Linear extrapolation

In mathematics, the process of fitting a straight line to a set of historical data points in a manner in which the error between the line and the data points is minimal. When the equation for such a line is determined, it can be used to estimate the value of future data points. If the historical fit is excellent, the forecast will be more believable. However, as in any forecast based on extrapolation, the underlying assumption, often implicit, is that the forces that were at work in the past will continue to be at work in the future and that new developments will not affect the extrapolation, which must ultimately be wrong. Linear extrapolations can be approximated by eye: simply placing a ruler on the historical data points and drawing a line that comes near all of them and extending that line into the future. One can speak of high inertia systems that are slow to change; here extrapolation for longer time periods is possible. Low inertia systems that are not well anchored in the recent past can change rapidly and therefore extrapolation must be done with caution. Extrapolations need not be linear: they can be based on equations that are higher order polynomials, cyclic, seasonal, etc.