Dangerous Curves Ahead: A Practical Approach to Curve Estimation in Regression

• In Event: 46.063 - Multiple Regression: Principles and Practices

Abstract

This session will address the need to examine the linear and curvilinear nature of data while conducting research and analyzing data. When correctly identifying the linear or curvilinear trend in data, researchers can uncover effects that are statistically significant, not otherwise found using only linear regression. In addition, with an added non-linear component, researchers may be able to ascertain greater predictive capacity with the regression equation.
The purpose of this session is to provide a practical approach to distinguishing between linear, quadratic, and cubic relationships in data. The following functions will be discussed and examples will be provided: Linear function (the IV and DV appear to trend in a linear pattern); Quadratic function (there is one bend in the regression line); and Cubic effects (there are two bends in the regression line).
Case examples and practical applications of the approach will be provided and discussed. Session participants will be able to determine the best model fit when using advanced regression techniques. A practical application model will be demonstrated using sample data to determine whether the predictive relationship of data fits a linear, quadratic, or cubic model. A step-by-step overview of the steps in SPSS will be provided in order to provide a practical, take home guide for the participants’ future research.
The SPSS Syntax, model summary table and data plots will be provided as examples of determining the predictive relationship of the model. As part of the SPSS example, a review of linear regression input, output, and data interpretation will be presented. After the overview of linear regression, quadratic and cubic effects will be examined and discussed. Participants will be able to run analysis on data and interpret output as a result of this demonstration.
This presentation lends itself to providing researchers with an additional tool in which to use while conducting research and data analysis. While many researchers may plot data to determine if there is a linear relationship, plotting alone should not be the mainstay for determining this relationship. This session will provide participants with a best practice tool when determining curvilinear relationships in regression analysis.

Author

• Lisa Raymon Besnoy, The University of Alabama