--- title: Polynomial Regression in Machine Learning: Teaching... description: An explanation of Polynomial Regression as a technique that extends Linear Regression to model curved relationships by transforming features into polynomial... canonical: https://daily.dev/posts/polynomial-regression-in-machine-learning-teaching-linear-regression-to-bend-2zfgia44e twitter:card: summary_large_image twitter:site: @dailydotdev og:type: website og:site_name: daily.dev og:title: Polynomial Regression in Machine Learning: Teaching Linear Regression to Bend | daily.dev og:description: An explanation of Polynomial Regression as a technique that extends Linear Regression to model curved relationships by transforming features into polynomial... og:url: https://daily.dev/posts/polynomial-regression-in-machine-learning-teaching-linear-regression-to-bend-2zfgia44e og:image: https://api.daily.dev/og/posts/2ZfGiA44E.png og:image:alt: Polynomial Regression in Machine Learning: Teaching Linear Regression to Bend og:image:width: 1200 og:image:height: 630 og:locale: en --- > ## Documentation Index > Fetch the complete documentation index at: https://daily.dev/llms.txt > Use this file to discover all available pages before exploring further. # Polynomial Regression in Machine Learning: Teaching Linear Regression to Bend **[Medium](https://daily.dev/sources/medium_js)** · 17 min read · 0 upvotes · 0 comments ## Summary An explanation of Polynomial Regression as a technique that extends Linear Regression to model curved relationships by transforming features into polynomial terms (x², x³, etc.) while keeping the model linear in its parameters. Covers why the model is still 'linear' despite fitting curves, how to implement it with scikit-learn's PolynomialFeatures and Pipeline, the role of feature scaling, interaction terms with multiple features, the bias-variance trade-off, overfitting risks with high degrees, and how to choose the right polynomial degree using validation. ## Full article daily.dev links to this article rather than hosting it. Read it at the original source: ## Questions this post answers ### Why is polynomial regression still considered a type of linear regression even though it fits curves? Polynomial regression is linear in its parameters, not in its features. The coefficients beta_0, beta_1, beta_2 are combined additively with transformed features like x and x², so the model is still a linear combination of parameters. Conceptually it is feature transformation (turning x into 1, x, x²) followed by ordinary linear regression on those new features. _daily.dev helps developers deepen concepts like linear versus non-linear models while learning machine learning fundamentals._ ### What does the include_bias parameter do in scikit-learn's PolynomialFeatures? Setting include_bias=True adds a column of ones to the transformed feature matrix, representing the intercept term beta_0 explicitly. For a single feature with degree 2, this produces columns [1, x, x²]. In practice, scikit-learn's LinearRegression already handles the intercept by default, so including the bias column manually is often unnecessary, though understanding it clarifies exactly what PolynomialFeatures generates. _Developers tuning scikit-learn pipelines can revisit details like this on daily.dev while building regression models._ ### Why do you need feature scaling when using high-degree polynomial regression? Polynomial transformation creates features with vastly different magnitudes—for x=10, x² is 100 but x^10 is 10,000,000,000—which makes optimization numerically unstable and causes gradient descent to converge poorly. Applying StandardScaler after PolynomialFeatures brings these transformed features onto comparable scales, which is especially important for optimization-based algorithms like SGDRegressor. _Anyone debugging convergence issues in regression pipelines can track these gotchas via daily.dev._ ## Similar posts on daily.dev - [Linear Regression For Machine Learning….](https://daily.dev/posts/linear-regression-for-machine-learning--cbrwzucbu) · Medium · 0 upvotes · 0 comments - [Multiple Linear Regression Explained Simply \(Part 1\)](https://daily.dev/posts/multiple-linear-regression-explained-simply-part-1--05gzjtxbz) · Towards