Average-Slope Regression

• Activity Number: 360
• Type: Contributed
• Date/Time: Tuesday, August 3, 2010 : 10:30 AM to 12:20 PM
• Sponsor: Biometrics Section
• Author(s): Brian G. Leroux*+ and Adam Omidpanah
• Companies: University of Washington and University of Washington
• Keywords: regression ; least-squares ; average slope

Abstract

The Average Slope is proposed as a nonparametric measure of linear association that extends the concept of linear regression coefficient to settings where a linear model is not assumed. This measure is motivated by the usual interpretation of a regression coefficient as the average difference between responses per unit difference in values of the predictor, holding other explanatory variables fixed. Comparisons are made between the Average Slope and the parameter estimated by Least Squares in various settings with misspecified models, measurement error in predictors, or high-leverage points. Methods of inference for the Average Slope are explored by simulations studies and application to real data sets. The results suggest that an estimator of the Average Slope has certain practical advantages over the Least Squares estimator.