R : Copyright 2005, The R Foundation for Statistical Computing
Version 2.1.1  (2005-06-20), ISBN 3-900051-07-0

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> invisible(options(echo = TRUE))
> qhat <- 8.6733
> rho <- c(0.97949, 0.96973, 0.95996)
> qi <- c(18.629, 12.790, 9.9702)
> 
> chi <- 3.841
> 
> r2 <- rho^2;
> r1 <- rho;
> r0 <- c(1,1,1) 
> 
> A <- cbind(r2,r1,r0)
> 
> print(qi - qhat)
[1] 9.9557 4.1167 1.2969
> 
> y <- qi - qhat - chi
> 
> #plot(rho,y)
> 
> x <- solve(A,y)
> 
> a <- x[1]
> b <- x[2]
> c <- x[3]
> 
> print( (-b - sqrt(b^2-4*a*c))/(2*a))
[1] 0.942392
> print( (-b + sqrt(b^2-4*a*c))/(2*a))
[1] 0.969094
> 
> #rho <- c(0.87988, 0.86035, 0.79980)
> #qi <- c(10.194, 10.634, 11.459)
> #rho <- c(0.87988, 0.87012, 0.86035)
> #qi <- c(10.194, 10.425, 10.634)
> #rho <- c(0.78027, 0.79004, 0.79980)
> #qi <- c(11.609, 11.537, 11.459)
> #rho <- c(0.88965, 0.87988, 0.87012)
> #qi <- c(9.9399, 10.194, 10.425)
> rho <- c(0.71973, 0.64941, 0.60059)
> qi <- c(11.939, 12.289, 12.544)
> 
> r2 <- rho^2;
> r1 <- rho;
> r0 <- c(1,1,1)
> 
> A <- cbind(r2,r1,r0)
> 
> print(qi - qhat)
[1] 3.2657 3.6157 3.8707
> 
> y <- qi - qhat - chi
> 
> plot(rho,y)
> 
> x <- solve(A,y)
> 
> a <- x[1]
> b <- x[2]
> c <- x[3]
> 
> print( (-b - sqrt(b^2-4*a*c))/(2*a))
[1] 0.6061805
> print( (-b + sqrt(b^2-4*a*c))/(2*a))
[1] 3.173266
> 
> proc.time()
[1] 0.82 0.12 0.97 0.00 0.01
>