Consider the four points (20,20), (30,50), (40,30),and (50,60).The least squares line is
= 5 + 50x.Explain what "least squares" means using these data as a specific example.
A)The line = 5 + 50x minimizes the sum of the vertical distances from the points to the line.
B)The line = 5 + 50x minimizes the sum of the squared vertical distances from the points to the line.
C)The line = 5 + 50x minimizes the sum of the squared horizontal distances from the points to the line.
D)The line = 5 + 50x minimizes the square of the standard deviation.
E)The line = 5 + 50x minimizes the sum of the squared difference between the x and y values.

Question

Consider the four points (20,20), (30,50), (40,30),and (50,60).The least squares line is 
= 5 + 50x.Explain what "least squares" means using these data as a specific example.
A)The line = 5 + 50x minimizes the sum of the vertical distances from the points to the line. 
B)The line = 5 + 50x minimizes the sum of the squared vertical distances from the points to the line. 
C)The line = 5 + 50x minimizes the sum of the squared horizontal distances from the points to the line. 
D)The line = 5 + 50x minimizes the square of the standard deviation. 
E)The line = 5 + 50x minimizes the sum of the squared difference between the x and y values.

Quizplus · Accepted Answer

"Least squares" refers to the method of finding a line that minimizes the sum of the squared vertical distances from the points to the line. Therefore, the best choice is B, which specifically states that the least squares line minimizes the sum of the squared vertical distances. The other choices are not accurate descriptions of the least squares method.

Consider the Four Points (20,20), (30,50), (40,30),and (50,60)