A quasar is a distant celestial object (at least 4 billion light-years away) that provides a powerful source of radio energy. The Astronomical Journal (July 1995) reported on a study of 90 quasars detected by a deep-space survey. The survey enabled astronomers to measure several different quantitative characteristics of each quasar, including redshift range, line flux (erg/cm2gˆ™ ˆ™ ˆ™s), line luminosity (erg/s), AB1450 magnitude, absolute magnitude, and rest-frame equivalent width. The data for a sample of 25 large (redshift) quasars are saved in the QUASAR file. (Several quasars are listed in the table.)

a. Hypothesize a first-order model for equivalent width y as a function of the first four variables shown in the table.

b. Fit the first-order model to the data. Give the least squares prediction equation.

c. Interpret the b estimates in the model.

d. Test the overall adequacy of the model, using α = .05.
e. Test to determine whether redshift (x1) is a useful linear predictor of equivalent width (y). Use α = .05.

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Absolute Rest-Frame Redshift Lie Flux Line Luminosity AB1450 Magnitude Equivalent Width (x2) (x3) 45.29 45.13 45.11 45.63 45.30 Quasar(X1) 2.81 3.07 3.45 3.19 3.07 -13.48 -13.73 -13.87 -13.27 13.56 19.50 19.65 18.93 18.59 19.59 26.27 26.26 -27.17 -27.39 26.32 82 92 114 4