Seismic intensity is, by definition, an index for the classification of the severity of earthquake effects observed in a settlement. However the experience of many decades of its use within functional relations with other parametric quantities have shown that it represents a quite reliable estimator of ground motion amplitude and that it can be confidently related to instrumentally measured quantities by a logarithmic relation. Most intensity attenuation relations from the literature model empirically the difference between epicentral intensity I_0 (defined as the maximum observed intensity or something less that that) and the intensity at the site. This means assuming that I_0 is actually the average intensity observed at the epicenter and that it scales with site intensity with coefficient equal to 1. We analyzed the Italian macroseismic dataset that can be obtained by combining the two major Italian macroseismic databases following the choices made by the compilers of the parametric catalog of Italian earthquakes. It contains about 50,000 observations from ancient times to 1992. We considered an attenuation equation with log-linear dependence with hypocentral distance (depth fixed to 10 km) and an additional empirical term proportional to I_0 I_s=a + b D + c log{D} + d I_0 We found that: i) the intensity data observed at sites located at distance larger than the one at which the expected average intensity is below the limit of diffuse perceptibility (degree IV) are clearly incomplete and might bias the resulting attenuation relation, ii) intensity data with uncertain estimates (i.e. VI-VII) have frequencies lower of about 30-50% than regular ones and thus must be modeled separately, iii) the average intensity at the epicenter is on average from one to two degrees lower than I_0, iv) epicentral intensity contributes to the attenuation relation with a coefficient significantly different from 1.0 (about 0.7-08) thus indicating the it cannot be considered a reference ground-motion level but rather an estimator of the energy of the earthquake, v) the statistical distribution of intensity residuals closely resembles a normal one but with a significant skewness that can be appropriately modeled by a modified Azzalini distribution.