The purpose of this work was to critically assess the potential and limitations of linear and rank correlation methods, not only relevant to laser-induced breakdown spectroscopy (LIBS), but to other spectroscopic techniques as well. Through computer simulations, it was demonstrated that a linear correlation is a more suitable technique for material identification than a rank correlation due to its better stability toward noise and better ability to detect small systematic variations in line intensities. The effect of noise on the results of correlation analysis has been studied. It was found that random noise causes correlation coefficients to be distributed normally, whereas flicker noise (random fluctuations in line intensities) results in a gamma distribution of correlation coefficients. Hence, the distribution of correlation coefficients can be used for detection of the type of noise that dominates correlated spectra. A potential of linear correlation analysis for plasma diagnostics has been demonstrated. It is based on a strong dependence of the linear correlation coefficient upon the line shapes of correlated spectral lines and, consequently, upon plasma parameters (plasma temperature, number densities).