Practice Model Fit (Intuition) in Math

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

Quick Recap

Model fit describes how closely a statistical model's predictions match the observed data — measured by residuals, R^2, or loss functions.

Does the model's predictions match reality? Good fit = close match.

Example 1

easy
A scatter plot of weight vs. height shows points loosely scattered around a line. Two measures of fit are given: R^2 = 0.65 and residuals with SD = 8 kg. Interpret both measures.

Example 2

medium
Residual plot for a linear model shows a clear U-shaped pattern. What does this indicate about the model, and what should be done?

Example 3

easy
Three models have R^2 values: Model A = 0.95, Model B = 0.50, Model C = 0.10. Rank them by goodness of fit and describe what each R^2 means.

Example 4

hard
A model has R^2 = 0.99 in-sample but shows a fanning residual plot (residuals grow larger as \hat{y} increases). What problem does this reveal, and what are its consequences?
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