In numeric methods, extrapolation of several samples can be done by using linear predictive models as given by the equation below. IF P=1, it means if there is only one prediction coefficient a₁=a, what is the optimum value of a (how do we calculate a), so that the MSE (mean (1/N) square error e²[n]) is minimum

mean_square_error=

is minimum for N values, where N is the total number of samples to be considered when calculating a_k coefficients and N>>P

rn] = $ar:rn ] + ein k=1 E [n] N n=1