# Adjusted R2 Validity for Big amounts of observations

I am working with a dataset that has a big amount of observations (2000). The purpose of my work is to find which dependent variables (x1, x2, x3...) are linked to my independent variable (y). I have discovered the adjusted R2 method and it seems pretty accurate for what I am looking for since it makes a ponderation of the influence of new variables in the prediction.

The equation for the Adjusted R2 method is shown in 1:

R2_Adj = 1 - [(1-R2)(n-1)/n-k-1] [1]

where:

• N is the number of points in your data sample.
• K is the number of independent regressor.

Apparently it should work. However, when I have a big amount of data: N = 2000 the difference between 1 or 2 regressors is sometimes not big enough to spot a good regressor and instead, sometimes the model accepts a 'bad' regressor as 'good'.

Do you know how can I fix this? Does it exist any other method similar to this one that allows to use this big amount of Data samples?

• how do you know it is not accepting good regressors and accepting bad regressors? Commented Nov 2, 2021 at 12:56
• I created my own dataset with the independent variable and 'good' and 'bad' regressors for it and this was the result Commented Nov 2, 2021 at 13:00
• just by chance this will sometimes happen. Or did you find a systematic problem? Commented Nov 2, 2021 at 13:02
• In my model It happens whenever I add a new regressor to the proper one. The adjusted regression value is higher for the 2 variables model (which contains a bug) than for the one variable model (which only contains the proper variable). But I can try to create a new dataset and check, thank you! Commented Nov 2, 2021 at 13:10
• I don't know much about adjusted R2, but if your goal is to find variables related to the outcome, than you can use p-values or other similar measures, no? Also, a question is if you want to put variables into one model or test them separately, which has different interpretations Commented Nov 2, 2021 at 13:16