---
title: What the Heck Is Best Subsets Regression, and Why Would I Want It?
description: What the Heck Is Best Subsets Regression, and Why Would I Want It?
image: https://blog.minitab.com/hubfs/B2BML%20-%20NEW%20FILE%20MANAGER%20STRUCTURE/Blog%20Images/Imported_Blog_Media/models_to_size_4_w640.jpg
---
English
- [English](https://blog.minitab.com/en/?hsLang=en)
- [Français](https://blog.minitab.com/fr/?hsLang=en)
- [Deutsch](https://blog.minitab.com/de/?hsLang=en)
- [Português](https://blog.minitab.com/pt/?hsLang=en)
- [Español](https://blog.minitab.com/es/?hsLang=en)
- [日本語](https://blog.minitab.com/ja/?hsLang=en)
- [한국어](https://blog.minitab.com/ko/?hsLang=en)
- [中文（简体）](https://blog.minitab.com/zh/?hsLang=en)
- [ Partners](https://www.minitab.com/en-us/company/partners/)
- [ Contact](https://www.minitab.com/en-us/company/contact-us/)
- [ Talk to Minitab](https://www.minitab.com/en-us/talk-to-minitab/)
- [ My Account](https://licensing.minitab.com/account/manage)
[](https://www.minitab.com/en-us/)
- Products
Back
[Products](https://www.minitab.com/en-us/products/)
[All Products](https://www.minitab.com/en-us/products/)
- [Minitab Solution Center](https://www.minitab.com/en-us/products/minitab-solution-center/)
- [Minitab Statistical Software](https://www.minitab.com/en-us/products/minitab/)
- [Minitab Connect](https://www.minitab.com/en-us/products/connect/)
- [Minitab Model Ops](https://www.minitab.com/en-us/products/model-ops/)
- [Minitab Education Hub](https://www.minitab.com/en-us/products/education-hub/)
- [Minitab Engage](https://www.minitab.com/en-us/products/engage/)
- [Minitab Workspace](https://www.minitab.com/en-us/products/workspace/)
- [Real-Time SPC](https://www.minitab.com/en-us/products/real-time-spc/)
- [Prolink Data Collection & SPC](https://www.minitab.com/en-us/products/prolink)
- [Simul8 Discrete Event Simulation](https://info.minitab.com/en/new-to-simul8?hsLang=en)
- [SPM](https://www.minitab.com/en-us/products/spm/)
- Solutions
Back
[Solutions](https://www.minitab.com/en-us/solutions/)
[All Solutions](https://www.minitab.com/en-us/solutions/)
- [Analytics](https://www.minitab.com/en-us/solutions/analytics/)
- [Statistics & Predictive Analytics](https://www.minitab.com/en-us/solutions/analytics/statistical-analysis-predictive-analytics/)
- [Data Science & Machine Learning](https://www.minitab.com/en-us/solutions/analytics/data-science-machine-learning/)
- [Business Analytics & Intelligence](https://www.minitab.com/en-us/solutions/analytics/business-analytics-intelligence/)
- [Statistical Process Control](https://www.minitab.com/en-us/solutions/analytics/statistical-process-control/)
- [Quality Analytics](https://www.minitab.com/en-us/solutions/analytics/quality-analytics/)
- [Live Analytics](https://www.minitab.com/en-us/solutions/analytics/live-analytics/)
- [Reliability & Life Data Analysis](https://www.minitab.com/en-us/solutions/analytics/reliability/)
- [Discrete Event Simulation](https://info.minitab.com/en/new-to-simul8?hsLang=en)
- [Process Mining](https://info.minitab.com/en/new-to-simul8?hsLang=en)
- [Key Capabilities](https://www.minitab.com/en-us/solutions/key-capabilities/)
- [Continuous Improvement](https://www.minitab.com/en-us/solutions/key-capabilities/continuous-improvement/)
- [Data Integration & Data Prep](https://www.minitab.com/en-us/solutions/key-capabilities/data-integration-data-prep/)
- [Diagramming & Mind Mapping](https://www.minitab.com/en-us/solutions/key-capabilities/diagramming-mind-mapping/)
- [Digital Twins](https://info.minitab.com/en/new-to-simul8?hsLang=en)
- [Model Deployment & ML Ops](https://www.minitab.com/en-us/solutions/key-capabilities/model-deployment-ml-ops/)
- [Innovation & Project Management](https://www.minitab.com/en-us/solutions/key-capabilities/innovation-project-management/)
- [Process Excellence: Detect, Correct & Prevent](https://www.minitab.com/en-us/solutions/key-capabilities/process-excellence/)
- [Featured Industries](https://www.minitab.com/en-us/solutions/industry/)
- [Academic](https://www.minitab.com/en-us/solutions/industry/academic/)
- [Energy & Natural Resources](https://www.minitab.com/en-us/solutions/industry/energy-resources/)
- [Government & Public Sector](https://www.minitab.com/en-us/solutions/industry/government/)
