--- title: "Linear Regression with Evenly-Spaced Abscissae" url: https://daily.dev/posts/linear-regression-with-evenly-spaced-abscissae-jcixvo2nn source_url: https://www.embeddedrelated.com/showarticle/1163.php type: article source: "EmbeddedRelated" published: 2026-05-31T07:47:59.023Z updated: 2026-05-31T09:05:29.367Z tags: ["python", "numpy", "linear-regression"] reading_time: 12 upvotes: 0 comments: 0 language: 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. # Linear Regression with Evenly-Spaced Abscissae **[EmbeddedRelated](https://daily.dev/sources/embeddedrelated)** · 12 min read · 0 upvotes · 0 comments ## Summary When x-coordinates (abscissae) are evenly spaced, the least-squares linear regression matrix simplifies dramatically. The intercept equals the plain mean of y values, and the slope is a weighted sum with arithmetic weights using the formula q = 12/(m³ - m). This eliminates the need for matrix solvers entirely. The post derives this from first principles using the normal equations, demonstrates it with NumPy examples, and provides a compact Python routine `linear_fit_equal_spacing` that computes slope and offset with a simple loop — useful for embedded or resource-constrained environments where matrix libraries may be unavailable. ## Full article daily.dev links to this article rather than hosting it. Read it at the original source: ## Similar posts on daily.dev - [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 - [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 - [The Anatomy of the Least Squares Method, Part Two](https://daily.dev/posts/the-anatomy-of-the-least-squares-method-part-two-9emh8plaz) · The Palindrome · 0 upvotes · 0 comments - [The Anatomy of the Least Squares Method](https://daily.dev/posts/the-anatomy-of-the-least-squares-method-zpx9l4ifa) · The Palindrome · 1 upvotes · 0 comments - [Linear Regression: The Simplest Model That Actually Works](https://daily.dev/posts/linear-regression-the-simplest-model-that-actually-works-gh0lpkiuu) · Medium · 0 upvotes · 0 comments --- Tags: [#python](https://daily.dev/tags/python), [#numpy](https://daily.dev/tags/numpy), [#linear-regression](https://daily.dev/tags/linear-regression) [View this post on daily.dev](https://daily.dev/posts/linear-regression-with-evenly-spaced-abscissae-jcixvo2nn)