  We analyse a sample of 21 active galactic nuclei (AGN) using data from the
Swift satellite to study the variability properties of the population in the
X-ray, UV and optical band. We find that the variable part of the UV-optical
emission has a spectrum consistent with a powerlaw, with an average index of
$-2.21\pm0.13$, as would be expected from central illumination of a thin disc
(index of -7/3). We also calculate the slope of a powerlaw from UV to X-ray
variable emission, $\alpha_{\rm OX,Var}$; the average for this sample is
$\alpha_{\rm OX,Var} = -1.06 \pm 0.04$. The anticorrelation of $\alpha_{\rm
OX}$ with the UV luminosity, $L_{\rm UV}$, previously found in the average
emission is also present in the variable part: $\alpha_{\rm OX,Var} = (-0.177
\pm 0.083) {\rm log} (L_{\rm \nu,Var} (2500\,\AA)) + (3.88 \pm 2.33)$.
Correlated variability between the emission in X-rays and UV is detected
significantly for 9 of the 21 sources. All these cases are consistent with the
UV lagging the X-rays, as would be seen if the correlated UV variations were
produced by the reprocessing of X-ray emission. The observed UV lags are
tentatively longer than expected for a standard thin disc.
