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I have a R-squared of 0.4787. I know it indicates the model does not fit very well with the observations, but that is what I got so far using R. My question is: does R-squared help to access statistical significance?

kjetil b halvorsen
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Betty
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    R2 isn't even a good indicator for goodness of fit. If you want to assess the statistical significance of the model you'd consult its F-score. – Robin Gertenbach Feb 25 '20 at 18:05
  • Hi @Betty, R square means the proportion of variance that can be explained by your predictors. This will really depend on the number of observations right? If you have a lot of observations, its rsquare can be low but hugely significant – StupidWolf Feb 25 '20 at 18:31
  • Likewise you might have a small number of observations, maybe like 0.5 for rsquare like what you have, by this is can somewhat by chance right. The answer is, first look at the number of observations, you can use F test and also the r square to determine how useful is the model to you – StupidWolf Feb 25 '20 at 18:32
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    Statistical significance of what? By the way, your $r^2$ might be quite excellent, depending on your goals. – Dave Feb 26 '20 at 02:31

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All else equal, the higher the $R^2$, the higher the $F$-stat and the lower the p-value.

That "all else equal" is crucial, however. If you increase the $R^2$ by throwing many parameters at the model, you affect the degrees of freedom and can wind up with a lower p-value in the $F$-test.

However, there is a loose relationship. Especially if I knew that I had been careful to have a reasonable number of parameters for the sample size, I would see a high $R^2$ as at least a positive signal. Then the $F$-test can account for the exact number of parameters compared to the sample size.

Unless you have a tiny sample size or a huge number of parameters for your sample size, that $R^2 = 0.4787$ is likely screaming out that you will have a significant $F$-test.

Dave
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