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Consider this residuals vs. fitted values plot:

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Would you say this have no problems and I can go on the linear regression? I am interpreting this as heteroscedasticity and with that should not go further, what do you think?

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    Welcome to Cross Validated! Please look at this related page for a guide to interpreting such plots. If that doesn't answer your question, please edit this question in light of that other question, to say more about why you think this represents heteroscedasticity. – EdM Sep 10 '23 at 19:04
  • No, it's not heteroscedasticity, but it does indicate that your DV is discrete and, therefore, either multinomial or ordinal logistic might be better. See https://stats.stackexchange.com/questions/25068/interpreting-plot-of-residuals-vs-fitted-values-from-poisson-regression – Peter Flom Sep 10 '23 at 19:29
  • You can tell that your observed data seems to take discrete values $0, 0.5, 0.75, 1, 1.25, 1.5, 1.75, 2$ but your predicted values are in roughly in the narrower range $0.9$ to $1.52$. There is nothing intrinsically wrong with this, except that the performance of your model is probably not great; you have found some sort of relationship but it does not seem strong enough to make good predictions of actual values. – Henry Sep 10 '23 at 20:35

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