If I have a yearly quantity (eg. 2000 - 45, 2001-67, 2002 - 38.....2010 - 38) and I need to find the least squares line for this relationship, what should I use for the X values?
Should I use the years as they are or is there anything else?
2026-04-02 15:38:30.1775144310
X values for least squares approximation
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As for the $x$ variable, you could use the current year but more common one will let the first quantity corresponds to $x=1$ and the second one to $x=2$, etc. Do not forget to add an intercept if the series does not start at $(x, y) = (0, 0)$.
If the quantity is on a yearly basis you actually have a time series. For such series there are a lot of other tools to use, see https://www.otexts.org/fpp/4/8. There is even a pretty good wikipedia page about trends: http://en.m.wikipedia.org/wiki/Trend_estimation