# Minimal number of points for a linear regression

What would be a "reasonable" minimal number of observations to look for a trend over time with a linear regression? what about fitting a quadratic model?

I work with composite indices of inequality in health (SII,RII), and have only 4 waves of the survey, so 4 points (1997,2001,2004,2008).

I am not statistician, but I have the intuitive impression 4 points are not sufficient. Do you have an answer, and/or references ?

Thanks a lot,

Françoise

• The usual rule of thumb is 10 points for each independent variable. – Peter Flom Sep 23 '12 at 12:26
• How are your indices measured? If they include estimates of variability, then two could be enough (using a t-test or its analog). The basic statistical principle that applies here is that when random variation is an unlikely explanation of what you are observing, then you have the right to attribute any apparent trend to non-random causes. When the trend is strong, very few data values may be needed to come to such a conclusion, all generic "rules of thumb" notwithstanding. – whuber Sep 24 '12 at 15:41

• yes, I agree. And it could well be the case in physics, say, or any area where a very high $R^2$ is expected and theory is strong and error is small. – Peter Flom Sep 23 '12 at 13:29