What constrained regression function shuld I use?
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I have a regression model log (r(i)) = a + b * log(A(i)) where A(i) is a vector and each element is known. Log is the nature log.
I need to find out a, b, and each element of r(i) such that the sum of r(i) equals to a constant k and the sum of error, i.e. sum(square[log (r(i)) – (a + b * log(A(i)))]) is minimized. Both a and b are scalars.
What regression model can I choose?
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Torsten
on 13 Mar 2015
Choose a and b such that
exp(a)*(A(1)^b+A(2)^b+...+A(n)^b)=k
Then sum (exp(a)*A(i)^b) = k is satisfied.
Now define r(i) = exp(a) * A(i)^b, and you are done.
Best wishes
Torsten.
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Simon Wang
on 13 Mar 2015
Edited: Simon Wang
on 13 Mar 2015
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Torsten
on 13 Mar 2015
Choose b=1, a=log(k/(A(1)+A(2)+...+A(n))) and define r(i)=exp(a)*A(i).
Then sum(square[log (r(i)) – (a + b * log(A(i)))]) is minimized (because it equals 0) and sum r(i)=k.
Best wishes
Torsten.
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