Explanation

In Ordinary Least Squares (OLS) regression, the objective is to find the line of best fit that minimizes the sum of the squared residuals (errors).

Key Points:

• Residuals are the differences between the actual observed values and the predicted values from the regression model
• Squared residuals are used to eliminate negative signs and give more weight to larger errors
• The sum of squared residuals (SSR) is what OLS minimizes

Mathematical Representation:

For a regression model: $y_i = \beta_0 + \beta_1 x_i + \epsilon_i$ Where:

• $y_i$ = actual stock returns
• $x_i$ = S&P 500 Index returns
• $\hat{y}_i$ = estimated stock returns from the model
• $\epsilon_i = y_i - \hat{y}_i$ = residuals

OLS minimizes: $\sum_{i=1}^{n} (y_i - \hat{y}_i)^2 = \sum_{i=1}^{n} \epsilon_i^2$

Why Other Options Are Incorrect:

• Option B: Incorrect because it squares the sum of differences rather than summing squared differences
• Option C: Incorrect because it focuses on S&P 500 returns rather than stock returns
• Option D: Incorrect because it deals with squared S&P 500 returns rather than squared residuals

Therefore, Option A correctly describes the OLS procedure as minimizing the sum of squared differences between actual and estimated stock returns.