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Problem-Solving and Data AnalysisVery hardReading a negative slope without overclaiming

Problem-Solving and Data Analysis practice question

For 30 cars, a scatterplot shows each car's mass, x, in kilograms, and its fuel economy, y, in kilometres per litre. The line of best fit has a slope of −0.004. Which statement is best supported?

  1. A. Heavier cars tend to have lower fuel economy; each additional kilogram is associated with a predicted decrease of 0.004 kilometres per litre.Correct
  2. B. The association between mass and fuel economy is positive.
  3. C. Each additional kilogram of mass causes a car's fuel economy to fall by 0.004 kilometres per litre.
  4. D. For each additional kilometre per litre of fuel economy, a car's mass decreases by 0.004 kilograms.

Answer: A. Heavier cars tend to have lower fuel economy; each additional kilogram is associated with a predicted decrease of 0.004 kilometres per litre.

A negative slope means y tends to fall as x rises: heavier cars, lower fuel economy. The slope's size, 0.004, is the predicted change in y per unit of x. 'Associated' is the right word for a line fitted to observed data.

Why the other answers are wrong

B. The association between mass and fuel economy is positive.
A negative slope is a negative association.
C. Each additional kilogram of mass causes a car's fuel economy to fall by 0.004 kilometres per litre.
A line of best fit describes an association in the data; it can't establish that mass CAUSES the change.
D. For each additional kilometre per litre of fuel economy, a car's mass decreases by 0.004 kilograms.
This reverses the roles of x and y. The slope is the change in y (fuel economy) per unit of x (mass).

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