## Excel in math and science

### Master concepts by solving fun, challenging problems.

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### Learn more effectively through short, conceptual quizzes.

## Our wiki is made for math and science

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Master advanced concepts through explanations,

examples, and problems from the community.

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Easy Math Editor

`*italics*`

or`_italics_`

italics`**bold**`

or`__bold__`

boldNote: you must add a full line of space before and after lists for them to show up correctlyparagraph 1

paragraph 2

`[example link](https://brilliant.org)`

`> This is a quote`

Remember to wrap math in \( ... \) or \[ ... \] to ensure proper formatting.`2 \times 3`

`2^{34}`

`a_{i-1}`

`\frac{2}{3}`

`\sqrt{2}`

`\sum_{i=1}^3`

`\sin \theta`

`\boxed{123}`

## Comments

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TopNewest\[\]To obtain \(r\) and \(K\) that minimizes \(\,J\), you just take derivative of \(\,J\) with respect to \(r\) and \(K\) and then set equal to \(0\). This technique is called minimizing the mean square error (

MSE) or chi-squared (\(\;\chi^2\)) minimization.\[\] \[ \begin{align} \frac{\partial J}{\partial r}&=0\tag1\\ \frac{\partial J}{\partial K}&=0.\tag2 \end{align} \] \[\]Next, plug in data in the table and solve those two non-linear equations. You can use either Newton-Raphson, Steffenson, or secant method. Of course you should use computer program like Matlab, SAS, R, etc to help you solve \(\,(1)\) and \(\,(2)\).Log in to reply