Examining some students on their final year projects defence. I discovered that a student had the Adjusted R² in the Regression analysis of her work to be greater than 99%. Could that be possible?
2. Can an adjusted R-squared exceed the associated, unadjusted R-squared? No, though they can be equal (as pointed out by Debopam Ghosh )
Here's one version of the most commonly used formula for adjusted R-squared:
Adjusted R2 = 1 – [(1-R2)*(n-1)/(n-k-1)]
where:
R2 = unadjusted/observed R-squared
n = sample size used in model
k = number of IVs included in the model
Note that, the ratio (n - 1) / (n - k - 1) will always be less than one for k = 1, 2, ...n - 1. So, unless the unadjusted R-squared = 1, the adjusted R-squared will be less than the unadjusted R-squared. As N increases, relative to k, the difference between the two values will decrease as well.
So, what this all means is that no; if R-squared = .990, adjusted R-squared cannot be .992.