information:filtering, structural:reformatting, stylistic:style_transfer
Linear

Linear extrapolation means creating a tangent line at the end of the known data and extending it beyond that limit. Linear extrapolation will only provide good results when used to extend the graph of an approximately linear function or not too far beyond the known data.

If the two data points nearest the point x ∗ {\displaystyle x_{*}} to be extrapolated are (x k − 1, y k − 1) {\displaystyle (x_{k-1},y_{k-1})} and (x k, y k) {\displaystyle (x_{k},y_{k})}, linear extrapolation gives the function:

(which is identical to linear interpolation if x k − 1 < x ∗ < x k {\displaystyle x_{k-1}<x_{*}<x_{k}}). It is possible to include more than two points, and averaging the slope of the linear interpolant, by regression -like techniques, on the data points chosen to be included. This is similar to linear prediction.