Our practical motivation is the analysis of potential correlations between spectral noise current and threshold voltage from common on-wafer MOSFETs. The usual strategy leads to the use of standard techniques based on Normal linear regression easily accessible in all statistical software (both free or commercial). However, these statistical methods are not appropriate because the assumptions they lie on are not met. More sophisticated methods are required. A new strategy based on the most novel nonparametric techniques which are data-driven and thus free from questionable parametric assumptions is proposed. A backfitting algorithm accounting for random effects and nonparametric regression is designed and implemented. The nature of the correlation between threshold voltage and noise is examined by conducting a statistical test, which is based on a novel technique that summarizes in a color map all the relevant information of the data. The way the results are presented in the plot makes it easy for a non-expert in data analysis to understand what is underlying. The good performance of the method is proven through simulations and it is applied to a data case in a field where these modern statistical techniques are novel and result very efficient.