Financial Risk Manager Part 1

The correct answer is B: By minimizing the sum of squared prediction mistakes.

Explanation:

Ordinary Least Squares (OLS) estimators in multiple regression models are derived by minimizing the sum of squared residuals (also called sum of squared errors or SSE). This is mathematically represented as:

$\min \sum_{i=1}^{n} (y_i - \hat{y}_i)^2$

Where:

• $y_i$ = actual value of the dependent variable
• $\hat{y}_i$ = predicted value from the regression model
• The difference $(y_i - \hat{y}_i)$ is the residual or prediction mistake

Why other options are incorrect:

A. Minimizing the absolute difference of the residuals - This describes Least Absolute Deviations (LAD) regression, not OLS. OLS squares the residuals, while LAD uses absolute values.

C. Minimizing the distance between the actual and fitted values - While this sounds similar, it's not specific enough. OLS specifically minimizes the sum of squared distances, not just any distance measure.

D. By equating the sum of squared errors to zero - This is incorrect. The sum of squared errors is minimized, not set to zero. Setting SSE to zero would imply a perfect fit, which is generally not achievable.

Key Concept: OLS estimation finds the parameter values that minimize the sum of squared prediction errors, which provides the best linear unbiased estimators (BLUE) under the Gauss-Markov assumptions.