A scatterplot shows the average resale price y, in dollars... | SAT Two-variable data: models and scatterplots Question, Answer Explained

Question bank / Two-variable data: models and scatterplots

Math · Problem-Solving and Data AnalysisHard

A scatterplot shows the average resale price $y$ , in dollars, of a certain phone model $x$ months after the model's release. The line of best fit for the data is $y = -12x + 600$ . At $15$ months after release, the actual average resale price was $\$357$ . The actual price was what percent less than the price predicted by the line of best fit?

$15\%$

$18\%$

$63\%$

$85\%$

Show answer and explanation

Answer: A

The predicted price at $x = 15$ is $-12(15) + 600 = 420$ dollars. The actual price was $420 - 357 = 63$ dollars less. As a percent of the predicted price, $\frac{63}{420} = 0.15$ , or $15\%$ .

Choice B divides the difference by the actual price, $357$ , but less than the predicted price means the predicted price is the base.

Why the other choices are wrong

B. This divides the 63 dollar difference by the actual price, 357, instead of by the predicted price, 420.
C. 63 is the difference in dollars, not a percent.
D. 85% is the actual price as a percent of the predicted price, not the percent decrease.

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