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

question 1

Multiple Choice

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.