Regression

Regression analysis estimates the relationship between variables, how a dependent variable changes with one or more independent variables.

In finance, a linear regression is used to estimate Beta by regressing a stock’s returns against market returns:

$$R_i=\alpha +\beta R_m+ϵ$$

Where:

• $R_i$ = Return of asset i (dependent variable)
• $R_m$ = Return of the market (independent variable)
• $\alpha$ = Intercept (asset’s return when market return is zero)
• $\beta$ = Slope (sensitivity of asset returns to market returns)
• $ϵ$ = Error term (unexplained variation)

Helps identify how much of a stock’s movements is explained by market movements versus Idiosyncratic Factors.