---
title: "Meaning & Key Takeaway of: Taking least squares is no longer…"
description: "\"“Taking least squares is no longer optimal, and the very idea of ‘accuracy’ has to be rethought. This simple fact is as important as it is neglected. T..."
image: "https://sms4smile.com/quotes/i/57d/leonard-a-smith-76113_nonlinear_taking-least-squares-is-no-longer-optima_2628469.jpg"
---

#  Taking least squares is no longer optimal, and the very…

![“Taking least squares is no longer optimal, and the very idea of ‘accuracy’ has to be rethought. This simple fact is as important as it is neglected. This problem is easily illustrated in the Logistic Map: given the correct mathematical formula and all the details of the noise model – random…” quote by Leonard A. Smith](https://sms4smile.com/quotes/i/57d/leonard-a-smith-76113_nonlinear_taking-least-squares-is-no-longer-optima_2628469.jpg)   [Download](https://sms4smile.com/quotes/i/57d/leonard-a-smith-76113_nonlinear_taking-least-squares-is-no-longer-optima_2628469.jpg) [Open image](https://sms4smile.com/quotes/i/57d/leonard-a-smith-76113_nonlinear_taking-least-squares-is-no-longer-optima_2628469.jpg)

> ““Taking least squares is no longer optimal, and the very idea of ‘accuracy’ has to be rethought. This simple fact is as important as it is neglected. This problem is easily illustrated in the Logistic Map: given the correct mathematical formula and all the details of the noise model – random numbers with a bell-shaped distribution – using least squares to estimate α leads to systematic errors. This is not a question of too few data or insufficient computer power, it is the method that fails. We can compute the optimal least squares solution: its value for α is too small at all noise levels. This principled approach just does not apply to nonlinear models because the theorems behind the principle of least squares repeatedly assume bell-shaped distributions.””

[Leonard A. Smith](https://sms4smile.com/quotes/author/leonard-a-smith/)

## About This Quote

This interpretation was drafted with AI assistance. It is one reading of the quote, not the author's own explanation.

Least‑squares fails for non‑Gaussian noise; new methods needed for accurate modeling.

**In simple terms:** Old methods don’t work for all data.

Key Takeaway

Adopt robust statistical techniques.

Themes

statistics modeling accuracy

Mood

analytical cautious

Type

academic technical

When to use this quote

- research
- engineering
- data analysis

Key Concepts

non‑linear models noise distribution

Questions to Reflect On

- When to replace least‑squares?
- What alternatives suit non‑Gaussian data?

A Different Perspective

Transition to new methods can be costly.

★ ★ ★ ★ ★   No ratings yet

[Model Random](https://sms4smile.com/quotes/about/model-random-2170314/) [Noise Model](https://sms4smile.com/quotes/about/noise-model-2170313/) [Nonlinear](https://sms4smile.com/quotes/about/nonlinear/) [Nonlinear Models](https://sms4smile.com/quotes/about/nonlinear-models-2170312/) [Squares Estimate](https://sms4smile.com/quotes/about/squares-estimate-2170315/)

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