There are many chemistry examples where a model Y is fit from X. Y and X may be multivariate, may be transformed variables (the natural logarithm often seen), polynomial functions etc. The simplest is the linear regression model fitting Y with X. Many models can be transformed so as to examine the fits using linear models. Rawski et al. (2016) considered fitting linear regression models for calibration in analytical chemistry. Y represents the signal and x the measured chemical property. Hanscam (2014) examines the Arrhenius equation in physical chemistry. Y is the natural logarithm of the rate constant; and x is a function of the inverse temperature (Kelvin). Shenker et al. (2005) present an improved procedure allowing quantitative propagation of uncertainty from literature derived values (LDVs) to final adjusted values (FAVs). The procedure is applied to partitioning properties for 30 organic chemicals. The authors use Y to represent the sum of squares of the adjustments applied to LDVs to achieve internal consistency using least squares and x the sum of squares of the adjustments applied to LDVs to achieve internal consistency. In instances where we examine relationships between the individual x variables from the X design matrix and in examples such as that mentioned above of Shenker et al. (2005); the Y and X can be interchanged. This poster asks then the question should we regress Y on X or X on Y? A SAS® macro program will be made available to answer this question, and further analyses conducted to compare least squares and robust regression estimates using M-estimation with Huber weighting and bisquare weighting of the residuals (SAS/STAT, 2018; SAS Studio, 2019).

There are many chemistry examples where a model Y is fit from X. Y and X may be multivariate, may be transformed variables (the natural logarithm often seen), polynomial functions etc. The simplest is the linear regression model fitting Y with X. Many models can be transformed so as to examine the fits using linear models. Rawski et al. (2016) considered fitting linear regression models for calibration in analytical chemistry. Y represents the signal and x the measured chemical property. Hanscam (2014) examines the Arrhenius equation in physical chemistry. Y is the natural logarithm of the rate constant; and x is a function of the inverse temperature (Kelvin). Shenker et al. (2005) present an improved procedure allowing quantitative propagation of uncertainty from literature derived values (LDVs) to final adjusted values (FAVs). The procedure is applied to partitioning properties for 30 organic chemicals. The authors use Y to represent the sum of squares of the adjustments applied to LDVs to achieve internal consistency using least squares and x the sum of squares of the adjustments applied to LDVs to achieve internal consistency. In instances where we examine relationships between the individual x variables from the X design matrix and in examples such as that mentioned above of Shenker et al. (2005); the Y and X can be interchanged. This poster asks then the question should we regress Y on X or X on Y? A SAS^®^ macro program will be made available to answer this question, and further analyses conducted to compare least squares and robust regression estimates using M-estimation with Huber weighting and bisquare weighting of the residuals (SAS/STAT, 2018; SAS Studio, 2019).

Should we regress Y on X or X on Y? Question for chemical applications

ACS Spring 2022

The official archive and repository for all ACS Meetings & Expositions abstracts and select posters or presentations.