If |r| = 1, the standard deviation of y is equal to the standard deviation of the residuals.

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Quizplus · Accepted Answer

The standard deviation of y is not necessarily equal to the standard deviation of the residuals. The value |r| = 1 indicates a perfect linear relationship between two variables, but the standard deviation of y measures the spread of the y values around their mean, while the standard deviation of the residuals measures the spread of the differences between observed and predicted y values. These are related but distinct concepts.

If |R| = 1, the Standard Deviation of Y Is