# Linear regression or average percent change?

I have 12 (1 year's worth) values and I want to determine the trend and represent the trend as a positive or negative figure. What is the difference in using linear regression versus the monthly percent change averaged?

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## 1 Answer

The monthly percentage change averaged will have the implicit assumption that the growth is exponential while a linear regression has the assumption that it is linear.

If you do it properly, the average monthly percentage change involves taking the 11th root of the product of the $1+\frac{P_i}{100}$ terms, in which case it will depend on the first and last terms only, ignoring all intermediate months.

It might be sensible if you drew a graph of your data before any numerical analysis, to see what the pattern might be.

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Drawing a graph isn't going to help the solution in this case. It needs to be automated. We're looking for a programmable algorithm - ultimately, the question is simply whether average percentage change vs. linear regression is going to be a more accurate representation. –  Rob Jun 23 '11 at 15:07