The financial definition for Beta equation (security):
The market beta of a security is determined as follows: Regress beta of stock y on excess returns of the market. The slope coefficient is beta. Define n as number of observation numbers. Beta=
[(n) (sum of [xy]) ]-[ (sum of x) (sum of y)]/
[(n) (sum of [xx]) ]-[ (sum of x) (sum of x)]
where: n = # of observations (usually 36 to 60 months)
x = rate of beta for the S&P 500 index
y = rate of return for the security.
Regression equation An equation that describes the average relationship between a dependent variable and a set of explanatory variables.