2 0 I LTE Back HW-3.pdf | - (4. Deep space survey of quasars. A quasar is a dist

Question

2 0 I LTE Back HW-3.pdf | - (4. 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 quasans several different quantitative characteristics of each quasar, including redshift range, line flux (erg/cm2's), ne luminosity (erg/s), AB145o magnitude, absolute magnitude, and rest frame equivalent width. The data for a sample of 25 large (redshift) quasars is listed in the table below (a) Hypothesize a first-order model for equivalent width, y, as a function of the first four variables detected by a deep space survey. The survey enabled astronomers to in the table. b) The first-order model is fit to the data using SAS. The printout is provided on the next page Give the least squares prediction equation. (c) Interpret the estimates in the model. (d) Test to determine whether redshift is a useful linear predictor of cquivalent widih (y), using (e) Locate R2 and on the SAS printout. Interpret these values, which statistic is the preferred measure of model fit? Explain. () Locate the global F-value for testing the overall model on the SPSS printout. Use the statistic to test the null hypothesis Ho: 1 = .-h-A+ 0. QUASAR REDSHIFT LINEFLUX LUMINOSITY AB1450 ABSMAG RFEWIDTH 2.81 13.48 13.73 13.87 19.5 -26.27 19.65 26.26 18.93 27.17 18.59 27.39 19.59 26.32 19.42 26.97 19.18 26.83 20.41 25.36 18.93 27.34 45.13 45.11 45.63 3.19 13.56 13.95 13.83 45.08 45.27 45.41 45.23 45.27 45.25 45.07 45.19 45.19 2.81 3.83 13.66 2.81 -13.5 -13.96 13.91 13.85 13.67 -13.93 -13.75 14.17 13.92 14.28 -13.82 14.08 -13.82 14.15 13.74 18.45 27.32 20.55 -25.94 20.45 25.65 19.7 26.51 9.5426.37 20.17 26.29 19.3 26.58 20.68 25.61 20.51 25.41 20.7 25.67 19.45 26.73 19.9 -26.02 1949 26.35 20.89 25.09 19.17 26.83 4.34 45.08 44.92 44.94 44.86 45.2 44.78 44.99 44.75 45.17 116 3.07 2.94

Explanation / Answer

A] The Hypothesis for this model is

H0 : The Mean effect of all variable is zero ( i.e. b0=b1=b2=b3=0)

against,

H1 : The mean effect of at least one variable is differant ( Not zero )

B]

The Fitted Model from above data is,

RFEWIDTH = 21088 + 108.4508 * REDSHIFT + 557.9098 * LINEFLUX - 340.1655 * LIMINOSITY+ 85.6810 * ABI450

C]

21088 = INTERCEPT

108.4508 = REDSHIFT

557.9098 = LINEFLUX

340.1655 = LIMINOSITY

85.6810 = ABI450

REDSHIFT = 108.4508 Means if REDSHIFT increase by one unit the response increase by 108.4508

E]

The p-value of REDSHIFT variable is 0.2359 which is less than 0.05

i.e Accept H0 at 5% level of significance

i.e The REDSHIFT variable is not significant i.e not usefull in model.

>>>>>>>>>>>>>>>>> Best Luck >>>>>>>>>>>>>>>>>

According to chegg rule i have solved only first four subparts

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