# Can the OLS residual variance suggest a polynomial relationship?

I am trying to figure out whether from the following graph of the OLS residuals that the linear relationship does not hold, and that probably a cubic relationship would do better? Since both in the beginning as in the middle the variance is larger, and two bends in a regression could lower the variance for these areas. Or is that something that is not determinable from this graph?

• The mean structure does not suggest either a cubic or quadratic term: they could not accurately reproduce what is shown. There are several ways it could be handled: allow the slope to change discontinuously at an unknown point (that adds two parameters) or add a (decaying) exponential term, which also needs two parameters. If you want to anticipate the outcome, eyeball the break (it's around $3/4$) and introduce a variable equal to time before the break and zero after the break. Although this doesn't account for uncertainty in estimating the break, it will show you a better fit. – whuber May 10 '13 at 22:00