A regression line is designed to minimize the distance between the observed data points and the line itself, which is why it passes through the means of x and y. This intersection at the means ensures that the line accurately reflects the central tendency of the data, enhancing its predictive power. By aligning with the average values, the regression line reduces the overall error in predictions. The concept emphasizes that the line of best fit is not just about individual points but about representing the overall trend effectively. Thus, passing through the means contributes to the accuracy and reliability of the regression analysis.