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I have carried out a linear regression. This is the form of the model:

bounded (0-1) response variable ~ factor1 (2 levels) + factor2 (5 levels) + interaction between factor1:factor2 + factor3 (2 levels)

Sample size is about 350.

I have plotted the residuals against the predicted values from that model:

enter image description here

As there is a distinct pattern in the residuals, it appears linear regression is not a suitable model. I have carried out several other linear regressions lately with different data, and I have repeatedly seen this pattern in the residuals.

Does this pattern provide information on what model would be best to use? Should an interaction term be added? Is there a predictor missing? Should a non-linear model be used? Or instead, does this particular pattern in the residuals actually not provide any indicators as to what model to use?

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  • $\begingroup$ What is your model? $\endgroup$
    – Peter Flom
    Dec 19, 2013 at 20:51
  • $\begingroup$ How do you mean? Unfortunately I can't post actual data if thats what you mean. $\endgroup$
    – luciano
    Dec 19, 2013 at 20:53
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    $\begingroup$ What is your dependent variable? What independent variables? How big is the sample? Are the variables continuous or categorical? that sort of thing. The actual context would be nice, too, even without data. $\endgroup$
    – Peter Flom
    Dec 19, 2013 at 20:55
  • $\begingroup$ Is your dependent variable naturally bounded? Sort of looks like it. And yeah, you need to provide more info. $\endgroup$ Dec 19, 2013 at 20:59
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    $\begingroup$ You should not be doing ordinary linear regression with a "bounded (0-1) response variable". Neither the assumption about linearity of the mean nor the constant variance assumption are likely to be true, except in some special cases, and even then usually only approximately. Is your bounded variable compositional data, or is it a proportion based on counts, or something else? $\endgroup$
    – Glen_b
    Dec 20, 2013 at 2:56

1 Answer 1

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Luciano: 1) at first glance, your residual plot seemingly shows heteroskedasticity of residuals. This violates one of the requirements of OLS. This often happens when factor variables are the only predictors. 2) But the most substantive issue rests on the consideration that OLS is unfit to deal with a binary dependent variable (if this is your case).

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