The curves corresponding to the simple logarithmic regressions and the curves of the hyperbolic regressions have very close paths. This is the reason why there is the problem of performing an analysis that allows the choice between the two types of regression of the most appropriate type for a particular case. The paper analyzed two hypothetical case studies (with computer-generated input data). For the first data set (cloud composed of 30 points) the most appropriate regression is the logarithmic regression, and for the second data set the hyperbolic regression is more appropriate. The selection of the optimal regression is performed with the help of Pearson correlation coefficients. The main objective of the paper is to present concisely but fully the calculation method by which the two different types of simple regressions are obtained, which are the logarithmic regression and the hyperbolic regression.