michael; id_orcid 0000-0002-4701-6283 Witt | University of Bristol; Bristol Robotics Laboratory; University of Westminster; … |
| 2026-10-21 | [The economic geography of Churches: housing market effects in Stockholm](https://doi.org/10.1007/s10824-026-09609-w) | [Journal of Cultural Economics](https://scholar4ai.com/journals/journal-of-cultural-economics.md) | Mats Wilhelmsson | KTH Royal Institute of Technology |
| 2026-10-20 | [Enhancing the resilience of entrepreneurs](https://doi.org/10.1007/s11365-026-01257-y) | [International Entrepreneurship and Management Journal](https://scholar4ai.com/journals/international-entrepreneurship-and-management-journal.md) | Ana Rosado-Cubero, Adolfo Hernández, Francisco José Blanco-Jiménez et al. | Universidad Complutense de Madrid; Universidad Rey Juan Carlos |
| 2026-10-17 | [The shapes of knowledge spillovers: the AC-KS model](https://doi.org/10.1007/s11187-026-01286-5) | [Small Business Economics](https://scholar4ai.com/journals/small-business-economics.md) | Gustavo A. Barboza, Alessandro Braga, Aubin Duchier | Loyola University New Orleans |
| 2026-10-17 | [LLM application in digital asset assessments: mixed methods research](https://doi.org/10.1007/s10115-026-02910-2) | [Knowledge and Information Systems](https://scholar4ai.com/journals/knowledge-and-information-systems.md) | Yann Thorens, Martin Angerer, Pejman Ebrahimi et al. | University of Liechtenstein |
| 2026-10-17 | [The role of immigrant caregivers in improving the welfare of elders and reducing public health costs](https://doi.org/10.1007/s00148-026-01216-5) | [Journal of Population Economics](https://scholar4ai.com/journals/journal-of-population-economics.md) | Lisa Capretti, Joanna Aleksandra Kopinska, Rama Dasi Mariani et al. | University of Rome Tor Vergata; Sapienza University of Rome; Roma Tre University |
| 2026-10-16 | [Sustainable finance versus non-sustainable finance and environmental sustainability: evidence from selected OECD economies](https://doi.org/10.1186/s40854-026-00981-2) | [Financial Innovation](https://scholar4ai.com/journals/financial-innovation.md) | Daniel Balsalobre‐Lorente, Magdalena Radulescu, Niu Rong et al. | Azerbaijan State University of Economics; Universidad Ecotec; University of Castilla-La Mancha; … |
| 2026-10-16 | [Resilient or unstable? Real rate regimes in emerging markets](https://doi.org/10.1007/s00181-026-02977-4) | [Empirical Economics](https://scholar4ai.com/journals/empirical-economics.md) | Türker BATMAZ, Alper Gormus, Elif Hilal Nazlıoğlu | Balıkesir University; Coastal Carolina University; Pamukkale University |
| 2026-10-15 | [Economic uncertainty and fertility cycles: baby boom and busts in twentieth century USA](https://doi.org/10.1007/s10887-026-09273-x) | [Journal of Economic Growth](https://scholar4ai.com/journals/journal-of-economic-growth.md) | Bastien Chabé-Ferret, Paula E. Gobbi | Luxembourg Institute of Socio-Economic Research; Middlesex University London; Université Libre de Bruxelles |
| 2026-10-15 | [Economic Inequality Reduces Sustainable Consumption: Cross-National and Experimental Evidence and Psychological Mechanisms](https://doi.org/10.1007/s10551-026-06437-y) | [Journal of Business Ethics](https://scholar4ai.com/journals/journal-of-business-ethics.md) | Steven A. Brieger, Jacob Hörisch, Xinyu Zhang | NEOMA Business School; Leuphana University of Lüneburg; University of Sussex |
| 2026-10-14 | [Does the widespread of mobile internet narrow the urban–rural labor income gap? Evidence from China](https://doi.org/10.1016/j.eap.2026.10.043) | [Economic Analysis and Policy](https://scholar4ai.com/journals/economic-analysis-and-policy.md) | Yunshu Shao | Korea University |
