What can be inferred if the residuals are not randomly distributed in the residual plot?

  • The data has no outliers
  • The data is perfectly linear
  • The linear regression model is a perfect fit for the data
  • The linear regression model is not a good fit for the data
If the residuals are not randomly distributed (e.g., if they form a pattern), it suggests that the linear regression model is not a good fit for the data. This could be because the relationship between the variables is not linear, or because the data exhibits heteroscedasticity (unequal variances of errors), among other reasons.
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