Refer to the Journal of Astrophysics & Astronomy (Mar./Jun. 2003) study of red shifts in quasi-stellar objects presented in Exercise. Recall that simple linear regression was used to model the magnitude (y) of a quasi-stellar object as a function of the redshift level (x). In addition to the least squares line, ŷ = 18.13 + 6.21x, the coefficient of correlation was determined to be r = .84.
a. Interpret the value of r in the words of the problem.
b. What is the relationship between r and the estimated slope of the line?
c. Find and interpret the value of r2.