Intrepreting Predicted R^2 Value

[Stu_Souten]

Hello all

I have created a linear regression model for some data which is y= 541.5 + 0.239 * x

I need to check how reliable this model is and one of the metrics I am using is the Predicted R^2, in this case it is 8%.

I know that the R^2 value tells you how well the model predicts new observations but I am trying to understand what my R^2 of 8% is telling me???

Is my R^2=8% telling me that my model is able to predict the response of new observations to an accuracy of 8% i.e. if I had a new x value of say 22, then using my regression model I would get a y value of 541.5+0.239*22 = 546.758, would it be correct to say that my predicted value of 546.758 is only 8% of the true value.

Does this makes sense?

Thank you for your help.

 

[Harry_the_cat]

An \(\displaystyle R^2\), the coefficient of determination, of 8% means that 8% of the variation in the dependent variable (y) can be explained by the variation in the independent variable (x). (Which implies that 92% can't be.)
Also, this means that R, which is Pearson's correlation coefficient, is \(\displaystyle \sqrt{0.08}\approx 0.28\) which is considered quite low.