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