Drive the expression for temperature coefficient of resistance?

To derive a value for thermal coefficient of resistance, I find the resistance R1 at one temperature T1, and the resistance R2 at temperature T2.

I can then express this coefficient as (R2 - R1) / [R1 (T2 - T1)] X 100% per degree.

Example: R1 = 50 ohms at T1 = 20 degC

R2 = 20 ohms at T2 = 500 degC

(R2 - R1) / [R1(T2 - T1)] X100% per deg = (20 - 50) / [50 (500 - 20)] X100% per deg

= - 0.125% per degC

But this assumes the change in resistance is linear. In fact, such changes often happen on a curve. To estimate the form of the curve, at least three temperature:resistance data pairs are needed.