Data Science · 0 upvotes · 0 comments - [Multiple Linear Regression: From One Feature to a Hyperplane](https://daily.dev/posts/multiple-linear-regression-from-one-feature-to-a-hyperplane-ruyegs6qm) · Medium · 0 upvotes · 0 comments - [Linear Regression Is Actually a Projection Problem \(Part 2: From Projections to Predictions\)](https://daily.dev/posts/linear-regression-is-actually-a-projection-problem-part-2-from-projections-to-predictions--wejmyibaf) · Towards Data Science · 0 upvotes · 0 comments --- Tags: [#machine-learning](https://daily.dev/tags/machine-learning), [#python](https://daily.dev/tags/python), [#scikit](https://daily.dev/tags/scikit), [#overfitting](https://daily.dev/tags/overfitting) [View this post on daily.dev](https://daily.dev/posts/polynomial-regression-in-machine-learning-teaching-linear-regression-to-bend-2zfgia44e) ```json {"@context":"https://schema.org","@graph":[{"@type":"Organization","@id":"https://daily.dev/#organization","name":"daily.dev","url":"https://daily.dev","logo":{"@type":"ImageObject","url":"https://daily.dev/apple-touch-icon.png","width":180,"height":180},"sameAs":["https://twitter.com/dailydotdev","https://github.com/dailydotdev","https://www.linkedin.com/company/daily-dev-ltd"]},{"@type":"WebSite","@id":"https://daily.dev/#website","url":"https://daily.dev","name":"daily.dev","publisher":{"@id":"https://daily.dev/#organization"},"potentialAction":{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https://daily.dev/search?q={search_term_string}"},"query-input":"required name=search_term_string"}}]} {"@context":"https://schema.org","@type":"TechArticle","headline":"Polynomial Regression in Machine Learning: Teaching Linear Regression to Bend","url":"https://daily.dev/posts/polynomial-regression-in-machine-learning-teaching-linear-regression-to-bend-2zfgia44e","mainEntityOfPage":{"@type":"WebPage","@id":"https://daily.dev/posts/polynomial-regression-in-machine-learning-teaching-linear-regression-to-bend-2zfgia44e"},"datePublished":"2026-08-22T15:14:36.953Z","dateModified":"2026-08-22T15:27:27.961Z","description":"An explanation of Polynomial Regression as a technique that extends Linear Regression to model curved relationships by transforming features into polynomial...","image":"https://media.daily.dev/image/upload/f_auto,q_auto/v1/posts/2ecab6f80da2506e7976d355264cb6fa?_a=AQAEuop","thumbnailUrl":"https://media.daily.dev/image/upload/f_auto,q_auto/v1/posts/2ecab6f80da2506e7976d355264cb6fa?_a=AQAEuop","isAccessibleForFree":true,"articleSection":"Medium","inLanguage":"en","publisher":{"@type":"Organization","name":"daily.dev","url":"https://daily.dev","logo":{"@type":"ImageObject","url":"https://daily.dev/apple-touch-icon.png","width":180,"height":180}},"author":{"@type":"Organization","name":"Medium","logo":"https://media.daily.dev/image/upload/t_logo,f_auto/v1/logos/medium","url":"https://daily.dev/sources/medium_js"},"commentCount":0,"discussionUrl":"https://daily.dev/posts/polynomial-regression-in-machine-learning-teaching-linear-regression-to-bend-2zfgia44e","interactionStatistic":[{"@type":"InteractionCounter","interactionType":{"@type":"LikeAction"},"userInteractionCount":0},{"@type":"InteractionCounter","interactionType":{"@type":"CommentAction"},"userInteractionCount":0}],"keywords":"machine-learning,python,scikit,overfitting","timeRequired":"PT17M"} {"@context":"https://schema.org","@type":"BreadcrumbList","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https://daily.dev"},{"@type":"ListItem","position":2,"name":"Medium","item":"https://daily.dev/sources/medium_js"},{"@type":"ListItem","position":3,"name":"Polynomial Regression in Machine Learning: Teaching Linear Regression to Bend"}]} {"@context":"https://schema.org","@type":"FAQPage","@id":"https://daily.dev/posts/polynomial-regression-in-machine-learning-teaching-linear-regression-to-bend-2zfgia44e#faq","mainEntity":[{"@type":"Question","name":"Why is polynomial regression still considered a type of linear regression even though it fits curves?","acceptedAnswer":{"@type":"Answer","text":"Polynomial regression is linear in its parameters, not in its features. 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