Find the least squares regression line for the given points. Then plot the points and sketch the regression line. $( - 2 , - 1 ) , ( 0,0 ) , ( 2,3 )$
A) $y = x + \frac { 2 } { 3 }$
B) $y = x - \frac { 2 } { 3 }$
C) $y = x - \frac { 1 } { 3 }$
D) $y = x - \frac { 1 } { 2 }$
E) $y = x + \frac { 1 } { 3 }$

Question

Quizplus · Accepted Answer

To find the least squares regression line, we first calculate the means of the x-values ($\bar{x}$) and y-values ($\bar{y}$). For the given points $(-2, -1)$, $(0, 0)$, and $(2, 3)$, $\bar{x} = 0$ and $\bar{y} = \frac{2}{3}$. Then, we calculate the slope ($m$) of the regression line using the formula $m = \frac{\sum (x_i - \bar{x})(y_i - \bar{y})}{\sum (x_i - \bar{x})^2}$. Plugging in the values, we find $m = 1$. Thus, the equation of the regression line is $y = mx + b$, where $b$ is the y-intercept. Since $\bar{y} = m\bar{x} + b$ and $\bar{x} = 0$, $b = \bar{y} = \frac{2}{3}$. Therefore, the least squares regression line is $y = x + \frac{2}{3}$.

Find the Least Squares Regression Line for the Given Points (−2,−1),(0,0),(2,3)( - 2 , - 1 ) , ( 0,0 ) , ( 2,3 )(−2,−1),(0,0),(2,3)

Find the Least Squares Regression Line for the Given Points $( - 2 , - 1 ) , ( 0,0 ) , ( 2,3 )$