Example 3 – polynomial regression

The polynomial regression can be considered a more generalized form of the linear regression. A polynomial relationship has the form:

y = a₀ + a₁x¹ + a₂x² + a₃x³ + ... + a_nxⁿ

A polynomial can have any number of terms, which is called the degree of the polynomial. For each degree of the polynomial, the independent variable, x, is multiplied by some parameter, a_n,, and the X-value is raised to the power n. A straight line is considered a polynomial of degree 1; if you update the preceding polynomial formula to remove all degrees above one, you are left with:

y = a₀ + a₁x

Where a₀ is the y-intercept and a₁ is the slope of the line. Despite the slight difference in notation, this is equivalent to y = mx + b.

Quadratic equations, which you may recall from high school math, are simply polynomials of degree 2, or y = a₀ + a₁x + a₂x². Cubic equations...