Underfitting (Intuition) Math Example 3

Follow the full solution, then compare it with the other examples linked below.

easy

A student uses

\hat{y} = 50

(the mean) to predict all exam scores. Training

R^2 = 0

. Explain why this represents maximum underfitting.

1
The 'model' $\hat{y} = 50$ makes the same prediction for everyone — ignores all predictors
2
$R^2 = 0$ : the model explains 0% of score variation — worst possible fit (besides being negative)
3
This is maximum underfitting: the simplest possible model, capturing no structure at all
4
Any model using actual predictors should outperform this baseline

Answer

Predicting the mean for all is maximum underfitting (R²=0); it uses no information from predictors.

The mean-only model is the baseline (null model) in regression.

R^2

measures how much better any model does compared to this baseline. A

R^2 = 0

means the model is no better than ignoring all predictors.

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.

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