Presenter: Derrick Rollins, Iowa State University

Title: Dynamic Regression – Proposing a New Modeling Framework in Regression When Response Behavior is Not Static but Dynamic

Abstract: The response (y) of a variable that is caused by the change of an input variable (x) changes in one of two basic ways – non-dynamically or dynamically. A non-dynamic response is when y changes to its new state immediately. Examples of non-dynamic responses are opening eyes (x) and seeing immediately (y) and turning on the car radio (x) and hearing it (y) immediately. A dynamic response is one where y does not immediately go to its final state from the input change. There are two basic types of dynamic responses – lagged and deadtime. One example of a lagged response is changing the setting on the thermostat that causes the room temperature to change immediately but takes a significant amount of time to reach the new room temperature. Another example is turning on a ceiling fan. The fan starts to turn as soon the switch is changed but takes a significant amount of time to get to the final blade speed. An example of dead time, i.e., time delay, is hearing thunder from a long-distance away. The lightening can be seen immediately and has a non-dynamic response, but the thunder is not heard until a significant time after the lightening is seen, and then there is an essentially instantaneously loud boom! Dynamic responses can have lag and time delay. For example, a control valve could “stick” (deadtime) before gradually moving (lag) to its new position. The premise of this work is the belief that when modeling data are collected sequentially over time, that a simple framework can be embedded into classical regression that can enhance modeling substantially when dynamics exist, with as little as one additional parameter, as this talk will illustrate using real modeling data. The goal of this work is the development of a simplistic and effective framework for inclusion into all levels of regression courses and I am hoping to get helpful feedback in the seminar to assist in the success of this goal.