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 was discovered and reported in the Journal of Astrophysics & Astronomy (Mar. / Jun. 2003). Physicist D. Basu (Carleton University, Ottawa) applied simple linear regression to data collected for a sample of over 6,000 quasi-stellar objects with confirmed redshifts. The analysis yielded the following results for a specific range of magnitudes:
ŷ = 18.13 + 6.21x, where y = magnitude and x = redshift level.
a. Graph the least squares line. Is the slope of the line positive or negative?
b. Interpret the estimate of the y-intercept in the words of the problem.
c. Interpret the estimate of the slope in the words of the problem.