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Linear regression aims to fit a line while ___________ the distance to each point. Fill in the blank.

  1. Maximizing

  2. Minimizing

  3. Optimizing

  4. Squaring

The correct answer is: Minimizing

Linear regression is a statistical method used to model the relationship between a dependent variable and one or more independent variables. The main goal is to find the best-fitting line that represents this relationship. In the context of linear regression, the process involves minimizing the distance from the data points to the fitted line. Specifically, this distance is typically measured using the squared differences between the observed values and the predicted values. By minimizing these squared distances, which is known as minimizing the sum of squared errors (or residuals), linear regression aims to produce a line that best captures the underlying trend of the data. This approach ensures that the line is as close as possible to all the data points, thus improving the accuracy of predictions made using the model. Therefore, minimizing these distances is a foundational concept in linear regression and directly leads to a more effective model. Other choices like maximizing, optimizing, or squaring do not accurately capture the primary objective of linear regression. While optimizing could be loosely connected, it is not specific enough to describe the method used in linear regression, which is explicitly about minimizing error distances.