Hubble's data in 1929 is actually quite poor, since individual galaxies have peculiar velocities of several hundred km/sec, and Hubble's data only went out to 1200 km/sec. This has led some people to propose quadratic redshift-distance laws, but the data shown below on Type Ia SNe from Riess, Press and Kirshner (1996)

[his figure]

extend beyond 30,000 km/sec and provide a dramatic confirmation of the Hubble law, v = dD/dt = H*D

The fitted line in this graph has a slope of 64 km/sec/Mpc. Since we measure the radial velocity using the Doppler shift, it is often called the redshift. The redshift z is defined such that: 1 + z = lambda(observed)/lambda(emitted)

where lambda is the wavelength of a line or feature in the spectrum of an object. In special relativity we know that the redshift is given by 1 + z = sqrt((1+v/c)/(1-v/c)) so v = cz + ...

but the higher order corrections (the "...") in cosmology depend on general relativity and the specific model of the Universe.