When the regression line is drawn through a scatter plot of the data, which of the following is true about the line?

The correct choice highlights a fundamental principle of linear regression, which is designed to minimize the sum of squared distances between the observed data points and the regression line. This method, known as "least squares," is used to find the best-fitting line that represents the relationship between two variables in a scatter plot.

By applying this approach, the line is positioned such that the vertical distances (or residuals) from the actual data points to the line are squared and summed. The aim is to adjust the slope and intercept of the line so that this sum of squares is as small as possible. This results in a line that not only fits the data well but also represents the overall trend most effectively. This is a key aspect of how regression is utilized to make informed predictions and decisions based on data.

The other options relate to different concepts that do not specifically define how the regression line is determined. For example, the statement about touching the maximum number of points does not apply since the regression line may not pass through all points. Likewise, having exactly half of the points above and below the line is not guaranteed in a regression analysis, as it depends on the data distribution. Lastly, while the line being closer to every point on average suggests a good fit, the definition