Illustration of the intrinsic color distribution P(C) implied by the Si II velocity distribution P_V(v) and an assumed linear relation between the mean intrinsic color and velocity. Bottom left: the Si II velocity distribution is a gamma distribution with a long tail toward high velocities. Top left: the red solid line is a mean linear relation with slope b = −0.03 mag (10³ km s⁻¹)⁻¹ and intercept at v = −11, 800 km s⁻¹ of c₀ = −0.10 mag, with a residual intrinsic scatter of σ_C = 0.02 mag (red dashed). The blue solid line is a mean constant relation with zero slope and some intrinsic scatter (blue dashed). Top right: with zero slope (blue line), the implied marginal intrinsic color distribution is Gaussian. With nonzero slope (red line), the intrinsic color distribution has a skewed distribution with a tail toward redder intrinsic color. The intrinsic mean and variance for the blue-line model were chosen so that the resulting red curve and blue curve P(C) distributions would match in mode and variance. The model with the strong linear trend implies a non-Gaussian intrinsic color distribution P(C) with a longer red (positive) tail and a shorter blue (negative) tail than the model with no trend.