Analyze regression to mean in heavy-tailed shares

Q: Analyze regression to mean in heavy-tailed shares

This question evaluates statistical reasoning about heavy-tailed metrics and cohort dynamics, covering concepts like regression to the mean, variance differences in extreme quantile cohorts, time-series seasonality, and temporal stability of quantiles.

Q: How do I approach Analytics & Experimentation interview questions?

Analytics & Experimentation questions require understanding of core concepts and practice. PracHub provides solutions with explanations to help you master analytics & experimentation interviews.

Q: What difficulty level is this interview question?

This is a medium difficulty Analytics & Experimentation question, commonly asked during Onsite rounds at Meta.

Q: What role is this question designed for?

This question is commonly asked for Data Scientist candidates at Meta during technical interviews.

Question

Cohort Dynamics of a Right-Skewed Daily Shares Metric

Context

You have a right-skewed metric: daily shares per user, with a long tail.
On Day 1, you form two cohorts based on each user's Day-1 value:
- p50 cohort: users around the 50th percentile of the Day-1 distribution.
- p95 cohort: users around the 95th percentile of the Day-1 distribution.
You then track each cohort’s mean daily shares for the next 14 days (e.g., Days 2–15), counting zeros for users who do not share.
Assume cohorts are formed using narrow bands around the quantiles to ensure sufficient sample size (e.g., ±1 percentile point).

Questions

(a) Predict how each cohort’s mean daily shares will evolve over the next 14 days and explain the roles of regression to the mean vs genuine behavioral differences.

(b) Which cohort should exhibit larger day-to-day variance and why?

(c) Describe how weekly seasonality (e.g., weekends) will appear in the cohort time series and how you would adjust for it.

(d) Outline an analysis to test whether quantiles (e.g., p50, p95) are temporally stable for this metric.

Analyze regression to mean in heavy-tailed shares

Quick Overview

Cohort Dynamics of a Right-Skewed Daily Shares Metric

Context

Questions

Solution

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