Compute the least-squares regression line for predicting y from x given the following summary statistics:
$$\begin{array} { l l l }
\bar { x } = 6.7 & s _ { x } = 1.6 & \bar { y } = 23.8 \
s _ { y } = 6.5 & r = 0.93 & \

\end{array}$$
A) $y = - 1.5133 + 3.7781 x$
B) $y = - 1.5133 + 0.2289 x$
C) $y = 0.2289 - 1.5133 x$
D) $y = 3.7781 - 1.5133 x$

Question

Compute the least-squares regression line for predicting y from x given the following summary statistics:
 $$\begin{array} { l l l } 
\bar { x } = 6.7 & s _ { x } = 1.6 & \bar { y } = 23.8 \
s _ { y } = 6.5 & r = 0.93 & \

\end{array}$$
A) $y = - 1.5133 + 3.7781 x$
B) $y = - 1.5133 + 0.2289 x$
C) $y = 0.2289 - 1.5133 x$
D) $y = 3.7781 - 1.5133 x$

Quizplus · Accepted Answer

The slope of the least-squares regression line is calculated as $b = r \frac{s_y}{s_x} = 0.93 \times \frac{6.5}{1.6} = 3.7781$. The intercept is calculated as $a = \bar{y} - b\bar{x} = 23.8 - 3.7781 \times 6.7 = -1.5133$. Thus, the equation is $y = -1.5133 + 3.7781x$.

Compute the Least-Squares Regression Line for Predicting Y from X xˉ=6.7sx=1.6yˉ=23.8sy=6.5r=0.93\begin{array} { l l l } \bar { x } = 6.7 & s _ { x } = 1.6 & \bar { y } = 23.8 \\s _ { y } = 6.5 & r = 0.93 & \\\end{array}xˉ=6.7sy​=6.5​sx​=1.6r=0.93​yˉ​=23.8​

Compute the Least-Squares Regression Line for Predicting Y from X $\begin{array} { l l l } \bar { x } = 6.7 & s _ { x } = 1.6 & \bar { y } = 23.8 \\s _ { y } = 6.5 & r = 0.93 & \\\end{array}$