We present 4 years of spectrophotometric monitoring data for two radio-quiet quasars , PG 0804+762 and PG 0953+414 , with typical sampling intervals of several months . Both sources show continuum and emission line variations . The variations of the H \beta line follow those of the continuum with a time lag , as derived from a cross-correlation analysis , of 93 \pm 30 days for PG 0804+762 and 111 \pm 55 days for PG 0953+414 . This is the first reliable measurement of such a lag in active galactic nuclei with luminosity L > 10 ^ { 45 } erg s ^ { -1 } . The broad line region ( BLR ) size that is implied is almost an order of magnitude larger than that measured in several Seyfert 1 galaxies and is consistent with the hypothesis that the BLR size grows as L ^ { 0.5 } .