onlineregression12:   One-predictor-variable nonlinear regression (max input 3000 characters)    ⇒   y = f(x)

Formulas

y= axb         log(y)= log(a) + b[log(x)]

u= log(x)        v= log(y)         v= log(a) + bu

v= α + βu         log(a)= α        b= β        a= 10α

β= [Σ(uv)-(ΣuΣv)/n]/{Σ(u2)-[(Σu)2/n]}

α= [Σv-(βΣu)]/n        y = 10αxβ

Reference

Ponce, V. M. 1989. Engineering Hydrology, Principles and Practices. Prentice Hall, page 240.
Example
INPUT DATA:

Enter array size n:     

Enter paired values of arrays y and x (separate each value with a comma; maximum string length is 3000 characters).

y:     

x:     

ECHO OF INPUT:

n =  

y(1) =  .   

x(1) =  .   

OUTPUT:

a =            b =            y = x

            

  Your request was processed at  09:45:36 pm on April 25th, 2025   [ 250425  21:45:36 ].

Thank you for running onlineregression12b.   Please call again.   [201004]