An orthogonal least-squares method was considered for linear correlations of data sets in which both variables are subject to unknown uncertainties in measurement. A previously reported method and an alternatively developed equivalent method were investigated. The orthogonal method was found to be sensitive to the relative numerical scales of the two variables, but its application is considered appropriate to data sets rescaled to dimensionless forms. A versatile computer program was developed for application of the method. It allows for the comparison of the orthogonal and standard least-squares methods and has the ability to produce publication quality plots. Results are given for one experimental data set.