Question C.1.3: Fit the power function y = bx^m to the data yi . The value o......

System Dynamics [1255330]

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

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The least-squares criterion is

J=\sum\limits_{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\limits_{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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