Underfitting (Intuition) Math Example 1
Follow the full solution, then compare it with the other examples linked below.
Example 1
easyA scatter plot shows a clear U-shaped relationship between and . A linear model is fitted and gets . Explain what underfitting is and how to fix this model.
Solution
- 1 Underfitting: the model is too simple to capture the U-shaped pattern — a line cannot represent a curve
- 2 : only 5% of variation explained — the model is nearly useless
- 3 Diagnosis: both training error and test error are high (model fails everywhere)
- 4 Fix: use a quadratic model which can capture U-shapes; check that improves significantly
Answer
Underfitting: linear model can't capture U-shape. Fix: use quadratic model to match the true curved relationship.
Underfitting (high bias) occurs when the model's functional form is too restrictive for the true relationship. Unlike overfitting (which needs simplification), underfitting requires a more flexible model class to capture the real pattern in the data.
About Underfitting (Intuition)
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.
Learn more about Underfitting (Intuition) →More Underfitting (Intuition) Examples
Example 2 medium
Compare two regression models on the same data: Model 1 (linear): training [formula], test [formula]
Example 3 easyA student uses [formula] (the mean) to predict all exam scores. Training [formula]. Explain why this
Example 4 hardA linear model for time-series stock prices has high residuals for all time periods. Identify this a