In this study, we modify the nonparametric regression method of Ghosh and Majumder to incorporate squared sums in conjunction with squared differences and use local linear polynomials instead of the Nadaraya-Watson estimator to perform a genome-wide linkage scan of rheumatoid factor (RF)-IgM, a quantitative phenotype correlated with rheumatoid arthritis affection status in the simulated data of Genetic Analysis Workshop 15 (GAW15). This evidence concerns the gene CD40LG and rheumatoid arthritis.