The beta of a stock is determined as follows:
(( n) (sum of (xy)) )-((sum of x) (sum of y))
(( n) (sum of (xx)) )-((sum of x) (sum of x))
where: n = number of observations (24-60 months)
x = rate of return for the S&P 500 Index
y = rate of return for the stock
The New York Times Financial Glossary
Financial and business terms. 2012.