I'm in AP Statistics, an introductory college course taught at high school. We learned that if a residual plot has a pattern, we must re-express the data until the residual plot is scattered. This is because a scattered residual plot indicates a linear correlation. But why is this the case?

For example, if all the data points are clustered along the line of best fit, the residual plot would show a pattern. In this case, the model closely matched the data points. But we learned that patterned residual plots show a lack of linear correlation, meaning the model is a poor one.

Please explain!!!

And if my question doesn't make any sense, please ask me to explain!!!

  • $\begingroup$ If by pattern you mean some tendency for the residuals to have the variance change as a function of the predictor variable this would indicate heteroscedasticity. Other patterns could indicate nonlinearity or other departures from the assumptions of the linear model. If the residuals look like random noise about the fitted line then the linear model could be appropriate even if they tend to be large but with the line having a nonzero slope. A strong linear model might mean small residuals, $\endgroup$ – Michael R. Chernick Oct 15 '17 at 23:33
  • $\begingroup$ Can you post some images of the patterns you have in mind? It's a little hard to guess from your verbal descriptions. $\endgroup$ – gung - Reinstate Monica Oct 16 '17 at 1:10

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