The Beta coefficient, or financial elasticity (sensitivity of the asset returns to market returns, relative volatility), is a key parameter in the Capital asset pricing model (CAPM).
The formula for the Beta of an asset is 
The β coefficient measures the asset's non-diversifiable risk, also called systematic risk or market risk, rm measure the rate of return of the market and ra measures the rate of return of the asset. On an individual asset level, measuring beta can give clues to volatility and liquidity in the marketplace. On a portfolio level, measuring beta is thought to separate a manager's skill from his willingness to take risk.
The beta coefficient was actually borne out of regression analysis. It is linked to a regression analysis of the return of the stock index (x-axis) versus the return of the asset (y-axis). That is, AssetReturn = β0 + β1 * IndexReturn. The beta coefficient being discussed is β1.
For example, in a year where the broad market or benchmark index returns 25%, suppose two managers gain 50%. Since this is theoretically possible merely by choosing a portfolio whose beta is exactly 2.0, we would expect a skilled portfolio manager to have built the portfolio with a beta somewhat less than 2, such that the excess return not explained by the beta is positive. If one of the managers has an average beta of 3.0 in his portfolio, and the other's is only 1.5, then the CAPM simply states that we are not being adequately compensated for the first manager's risk, whereas the second manager has done more than expected of him and appears capable of generating superior returns.
