I am working on a regression problem, where I achieved a very low MSE, which usually means that R2 coefficient should be close to 1, especially that the regressed curve is very close to the true curve.
The problem is the R2 is very low, even though the MSE is very low. What does this mean from the data nature perspective ?? and Why can this happen??
I understand that R2 equals MSE divided by variance, which implies that low R2 means either low MSE or very high variance. I hope somebody can explain this!
I could be misunderstanding your question. But R2 is your Sum of squares explained (aka regression) divided by your total variance. It is not your MSE divided by variance as you noted above. Therefore, the size of MSE has no direct relation to R2. It seems like you have a very small sum of squares explained/regression that is causing you to have a small R2. Because mean squares are impacted by DF as mentioned above (they are simply sum of squares divided by degrees of freedom), the size of the Mean Squares for either explained or error don't make a lot of sense to interpret without considering the other. Their relative size of one to another is more important than their absolute size (which is how we get f values). As pointed out above, a small MSE could have a lot do to with the number of degrees of freedom you have as well as the amount of unexplained variance you have. Without seeing the results, it seems like you have a relatively (to sum of squares explained/regression) large sum of squares error, but a lot of degrees of freedom, which is causing a small MSE and a small R2. Best of luck.
MSE =Error sum of squares/d.f(Residual space), MSE is unbiased estimator of error variance under standard assumptions of the linear model.
MSE can be low in situation of under fitting, where there are too many degrees of freedom available to Residual space and too few to the Regressor space, this in turn can lead to small R2 also if the contributing regressors in the present regression model do not contribute to much of data variation.
I could be misunderstanding your question. But R2 is your Sum of squares explained (aka regression) divided by your total variance. It is not your MSE divided by variance as you noted above. Therefore, the size of MSE has no direct relation to R2. It seems like you have a very small sum of squares explained/regression that is causing you to have a small R2. Because mean squares are impacted by DF as mentioned above (they are simply sum of squares divided by degrees of freedom), the size of the Mean Squares for either explained or error don't make a lot of sense to interpret without considering the other. Their relative size of one to another is more important than their absolute size (which is how we get f values). As pointed out above, a small MSE could have a lot do to with the number of degrees of freedom you have as well as the amount of unexplained variance you have. Without seeing the results, it seems like you have a relatively (to sum of squares explained/regression) large sum of squares error, but a lot of degrees of freedom, which is causing a small MSE and a small R2. Best of luck.
I am agree with Mr. Eric. It depends on the data used for study. How much variation between data and how much data is used for study.
Dear Ahmad
As Shanti and Eric mentioned this problem is related to your data. If you share your scatter plot and regression line, then I can better explain the reason of the problem.
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