A ball is released in free fall, and its height is measured by a motion detector over a 3-second period. The time and height (in meters) are stored into the graphing calculator. A sample of the data points is shown, as well as the scatter plot for all the points.
The scatter plot shows a series of parabolic arches. The TRACE command was used to find the two lowest points and the highest point for one complete bounce, and a quadratic regression [STAT CALC 5:QUADREG] was performed for these data.
Even with the relatively crude equipment with which the measurements were taken, the leading coefficient −4.49 is very close to the theoretical gravitational coefficient of −4.9 meters per second per second (m/sec/sec).