*This program computes a confidence interval for the 
squared multiple correlation coefficient for the design
in which values of the independent variables are sampled.
To use the program you input
n--the sample size
k--the number of predictors
rsq--the sample squared multiple correlation coefficient
conlevel--the confidence level for the interval;
data;
n=117;
k=2;
rsq=.1245;
conlev=.95;
pul=(1-conlev)/2;
pll=1-(1-conlev)/2;
df1=n-1;
df2=n-k-1;
		rtildesq=rsq/(1-rsq);
		switch=0;
		switch1=0; 
        test=probf((n-k-1)*rtildesq/k,k,n-k-1); 
		if test <=pul then do; 
           switch=1;
		   llrhosq=0;
           ulrhosq=0;
		   ulrhotildesq=0;
           llrhotildesq=0;
		end;
		if test <=pll then do; 
           switch1=1;
		   llrhosq=0;
		   llrhotildesq=0;
        end;
x2=.99999;
x1=.00001;
x3=.5;
diff3=1;
if switch=0 then do while (abs(diff3)>.00001);
            x3=(x1+x2)/2;
		    yy=x3/(1-x3);
			gamma=sqrt(1+yy);
		    phi1=df1*(gamma**2-1)+k;
			phi2=df1*(gamma**4-1)+k;
			phi3=df1*(gamma**6-1)+k;
			g=(phi2-(sqrt(phi2**2-phi1*phi3)))/phi1;
			nu=(phi2-2*yy*gamma*(sqrt(df1*df2)))/g**2;
			lambdau=yy*gamma*(sqrt(df1*df2))/g**2;
			limit=df2*rtildesq/(nu*g);
			diff3=probf(limit,nu,df2,lambdau)-pul;
		    yy=x1/(1-x1);
			gamma=sqrt(1+yy);
		    phi1=df1*(gamma**2-1)+k;
			phi2=df1*(gamma**4-1)+k;
			phi3=df1*(gamma**6-1)+k;
			g=(phi2-(sqrt(phi2**2-phi1*phi3)))/phi1;
			nu=(phi2-2*yy*gamma*(sqrt(df1*df2)))/g**2;
			lambdau=yy*gamma*(sqrt(df1*df2))/g**2;
			limit=df2*rtildesq/(nu*g);
			diff1=probf(limit,nu,df2,lambdau)-pul;
            if diff1*diff3<0 then x2=x3;else x1=x3;
			ulrhosq=x3;
end;*for do while;
x2=.99999;
x1=.00001;
x3=.5;
if switch =0 & switch1=0 then do;
    yy=x3/(1-x3);
    gamma=sqrt(1+yy);
    phi1=df1*(gamma**2-1)+k;
    phi2=df1*(gamma**4-1)+k;
    phi3=df1*(gamma**6-1)+k;
    g=(phi2-(sqrt(phi2**2-phi1*phi3)))/phi1;
    nu=(phi2-2*yy*gamma*(sqrt(df1*df2)))/g**2;
    lambdau=yy*gamma*(sqrt(df1*df2))/g**2;
    limit=df2*rtildesq/(nu*g);
    diff3=probf(limit,nu,df2,lambdau)-pll;
	do while (abs(diff3)>.00001);
	        x3=(x1+x2)/2; 
            yy=x3/(1-x3);
			gamma=sqrt(1+yy);
		    phi1=df1*(gamma**2-1)+k;
			phi2=df1*(gamma**4-1)+k;
			phi3=df1*(gamma**6-1)+k;
			g=(phi2-(sqrt(phi2**2-phi1*phi3)))/phi1;
			nu=(phi2-2*yy*gamma*(sqrt(df1*df2)))/g**2;
			lambdau=yy*gamma*(sqrt(df1*df2))/g**2;
			limit=df2*rtildesq/(nu*g);
			diff3=probf(limit,nu,df2,lambdau)-pll;
		    yy=x1/(1-x1);
			gamma=sqrt(1+yy);
		    phi1=df1*(gamma**2-1)+k;
			phi2=df1*(gamma**4-1)+k;
			phi3=df1*(gamma**6-1)+k;
			g=(phi2-(sqrt(phi2**2-phi1*phi3)))/phi1;
			nu=(phi2-2*yy*gamma*(sqrt(df1*df2)))/g**2;
			lambdau=yy*gamma*(sqrt(df1*df2))/g**2;
			limit=df2*rtildesq/(nu*g);
			diff1=probf(limit,nu,df2,lambdau)-pll;
            if diff1*diff3<0 then x2=x3;else x1=x3;
			llrhosq=x3;
end;*for do while;
end;
llrhosq=round(llrhosq,.001); 
ulrhosq=round(ulrhosq,.001);  
proc print;
var n k rsq conlev llrhosq ulrhosq ;
quit;