Problem:
Using the accompanying Java applet, find and graph the third degree polynomial
model which best approximates the data:
Horizontal Distance  Release Height 
573  1000 
534  800 
495  600 
451  450 
395  300 
337  200 
253  100 

[Extracted from Galileo's Gravity and Motion Experiments.]
Visualization:
This exploration illustrates the least squares algorithm which obtains the
third degree polynomial which best approximates the data listed above. If you
already have not done so, then
click here to activate the Java applet.
 First, we enter the data above in the area in the left hand side of the
applet. Use your mouse to click and place a cursor in this area.
 Type in 573,1000 followed by the Enter key.
(573 and 1000 are separated by a comma.)
 Type in 534,800 followed by the Enter key.
 Continue to enter the remaining five pairs of numbers.
 On the bottom right hand side of the Applet screen you should see the
word Linear; click on the nearby arrowhead.
 You will then see a list of three items; click on Cubic.
 Press on the Compute button at the bottom lefthand
side of the Applet screen. The Applet will draw the collection of data points,
the graph of the cubic and give you the equation of the cubic.
Note: If you want to use this Applet for other data
sets then you must have at least four pairs of data to use the cubic
option, three pairs of data to use the quadratic option and two
pairs of data to use the linear option.
Acknowledgment:
The code for the Java Applet is a modification of code written by
Bryan Lewis at the Department of Mathematics, Kent State University and which is
available on his page Simple Least Squares Data Fitting Applet.