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MATHEMATICS The confidence interval for R or R squared is based on the normal probability distribution. To use that distribution Fisher's transformation needs to be applied to R: Z = 0.5 * ln [ (1R) / (1+R) ] where Z is the transformed R value. Z has been proved to follow a normal distribtion with standard deviation (S) defined by: S squared = 1/(N3) where N is the number of data sets. With S, confidence intervals for Z can be found as follows: ZL = Z  F * S ZU = Z + F * S where ZL is the lower confidence limit of Z, ZU is the upper confidence limit, and F is a factor dependeing on the degree of confidence desired: For 50% confidence F = 0.674 For 75% confidence F = 1.150 For 90% confidence F = 1.65 For 95% confidence F = 1.96 For 97.5% confidence F = 2.24 For 99% confidence F = 2.58 For 99.9% confidence F = 3.29 After finding ZL and ZU, these values must be transformed back to RL and RU, RL being the lower confidence limit of R and RU the upper confidence limit. We have: RL = [exp(2*ZL)1] / [exp(2*ZL) +1]; RU = [exp(2*ZU)1] / [exp(2*ZU) +1]; The upper and lower confidence limits of R squared can now be found using the squared values of RL and RU. 
