# Question: When we use R2 for a random sample to estimate

When we use R2 for a random sample to estimate a population R2, it’s a bit biased. It tends to be a bit too large, especially when n is small. Some software also reports Adjusted R2 = R2 - {p/[n - (p + 1)]}(1 - R2), where p = number of predictor variables in the model. This is slightly smaller than R2 and is less biased. Suppose R2 = 0.500 for a model with p = 2 predictors. Calculate adjusted R2 for the following sample sizes: 10, 100, 1000. Show that the difference between adjusted R2 and R2 diminishes as n increases.

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