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Problem-Solving and Data AnalysisVery hardLimits of a fitted linear model

Problem-Solving and Data Analysis practice question

A researcher fits the model y = 20 − 0.5x to data on x, the daily outdoor temperature in degrees Celsius between 0 and 30, and y, a household's daily heating cost in dollars. Which statement is best supported?

  1. A. Within the observed range, each 1-degree rise in temperature is associated with a 0.5-dollar fall in heating cost, and the model should not be relied on for temperatures outside 0 to 30 degrees.Correct
  2. B. At 60 degrees the household would be paid 10 dollars for heating.
  3. C. Raising the temperature causes heating costs to fall by exactly 0.5 dollars.
  4. D. The household spends 20 dollars a day on heating on average.

Answer: A. Within the observed range, each 1-degree rise in temperature is associated with a 0.5-dollar fall in heating cost, and the model should not be relied on for temperatures outside 0 to 30 degrees.

A fitted line describes an association within the data's range.

Why the other answers are wrong

B. At 60 degrees the household would be paid 10 dollars for heating.
This extrapolates far outside the data to an absurd result.
C. Raising the temperature causes heating costs to fall by exactly 0.5 dollars.
Association is not exact causation.
D. The household spends 20 dollars a day on heating on average.
20 is the predicted cost at 0 degrees, not an average.

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