Using a sample of 228 optically selected Active Galactic Nuclei ( AGNs ) in the 0.01–6.3 redshift range with a high fraction of X-ray detections ( 81–86 % ) , we study the relation between rest-frame UV and soft X-ray emission and its evolution with cosmic time . The majority of the AGNs in our sample ( 155 objects ) have been selected from the Sloan Digital Sky Survey ( SDSS ) in an unbiased way , rendering the sample results representative of all SDSS AGNs . The addition of two heterogeneous samples of 36 high-redshift and 37 low-redshift AGNs further supports and extends our conclusions . We confirm that the X-ray emission from AGNs is correlated with their UV emission , and that the ratio of the monochromatic luminosity emitted at 2 keV compared to 2500 Å decreases with increasing luminosity ( \alpha _ { \textrm { \scriptsize { ox } } } = -0.136 l _ { \textrm { \scriptsize { uv } } } +2.616 , where l _ { \textrm { \scriptsize { uv } } } is in \log units ) , but does not change with cosmic time . These results apply to intrinsic AGN emission , as we correct or control for the effects of the host galaxy , UV/X-ray absorption , and any X-ray emission associated with radio emission in AGNs . We investigate a variety of systematic errors and can thereby state with confidence that ( 1 ) the \alpha _ { \textrm { \scriptsize { ox } } } – l _ { \textrm { \scriptsize { uv } } } anti-correlation is real and not a result of accumulated systematic errors and ( 2 ) any \alpha _ { \textrm { \scriptsize { ox } } } dependence on redshift is negligible in comparison . We provide the best quantification of the \alpha _ { \textrm { \scriptsize { ox } } } – l _ { \textrm { \scriptsize { uv } } } relation to date for normal radio-quiet AGNs ; this should be of utility for researchers pursuing a variety of studies .