Exact Fit:

Polynomial Fitting

Polynomial fitting gives one variable as a function of another. If n is the degree of the polynomial then n + 1 data points are needed to find the equation.

Linear Equation (First Degree Polynomial)

y = f (x) = a₀ + a₁ x

i.e.,      y₀ = a₀ + a₁ x₀ and y₁ = a₀ + a₁ x₁

Therefore a₀ and a₁ values can be obtained by using 2 data points. If the two data points are P₁ (x₁   y₁) and P₂ (x₂   y₂).

a₀  = (x₁ y₂  + y₁ x₂ )/(x₂-x₁ ) ; a = ( y₂  - y₁ )/ (x₂   - x₁)

Quadratic Equation (Second Degree)

y = a₀ + a₁ x + a₂ x².

 The same in the matrix form is

The result of this set of three simultaneous equations shall yield values of a₀, a₁ and a₂.