Redshifts of quasi-stellar objects. Refer to the Journal of Astrophysics&Astronomy (Mar./Jun. 2003) study of redshifts in quasi-stellar objects presented in Exercise.
Redshifts of quasi-stellar objects. 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.
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, 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.
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