Deep space survey of quasars. A first-order model was used to relate a quasar’s

Question

Deep space survey of quasars. A first-order model was used to relate a quasar’s equivalent width (y) to redshift (x_1), line flux (x_2), line luminosity (x_3), and AB1450 (x_4). A portion of the SPSS spreadsheet showing 95% prediction intervals for y for the first five observations in the data set is reproduced on p. 194. and here it is:

quasar

Redshift

Lineflux

Linelum

Ab1450

Rfewidth

lcl_95

ucl_95

1

  

2

   

3

   

4

  

5

    5

   3.07

-13.56

45.30

19.59

114

90.69

158.57

Interpret the interval corresponding to the fifth observation.

quasar

Redshift

Lineflux

Linelum

Ab1450

Rfewidth

lcl_95

ucl_95

1

  

2

   

3

   

4

  

5

    5

   3.07

-13.56

45.30

19.59

114

90.69

158.57

Explanation / Answer

alpha = 1 - 0.95 = 0.05

alpha / 2 = 0.025

we find a value of Z for 0.025 in tables

Z= 1.96

interval will be

0.194 +/- 1.96 * srqt (0.194*0.806 / 5 )

0.194 +/- 0.3466

-0.1526 , 0.5206

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