| 2026-10-13 | [Climate disclosure and risk premium in the European bond market](https://doi.org/10.1007/s40822-026-00401-x) | [Eurasian economic review :](https://scholar4ai.com/journals/eurasian-economic-review.md) | Matteo Mazzarano, Gianni Guastella, Stefano Pareglio et al. | Università Cattolica del Sacro Cuore; Athens University of Economics and Business; University of Bologna; … |
| 2026-10-13 | [Training and productivity in micro-firms](https://doi.org/10.1016/j.respol.2026.105637) | [Research Policy](https://scholar4ai.com/journals/research-policy.md) | Marco Rispoli, Federico Tamagni | Prometeia (Italy); Scuola Superiore Sant'Anna |
| 2026-10-12 | [Correction: Trade and local labor market outcomes in Mexico: disentangling the channels and the role of geography, sectors, and trade types](https://doi.org/10.1007/s10290-026-00665-0) | [Review of World Economics](https://scholar4ai.com/journals/review-of-world-economics.md) | Emmanuel Vázquez, Deborah Elisabeth Winkler | Universidad Nacional de La Plata; World Bank Group |
| 2026-10-12 | [The influence of inflation on commercial bank performance: a systematic review](https://doi.org/10.1186/s43093-026-01013-2) | [Future Business Journal](https://scholar4ai.com/journals/future-business-journal.md) | Safwan Al-Dhobee, Mohammed Al-Rafaik, Ali Al-Oluki et al. | Sana'a University; Thamar University; Al-Razi University |
| 2026-10-10 | [Feasible GLS for time series regression](https://doi.org/10.1016/j.jeconom.2026.106346) | [Journal of Econometrics](https://scholar4ai.com/journals/journal-of-econometrics.md) | Pierre Perron Z, Emilio González-Coya | Boston University |
| 2026-10-10 | [Innovation bridging sustainability: the role of digital finance, institutional policy stringency, and climate physical risks for advancing energy transformation](https://doi.org/10.1186/s40854-026-00972-3) | [Financial Innovation](https://scholar4ai.com/journals/financial-innovation.md) | Huma Iftikhar, Luo Guang, Ningyu Qian | Huazhong University of Science and Technology |
| 2026-10-10 | [So similar, yet so different: comparing the US GAAP and IFRS experience at eliciting greater transparency on pension asset disclosures](https://doi.org/10.1007/s11142-026-09992-x) | [Review of Accounting Studies](https://scholar4ai.com/journals/review-of-accounting-studies.md) | Divya Anantharaman, Elizabeth Chuk, Tonni Shijun Xia | Rutgers, The State University of New Jersey; University of California, Irvine; San Diego State University |
| 2026-10-10 | [When heat hits: Short-run saving and withdrawal behavior among microfinance clients in Benin](https://doi.org/10.1016/j.worlddev.2026.107578) | [World Development](https://scholar4ai.com/journals/world-development.md) | Anna Mader, Oliver Mußhoff | Humboldt-Universität zu Berlin |
| 2026-10-10 | [The unseen pain of the Vietnam War: long-term effects of Agent Orange on labor market outcomes](https://doi.org/10.1007/s00148-026-01217-4) | [Journal of Population Economics](https://scholar4ai.com/journals/journal-of-population-economics.md) | Luu Duc Toan Huynh, Po Yin Wong | Queen Mary University of London |
| 2026-10-09 | [Product market competition and target difficulty: The role of innovation](https://doi.org/10.1016/j.iref.2026.105958) | [International Review of Economics & Finance](https://scholar4ai.com/journals/international-review-of-economics-finance.md) | Seul Gi Oh |  |
| 2026-10-09 | [The impact of pension fund market entry reform on household risk asset allocation: A financial analysis based on lifecycle theory](https://doi.org/10.1016/j.iref.2026.105964) | [International Review of Economics & Finance](https://scholar4ai.com/journals/international-review-of-economics-finance.md) | Guang Guo, Ying Liu, Wenhao Ling | Henan University |
| 2026-10-09 | [Place-based variation in health care: evidence from mandatory movers in the U.S. military health system](https://doi.org/10.1016/j.jhealeco.2026.103192) | [Journal of Health Economics](https://scholar4ai.com/journals/journal-of-health-economics.md) | Roxana Leal, Wei Luan, Jonathan Skinner et al. | Institute For Defense Analyses; Dartmouth College; Dartmouth Hospital |
