The precise geometric levelling is the main method for solving many scientific and engineering tasks related to the recent vertical movements of the Earth’s crust, the changes in slopes and levels of the oceans and seas, defining of continental and / or state reference height systems, validation of global geopotential models, monitoring of engineering construction, etc. Despite being in use more than a century, there are some incorrect beliefs about accumulation of uncertainties in the results obtained by this geodetic method. These mistaken theories cast their damage over the methodology of execution of measurements, the assessment of the accuracy, processing of the observation data and so on. The purpose of the current research is to throw light on one of the popular beliefs regarding accumulation of differences between both measurements of heights between terminal benchmarks in the precise levelling lines. In the research, the accumulation of the absolute values of the differences between both height measurements in the lines |D| is analyzed by multiple regression. As independent variables we use the square root of the length of leveling lines √L, the length of leveling lines L, the sum of the absolute heights in levelling sections in the lines ∑▒〖|h|〗, and the absolute value of the height difference between terminal benchmarks |H|. In the interest of plausibility, we analyzed the levelling data from different campaigns in two countries with contrasting climate and geological formations, those of the Third precise levelling of Bulgaria /1975-1984/, the Second precise levelling of Finland /1935-1955/ and the Third precise levelling of Finland /1984-2006/. The results from our analyses show that the multiple coefficients of determination of the differences |D| in respect of independent variables √L, L, ∑▒〖|h|〗 and |H| are 0.29, 0.36 and 0.28 for the Third precise levelling of Bulgaria, the Second precise levelling of Finland and Third precise levelling of Finland, respectively. The most important independent variable for explaining the differences |D| in the analyzed levelling networks, which is the only one statistically significant at 99% confidence level, is the sum of the absolute heights in levelling sections in the lines ∑▒〖|h|〗. The traditionally supposed variable, the square root of the length of leveling lines √L, is not statistically significant even at 90% confidence level in the case of each mentioned above network. The major conclusion, which we can make on the basis of the research results, is that under 40% of accumulation of the differences |D| between both measurements of heights in the precise levelling lines, we can explain by √L, L, ∑▒〖|h|〗 and |H|. Therefore, we need some new approaches in order to define the maximum accepted values of the differences |D| and levelling accuracy estimators.

Multiple regression, precise levelling, accuracy control