Refer to the Journal of Astrophysics & Astronomy (Mar./Jun. 2003) study of redshifts in Quasi-Stellar Objects (QSOs), Exercise 10.4. Recall that simple linear regression was used to model the magnitude (y) of a QSO as a function of redshift level (x). In addition to the least-squares line, ŷ = 18.13 + 6.21x, the coefficient of correlation was determined as 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 the value of r² and interpret its value

Data from Exercise 10.4

Astronomers call a shift in the spectrum of galaxies a “redshift.” A correlation between redshift level and apparent magnitude (i.e., brightness on a logarithmic scale) of a Quasi-Stellar Object (QSO) was discovered and reported in the Journal of Astrophysics & Astronomy (Mar./Jun. 2003). Simple linear regression was applied to data collected for a sample of over 6,000 QSOs with confirmed redshift.