Find the least squares regression line for the points $$( 1,0 ) , ( 2,2 ) , ( 9,4 )$$
A) $y = \frac { 8 } { 19 } x + \frac { 6 } { 19 }$
B) $y = \frac { 8 } { 19 } x + \frac { 3 } { 19 }$
C) $y = \frac { 8 } { 19 } x + \frac { 6 } { 67 }$
D) $y = \frac { 8 } { 67 } x + \frac { 6 } { 19 }$
E) $y = \frac { 8 } { 67 } x + \frac { 6 } { 67 }$

Question

Find the least squares regression line for the points $$( 1,0 ) , ( 2,2 ) , ( 9,4 )$$ 
A) $y = \frac { 8 } { 19 } x + \frac { 6 } { 19 }$
B) $y = \frac { 8 } { 19 } x + \frac { 3 } { 19 }$
C) $y = \frac { 8 } { 19 } x + \frac { 6 } { 67 }$
D) $y = \frac { 8 } { 67 } x + \frac { 6 } { 19 }$
E) $y = \frac { 8 } { 67 } x + \frac { 6 } { 67 }$

Quizplus · Accepted Answer

To find the least squares regression line, we first calculate the means of the x-values ($\bar{x}$) and the y-values ($\bar{y}$). For the given points, $\bar{x} = \frac{1+2+9}{3} = 4$ and $\bar{y} = \frac{0+2+4}{3} = 2$. Then, we calculate the slope ($m$) using the formula $m = \frac{\sum (x_i - \bar{x})(y_i - \bar{y})}{\sum (x_i - \bar{x})^2}$. Substituting the given points, we find $m = \frac{8}{19}$. Finally, we find the y-intercept ($b$) using the formula $b = \bar{y} - m\bar{x}$, which gives $b = \frac{6}{19}$. Therefore, the least squares regression line is $y = \frac{8}{19}x + \frac{6}{19}$.

Find the Least Squares Regression Line for the Points (1,0),(2,2),(9,4)( 1,0 ) , ( 2,2 ) , ( 9,4 )(1,0),(2,2),(9,4)

Find the Least Squares Regression Line for the Points $( 1,0 ) , ( 2,2 ) , ( 9,4 )$