R squared when every observation appears twice
Question
An OLS regression yields . If each observation is duplicated, so every point appears twice, and the regression is rerun, what is the new ? Enter if it cannot be determined.
Short answer
. The fitted line and the mean of are unchanged, so both the residual and total sums of squares exactly double, leaving their ratio and hence the same.
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Open the worked solutionLessons behind this question
- Simple Linear Regression: OLS Estimators and Geometry
- Multiple Linear Regression
- Populations, Samples, and Sampling Distributions
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