Find the least squares regression line for the points (1,0) , (6,6) , (11,12).
A) $y = \frac { 6 } { 5 } x - \frac { 6 } { 5 }$
B) $y = \frac { 6 } { 5 } x - \frac { 30 } { 133 }$
C) $y = \frac { 30 } { 133 } x - \frac { 6 } { 5 }$
D) $y = \frac { 30 } { 133 } x - \frac { 30 } { 133 }$
E)none of the above

Question

Quizplus · Accepted Answer

The least squares regression line is given by the equation y = mx + b, where m is the slope and b is the y-intercept. The slope is calculated as the average change in y divided by the average change in x, and the y-intercept is calculated as the average value of y minus the product of the slope and the average value of x.For the given points, the average change in y is (6 - 0) / (6 - 1) = 1, and the average change in x is (11 - 6) / (11 - 1) = 1. Therefore, the slope is m = 1.The average value of y is (0 + 6 + 12) / 3 = 6, and the average value of x is (1 + 6 + 11) / 3 = 6. Therefore, the y-intercept is b = 6 - 1 * 6 = 0.Therefore, the least squares regression line is y = 1x + 0, which is equivalent to y = x.

Find the Least Squares Regression Line for the Points (1,0) y=65x−65y = \frac { 6 } { 5 } x - \frac { 6 } { 5 }y=56​x−56​

Find the Least Squares Regression Line for the Points (1,0) $y = \frac { 6 } { 5 } x - \frac { 6 } { 5 }$