Question

Which of these best describes the least squares regression line – that is, the regression line obtained using the method of least squares? A. It is the line which makes the sum of the squared distances perpendicular to the line as small as possible. B. It is the line which best splits the data in half, with 50% of the data points lying above the regression line and 50% of the data points lying below the regression line. C. It is the line which makes the sum of the squared horizontal differences between the observed values and predicted values as small as possible. D. It is the line which makes the sum of the squared distances to the line, in the vertical direction (or y direction) as small as possible. E. More than one of these best describes the least squares regression line.

          Which of these best describes the least squares regression line – that is, the regression line obtained using the method of least squares?



 A. It is the line which makes the sum of the squared distances perpendicular to the line as small as possible.


 B. It is the line which best splits the data in half, with 50% of the data points lying above the regression line and 50% of the data points lying below the regression line.


 C. It is the line which makes the sum of the squared horizontal differences between the observed values and predicted values as small as possible.


 D. It is the line which makes the sum of the squared distances to the line, in the vertical direction (or y direction) as small as possible.


 E. More than one of these best describes the least squares regression line.

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