R-squared from sums of squares, a strong fit

Question

A regression of house price on floor area reports 	ext{SST} = 800, \qquad 	ext{SSE} = 200. Find R-squared and interpret it.

Accepted Answer

R-squared is the share of the total variation in y that the model explains: R^2 = 1 - \frac{	ext{SSE}}{	ext{SST}} = 1 - \frac{200}{800} = 1 - 0.25 = 0.75. The error keeps only a quarter of the variation (	ext{SSE}/	ext{SST} = 0.25), so the model explains the other three quarters: R^2 = 0.75, meaning about 75\% of the variation in house price is explained by floor area, with 25\% unexplained. That is a fairly strong fit for real data, but "strong" is context-dependent, and a high in-sample R^2 is not by itself proof the model will predict well on new houses. Takeaway. R^2 = 1 - 200/800 = 0…

R-squared from sums of squares, a strong fit

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