TABLE OF CONTENTS In many situations it is necessary to discover or develop a relationship between two measured variables. This occurs in the study of physics, biology, economics, engineering, and so on. Often, however, neither a priori nor theoretical knowledge is available regarding these variables or their relationship is very complicated. Examples include the relationship between the heights of parents and children, cigarette smoking and cancer, operating temperature and rotational speed in an electric motor, and resistivity and deformation in a strain gauge transducer. Thus, one must resort to empirical modeling of the potential relationship. Techniques for empirical modeling have been available for quite some time and are alternatively called curve fitting in engineering and numerical methods, regression analysis in statistics, or time series forecasting in economics. The fundamental principles for modeling are very similar in all of these areas.
Examine now a few applications that are interesting to physiologists, engineers, or educators. In Figure 2.1 are plotted two sets of measurements from walking studies relating step length to body height in men and women. The plot of the measured data points is called a scatter diagram. There is clearly an increasing trend in the data even though there may be several values of step length for a certain height. Straight lines, also drawn in the figure, should be good approximations for these sets of data. Notice that for a certain height, no step length values either for men or women are predicted exactly. There is...
