In Perlmutter et al. (1999), it is checked that B-Vrest-frame colors of nearby and distant type agree on average, and the color measurement is not used event per event.

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http://www.ctio.noao.edu/wsne

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... SNLS

http://cfht.hawaii.edu/SNLS

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... features

Most of the SN Ia photometric reductions transform instrumental magnitudes into standard magnitudes using color equations, derived from standard stars observations. This assumes that color rather than spectral features dominates cross-filter corrections.

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... $0.16 \pm 0.03$

Note that this number takes into account the number of parameters in the fit. The measured rms value is $0.14 \pm 0.03$ .

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... fit

The uncertainties on the distance estimate formally depend on $\alpha$ and $\beta$ , and increase with them. As a consequence, the $\chi^2$ minimum is biased toward large values of these parameters. We therefore computed the uncertainties with the initial values, and use the result of the fit at the final iteration.

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... $\alpha = 0.88$

b=0.52 translates to $\alpha\simeq 0.88$ when using stretch and the first order relation $(\Delta M_{15}-1.1) \simeq 1.7 (1-s)$ .

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...Phillips et al. (1999)

The proposed relation is $\frac{{\rm d}c}{{\rm d}\Delta M_{15}} = 0.114 \pm 0.037$ . With the approximate relation $\frac{{\rm d}\Delta M_{15}}{{\rm d} s_B} \simeq -1.7$ (at s_B = 1), we expect ${\rm d}c/{\rm d}s \simeq -0.2$ .

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