LPC Order

The accuracy of the predictor improves with an increase of order $N$:

The smallest value of $N$ that will yield sufficiently quality in the speech representation is related to

1. the highest frequency in the speech,
2. the number of formant peaks expected and
3. the sampling rate.

There is no exact relationship for determining what value of $N$ should be used, but in general it's between 10 and 20 or the sampling rate in kHz plus 4 (for $fs = 15$kHz, you might use a $N = 19$).

Schemes for determining predictors by minimizing the residual work either explicitly or implicitly.

A more rigorous treatment of the subject can be found in J. Makhoul's tutorial³