Consider the four points (20,20) ,(30,50) ,(40,30) ,and (50,60) .The least squares line is $y^=5+50x\hat{y} = 5 + 50 x$ Explain what "least squares" means using these data as a specific example.

A) The line $y^\hat{y}$ = 5 + 50x minimizes the sum of the vertical distances from the points to the line.
B) The line $y^\hat{y}$ = 5 + 50x minimizes the sum of the squared vertical distances from the points to the line.
C) The line $y^\hat{y}$ = 5 + 50x minimizes the sum of the squared horizontal distances from the points to the line.
D) The line $y^\hat{y}$ = 5 + 50x minimizes the square of the standard deviation.
E) The line $y^\hat{y}$ = 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

y^=5+50x\hat{y} = 5 + 50 x

Explain what "least squares" means using these data as a specific example.

A) The line

y^\hat{y}

= 5 + 50x minimizes the sum of the vertical distances from the points to the line.
B) The line

y^\hat{y}

= 5 + 50x minimizes the sum of the squared vertical distances from the points to the line.
C) The line

y^\hat{y}

= 5 + 50x minimizes the sum of the squared horizontal distances from the points to the line.
D) The line

y^\hat{y}

= 5 + 50x minimizes the square of the standard deviation.
E) The line

y^\hat{y}

= 5 + 50x minimizes the sum of the squared difference between the x and y values.

yusof asefi · Accepted Answer

Final Answer : B, Explanation :  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.

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