EPM regression principle. The EPM uses multiple spectroscopic observations to measure the ratio of the photospheric angular diameter θ (Eq. (4)) and the photospheric velocity v_ph for different times. These measurements (shown in blue) fall on a straight line (red). We can determine the SN luminosity distance D_L from the inverse of the slope of this line and the time of explosion from the intercept (see Eq. (5)).