A continuous check has been made on the masonry wall on which Leonardo painted the 'Last Supper', recording measurements of temperatures, displacements, forces, etc. over about two years. Some of these quantities were chosen to perform a statistical analysis of relevant physical relationships; in particular the time dependence of the displacements has been carefully studied. The present work illustrates the statistical methods and the relationships found and gives an assessment on the safety of the painting on the basis of the examined data.