In the numerical integrations of the outer planets, when the inner planets are not considered, the initial conditions are determined by least square adjustment with a complete ephemeris. In the present work, we compute the resulting uncertainty on the initial conditions by the analysis of the very simple problem which consists in fitting by least squares a straight line to a sine curve. Explicit formulae for the computation of the error due to the fitting process are given. In particular, fitting over an integer number of periods is very close to the worst case. The determination of the initial conditions in the LONGSTOP project is analysed as an example. It is shown that the uncertainty on the main frequencies of the secular system due to the determination of the initial conditions is of the order of 0.01 arcsec/year.