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Category > Business & Finance Posted 07 May 2017 My Price 10.00

Deep space survey of quasars

 

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 (x1is 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)    

a

 
Locate R2 and R2

 

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 -value for testing the over- all model on the SPSS printout. Use the statistic to test the null hypothesis H0β1 =

β2 = ··· = β4 = 0.

 

 

 
 

Answers

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Status NEW Posted 07 May 2017 10:05 AM My Price 10.00

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