# Although not reported in the paper it is possible to generate estimates of the confidence interval around the R2.
# This can be done by simulating betas and generating estimated R2s for each simulation. 
#
# Approximate estimates can also be produced using only information on the degrees of freedom for each model. 
# An example of how this is done is given below.
#
# The (R) code below generates confidence intervals for the Adj R by exploiting the following relation between the the R2 and the ADJR2:
# R2 = (p)/(n - 1) + ((n - p - 1)/( n - 1))ADJR2
#
# Note that the CI is constructed based on the *approximate* SE of Rsq: sersq <- sqrt((4*rsq*(1-rsq)^2*(n-k-1)^2)/((n^2-1)*(n+3)))
# For more details See R documentation: CI.Rsq {psychometric}


library(psychometric)


DATA <-matrix(c(
0.14,	0.36,	0.18,	0.13,	0.49,	0.18,	0.02,	0.13,	0.22,	0.43,	0.3,	0.38,
134,	133,	138,	144,	142,	131,	132,	128,	143,	81,	126,	138,
37,	40,	40,	40,	40,	39,	39,	40,	40,	29,	37, 	40

),12)


Y<-matrix(-1, nrow(DATA), 3)
for(k in 1:nrow(DATA)){
	R2<- (DATA[k,3])/(DATA[k,2] - 1) + ((DATA[k,2] - DATA[k,3]-1)/( DATA[k,2] - 1))*DATA[k,1]
	T<- CI.Rsq(R2, DATA[k,2], DATA[k,3], level = 0.95)
	Y[k,1] <- (T[1,3] - (DATA[k,3])/(DATA[k,2] - 1))/((DATA[k,2] - DATA[k,3]-1)/( DATA[k,2] - 1))
	Y[k,2] <- (T[1,1] - (DATA[k,3])/(DATA[k,2] - 1))/((DATA[k,2] - DATA[k,3]-1)/( DATA[k,2] - 1))
	Y[k,3] <- (T[1,4] - (DATA[k,3])/(DATA[k,2] - 1))/((DATA[k,2] - DATA[k,3]-1)/( DATA[k,2] - 1))
	}
Y