online regression, one-predictor-variable nonlinear linear regression, x-y regression, Victor Miguel Ponce, 300 characters in input

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

Formulas

y= ax^b         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= 10^α
β= [Σ(uv)-(ΣuΣv)/n]/{Σ(u²)-[(Σu)²/n]}
α= [Σv-(βΣu)]/n        y = 10^αx^β

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 07:49:04 am on December 18th, 2025   [ 251218  07:49:04 ].

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