What is the least squares regression line?

The least squares regression line is defined specifically as the line that minimizes the sum of the squared differences between the predicted values (the values given by the regression line) and the observed values (the actual data points). This method is used to find the best-fitting line through a set of data in a scatterplot, ensuring that the overall distance between the line and the data points is as small as possible. By squaring the differences, the method emphasizes larger errors, which helps in providing a more accurate fit. This approach is fundamental to linear regression and helps in predicting outcomes based on the relationship observed in the data.

Other descriptions may miss the key aspect of minimization or focus on concepts that aren't relevant to the least squares criterion, thus illustrating why those options do not accurately capture the definition of the least squares regression line.