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I have seen a tutorial video where a person is advising to check for heteroscedasticity in a regression by plotting the IV against the DV. Is this a problem? Are there any drawbacks with this approach?

I know that I was always told to plot the standardised residual against the predicted values.

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If there is one and only one predictor or covariate or independent variable $x$ then a scatter plot of the response or dependent variable $y$ versus $x$ is a good way of checking the relationship in several respects, including but not only

  • whether the relationship between the variables is approximately linear as is needed for linear regression $y = b_0 + b_1 x$ to make sense.

  • whether there are any of the following which can complicate analysis: skewness or long-tailed distribution of either variable; heteroscedasticity of variation around a putative regression line; gaps or granularity in the distribution; possible univariate or bivariate outliers.

In each case other plots may be even better, including plots focused directly on either univariate distribution or plots based on residuals.

If there are two or more predictors then it is unlikely that one plot can be used to show all aspects of behaviour. Usually it is better to plot residuals in a focused way. The most useful single plot can be a plot of residuals (vertical axis) versus fitted or predicted values (horizontal axis) which can always be drawn, regardless of how many predictors there are.

Note on terminology:

  • The terms dependent variable (sometimes DV) and independent variable (sometimes IV) remain widespread, despite repeated suggestions that they should be dropped in favour of others that are more evocative. Objections to those terms include: "dependence" and "independence" are already overloaded terms in probability and statistics; many beginning students have found it hard to remember the difference, to their own confusion and others'; the abbreviations DV and IV are respectively in common use as meaning "Deo volente" (God willing) and in specific econometric use as meaning "instrumental variable".

  • The terms against and versus divide the world. Some of us, including this writer, think of plotting what is on the vertical axis versus what is on the horizontal axis, which can be justified as sanctioned by mathematical and physical tradition and logic. Others flip it round: for example, economists presumably have reasons for how they plot supply, demand and price.

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  • $\begingroup$ +1 If the economists are going to create ambiguous abbreviations, that's on them: the rest of the world shouldn't have to change theirs in response! But I love the alternative meaning of "DV" and find it perfectly descriptive of the apparent behavior of many DVs in regressions, as well as the feelings one sometimes gets when trying to model their behavior. :-). $\endgroup$
    – whuber ♦
    Commented Oct 3, 2014 at 15:53
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    $\begingroup$ @whuber One comment was more in jest than the other. In some economic circles the use of instrumental variables seems to be largely an act of faith, so there may be a more than tangential connection. $\endgroup$
    – Nick Cox
    Commented Oct 3, 2014 at 15:55
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Plotting the IV against the DV is only a good check for heteroskedasticity in a simple linear regression. In a multiple regression, heteroskedasticity refers to different variances of the residuals in any subgroup, which might be identifiable only with multiple IVs entered into the model

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  • $\begingroup$ I would like to point to a possible ambiguity in this characterization of heteroscedasticity: the variance of the response variable, when broken down by subgroups, will almost always appear to be heteroscedastic in a multiple regression. You must be referring to the variances after controlling for all the variables--that is, the residual variances (even though you haven't mentioned residuals at all). But then what is "identifiable only with multiple IVs" supposed to mean? $\endgroup$
    – whuber ♦
    Commented Oct 3, 2014 at 15:56

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