What is a characteristic of the regression line in relation to a scatter plot?

The characteristic that accurately describes the regression line in relation to a scatter plot is that it minimizes the sum of squared distances between the actual data points and the regression line itself. This method, known as the least squares criterion, is fundamental to linear regression analysis.

When you fit a regression line to a scatter plot of data, the goal is to determine the line that best represents the relationship between the independent variable and the dependent variable. This is quantitatively achieved by ensuring that the total of the squares of the vertical distances (the residuals) from each data point to the line is as small as possible. Thus, the regression line provides the best linear approximation of how the two variables interact and allows for predictions to be made based on it.

In contrast, the notion that the regression line touches the maximum number of points for a single line complicates the understanding of regression. A well-fitted regression line does not necessarily pass through any data points at all; it summarizes the trend of the data rather than intersecting with each point.

The statement about the regression line being always perfectly horizontal or vertical is also inaccurate. A regression line can take on various slopes depending on the relationship between the variables, meaning it does not have to conform to such constraints. A