Explain p-values and interpret regressions

##### Question This is a statistics rapid-fire onsite for a Data Scientist role. Answer each part clearly and precisely — first as if explaining to a Product Manager, then for a technical audience. **Part A — p-values** 1. Explain **what a p-value is** in plain language (PM-friendly). 2. Give the **formal definition** of a p-value. 3. How should a p-value be **interpreted**, and what are the **common misinterpretations** to avoid? 4. If you run an A/B test and obtain **p = 0.03** for the primary metric, what decision would you make? What additional context would you request before shipping? **Part B — Linear regression with confounding** 5. You fit a linear regression with multiple features and suspect **confounding factors** exist. How do you interpret each parameter (coefficient)? 6. What does **“controlling for other variables”** actually mean, and when can that interpretation fail? 7. What is the difference between an **associational** and a **causal** interpretation of a coefficient? 8. What checks or approaches would you use to **reduce confounding bias**? **Part C — L1 vs L2 regularization** 9. What are **L1 (Lasso)** and **L2 (Ridge)** regularization, and how do they differ in effect? 10. When and why would you prefer one over the other (feature selection, multicollinearity, prediction vs interpretability)? 11. How would you **select the regularization strength** (λ), and what are the practical tradeoffs?