Given x and y vectors in quick variables 1 and 2 as before, the first job is to form the matrix that describes the problem.

Thus we want a @c{$19\times2$} 19x2 matrix with our x vector as one column and ones as the other column. So, first we build the column of ones, then we combine the two columns to form our A matrix.

2: [1.34, 1.41, 1.49, ... ] 1: [ [ 1.34, 1 ] 1: [1, 1, 1, ...] [ 1.41, 1 ] . [ 1.49, 1 ] ... r 1 1 v b 19 RET M-2 v p v t s 3

Now we compute @c{$A^T y$} trn(A) * y and @c{$A^T A$} trn(A) * A and divide.

1: [33.36554, 13.613] 2: [33.36554, 13.613] . 1: [ [ 98.0003, 41.63 ] [ 41.63, 19 ] ] . v t r 2 * r 3 v t r 3 *

(Hey, those numbers look familiar!)

1: [0.52141679, -0.425978] . /

Since we were solving equations of the form @c{$m \times x + b \times 1 = y$}
m*x + b*1 = y, these
numbers should be m and b, respectively. Sure enough, they
agree exactly with the result computed using `V M` and `V R`!

The moral of this story: `V M` and `V R` will probably solve
your problem, but there is often an easier way using the higher-level
arithmetic functions!

In fact, there is a built-in `a F` command that does least-squares
fits. See section Curve Fitting.

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