A Comparison of multiple linear regression and quantile regression for modeling the internal bond of medium density fiberboard
Young, T. M., L.B. Shaffer, F.M. Guess, H. Bensmail, and R.V. León.  2008.  Forest Products Journal. 58(4):39-48.

Multiple Linear Regression (MLR) and Quantile Regression (QR) models were developed for the Internal Bond (IB) of Medium Density Fiberboard (MDF). The data set aligned the IB of MDF came from 184 different independent variables that corresponded to on-line sensors. MLR models were developed for MDF product types that were distinguished by thickness in inches, i.e., 0.750 inches, 0.6875 inches, 0.625 inches, and 0.500 inches. A best model criterion wasused with all possible subsets. QR models were developed for each product type for the most common independent variable of the MLR models for comparison. The adjusted coefficient of determination (R2a) of the MLR models range from 72% with 53 degrees of freedom to 81% with 42 degrees of freedom. The Root Mean Square Errors (RMSE) ranged from 6.05 pounds per square inch (psi) to 6.23 psi, the maximum Variance Inflation Factor (VIF) was 5.6 and all residual patterns were homogeneous. A common independent variable for the 0.750 inch and 0.625 inch MLR models was“Refiner Resin Scavenger %”. QR models for 0.750 inch and 0.625 inch indicate similar slopes for the median and average with different slopes at the 5th and 95th percentiles. “Face Humidity” was a common independent variable for the 0.6875 inch and 0.500 inch MLR models. QR models for 0.6875 inch and 0.500 inch indicate different slopes for the median and average, and instability in IB in the outer 5th and 95th percentiles. The use of QR models to investigate the percentiles of the IB of MDF suggests significant opportunities for manufacturers for continuous improvement and cost savings.