We present noncompetitive adsorption as "particles in a box with one sticky wall." We start with a general model that can be modeled as a simple ordinary differential equation (ODE). To verify the ODE students run a computer simulation. The ODE's solution imperfectly fits the simulation's data. This leads to the diffusion partial…

Through a series of explorations, this article will demonstrate how the Kentucky Derby winning times dataset provides various opportunities for introductory and advanced topics, from data processing to model building. Although the final goal may be a prediction interval, the dataset is rich enough for it to appear in several places in an…

This project allows students to better understand the scope and pace of climate change by conducting their own analyses. Using data readily available from NASA and NOAA, students can apply their knowledge of regression models (or of the modeling of rates of change). The results lend themselves to a writing assignment in which students demonstrate…

The purpose of our modeling effort is to predict future outcomes. We assume the data collected are both accurate and relatively precise. For our oscillating data, we examined several mathematical modeling forms for predictions. We also examined both ignoring the oscillations as an important feature and including the oscillations as an important…

In 1974, the National Football League (NFL) initiated a sudden death overtime rule for games ending in a tie score at the end of regulation time. The rule states that the sudden death system of determining the winner shall prevail when the score is tied at the end of the regulation playing time of all NFL games. The team scoring first during…

The white picket fence is an integral component of the iconic American townscape. But, for mathematics students, it can be a mathematical challenge. Picket fences in a variety of styles serve as excellent sources to model constant, step, absolute value, and sinusoidal functions. "Principles and Standards for School Mathematics" (NCTM 2000)…

The paper reports some initiatives to freshen up the typical undergraduate business forecasting course. These include (1) students doing research and presentations on contemporary tools and industry practices such as neural networks and collaborative forecasting (2) insertion of Logistic Regression in the curriculum (3) productive use of applets…

One of the innovative approaches in the use of hierarchical linear models (HLM) is to use HLM for Slopes as Outcomes models. This implies that the researcher considers that the regression slopes vary from cluster to cluster randomly as well as systematically with certain covariates at the cluster level. Among the covariates, group indicator…

Uses examples of hierarchical linear modeling (HLM) at local and national levels to illustrate proper applications of HLM and dummy variable regression. Raises cautions about the circumstances under which hierarchical data do not need HLM. (SLD)

A simplified mathematical model for the calculation of imprecision associated with the construction of a calibration line is presented. The model also aims at a discussion on variables that really affect it and to integrate the resulting imprecision with that caused by the other steps in the analytical method in order to calculate a real…

The dataset presented here illustrates to students the utility of logistic regression. Its analysis results in a fit that explains much of how senators vote on a particular bill, and allows for quantification of the effects of ideology and money on the vote. A number of interesting quantitative interpretations follow from a good fit. A successful…

A linear regression function is developed for use in a classification procedure. The procedure is applied to faculty merit review data, resulting in an interpretable regression function and within-sample classifications as good as a four-funtion discriminant analysis. (Author/BW)

Spreadsheets to explore regression with an algebra 2 class in a medium-sized rural high school are presented. The use of spreadsheets can help students develop sophisticated understanding of mathematical models and use them to describe real-world phenomena.

Students in statistics service courses are frequently exposed to dogmatic approaches for evaluating the role of randomization in statistical designs, and inferential data analysis in experimental, observational and survey studies. In order to provide an overview for understanding the inference process, in this work some key statistical concepts in…

In discussions with leading educators from many different fields, MAA's CRAFTY (Curriculum Renewal Across the First Two Years) committee found that one of the most common mathematical themes in those other disciplines is the idea of fitting a function to a set of data in the least squares sense. The representatives of those partner disciplines…