onlineregression14:   Multiple nonlinear regression   ⇒   y = f(x1, x2)

Formulas

u = log(x1)           v = log(x2)           w = log(y)

t1 = n∑wv - ∑w∑v           t2 = n∑u∑v - ∑u∑v          t3 = n∑v2 - (∑v)2

t4 = n∑wu - ∑w∑u           t5 = n∑uv - ∑u∑v           t6 = n∑u2 - (∑u)2

t7 = n∑v2 - (∑v)2

β1 = (t1*t2 - t3*t4)/(t5*t5 - t6*t7)          β2 = (t4 - β1*t6)/t2

α = (∑w - β1∑u - β2∑v)/n          a = 10[(∑w - β1∑u - β2∑v)/n]

b1 = β1          b2 = β2          y = a x1b1 x2b2

Reference

Ponce, V. M. 1989. Engineering Hydrology, Principles and Practices. Prentice Hall, page 241-243.
Example
INPUT DATA:

Enter array size n:     

Enter corresponding values of arrays y, x1 and x2 (separate each value with a comma; maximum string length is 300 characters).

y:     

x1:     

x2:     

ECHO OF INPUT:

n =  

y(1) =  .   

x1(1) =  .   

x2(1) =  .   

OUTPUT:

a =            b1 =            b2 =                      y = x1 x2

            

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