Analyze Linear Regression Changes with Duplicated Observations

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.