SAT Math · Two-variable data: models and scatterplots · medium
A linear model predicts a plant's height, in centimeters, as h(w) = 2.5w + 8, where w is the number of weeks since data collection began,…
A linear model predicts a plant's height, in centimeters, as , where is the number of weeks since data collection began, with ranging from 2 to 20 in the original study. What is the plant's predicted height at , and is this prediction reliable given the study's scope?
Answer and explanation
Answer: A: 8; not reliable, since w=0 is outside the range of data actually observed
Evaluate the model at : centimeters. The second part asks about reliability. The study only collected data for weeks 2 through 20, so lies outside the observed range. Predicting there is extrapolation, and nothing in the data shows that the straight-line pattern continues backward to the start. That makes A correct. Choice B treats any value the equation can accept as trustworthy, which ignores the range of the data. Choice C gets the height wrong ( is 8, not 0) and invents a reason. Choice D computes 10.5 by plugging in , and also treats the equation as sufficient.
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