Computing R-squared from the error and total spread

Question

For a fitted regression, the total variation in $y$ around its mean is measured by the total sum of squares, and the variation the model fails to capture is the error (residual) sum of squares:

$\text{SST} = 500, \qquad \text{SSE} = 200.$

What is the R-squared of the model, and what does it mean in words?

Accepted Answer

R-squared answers one question: of all the up-and-down variation in y, what fraction did the model manage to explain? Start from the total variation (SST), see how much is left over as error (SSE), and the rest is what the model explained. R^2 = 1 - \frac{	ext{SSE}}{	ext{SST}} = 1 - \frac{200}{500} = 1 - 0.4 = 0.6. So R^2 = 0.6, or 60\%. In plain words: the model explains about 60\% of the variation in y, and the remaining 40\% is still unexplained (left in the errors). The fraction 	ext{SSE}/	ext{SST} = 0.4 is exactly the share of variation the model missed, and one minus that is the sha…

Computing R-squared from the error and total spread

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