Why do we see a gravitational redshift in the spectrum of the sun?

When we talk about the visible electromagnetic spectrum, we know it starts in violet-blue and ends in red.  

In this context the astronomer Edwin Powell Hubble observed several celestial bodies, and when obtaining the spectra of distant galaxies he observed that the spectral lines were displaced towards the red one (red shift), whereas the nearby stars showed a spectrum displaced to the blue one.  

From there, it was deduced that the farther a body in the universe is, the more redshifted it is in its spectrum. This effect is due to the dilation and contraction of time by speed according to the relativity.  

Now, the Sun is a massive star and the Earth is at certaind distance from it, therefore time passes slower in the Sun than on Earth. This causes the spectrum of the Sun to present lines with a lower frequency or longer wavelength than normal, that is, more towards red.