Which of the following describes a line of best fit?

A line of best fit, often used in statistical analysis and data visualization, represents a trend within a set of data points plotted on a graph. The purpose of this line is to summarize the relationship between the variables involved.

The concept of minimizing the distance from all data points in a scatter plot is central to determining the line of best fit. Specifically, the line is drawn such that the sum of the squares of the vertical distances (residuals) from the data points to the line is minimized. This approach ensures that the line most accurately reflects the trend presented by the data, making it a valuable tool for prediction and analysis.

In contrast, a line that perfectly intersects all data points would suggest that there is no variance or error in the data, which is rarely the case in real-world scenarios. Similarly, a line that shows the average of all data points might not accurately capture the relationship or trend between those points, and a line that simply connects the highest and lowest data points fails to illustrate the underlying pattern or distribution of the data. Thus, the line of best fit is specifically designed to best approximate and represent the overall trend in the dataset, making the option that highlights minimizing the distance from all data points the correct choice.