R-squared from the explained sum of squares directly

Question

A regression reports the total spread of y and the part the model explains directly: 	ext{SST} = 400, \qquad 	ext{SSR (explained)} = 360. Find R-squared.

Accepted Answer

The total variation splits into two pieces: the part the model explains (the regression, or explained, sum of squares SSR) plus the part it leaves in the errors (SSE). So 	ext{SST} = 	ext{SSR} + 	ext{SSE}. R-squared is just the explained part as a fraction of the total, which you can read off directly when SSR is given: R^2 = \frac{	ext{SSR}}{	ext{SST}} = \frac{360}{400} = 0.9. So the model explains 90\% of the variation. Notice this matches the other formula: the leftover error is 	ext{SSE} = 400 - 360 = 40, and 1 - 40/400 = 1 - 0.1 = 0.9 gives the same answer. The two forms, explained…

R-squared from the explained sum of squares directly

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