I'm reading about the assumptions of taking a linear fit between two variables from here, and that source says:
For diagnosing non-linearity:
nonlinearity is usually most evident in a plot of observed versus predicted values or a plot of residuals versus predicted values.
For diagnosing heteroscedasticity:
look at a plot of residuals versus predicted values.... Be alert for evidence of residuals that grow larger either as a function of time or as a function of the predicted value.
From the discussion on that page, I'm not clear on the differences between non-linearity and heteroscedasticity. I would think that fitting a straight line to, say, a parabola would violate non-linearity (of course) and therefore be heterscedastic. I can't think of an example which would violate one assumption, but not the other. Or are they independent qualities?