If the line of best fit predicts a higher y-value than the observed y for a data point, what is the sign of the residual y - ŷ?

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Multiple Choice

If the line of best fit predicts a higher y-value than the observed y for a data point, what is the sign of the residual y - ŷ?

Explanation:
Residuals are the difference between what’s observed and what the line of best fit predicts: y − ŷ. If the line predicts a higher value than what’s observed, you’re subtracting a larger number from a smaller one, which gives a negative result. So the residual y − ŷ is negative when ŷ > y. This also means the point lies below the fit line. If the prediction were lower than the observation, the residual would be positive; if it matched exactly, it would be zero.

Residuals are the difference between what’s observed and what the line of best fit predicts: y − ŷ. If the line predicts a higher value than what’s observed, you’re subtracting a larger number from a smaller one, which gives a negative result. So the residual y − ŷ is negative when ŷ > y. This also means the point lies below the fit line. If the prediction were lower than the observation, the residual would be positive; if it matched exactly, it would be zero.

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