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You have been introduced to the notion that R^2 can capture “the % of variation in Y explained by the regression model.” This interpretation holds for simple and multivariate regression (as you have seen: as long as the model contains an intercept.) It is important to note, however, that R^2 cannot be used formally to hypothesis test whether a model is “good” or “not.” Therefore, the magnitude is often open to interpretation. I have noticed that there is often a desire to identify a “global value for R^2” that suggests the model is “good.” (Global in the sense that the value could be used across all models, 0.70? 0.80? 0.90?) Often I am asked, “what is a good value for R^2?”
