R-squared for a weak model, most variation unexplained

Question

A regression of daily mood score on hours of sunlight reports 	ext{SST} = 1000, \qquad 	ext{SSE} = 550. Find R-squared and say what it tells you.

Accepted Answer

Compute the fraction of variation the model explains: R^2 = 1 - \frac{	ext{SSE}}{	ext{SST}} = 1 - \frac{550}{1000} = 1 - 0.55 = 0.45. So R^2 = 0.45: sunlight explains about 45\% of the variation in mood, and 55\% remains unexplained (people's moods depend on much more than sunshine). Is a low R-squared "bad"? Not necessarily. For messy human behavior, explaining nearly half the variation with a single input can be a genuinely useful finding. Whether an R-squared is good depends entirely on the field and the goal, not on some universal threshold. Takeaway. R^2 = 1 - 550/1000 = 0.45; a "low" …

R-squared for a weak model, most variation unexplained

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