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?
[edit after comments]
The mean structure does suggest a quadratic term, and possibly a cubic term, however this last one seems small.