Linear algebra with a linear model (Matlab)

Question

Given the equation

$$r = B + e(r\cos(\theta))$$

and the corresponding data:

$\theta: 0.88; 1.1; 1.42; 1.77; 2.14$ and $r: 3; 2.4; 1.65; 1.25; 1.01$

How do you input these data for matlab to solve for $B$ and $e$?

Answer 1

Cleve Moler's Numerical Computing with MATLAB has this excellent chapter on how to do least squares; you can adapt any of the methods discussed there. To give you a few nudges on how to do your code: you have r as a dependent variable, and you can construct a new independent variable rc=r.*cos(theta);, where r and theta are appropriately constructed arrays. You can use [] to form the columns of the matrix required for the linear regression, and then use \ to get the least squares solution.

Or, there's polyfit()...

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OP seems to have some difficulty seeing how least squares applies here, so here's a hint on how to assemble the equations:

$$\begin{pmatrix}1&r_1\cos\,\theta_1\\1&r_2\cos\,\theta_2\\1&r_3\cos\,\theta_3\end{pmatrix}\begin{pmatrix}B\\e\end{pmatrix}=\begin{pmatrix}r_1\\r_2\\r_3\end{pmatrix}$$