What method does linear regression primarily use to determine the best-fitting line?

Linear regression primarily employs the method of minimizing the squared distances to the points, which is known as the least squares method. This technique aims to find the line that best represents the data by minimizing the sum of the squares of the vertical distances (residuals) from each of the data points to the line itself.

By focusing on squared distances, linear regression effectively emphasizes larger errors compared to smaller ones, ensuring that the model fits the overall trend of the data rather than just accommodating individual outliers or errors. This approach leads to a unique solution for the best-fitting line, enabling predictions and insights based on the established relationship between the independent and dependent variables.

The alternative methods mentioned, such as maximizing the total distance from points, finding the midpoint of all data points, or calculating the average of all points, do not align with the principles of how linear regression operates. These methods would not yield a line that minimizes the errors effectively and thus would not serve the purpose of linear regression when determining the best fit for a dataset.