Astronomer Edwin Hubble postulated a relationship between the distance between Earth and the velocity at which a galaxy appears to be traveling away from Earth. The following table shows observations of seven galaxies. Distance is measured in megaparsecs (1 Mpc is approximately 3,260 light-years), and velocity is measured in kilometers per second.Distance (Mpc)Velocity (km/s)51.84,59012.21,23427117,69546.23,75258.25,11846.23,75229.11,734(a)Find the equation of linear regression line for the data where distance is the independent variable, x, and velocity is the dependent variable. (Round your numerical answers to two decimal places.)ŷ = (b)Using the equation from part (a), estimate the velocity (in kilometers per second) at which a galaxy 110 Mpc from Earth is traveling. (Round your answer to the nearest whole number.)km/s

Distance (Mpc) Velocity (km/s) 51.8 4,590 12.2 1,234 271 17,695 46.2 3,752 58.2 5,118…

Answered: Astronomer Edwin Hubble postulated a…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

Astronomer Edwin Hubble postulated a relationship between the distance between Earth and the velocity at which a galaxy appears to be traveling away from Earth. The following table shows observations of seven galaxies. Distance is measured in megaparsecs (1 Mpc is approximately 3,260 light-years), and velocity is measured in kilometers per second.

Distance (Mpc)	Velocity (km/s)
51.8	4,590
12.2	1,234
271	17,695
46.2	3,752
58.2	5,118
46.2	3,752
29.1	1,734

(a)

Find the equation of linear regression line for the data where distance is the independent variable, x, and velocity is the dependent variable. (Round your numerical answers to two decimal places.)

ŷ =

(b)

Using the equation from part (a), estimate the velocity (in kilometers per second) at which a galaxy 110 Mpc from Earth is traveling. (Round your answer to the nearest whole number.)

km/s

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