What statistical approach does the Capital Asset Pricing Model primarily use?

The Capital Asset Pricing Model (CAPM) primarily utilizes simple linear regression to establish the relationship between the expected return of a security and its systematic risk as represented by beta. In this framework, the expected return is modeled as a linear function of the market return and the risk-free rate.

By applying simple linear regression, CAPM enables investors and analysts to determine the expected return on an asset given its risk compared to the overall market. The model's formula clearly demonstrates this relationship: the expected return is equal to the risk-free rate plus the beta of the asset multiplied by the market risk premium.

This method is favored in the CAPM because of its straightforwardness and its practical ability to derive insights from empirical data about how asset returns correlate with market movements, thereby aiding in the risk assessment and asset pricing decision processes. Utilizing complex approaches, such as multivariate regression or non-linear techniques, would not align with the basic premise and objectives of CAPM, which aims to provide a clear and simple explanatory model.