Analyze regression to mean in heavy-tailed shares

Per-user daily shares follow a right-skewed distribution with a long tail. On the first day, split users into two cohorts based on the Day-1 daily-share distribution: those at the 50th percentile (p50) and those at the 95th percentile (p95). Over the next 14 days, (a) forecast how each cohort’s mean daily shares will evolve and explain the role of regression to the mean versus genuine behavioral differences. (b) Which cohort would you expect to show greater day-to-day variance, and why? (c) Describe how weekly seasonality, such as weekend effects, will appear in the cohort time series and how you would adjust for it. (d) Outline an analysis to test whether quantiles like p50 and p95 are temporally stable for this metric.

Overview: This question tests 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.

Read the full data scientist interview experience this question came from.