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My answer key responds with a large $R^2$ and a residual plot with no pattern.

The residual plot with no pattern makes sense. However, is having a large $R^2$ necessary? A linear model can be appropriate, but weak, with a low $r$ value, thus it follows that a model can be appropriate, although weak with a low $R^2$ value.

Is the answer key padding with extra information?

(Note, I'm currently in AP Statistics, and I'm sorry if this is a really basic question! Thank you for taking your time, though!)

Nick Stauner
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iamashortgiraffe
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  • Some perspective on this is afforded in the thread at http://stats.stackexchange.com/questions/13314/is-r2-useful-or-dangerous. – whuber Dec 31 '13 at 18:01
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    I am not sure what your question is. – Peter Flom Dec 31 '13 at 18:25
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    The $R^2$ tells you nothing about the appropriateness of a linear model - even a very high $R^2$ doesn't say the model is linear and a ver low $R^2$ doesn't imply it isn't. It's perfectly possible for the "true" model to be linear but have an $R^2$ that's very close to zero. – Glen_b Dec 31 '13 at 19:18

1 Answers1

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The answer key is incorrect. As Glen_b noted, a true linear relationship will not necessarily produce a high $R^2.$ Noisy data is one cause, for example. Correspondingly, a high $R^2$ does not guarantee linearity. Other models could still be better.

soakley
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