Adjusted R2 and R2 CIs

[TomiSzucs]

Currently we use the following formulas for calculating adjusted r-squared confidence intervals:
Olkin, I. and Finn, J.D. (1995). Correlations Redux. Psychological Bulletin, 118(1), pp. 155-164.
See also: https://www.danielsoper.com/statcalc/formulas.aspx?id=28

Standard error calculations are based on: Cohen, J., Cohen, P., West, S.G., and Aiken, L.S. (2003). Applied Multiple Regression/Correlation Analysis for the Behavioral Sciences (3rd edition). Mahwah, NJ: Lawrence Earlbaum Associates. pp. 88
See also: https://stats.stackexchange.com/questions/175026/formula-for-95-confidence-interval-for-r2

These formulas are originally defined for r-squared. Our working assumption is that since the adjusted r-squared and the r-squared metric are both estimates of the magnitude of variance accounted for by the regressors, the same interval estimation can be used for both. Validate if this is the case, change if not.