Скачать или смотреть Data fitting explained (part 3) | Polynomial models, quadratic and cubic curves

In part 3 of the data fitting series, we explore polynomial models, which allow us to describe curved relationships in data.
You’ll learn how polynomial models extend linear models by adding powers of x, and how the degree of a polynomial controls the number of bends in the curve. We explain quadratic models, which create a single smooth bend, and cubic models, which can produce S-shaped curves with two turning points.
Practical examples are used throughout, including projectile motion, optimisation problems, tablet compression, and thermal analysis, to show how polynomial models are applied in real scientific and engineering contexts. We also introduce a simple rule of thumb that helps you decide which polynomial degree is appropriate for your data.
This video helps you recognise when linear models are no longer sufficient and how to choose polynomial models without overcomplicating the analysis.

0:00 Introduction to polynomial models
0:30 What polynomial models are
1:05 Quadratic models explained
1:55 Quadratic real-world examples
2:45 Cubic models explained
3:35 Cubic real-world examples
4:25 Polynomial degree rule of thumb
5:10 Practical formulation examples
5:50 Common mistakes with polynomials
6:20 What’s next: exponential behaviour

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