- [Healthcare](https://www.minitab.com/en-us/solutions/industry/healthcare/)
- [Insurance](https://www.minitab.com/en-us/solutions/industry/insurance/)
- [Manufacturing & Industrial](https://www.minitab.com/en-us/solutions/industry/manufacturing-industrial/)
- [Services](https://www.minitab.com/en-us/solutions/industry/service-industries/)
- [Software & Technology](https://www.minitab.com/en-us/solutions/industry/software-technology/)
- [Construction](https://www.minitab.com/en-us/solutions/industry/construction/)
- [Featured Roles](https://www.minitab.com/en-us/solutions/role/)
- [Engineering](https://www.minitab.com/en-us/solutions/role/engineering/)
- [Business Analysis](https://www.minitab.com/en-us/solutions/role/business-analysts/)
- [Information Technology](https://www.minitab.com/en-us/solutions/role/information-technology/)
- [Supply Chain](https://www.minitab.com/en-us/solutions/role/supply-chain/)
- [Customer Service & Contact Center](https://www.minitab.com/en-us/solutions/role/customer-service-contact-center/)
- [Human Resources](https://www.minitab.com/en-us/solutions/role/human-resources/)
- [Marketing](https://www.minitab.com/en-us/solutions/role/marketing/)
- [Research and Development](https://www.minitab.com/en-us/solutions/role/research-and-development/)
- Resources & Services
Back
[Resources & Services](https://www.minitab.com/en-us/resources-services/)
[All Resources & Services](https://www.minitab.com/en-us/resources-services/)
- [Resources](https://www.minitab.com/en-us/resources-services/resources/)
- [Case Studies](https://www.minitab.com/en-us/resources-services/resources/case-studies/)
- [eBooks & White Papers](https://www.minitab.com/en-us/resources-services/resources/ebooks-and-white-papers/)
- [Blog](https://blog.minitab.com/blog/?hsLang=en)
- [Data Sets](https://www.minitab.com/en-us/resources-services/resources/data-set/)
- [Webinars & Events](https://www.minitab.com/en-us/resources-services/resources/events/)
- [Education Hub](https://www.minitab.com/en-us/resources-services/resources/education-hub/)
- [Services](https://www.minitab.com/en-us/resources-services/services/)
- [Training](https://www.minitab.com/en-us/resources-services/services/training/)
- [Deployment](https://www.minitab.com/en-us/resources-services/services/deployment/)
- [Consulting](https://www.minitab.com/en-us/resources-services/services/statistical-consulting/)
- [Self-Paced Learning](https://www.minitab.com/en-us/resources-services/services/self-paced-learning/)
- [Continuing Education](https://www.minitab.com/en-us/resources-services/services/continuing-education/)
- Support
Back
[Support](https://www.minitab.com/en-us/support/)
[Technical Support](https://www.minitab.com/en-us/support/)
- [Subscriptions & Activation](https://www.minitab.com/en-us/support/subscriptions-and-activation/)
- [Minitab Quick Start](https://www.minitab.com/en-us/support/quick-start/)
- [Training](https://www.minitab.com/en-us/resources-services/services/training/)
- [Installation Support](https://www.minitab.com/en-us/support/installation/)
- [Support Videos](https://www.minitab.com/en-us/support/videos/)
- [Support Documentation](https://www.minitab.com/en-us/support/documents/)
- [Software Updates](https://www.minitab.com/en-us/support/software-updates/)
- [Product Downloads](https://www.minitab.com/en-us/support/downloads/)
- [Support Policy](https://www.minitab.com/en-us/support/policy/)
- Company
Back
[Company](https://www.minitab.com/en-us/company/)
[Company](https://www.minitab.com/en-us/company/)
- [About Us](https://www.minitab.com/en-us/company/our-company/)
- [Leadership Team](https://www.minitab.com/en-us/company/leadership-team/)
- [Partners](https://www.minitab.com/en-us/company/partners/)
- [Careers](https://www.minitab.com/en-us/company/careers/)
- [Contact](https://www.minitab.com/en-us/company/contact-us/)
- [News](https://www.minitab.com/en-us/company/press-releases/)
[Try/Buy](https://www.minitab.com/en-us/try-buy/)
- [Statistics](https://blog.minitab.com/en/blog/tag/statistics)
- [Data Analysis](https://blog.minitab.com/en/blog/tag/data-analysis)
-
- [Quality Improvement](https://blog.minitab.com/en/blog/tag/quality-improvement)
- [Subscribe](https://info.minitab.com/blog/subscribe?hsLang=en)
## Notice
You are now leaving minitab.com.
