Example

$$A=\left[\begin{array} {cc} 1000 & 1 \ 2000 & 1 \ 3000 & ... ... 1 \ 8000 & 1 \ 9000 & 1 \ 10000 & 1 \end{array} \right],$$

$$b=\left[\begin{array} {c} 0.16 \ 0.63 \ 1.44 \ 2.56 \... ....73 \ 7.84 \ 10.28 \ 12.98 \ 16.32 \end{array} \right].$$

Form A^T A x = A^T b, solve for x:

$$x= \left[\begin{array} {c} 0.001779818 \ -3.596 \end{array} \right].$$

Thus, $t \approx 0.001779818 n -3.596$ is the best fit to the data in a least squares sense.

The best quadratic is much better: $t \approx 1.67803\times 10^{-7} n^2 -6.601515\times 10^{-5} n + 0.09566667$.