Define the least-squares problem

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Reference no: EM131760976

Question: (Lotka's law and least squares) Lotka's law describes the frequency of publication by authors in a given field. It states that X aY = b, where X is the number of publications, Y the relative frequency of authors with X publications, and a and b are constants (with b > 0) that depend on the specific field. Assume that we have data points (Xi, Yi), i = 1, . . . , m, and seek to estimate the constants a and b.

1. Show how to find the values of a, b according to a linear leastsquares criterion. Make sure to define the least-squares problem involved precisely.

2. Is the solution always unique? Formulate a condition on the data points that guarantees unicity.

Reference no: EM131760976

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