Redshifts of quasi-stellar objects. Refer to the Journal of Astrophysics&Astronomy (Ma...

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?

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b. Interpret the estimate of the y -intercept in the words of the problem.

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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.

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b. What is the relationship between r and the estimated slope of the line?

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c. Find and interpret the value of r2.