Explanation

Ordinary Least Squares (OLS) regression aims to minimize the sum of squared differences between the actual values of the dependent variable and the estimated values from the regression model.

In this specific case:

• Dependent variable: Stock's return (what we're trying to predict)
• Independent variable: S&P 500 return (the predictor)
• OLS objective: Minimize the sum of squared differences between the actual stock returns and the estimated stock returns from the regression equation

Let's analyze why the other options are incorrect:

Option A: Incorrect - This describes minimizing differences related to the S&P 500 returns (independent variable), not the stock returns (dependent variable).

Option B: Incorrect - This describes minimizing the square of the sum of differences, but OLS minimizes the sum of squared differences, not the square of the sum.

Option C: Incorrect - This involves squared S&P 500 returns, which is not the objective of OLS regression.

Option D: Correct - This accurately describes the OLS objective: minimizing the sum of squared residuals (differences between actual and estimated values of the dependent variable).

The mathematical formulation for OLS is: $\min \sum_{i=1}^{n} (Y_i - \hat{Y}_i)^2$ Where:

• $Y_i$ = actual stock return
• $\hat{Y}_i$ = estimated stock return from regression
• The sum is over all observations (i = 1 to n)