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

A linear model predicts that a company will sell 50 units in a given month. The company actually sold 42 units that month. What is the…

A linear model predicts that a company will sell 50 units in a given month. The company actually sold 42 units that month. What is the sign of the residual (actual minus predicted), and where does this observation lie relative to the model's line?

Answer and explanation

Answer: C: The residual is negative, and the observation lies below the line.

The residual is actual minus predicted: 42−50=−842 - 50 = -8. It is negative because the company sold fewer units than the model predicted. A point whose actual value is below the predicted value lies below the model's line, since the line gives the predicted value at that xx. That makes C correct. Choice A has a positive residual, which would mean the company sold more than predicted. Choice B correctly gets the sign but misplaces the point above the line. Choice D is wrong because a residual of zero would require the actual and predicted values to be exactly equal.

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