Problem-Solving and Data AnalysisVery hardLimits of predictions from a model
Problem-Solving and Data Analysis practice question
A researcher collected data on the height of a tree, in metres, at each year of its age for ages 1 through 10, and found a line of best fit for the data. She then used the line to predict the tree's height at age 40.
Which of the following is the best criticism of this prediction?
- A. The prediction reaches far outside the range of ages in the data, where the linear pattern may no longer hold.Correct
- B. A line of best fit can describe data but can never be used to make any prediction.
- C. The prediction must be wrong because age 40 does not appear in the researcher's data.
- D. A scatterplot cannot be used to show a relationship between two variables.
Answer: A. The prediction reaches far outside the range of ages in the data, where the linear pattern may no longer hold.
The data cover ages 1 to 10, so that is the range the line was fitted to and the only range it is evidence about. Extending it to age 40 assumes the same steady growth continues four times beyond anything observed, which trees do not do indefinitely.
Why the other answers are wrong
- B. A line of best fit can describe data but can never be used to make any prediction.
- Prediction is exactly what a line of best fit is for. The problem is not predicting, it is predicting far outside the data that justified the line.
- C. The prediction must be wrong because age 40 does not appear in the researcher's data.
- A model routinely predicts at values that were not measured — that is its purpose. The issue is the distance from the observed range, not the absence of that exact age.
- D. A scatterplot cannot be used to show a relationship between two variables.
- Showing the relationship between two variables is precisely what a scatterplot does, and it is the basis for fitting the line in the first place.
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