Refer to The Astronomical Journal (July 1995) study of quasars detected by a deep space survey, Exercise 11.72. Recall that several quantitative independent variables were used to model the quasar characteristic, rest frame equivalent width (y). The data for 25 quasars are saved in the QUASAR file. (Data for the first five quasars are listed in the table.

a. Write a complete second-order model for y as a function of redshift (x₁), line flux (x₂), and AB₁₄₅₀ (x₄).

b. Fit the model, part a, to the data using a statistical software package. Is the overall model statistically useful for predicting y?

c. Conduct a test to determine if any of the curvilinear terms in the model, part a, are statistically useful predictors of y.

Data from Exercise 11.72

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/cm²·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.

Transcribed Image Text:

N QUASAR (First five quasars shown) Line Absolute Rest Frame Quasar Redshift (X1) Lineflux (X2) Luminosity (X3) AB1450 Xa) Magnitude (Xs) Equivalent Width (y) 2.81 -13.48 45.29 19.50 -26.27 117 2 3.07 - 13.73 45.13 19.65 -26.26 82 3 3.45 - 13.87 45.11 18.93 -27.17 33 3.19 - 13.27 45.63 18.59 -27.39 92 3.07 - 13.56 45.30 19.59 -26.32 114 4.