Many objective functions have been proposed in X-ray crystallography to solve the molecular replacement (MR) problem and other optimization problems. In this paper, we establish the equivalence between optimizing two target functions: a commonly used correlation coefficient and a least squares function. This equivalence may be in neighborhoods about the global optima or the entire MR variable space depending on whether the average values of the observed and calculated data are subtracted from observed and calculated data. In addition, we also present an argument that the correlation coefficient between structure factor magnitudes is likely to perform better than the correlation coefficient between intensities. This was confirmed by the MR program SOMoRe, especially when low-resolution data were used.