Practice Underfitting (Intuition) in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
Underfitting occurs when a model is too simple to capture the true pattern in the data, performing poorly on both training data and new data.
The model misses important structure—it's not learning enough.
Example 1
easyA scatter plot shows a clear U-shaped relationship between x and y. A linear model is fitted and gets R^2 = 0.05. Explain what underfitting is and how to fix this model.
Example 2
mediumCompare two regression models on the same data: Model 1 (linear): training R^2=0.40, test R^2=0.38. Model 2 (cubic): training R^2=0.95, test R^2=0.35. Diagnose each model.
Example 3
easyA student uses \hat{y} = 50 (the mean) to predict all exam scores. Training R^2 = 0. Explain why this represents maximum underfitting.
Example 4
hardA linear model for time-series stock prices has high residuals for all time periods. Identify this as underfitting and explain why stock prices might inherently have an upper bound on R^2 regardless of model complexity.