Reddening and the Shape of the Variable Component of the Continua of
  Active Galactic Nuclei From the Optical to the Far Ultraviolet. I
  We analyze the photometric variability of over 6,000 active galactic nuclei
(AGNs) from the Sloan Digital Sky Survey Stripe 82. We recover the spectral
energy distribution (SED) of the variable flux as a function of wavelength. For
rest wavelengths longer than $\sim 2200$ Angstroms we find that the SED of the
variable component of the bluest AGNs is in agreement with the $F_{\nu} \propto
\nu^{+1/3}$ spectrum predicted for an externally-illuminated accretion disc. We
confirm there is some residual variable emission corresponding to the "small
blue bump" and other broad-line region variability. We interpret steeper
optical spectra of the variable component as being due to intrinsic reddening.
This is supported by the correlation of the Balmer decrement with the colour
excess of the variable component. We find that the median reddening of the SDSS
AGNs in Stripe 82 is $E(B-V) \thickapprox 0.17$ in agreement with the reddening
derived from the Balmer decrement.
