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While learning about regression, I was told as a prerequisite for significance testing you must test for normality and homogeneity. I can do this by plotting Q-Q plots and residuals to fitted values, and then easily tell just by looking at them whether or not they indicate normality or homogeneity.

However, what about cases where it isn't immediately clear? For example, I observe the Q-Q plot to be neither clearly straight or clearly skewed. Similarly for the residuals to fitted values plot, it is not clear whether or not the cloud of points is unstructured or structured.

Do methods exist to definitively tell me if I should accept the data as normal/homogeneous? Or am I missing something, and such methods wouldn't very useful?

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