... the variation accounted for by the least squares regression line. The expression 1 − r2 is the fraction of variation that is left in the residuals. If r2 = 0, the regression line describes none of the variation in the data. In this case, the slope b1 = r (sy/sx) is also zero and the fitted line is flat. If r2 = 1, the line represents all of the variation and se = 0.

For the diamonds, r2 = 0.712 ≈ 0.5 and 1 − r2 = 0.5. Because 0 ≤ r2 ≤ 1, this summary is often described on a percentage scale. For example, we might say “The fitted line explains 50% of the variation in price.”

Summarizing the Fit of a Line

The quantity r2 is a popular summary of a regression ...

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