Discussing linear regression feature representations during a Data Scientist interview.

Given two original regressors x1 and x2, model a is linear in x1 and x2. Model b is linear in the transformed features x1 + x2 and x1 - x2. Are models a and b equivalent? Provide a mathematical explanation. If you have more than 1,000 predictors and want to fit a linear model, what problems might occur and how would you mitigate them?

Recall that linear transforms of features can represent same subspace; consider rank, multicollinearity, over-parameterization; mention overfitting, regularization, dimensionality reduction for many predictors.

Databricks Data Scientist interview question: Explain Linear Regression Feature Transformation Equivalence. {"blocks": [{"key": "8f3e062c", "text": "Scenario", "type": "header-two", "depth": 0, "inlineStyleRanges": [], "entityRanges": [], "data": {...