Click Continue to proceed to:
Continue
Go Back
# What the Heck Is Best Subsets Regression, and Why Would I Want It?
[Cody Steele](https://blog.minitab.com/en/blog/author/cody-steele) | 12/19/2012
Topics: [Regression Analysis](https://blog.minitab.com/en/blog/tag/regression-analysis)
- [Share](https://www.linkedin.com/shareArticle?mini=true&url=https://blog.minitab.com/en/blog/statistics-and-quality-improvement/what-the-heck-is-best-subsets-regression-and-why-would-i-want-it)
- [Share](https://www.facebook.com/sharer.php?u=https://blog.minitab.com/en/blog/statistics-and-quality-improvement/what-the-heck-is-best-subsets-regression-and-why-would-i-want-it)
Last time, [we used stepwise regression to come up with models for the gummi bear data](https://blog.minitab.com/blog/statistics-and-quality-improvement/gummi-bear-doe-stepwise-model-selection?hsLang=en). Stepwise regression is a great tool, but it has a downside: when we use stepwise selection in design of experiments, especially if we focus on only the last step, we can miss interesting models that might be useful.
One way to look at more models is to use Minitab’s Best Subsets feature. Instead of identifying a single model based on statistical significance, Minitab’s Best Subsets feature shows a number of different models, as well as some statistics to help us compare those models.
To get the idea, let’s look at some smaller models.
The variables column (Vars) shows how many terms are in the model. In this case, I requested that Minitab print two models with 1–4 terms. Here are the statistics that Minitab provides to help you choose a model:
- R2 is for when you compare models with the same number of terms. Higher is better.
- Adjusted R2 is for when you compare models with different numbers of terms. Higher is better.
- Mallows’ Cp is for when you compare models with the same or different numbers of terms, provided all of the models came from the same initial set of terms. If you change the predictors and run best subsets a second time, you cannot use Mallows’ Cp to compare the models. The smaller the Mallows’ Cp, the better it is for prediction. The closer it is to the printed number of variables + 1 (for the intercept term), the less biased the estimates of the coefficients are.
- S is an estimate of the variability about the regression line. Smaller is better.
In the output above, the model with
- the position of the fulcrum
- the angle of the catapult
- the number of rubber band windings, and
- the interaction between the position of the catapult, the position of the gummi bear, and the number of rubber band windings
has the best statistics. However, the statistics for the other 4-predictor model are so close that it would be hard to say that one is practically better than the other.
With a smaller number of models to work with, you can use Minitab to check the predicted R2 values. Predicted R2 is similar to the other R2 type statistics, but estimates how well a model predicts new observations. Often, this criterion about new observations is the most appealing assessment to use. We want the model to predict what will happen when we launch a new gummi bear. As it turns out, the predicted R2 values are nearly equal for both four-term models: 77.09%. Based on these statistics, there’s no reason to think that one model will outperform the other, even though their predictions can vary considerably.
Next time, I’ll plan to take a look at some larger models to see if we can do better on the predictions. If you’re ready for more statistics now, take a look at what [Jim Colton can show you about some common misconceptions about R2](http://www.minitab.com/en-us/Published-Articles/Some-Misconceptions-about-R2/).
## You Might Also Like
[How One Hotel Used Data to Improve Guest Satisfaction](https://blog.minitab.com/en/blog/how-one-hotel-used-data-to-improve-guest-satisfaction?hsLang=en)
[Brainstorm](https://blog.minitab.com/en/blog/tag/brainstorm) | 9 Minute Read
[Enhancing Accelerated Underwriting Efficiency with Predictive Analytics](https://blog.minitab.com/en/blog/enhancing-accelerated-underwriting-efficiency-with-predictive-analytics?hsLang=en)
[Regression Analysis](https://blog.minitab.com/en/blog/tag/regression-analysis) | 3 Minute Read
[Predictive Analytics and Determining Patient Length of Stay at Time of Admission](https://blog.minitab.com/en/blog/predictive-analytics-and-determining-patient-length-of-stay-at-time-of-admission?hsLang=en)
[Regression Analysis](https://blog.minitab.com/en/blog/tag/regression-analysis) | 5 Minute Read
---
- [Careers](https://www.minitab.com/en-us/company/careers/)
- [Trust Center](https://www.minitab.com/en-us/trust-center/)
- [Suppliers](https://www.minitab.com/en-us/suppliers/)
- [Site Map](https://www.minitab.com/en-us/site-map/)
- [](https://www.linkedin.com/company/minitab/)
- [](https://www.facebook.com/Minitab/)
- [](https://www.youtube.com/user/MinitabInc)
- [](https://www.instagram.com/minitab/)
---
© 2025 Minitab, LLC. All Rights Reserved.
- [Terms of Use](https://www.minitab.com/en-us/legal/terms-of-use/)
- [Privacy Policy](https://www.minitab.com/en-us/legal/privacy-policy/)
- [Legal](https://www.minitab.com/en-us/legal/)
- Cookies Settings