The correlation of earthquakes with tremor and slow slip has not been clearly quantified. We investigate 12-year earthquake and tremor catalogs for Southwest Japan, and find that nearby small intraslab earthquakes are weakly correlated with tremor. In particular, the intraslab earthquakes with magnitudes ≥2.7 tend to be followed by tremor more often than expected at random by a factor of two to six. The excess number of tremor before earthquakes is not as significant, although marginally more than expected. The underlying physical mechanism of the observed triggering of tremor and inferred slow slip by earthquakes is most likely to be the dynamic stress changes (several to several tens of kPa) rather than the much smaller static stress changes. The rate of triggering of tremor by earthquakes is similar to, although somewhat lower than, rates observed for similar amplitude stress changes due to the lower-frequency teleseismic surface waves and tidal stressing.