What Factors Influence the Equation for a Bouncing Ball's Range?

[keishuu]

Homework Statement

I was wondering if someone could aid me in finding a general equation for this data. In my physics lab we had to drop a small steel ball over a steel bounce plate and record the range from the base of the bounce plate that it went. This was done 18 times from several heights and then averaged. I know I need to take into account the coefficient of restitution, what else should I take account of and do you have any suggestions about how to get a good equation going through this data.
Any suggestions? Thanks

Homework Equations

The Attempt at a Solution

I've included a graph of the data below

 

[Defennder]

If I recall correctly, MS Excel does have a "fit polynomial to curve" function, after you sketch a graph of the data you have. You can even choose the value of the highest order polynomial you want to approximate your curve with.

 

[keishuu]

I have to determine this using theory not using excel. Can someone please help me?

 

[keishuu]

Here is a better description of the problem