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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.

and

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?

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  • $\begingroup$ I think this plot of residuals shows non-linearity and homoscedasticity: rcompanion.org/handbook/images/image103.png. (Caveat: my image.) $\endgroup$ – Sal Mangiafico Oct 5 '18 at 2:23
  • $\begingroup$ You're right, it does. Thank you, I was misinterpreting the meaning of heteroscedasticity. $\endgroup$ – Jim421616 Oct 5 '18 at 2:24
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Non-linearity is different from heteroscedasticity in a matter of variance. When you have non-linear data the variance not necessarily is changing, however data has non-linear pattern along the independent variable:

enter image description here

Heteroscedasticity is when your dependent variable's variance is growing or shrinking along the independent variable:

enter image description here

EDIT: Note that not every non-linear data is heteroscedastic, same as not every heteroscedastic data is non-linear, however you may have both or neither at the same time.

I hope that helps.

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