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 = (∑y - β1∑x1 - β2∑x2)/n          a = 10[(∑y - β1∑x1 - β2∑x2)/n]

b1 = β1          b2 = β2          y = a x1b1 x2b2

Reference


SAMPLE INPUT DATA:

Array size n:  12

Corresponding values of arrays y, x1 and x2 (you can cut and paste sample arrays into form).

y:    89,75,57,34,101,121,68,79,25,59,96,12

x1:    3245,2567,2783,1234,5345,5329,3002,2976,1034,2984,3892,534

x2:    0.008,0.011,0.009,0.015,0.006,0.007,0.008,0.010,0.018,0.010,0.007,0.020


SAMPLE OUTPUT:

a = 0.038671        b1 = 1.176878        b2 = 0.46380


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