SAT Two-variable data: models and scatterplots Practice Question 1 (Medium) | SAT Owl

Question bank / Two-variable data: models and scatterplots

Math · Problem-Solving and Data AnalysisMedium

A botanist recorded the height $h$ , in centimeters, of a sunflower each week for $10$ weeks. The line of best fit for the data is $h = 2.4w + 15$ , where $w$ is the number of weeks after the botanist began recording. Which of the following is the best interpretation of $2.4$ in this context?

A

The predicted height of the sunflower, in centimeters, when the botanist began recording

B

The predicted total growth of the sunflower, in centimeters, over the $10$ weeks

C

The predicted increase in the sunflower's height, in centimeters, for each additional week

D

The predicted number of weeks it takes the sunflower to grow $1$ centimeter

Show answer and explanation

Answer: C

In a linear model $h = mw + b$ , the slope $m$ is the change in $h$ for each increase of $1$ in $w$ . Here the slope is $2.4$ , so the model predicts the sunflower grows $2.4$ centimeters each week. The value $15$ , not $2.4$ , is the predicted height at $w = 0$ .

Choice A describes the $y$ -intercept, $15$ , rather than the slope.

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