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AssignmentMultiple Choice

Calculating the Least-Squares Regression Line

Question 1 • CA-Statistics and Probability A

The line of best fit is also called the least-squares regression line. Which statement best explains that name?

Answer
A
The line is located on a scatterplot so that it minimizes the squared distances from the points to the line.
B
The line represents the place on the scatterplot that connects the points in the smallest square possible.
C
The line is located on a scatterplot so that it maximizes the squared distances from the points to the line.
D
The line represents the place on the scatterplot that crosses through the greatest number of points.

Explanation

The least-squares regression line is chosen to make the sum of the squared residuals as small as possible. A residual is the vertical difference between a data point and the line, so squaring and minimizing those differences gives choice A: the line minimizes the squared distances from the points to the line. It does not need to pass through the greatest number of points.

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