Choose linear regression or decision tree appropriately

Q: Choose linear regression or decision tree appropriately

This is a Machine Learning interview question from TikTok for Data Scientist roles. View the full question and solution on PracHub.

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Question

Choose Between Linear Regression and a Decision Tree Under a Hinge and Interaction DGP

Context

You have 100,000 i.i.d. observations with features x1 (range 0–100), x2, x3, and target y. The true data-generating process (unknown to you) is piecewise linear with a hinge at x1 = 50 and an interaction between x2 and x3:

y ≈ 3·x1 + 20·I[x1 > 50] + 2·(x2·x3) + ε
Heteroskedastic noise: Var(ε | x1) = 0.01·(1 + x1)

Task

Design an analysis to decide between linear regression and a decision tree. Specify:

Feature engineering and tests you would run for linearity (e.g., spline basis for x1, x2:x3 interaction) and how you would check residual diagnostics for heteroskedasticity.
A fair comparison protocol (CV split, identical preprocessing) and metrics.
How you would enforce monotonicity or interaction constraints in a tree-based model to reflect domain knowledge.
Which model you expect to generalize better here and why, including bias–variance reasoning and how you would quantify it with learning curves.

Choose linear regression or decision tree appropriately

Choose Between Linear Regression and a Decision Tree Under a Hinge and Interaction DGP

Context

Task

Solution (Locked)

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