In "An Introduction to Statistical Learning" (or actually anywhere else) R^2 (when close to 1) is defined as:

"R^2 value close to 1 indicates that the model explains a large portion of the variance in the response variable."

If R^2 is close to 1, the model is considered to fit the data well. Using the formula for R^2 (1-(RSS/TSS)) this makes sense.

But what confuses me: If the model doesn't explain the variance (i.e. R^2 goes towards 0), doesn't it then mean that the variance lies within the data, i.e. that the data has an inherently large variance? Consequently, if the data has a large variance, the model cannot make it any better?

  • This particular model maybe cannot make it better, but some other might. But yes, $R^2$ is tied to the data, and if the data is highly variable you can expect in general that $R^2$ is going to be low, but not necessarily. – user2974951 Dec 4 at 10:20

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