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4.11 Deep space survey of quasars. 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 quan- titative characteristics of each quasar, including
redshift range, line flux (erg/cm2 · s), line luminos- ity (erg/s), AB1450 magnitude, absolute magnitude, and rest frame equivalent width. The data for a
sample of 25 large (redshift) quasars is listed in the table on p. 187.
(a) Hypothesize a first-order model for equivalent width, y, as a function of the first four variables in the table.

|
QUASAR |
|
|
LINE |
|
ABSOLUTE |
REST FRAME |
|
|
REDSHIFT |
LINE FLUX |
LUMINOSITY |
AB1450 |
MAGNITUDE |
EQUIVALENT WIDTH |
|
QUASAR |
(x1) |
(x2) |
(x3) |
(x4) |
(x5) |
y |
|
1 |
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 |
|
4 |
3.19 |
−13.27 |
45.63 |
18.59 |
−27.39 |
92 |
|
5 |
3.07 |
−13.56 |
45.30 |
19.59 |
−26.32 |
114 |
|
6 |
4.15 |
−13.95 |
45.20 |
19.42 |
−26.97 |
50 |
|
7 |
3.26 |
−13.83 |
45.08 |
19.18 |
−26.83 |
43 |
|
8 |
2.81 |
−13.50 |
45.27 |
20.41 |
−25.36 |
259 |
|
9 |
3.83 |
−13.66 |
45.41 |
18.93 |
−27.34 |
58 |
|
10 |
3.32 |
−13.71 |
45.23 |
20.00 |
−26.04 |
126 |
|
11 |
2.81 |
−13.50 |
45.27 |
18.45 |
−27.32 |
42 |
|
12 |
4.40 |
−13.96 |
45.25 |
20.55 |
−25.94 |
146 |
|
13 |
3.45 |
−13.91 |
45.07 |
20.45 |
−25.65 |
124 |
|
14 |
3.70 |
−13.85 |
45.19 |
19.70 |
−26.51 |
75 |
|
15 |
3.07 |
−13.67 |
45.19 |
19.54 |
−26.37 |
85 |
|
16 |
4.34 |
−13.93 |
45.27 |
20.17 |
−26.29 |
109 |
|
17 |
3.00 |
−13.75 |
45.08 |
19.30 |
−26.58 |
55 |
|
18 |
3.88 |
−14.17 |
44.92 |
20.68 |
−25.61 |
91 |
|
19 |
3.07 |
−13.92 |
44.94 |
20.51 |
−25.41 |
116 |
|
20 |
4.08 |
−14.28 |
44.86 |
20.70 |
−25.67 |
75 |
|
21 |
3.62 |
−13.82 |
45.20 |
19.45 |
−26.73 |
63 |
|
22 |
3.07 |
−14.08 |
44.78 |
19.90 |
−26.02 |
46 |
|
23 |
2.94 |
−13.82 |
44.99 |
19.49 |
−26.35 |
55 |
|
24 |
3.20 |
−14.15 |
44.75 |
20.89 |
−25.09 |
99 |
|
25 |
3.24 |
−13.74 |
45.17 |
19.17 |
−26.83 |
53 |
Source: Schmidt, M., Schneider, D. P., and Gunn, J. E. ‘‘Spectroscopic CCD surveys for quasars at large redshift,’’ Astronomical Journal, Vol. 110, No. 1, July 1995, p. 70 (Table 1). Reproduced by permission of the American Astronomical Society.
(b) The first-order model is fit to the data using SPSS. The printout is provided on p. 188. Give the least squares prediction equation.
(c) Interpret the β estimates in the model.
(d)
Test to determine whether redshift (x1) is a useful linear predictor of equivalent width (y), using α = .05.
(degrees), and depth (feet) of each well was mea- sured. The data are saved in the ASWELLS file. (The first and last five observations are listed below.)
(e) ![]()
|
on the SPSS printout.
WELLID LATITUDE LONGITUDE DEPTH ARSENIC
Interpret these values. Which statistic is the preferred measure of model fit? Explain.
(f) Locate the global F -value for testing the over- all model on the SPSS printout. Use the statistic to test the null hypothesis H0: β1 =
β2 = ··· = β4 = 0.
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