Why Changing a Regression Model Changes the Projection

📰 Medium · Data Science

Learn how changing a regression model affects the projection and fit of the data, and understand the geometric interpretation of linear regression

intermediate Published 15 Apr 2026

Action Steps

Compare different least-squares models to understand how changing the model affects the subspace and fit
Visualize the geometric interpretation of linear regression to understand the relationship between the model and the data
Apply the concepts to real-world data to see how changing the model affects the projection and fit
Evaluate the performance of different models using metrics such as mean squared error or R-squared
Refine the model by iterating on the process and selecting the best model for the specific problem

Who Needs to Know This

Data scientists and analysts can benefit from this article to improve their understanding of regression models and their applications, and to effectively communicate with team members and stakeholders

Key Insight

💡 Changing a regression model changes the subspace and therefore changes the fit, highlighting the importance of model selection and evaluation

Key Takeaways

Learn how changing a regression model affects the projection and fit of the data, and understand the geometric interpretation of linear regression

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Title: Why Changing a Regression Model Changes the Projection

URL Source: https://medium.com/graphmath/why-changing-a-regression-model-changes-the-projection-4b396d28fb02?source=rss------data_science-5

Published Time: 2026-04-15T00:33:09Z

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# Why Changing a Regression Model Changes the Projection | by Eteri Byazrova | GraphMath | Apr, 2026 | Medium

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# Why Changing a Regression Model Changes the Projection

## Keeping the data fixed, we compare three least-squares models to show how changing the model changes the subspace — and therefore changes the fit

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_(in collaboration with_[_Yuri Morozov_](https://medium.com/@yumorozov)_)_

Linear regression is often presented as a formula for fitting a line to data. Geometrically, it is a pro

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Why Changing a Regression Model Changes the Projection

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