Mathematical Modeling and Real-Life Data

Today in Calculus, we looked at three different types of regression equations that can be used to model data. Linear regression was first. The students measured each others’ forearm lengths and their heights. You can have a good conversation about which should be independent and which dependent. We decided the forearm lengths were independent, and height was dependent. We put the data into our TI-84 Lists, determined appropriate window parameters, and plotted the data. Then we used the LinReg feature to graph a line of best fit:


The next regression equation we investigated was the quadratic one. For this one, I used the old favorite, the water fountain stream:


We pasted it into GeoGebra and put some points on the path of the water. Using those points and the QuadReg feature of the TI-84, we came up with an excellent model:


Finally, we used the sunrise and sunset times of the fifteenth day of each month in Nashville, TN to see how a sinusoidal function can model data. (I grabbed the data from the US Naval Observatory.) Students converted the times that were in hours:minutes to decimal hours (16 + 56/60) – (6+57/60). We entered the months (January = 1, February = 2, etc.) and length of daylight into the calculator’s lists and used SinReg to determine the sinusoidal function that best fits the data. If time permits, it’s a nice exercise for the students to figure out the amplitude, period, phase shift, and translation themselves, and compare their function to the calculator’s.


This set of exercises took about 50 minutes, and the girls got pretty excited when they saw how closely their functions matched the data, and how they can use them to determine other points.