Problem-Solving and Data AnalysisVery hardExtrapolation caution
Problem-Solving and Data Analysis practice question
A line of best fit relating a child's age x (from 2 to 10 years) to height y in centimetres is y = 6x + 78. Which statement about using this model is most appropriate?
- A. It gives reasonable predictions for ages 2 to 10 but should not be used to predict the height of a 40-year-old.Correct
- B. It predicts that a 40-year-old is 318 cm tall, which must be correct.
- C. It shows that height causes age to increase.
- D. It cannot be used for any age because the data are only a sample.
Answer: A. It gives reasonable predictions for ages 2 to 10 but should not be used to predict the height of a 40-year-old.
A fitted line is reliable within the range of the data; extrapolating to 40 gives an absurd 318 cm.
Why the other answers are wrong
- B. It predicts that a 40-year-old is 318 cm tall, which must be correct.
- 318 cm is impossible; the model does not apply at 40.
- C. It shows that height causes age to increase.
- Correlation says nothing about causation, and the direction is absurd.
- D. It cannot be used for any age because the data are only a sample.
- Within its range the model is useful.
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