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

dxiv - that is the entire point and hence the requirement for a constant of proportionality! — William White, Apr 02 '18 at 20:50
No, point is that one constant does not suffice, since $T$ and $T^2$ have different units, so adding them violates dimensional homogeneity in the first place. See the posted answer instead. — dxiv, Apr 02 '18 at 21:10

score 1 · Answer 1 · answered Apr 02 '18 at 20:40

1

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

answered Apr 02 '18 at 20:40

Vincenzo Tibullo

1 Answers1