Analyze Linear Regression Changes with Duplicated Observations
Overview
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.
Google
Jul 12, 2025, 6:59 PM
Data Scientist
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Statistics & Math
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Linear Regression, p-values, and Chi-square with Large Samples
Context
You are analyzing regression and goodness-of-fit results. Consider what happens if you mechanically duplicate each row of your dataset (same X and y repeated once), how to interpret p-values in practice, and how very large samples affect chi-square tests.
Questions
- If every observation in a linear regression dataset is duplicated (each row repeated once), how do the coefficient estimates and their standard errors change? Show the math.
- 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/adjustment can keep results interpretable?
Solution
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