Dimensional analysis / units for best fit curves

Question

I am doing a lot of curve fitting from experimental and modelling data.

If I have a polynomial of the form which takes a temperature T and outputs a pressure Pa

(Temp^2 + Temp + constant) = Pressure

then of course the units of left and right hand side of the equation do not match.

I need something like

(Temp^2 + Temp + constant)x = Pa

where x is a constant of proprtionality with the correct units.

(I am measuring temperture in Kelvin and pressure in pascals). How does this work for ever higher order polynomials?

regards

Answer 1

You need a fitting curve like $$ p = aT^2+bT+c $$ with

• [c]=pressure
• [b]=pressure/temperature
• [a]=pressure/temperature^2