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

Question

Quizplus · Accepted Answer

Least squares refers to the method of finding the line that minimizes the sum of the squared vertical distances from the points to the line. Therefore, the best choice is B which states that the least squares line minimizes the sum of the squared vertical distances from the points to the line.

Consider the Four Points (20,20),(30,50),(40,30),and (50,60) y^=5+50x\hat{y} = 5 + 50 xy^​=5+50x

Consider the Four Points (20,20),(30,50),(40,30),and (50,60) $\hat{y} = 5 + 50 x$