This paper focuses on the Least Square (LS) regression using the mean and Quantile (M) regression analysis using median which is based on "well-Known" parametric estimation methodologies. Data from Oregon and California highway bridges were used for the comparison of the two methods. Relationships were developed to predict the unit cost of FRP repair work and FRP cost was found to have a high degree of correlation with FRP area for both Oregon and California. It was observed that the Cost Estimating Relationships (CERs) obtained by Quantile (M) regression method had the smaller Mean Absolute Deviation (MAD) values and lower Mean Absolute Percentage Error (MAPE) values than Least Square (LS) regression. The stuudy showed that Quantile Regression is much less sensitive to outliers than Least Squares Regression.