| 2026-10-08 | [Living labs as entrepreneurial ecosystem architectures evidence from Horizon 2020 and Horizon Europe](https://doi.org/10.1007/s11365-026-01258-x) | [International Entrepreneurship and Management Journal](https://scholar4ai.com/journals/international-entrepreneurship-and-management-journal.md) | Giusy Sica, Chiara Spiniello, Maria Palazzo et al. | Mercatorum University; European Southern Observatory; University of Naples Federico II |
| 2026-10-08 | [When women take all: Direct election and female leadership](https://doi.org/10.1016/j.jebo.2026.107791) | [Journal of Economic Behavior & Organization](https://scholar4ai.com/journals/journal-of-economic-behavior-organization.md) | Davide Cipullo | Università Cattolica del Sacro Cuore; Enel (Italy) |
| 2026-10-08 | [Behavioral drivers of cryptocurrency markets: A systematic review](https://doi.org/10.1016/j.jbef.2026.101265) | [Journal of Behavioral and Experimental Finance](https://scholar4ai.com/journals/journal-of-behavioral-and-experimental-finance.md) | Sebastian Steindl, Hans Rüdiger Kaufmann, Bernd Britzelmaier | University of Nicosia; Pforzheim University of Applied Sciences |
| 2026-10-08 | [Is the relationship between climate policy uncertainty and cash holding nonlinear?](https://doi.org/10.1016/j.najef.2026.102730) | [The North American Journal of Economics and Finance](https://scholar4ai.com/journals/the-north-american-journal-of-economics-and-finance.md) | Augustinos I. Dimitras, Efstathios Magerakis, George Peppas | Hellenic Open University |
| 2026-10-07 | [Artificial intelligence technologies, skills demand and employment: Evidence from linked job ads](https://doi.org/10.1016/j.labeco.2026.102974) | [Labour Economics](https://scholar4ai.com/journals/labour-economics.md) | Lennert Peede, Michael Stops | Institut für Arbeitsmarkt und Berufsforschung |
| 2026-10-07 | [The conditional value relevance of ESG and innovation disclosures: a multi-method analysis of European firms combining panel econometrics and machine learning](https://doi.org/10.1007/s10479-026-07442-0) | [Annals of Operations Research](https://scholar4ai.com/journals/annals-of-operations-research.md) | Andreas Errikos Delegkos, Evangelia Arsenou, Dionisis Cavouras et al. | University of West Attica; University College Dublin |
| 2026-10-07 | [Geopolitical risk and the spatial convergence of renewable energy consumption: Evidence from 1996 to 2026](https://doi.org/10.1016/j.iref.2026.105920) | [International Review of Economics & Finance](https://scholar4ai.com/journals/international-review-of-economics-finance.md) | Liu He, 邹佰峰, Xing Chiang | Northeast Agricultural University; Northeast Forestry University; City University of Macau |
| 2026-10-07 | [Governance effectiveness of new rural elites and evaluation of rural revitalization outcomes: Evidence from 1302 samples in China](https://doi.org/10.1016/j.iref.2026.105951) | [International Review of Economics & Finance](https://scholar4ai.com/journals/international-review-of-economics-finance.md) | Yulin Tong, Yinghan Zhu, Ji Yiduo et al. | Nanchang University |
| 2026-10-06 | [CSR focus under competitive pressure: The role of national institutions](https://doi.org/10.1016/j.jwb.2026.101784) | [Journal of World Business](https://scholar4ai.com/journals/journal-of-world-business.md) | Limin Fu, Dirk Michael Boehe, Mariano L.M. Heyden | Monash University; Université Mohammed VI Polytechnique |
| 2026-10-06 | [Sentiment interactions in financial markets: Conditional volatility, feedback, and shock propagation](https://doi.org/10.1016/j.iref.2026.105946) | [International Review of Economics & Finance](https://scholar4ai.com/journals/international-review-of-economics-finance.md) | Md Tanvir Hasan | University of Dhaka; University of Glasgow |