comment  This program computes a confidence interval for the 
comment  squared multiple correlation coefficient for the design
comment  in which values of the independent variables are sampled.
comment  To use the program you input
comment  n--the sample size
comment  k--the number of predictors
comment  rsq--the sample squared multiple correlation coefficient
comment  conlevel--the confidence level for the interval.
NEW file.
INPUT PROGRAM.
compute n= 50.
compute k=5.
compute rsq=0.30.
compute conlev=.95.
compute #pul=(1-conlev)/2.
compute #pll=1-(1-conlev)/2.
compute #df1=n-1.
compute #df2=n-k-1.
compute #rtildsq=rsq/(1-rsq).
compute #switch=0.
compute #switch1=0. 
compute #test=cdf.f((n-k-1)*#rtildsq/k,k,n-k-1). 
do if (#test <=#pul).
compute           #switch=1.
compute           llrhosq=0.
compute           ulrhosq=0.
end if.
do if	(#test <=#pll). 
compute           #switch1=1.
compute           llrhosq=0.
end if.
compute #x2=1.0.
compute #x1=.00.
compute #diff3=1.
do if     #switch=0.
loop if     (abs(#diff3)>.00001).
compute           #x3=(#x1+#x2)/2.
compute           #yy=#x3/(1-#x3).
compute           #gamma=sqrt(1+#yy).
compute           #phi1=#df1*(#gamma**2-1)+k.
compute           #phi2=#df1*(#gamma**4-1)+k.
compute           #phi3=#df1*(#gamma**6-1)+k.
compute           #g=(#phi2-(sqrt(#phi2**2-#phi1*#phi3)))/#phi1.
compute	#nu=(#phi2-2*#yy*#gamma*(sqrt(#df1*#df2)))/#g**2.
compute	#lambdau=#yy*#gamma*(sqrt(#df1*#df2))/#g**2.
compute	#limit=#df2*#rtildsq/(#nu*#g).
compute	#diff3=ncdf.f(#limit,#nu,#df2,#lambdau)-#pul.
compute            #yy=#x1/(1-#x1).
compute	#gamma=sqrt(1+#yy).
compute           #phi1=#df1*(#gamma**2-1)+k.
compute	#phi2=#df1*(#gamma**4-1)+k.
compute	#phi3=#df1*(#gamma**6-1)+k.
compute	#g=(#phi2-(sqrt(#phi2**2-#phi1*#phi3)))/#phi1.
compute	#nu=(#phi2-2*#yy*#gamma*(sqrt(#df1*#df2)))/#g**2.
compute	#lambdau=#yy*#gamma*(sqrt(#df1*#df2))/#g**2.
compute	#limit=#df2*#rtildsq/(#nu*#g).
compute	#diff1=ncdf.f(#limit,#nu,#df2,#lambdau)-#pul.
do if (#diff1*#diff3<0).
compute  #x2=#x3.
else. 
compute #x1=#x3.
end if.
end loop.
compute ulrhosq=#x3.
end if.
compute #x2=1.0.
compute #x1=.00.
compute #diff3=1.
do if #switch =0 & #switch1=0.
loop if (abs(#diff3)>.00001).
compute	  #x3=(#x1+#x2)/2. 
compute             #yy=#x3/(1-#x3).
compute	  #gamma=sqrt(1+#yy).
compute	  #phi1=#df1*(#gamma**2-1)+k.
compute	  #phi2=#df1*(#gamma**4-1)+k.
compute	  #phi3=#df1*(#gamma**6-1)+k.
compute	  #g=(#phi2-(sqrt(#phi2**2-#phi1*#phi3)))/#phi1.
compute	  #nu=(#phi2-2*#yy*#gamma*(sqrt(#df1*#df2)))/#g**2.
compute	  #lambdau=#yy*#gamma*(sqrt(#df1*#df2))/#g**2.
compute	  #limit=#df2*#rtildsq/(#nu*#g).
compute	  #diff3=ncdf.f(#limit,#nu,#df2,#lambdau)-#pll.
compute	  #yy=#x1/(1-#x1).
compute	  #gamma=sqrt(1+#yy).
compute	  #phi1=#df1*(#gamma**2-1)+k.
compute	  #phi2=#df1*(#gamma**4-1)+k.
compute	  #phi3=#df1*(#gamma**6-1)+k.
compute	  #g=(#phi2-(sqrt(#phi2**2-#phi1*#phi3)))/#phi1.
compute	  #nu=(#phi2-2*#yy*#gamma*(sqrt(#df1*#df2)))/#g**2.
compute	  #lambdau=#yy*#gamma*(sqrt(#df1*#df2))/#g**2.
compute	  #limit=#df2*#rtildsq/(#nu*#g).
compute	  #diff1=ncdf.f(#limit,#nu,#df2,#lambdau)-#pll.
do if                    #diff1*#diff3<0.
compute             #x2=#x3.
else.                  
compute             #x1=#x3.
end if.
end loop.
compute	llrhosq=#x3.
end if.
end case.
END FILE.
END INPUT PROGRAM.
execute.
list variables=n k rsq conlev llrhosq ulrhosq/cases=1/format=numbered. 
execute.