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Question C.2.3: Fit the power function y = bx^m to the data yi. The value of...

Fit the power function y = bx^m to the data y_i. The value of m is known.

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The least-squares criterion is

J=\sum_{i=1}^n\left(b x^m-y_i\right)^2

To obtain the value of b that minimizes J, we must solve 𝜕J/𝜕b = 0.

\frac{\partial J}{\partial b}=2 \sum_{i=1}^n x_i^m\left(b x_i^m-y_i\right)=0

This gives

b=\frac{\sum_{i=1}^n x_i^m y_i}{\sum_{i=1}^n x_i^{2 m}}                (1)

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