In stock market investing, beta is a widely used empirical measure of the riskiness of a particular stock or sector relative to the market as a whole. For example, an advertising stock has beta > 1 if it tends to outperform during a stock market rally but under-performs during a sell-off. On the other hand, a utility stock has beta < 1 if it tends to follow the direction of the market but with reduced volatility.
I have not seen it used before, but “beta” might also be a useful measure of agricultural risk. Simply replace stock prices by crop yields of some agricultural unit (such as farm or county). The map shows the results of a calculation of corn yield “betas” at county level for six US corn belt states for the period 1910-2012. Data are from the National Agricultural Statistics Service (NASS). Here the benchmark index against which the yields of each county are compared is the total annual corn belt yield.
High values of beta are found in the Missouri River basin, and low values in Eastern Indiana.
 Mathematically where are individual stock and market returns respectively.