SAT Math · Two-variable data: models and scatterplots · medium

A linear model was used to predict the weight of four different animals based on their length. The residuals (actual minus predicted…

+2 Animal 1 -1 Animal 2 +5 Animal 3 -3 Animal 4 + - Residual (actual - predicted), lbs
A linear model was used to predict the weight of four different animals based on their length. The residuals (actual minus predicted weight) for the four animals were +2+2, −1-1, +5+5, and −3-3 pounds. Which animal's weight was modeled LEAST accurately?

Answer and explanation

Answer: D: The animal with a residual of +5 pounds

Prediction accuracy depends on the size of the error, not its direction. A residual of −3-3 and a residual of +3+3 are equally far from the line. Compare the absolute values: ∣+2∣=2|+2| = 2, ∣−1∣=1|-1| = 1, ∣+5∣=5|+5| = 5, ∣−3∣=3|-3| = 3. The largest is 5, so the animal with a residual of +5+5 pounds was modeled least accurately, choice D. Choice A (−1-1) is the most accurate, with the smallest error. Choice B (−3-3) is the tempting choice if you treat the most negative value as the worst. Choice C is false, since the errors differ.

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