Practice Prediction in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

Quick Recap

A prediction is a model-based estimate of an unknown or future value, accompanied by a measure of confidence or uncertainty.

Every prediction uses patterns from the past to extrapolate forward — good predictions come with explicit uncertainty bounds, not false precision.

Example 1

medium
A linear regression model gives \hat{y} = 2.5x + 10 where x = hours studied and y = test score. Predict the score for a student who studies 8 hours, and explain why this is a prediction, not a guarantee.

Example 2

hard
A model predicts house prices. In-sample R^2 = 0.92, but out-of-sample R^2 = 0.45. Explain what this means and identify the problem with the model.

Example 3

easy
Using the model \hat{y} = 3x - 5, predict y when x = 4 and x = 0. Then find x when \hat{y} = 25.

Example 4

hard
Why is extrapolation (predicting outside the observed range) dangerous? Give an example where extrapolating from a linear model would give a clearly unreasonable prediction.
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