I have a set of three measurements $(x_i, y_i)$ where the x-values are equally spaced. I am interested in extracting the linear slope between these three points (while the intercept has no physical meaning, as there is an unknown offset).

Nevertheless, a least-squares linear fit of these three points would result in the slope being computed simply as $m = \frac{y_3-y_1}{x_3-x_1}$ because $x_2 = \bar{x}$.

Is there any method that include the information from $x_2$ in the computation of the slope?

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