A frequently-used approach to the analysis of data in experimental design models when some of the observations are missing is to estimate the missing pieces of data and then to proceed with the analysis, making adjustments to take this estimation into account. The standard procedure for estimating the missing values is to minimize the residual sum of squares. In this note the criterion of minimum residual sum of squares is discussed and it is proved that (even when there is more than one missing value) estimation of missing values in a linear statistical model by minimization of the residual sum of squares is equivalent to setting the corresponding residuals equal to zero.