Practice Underfitting (Intuition) in Math

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

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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 structureβ€”it's not learning enough.

Showing a random 20 of 50 problems.

Example 1

medium
A residual plot of a linear fit shows a clear curved pattern. Is the model overfit or underfit, and why?

Example 2

medium
A scatter plot shows a clear parabolic relationship. You fit y=a+bxy = a + bx and get R2=0.10R^2 = 0.10. What model would you try next, and why?

Example 3

medium
As complexity increases from very low, both train and test error fall together at first. What were they suffering from at low complexity?

Example 4

medium
A learning-curve plot shows train and test error very close and both high, flat across sample size. What does this suggest?

Example 5

easy
To fix underfitting, should you make the model more or less complex?

Example 6

easy
A model gets R2=0.08R^2 = 0.08 on training data and R2=0.06R^2 = 0.06 on test data. Underfit or overfit?

Example 7

easy
Train accuracy 55%55\%, test accuracy 54%54\%. Best diagnosis?

Example 8

easy
A student uses y^=50\hat{y} = 50 (the mean) to predict all exam scores. Training R2=0R^2 = 0. Explain why this represents maximum underfitting.

Example 9

hard
A neural network is trained for only 2 epochs. Both train and validation loss remain high. Best next action?

Example 10

challenge
An analyst applies kk-means with k=2k = 2 to a dataset that obviously has 55 natural clusters, then concludes 'there are only two types of customers.' Critique this conclusion in terms of underfitting.

Example 11

medium
A linear classifier achieves 50%50\% accuracy on a 2D dataset that is clearly arranged in concentric circles. Underfit or overfit?

Example 12

easy
Fitting a straight line to data that clearly follows a curve is an example of ___.

Example 13

medium
A decision tree limited to depth 1 (a 'stump') is fit to a complex dataset. Predicted accuracy β‰ˆ55%\approx 55\%. Cause?

Example 14

medium
A linear model gives R2=0.30R^2=0.30 on data that visibly follows a parabola. What does the low R2R^2 plus visible curve suggest?

Example 15

easy
Predicting the mean y^=yˉ\hat y = \bar y for every input gives training R2=0R^2 = 0. What kind of fit is this?

Example 16

hard
In a regression task, residuals plotted against xx show a clear pattern (curve). What does that pattern reveal about the current model?

Example 17

easy
To fix underfitting you should usually make the model ___.

Example 18

challenge
Total error =bias2+variance=\text{bias}^2+\text{variance}. A model has bias 6, variance 1 (so error 37); adding capacity changes it to bias 2, variance 5. Did total error improve, and was the original underfit?

Example 19

easy
A simple model fails to find a pattern. Does that prove no pattern exists?

Example 20

medium
You apply heavy regularization (Ξ»=106\lambda = 10^6) to a linear model. Most coefficients shrink to nearly zero. What happens to bias and variance?
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Related Concepts

Model Fit (Intuition)