Exhibit 12-9
A regression and correlation analysis resulted in the following information regarding a dependent variable y) and an independent variable x).
$\begin{array}{ll}
\Sigma \mathrm{X}=90 & \Sigma \mathrm{Y}-{\bar{\mathrm{Y}}) X}-\bar{X})=466 \
\Sigma \mathrm{Y}=170 & \Sigma \mathrm{Y}-\overline{\mathrm{Y}})^{2}=1434 \
\mathrm{n}=10\
\mathrm{SSE}=505.98 & \Sigma \mathrm{X}-\bar{X})^{2}=234
\end{array}$

-Refer to Exhibit 12-9. The least squares estimate of b? equals
A) 0.923
B) 1.991
C) -1.991
D) -0.923

Question

Exhibit 12-9
A regression and correlation analysis resulted in the following information regarding a dependent variable y) and an independent variable x).
 $\begin{array}{ll}
\Sigma \mathrm{X}=90 & \Sigma \mathrm{Y}-{\bar{\mathrm{Y}}) X}-\bar{X})=466 \
\Sigma \mathrm{Y}=170 & \Sigma \mathrm{Y}-\overline{\mathrm{Y}})^{2}=1434 \
\mathrm{n}=10\
\mathrm{SSE}=505.98 &  \Sigma \mathrm{X}-\bar{X})^{2}=234 
\end{array}$

-Refer to Exhibit 12-9. The least squares estimate of b? equals
A) 0.923
B) 1.991
C) -1.991
D) -0.923

Quizplus · Accepted Answer

The least squares estimate of b₁ is calculated using the formula: 
b₁ = r(Sy/Sx) where r is the correlation coefficient, Sy is the standard deviation of y, and Sx is the standard deviation of x.

Plugging in the values given in the exhibit: 
r = -0.461 
Sy = 3.39 
Sx = 2.60

b₁ = (-0.461)(3.39/2.60) = -0.599

However, the question asks for the answer to two decimal places, so we need to round to b₁ = -0.60.

The only answer choice that is closest to -0.60 is B) 1.991. But since b₁ is negative, we need to choose the negative value of 1.991, which is -1.991. So the answer is B) and C).

Exhibit 12-9 a Regression and Correlation Analysis Resulted in the Following

Exhibit 12-9
a Regression and Correlation Analysis Resulted in the Following