Science Buddies: "Ask an Expert"

In the advanced part of our project (soccer: geometry of goal scoring) it says that we can make a mathematical expression to predict our success rate as a function of an angle but measured as a percentage of our success rate on straight-on shots. What type of expression would we use in this case? Also does this expression have to do with probability? How do we compare this expression to the result?
From,
Caitlin McCarthy and Lillie Hill

Hi soccerperson10,

I suggest making a scatterplot of angle on the x-axis and % of successful shots on the y-axis. The way that the data plot on that graph will tell you what form the function will have. For example, if you see a linear relationship between % success and angle, then you are looking for a function that has the equation of a line: success = m(angle) + b. If you plot the logarithm of % success versus the logarithm of angle and see a straight line, then you are looking a function of the form success = (angle)^power. You can also try log-linear axes. If the data look straight on a log-linear plot, you are looking at an exponential relationship.

To get a better handle on how you would actually do about finding the equation to describe the relationship, do some research on "least squares regression". This is a statistical method for determining the equation that best describes your data. If you see a linear relationship on a scatterplot, then you can apply least squares directly. If the relationship is nonlinear, you will need to look into "transformations to achieve linearity". Talk to your math teacher and ask him or her is he or she has a textbook about statistics--look at the chapter on regression. Make sure you also understand the correlation coefficient (usually denoted r). If after doing some research you have specific questions about how to apply regression to your dataset, post back and I'll be happy to help you further.

This YouTube video gives a decent explanation of the linear case. Your independent variable is angle and your dependent variable is % success.
http://www.youtube.com/watch?v=zPG4NjIkCjc