Which statement correctly distinguishes parametric models from nonparametric models with examples?

• A. K-NN is parametric.
• B. Parametric models have fixed parameters; nonparametric adapt with data.
• C. Parametric models grow with data; nonparametric fixed.
• D. Linear regression is nonparametric.

Answer: (B)

The main idea here is the difference in how model complexity is handled: parametric models fix the number of parameters in advance, while nonparametric models let complexity adapt with the data. In a parametric approach, you commit to a specific form and a finite set of parameters (for example, linear regression with just a slope and an intercept). No matter how much data you collect, you’re estimating those same parameters. That makes the model simple and data-efficient when the assumed form fits well, but it can miss patterns if the true relationship is more complex.

Nonparametric models don’t fix a finite parameter count in advance; their capacity can grow as you gather more data. This lets them capture more intricate patterns because the model can become more flexible with more information. A common example is K-nearest neighbors, which uses the training data directly and expands its local decision rules as more examples are added, increasing its flexibility. Kernel density estimation and certain tree-based methods reflect the same idea: their ability to fit data improves as the dataset grows.

So the best statement is that parametric models have fixed parameters, while nonparametric models adapt with data. The other descriptions conflict with how these two families manage complexity: linear regression is parametric, not nonparametric, and K-NN is nonparametric, not parametric.