Non-polynomial Forms and Linearisation:

Also the method of least squares is applicable to other forms of functions. For instance, periodic procedure might be represented as f (x) = A sin (ω x) + B cos (ω x),

Here A, B are coefficients to be find out. Various important non-polynomial forms might be linearised and linear regression might be applied such like

Exponential f (x) = A e^ax ⇒ ln [f (x)] = ln (A) + a x

Power law f (x) = B x^b ⇒ ln [f (x)] = ln B + b ln (x)

If we represent Y = ln [f (x)] and X = x (or) ln (x) after that the above equations become linear like Y = C + DX. The above described equation is linear along intercept C = ln (A) or ln (B) & slope D = a (or) b. Therefore from the linear fit the constants are measured.

It might be noted down that various heat transfer correlation might be taken as power law variations in terms of parameters such like R_e, P_r and G_r.