In classical data analysis, data are single values. This is the case if you consider a dataset of n patientswhich age and size you know. But what if you record the blood pressure or the weight of each patient during aday ? Then, for each patient, you do not have a single-valued data but a set of values since the blood pressureor the weight are not constant during the day.Suppose now that you do not want to record blood pressure a thousand times for each patient and to storeit into a database because your memory space is limited. Therefore, you need to aggregate each set of valuesinto symbols: intervals (lower and upper bounds only), box plots, histograms or even distributions (distributionlaw with mean and variance)...Thus, the issue is to adapt classical statistical tools to symbolic data analysis. More precisely, this articleis aimed at proposing a method to fit a regression on Gaussian distributions. This paper is divided as follows:first, it presents the computation of the maximum likelihood estimator and then it compares the new approachwith the usual least squares regression.