Analyze Linear Regression Changes with Duplicated Observations
Company: Google
Role: Data Scientist
Category: Statistics & Math
Difficulty: medium
Interview Round: Technical Screen
##### Scenario
Statistical considerations when analysing linear regression output and goodness-of-fit tests.
##### Question
If every observation in a linear-regression dataset is duplicated, how do the coefficient estimates and their standard errors change? Explain mathematically. In practical terms, what does a p-value represent and what common misinterpretations should be avoided? How does a very large sample size influence a chi-square test, and what penalty or adjustment can keep results interpretable?
##### Hints
Recall that estimates stay the same but SE scales with √n; discuss effect size vs. significance.
Quick Answer: This question evaluates understanding of linear regression inference (including how estimators and standard errors behave when observations are duplicated), correct interpretation of p-values, and the influence of very large samples on chi-square tests, situating it in the Statistics & Math domain of statistical inference and hypothesis testing.