Financial Risk Manager Part 1

The coefficient of determination (R²) has the following properties:

1. Range: R² takes values between 0% and 100% inclusive (0 ≤ R² ≤ 1). A value of 0% means the model explains none of the variability, while 100% means it explains all variability.

2. Effect of additional variables: R² generally increases when additional independent variables are added to the regression model, even if those variables are not statistically significant. This is why adjusted R² is often used to penalize for adding irrelevant variables.

3. Ordinary Least Squares (OLS): OLS estimation maximizes R². The OLS method finds the parameter estimates that minimize the sum of squared residuals, which is equivalent to maximizing R².

Since all three statements A, B, and C are true, the correct answer is D: All of the above are correct.

The coefficient of determination (R²) measures the proportion of variability in the dependent variable that is explained by the independent variables in the regression model: R² = SS_REG / SS_TOT = 1 - (SS_RES / SS_TOT), where SS_REG is the regression sum of squares, SS_RES is the residual sum of squares, and SS_TOT is the total sum of squares.