What is the least squares regression line?

The least squares regression line is defined as the line that minimizes the sum of the squares of the vertical distances (errors) between the observed data points and the predicted values on the line. This means that for each data point, the vertical distance from the point to the line is calculated, and these distances are squared to ensure that they are all positive and to give more weight to larger errors. The goal is to find the slope and intercept of the line that results in the smallest possible value for this sum of squared distances. This method is fundamental in statistical analysis for making predictions and understanding relationships between variables.

While the other choices reference aspects of data analysis or linear relationships, they do not accurately capture the primary function of the least squares regression method. For instance, averaging data points does differ from the least squares method, as it does not specifically focus on minimizing distance errors. Similarly, predicting future data points is a benefit of having a regression line but does not define it. A line passing through the origin indicates no intercept, which is not a requirement for a least squares regression line unless specified by the data itself.