1. Mathematical Sciences
Regression Analysis
and Football
Ranking Systems
D. P. Dwiggins, PhD
Department of
Mathematical Sciences
Cantor Sect Seminar
October 12, 2006
October 12, 2006

2. Regression Analysis
Given a collection of data,

3. Regression Analysis
Impose a linear relation on the data points:

4. Regression Analysis
Find an equation for the line by “regressing” the data points back to the imposed linear relation:

5. Least Squares Method Let between the predicted value for Yi and the
actual value (ei is also called the residual).
denote the error
Let S denote a measure of the total error between
the data points and the regression line.
will not work, as the positive errors will cancel the negative errors and this sum will always equal zero.
is a possibility, but awkward to use because the absolute value function is non-differentiable at its local minimum.

6. Least Squares Method Least Squares Regression finds the equation
for the regression line by minimizing the
sum of the squares of the errors:
S is minimized by taking derivatives of S with respect to A and B, setting these derivatives equal to zero, and solving the resulting equations for A and B.