Non-polynomial Forms and Linearisation:
The method of least squares is also applicable to other forms of functions. For instance, periodic process can be represented as f (x) = A sin (ω x) + B cos (ω x), where A, B are coefficients to be find out. Many significant non-polynomials forms might be linearised and linear regression might be applied such as
Exponential f (x) = A eax ⇒ ln [f (x)] = ln (A) + a x
Power law f (x) = B xb ⇒ ln [f (x)] = ln B + b ln (x)
If we define Y = ln [f (x)] and X = x (or) ln (x) then the above equations become linear as Y = C + DX. The above equation is linear with intercept C = ln (A) or ln (B) and slope D = a (or) b. Therefore from the linear fit the constants are calculated.
It can be noted that many heat transfer correlation may be taken as power law variations in terms of parameters such like Re, Pr and Gr.