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 + ... + anxn
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, an,, 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...