Quantile Regression with Applications in Agriculture and Temperature Study

Across disciplines, researchers are often interested in gaining a deeper understanding of trends in the tails of a distribution or comparing trends across a range of quantiles in a distribution. Typical ordinary least squares (OLS) regression models do not permit this type of investigation and limit our understanding of a given data set to its mean trends. Quantile regression was developed by Koenker and Bassett in 1978 to solve this problem of needing to better understand trends in location, shape and skewness across quantiles. In this project we will investigate quantile regression as a method and utilize it to conduct case studies investigating the change in corn and rice yields in the United States and temperatures in Minnesota over the last 50 years. In the agricultural study, we discover that greater deviations in temperature from the average have adverse effects on growth rate of rice and corn yields and this adverse effect is much more pronounced at lower quantiles of percentage change in yield. In the temperature study across several locations in Minnesota, we see a consistent pattern of damping of the seasonal cycles but different responses as global temperature increases. Applying quantile regression, consequently, allows us to see a richer picture than what would be obtained through OLS models