Prediction Math Example 4
Follow the full solution, then compare it with the other examples linked below.
Example 4
hardWhy is extrapolation (predicting outside the observed range) dangerous? Give an example where extrapolating from a linear model would give a clearly unreasonable prediction.
Solution
- 1 Extrapolation danger: the linear relationship may only hold within the observed range; outside that range, the true relationship may be curved or have a different slope
- 2 Example: a model predicts height from age 5–15 as cm
- 3 Extrapolating to age 50: cm (nearly 10 feet!) — clearly impossible
- 4 The linear model only applies to the range years; the relationship flattens after growth stops
Answer
Extrapolation produces unreliable predictions; example: predicting adult height using a child growth linear model gives absurd results.
Extrapolation assumes the model extends beyond its valid range — an assumption that is often false. Always restrict predictions to the range of observed data and use domain knowledge to evaluate whether extrapolated predictions make sense.
About Prediction
A prediction is a model-based estimate of an unknown or future value, accompanied by a measure of confidence or uncertainty.
Learn more about Prediction →More Prediction Examples
Example 1 medium
A linear regression model gives [formula] where [formula] = hours studied and [formula] = test score
Example 2 hardA model predicts house prices. In-sample [formula], but out-of-sample [formula]. Explain what this m
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