Below are the productivity, dexterity, and job satisfaction ratings of ten randomly selected employees.
$\begin{array} { l | l l l l l l l l l l }
\text { Productivity } ( \boldsymbol { P } ) & 23 & 25 & 28 & 21 & 21 & 25 & 26 & 30 & 34 & 36 \
\hline \text { Dexterity } ( \boldsymbol { D } ) & 43 & 53 & 59 & 42 & 47 & 53 & 55 & 63 & 67 & 75 \
\hline \text { Satisfaction } ( \boldsymbol { S } ) & 56 & 58 & 60 & 50 & 54 & 61 & 59 & 63 & 67 & 69
\end{array}$
Find the multiple regression equation that expresses the job satisfaction scores in terms of the productivity and dexterity scores.
A) $\hat { S } = 28.28 + 0.0860 P + 0.517 D$
B) $\hat { S } = 28.28 + 0.011 P + 0.437 D$
C) $\hat { S } = 28.28 + 0.237 P + 0.728 D$
D) $\hat { S } = 28.28 + 0.517 P + 0.0860 D$

Question

Below are the productivity, dexterity, and job satisfaction ratings of ten randomly selected employees.
$\begin{array} { l | l l l l l l l l l l } 
\text { Productivity } ( \boldsymbol { P } ) & 23 & 25 & 28 & 21 & 21 & 25 & 26 & 30 & 34 & 36 \
\hline \text { Dexterity } ( \boldsymbol { D } ) & 43 & 53 & 59 & 42 & 47 & 53 & 55 & 63 & 67 & 75 \
\hline \text { Satisfaction } ( \boldsymbol { S } ) & 56 & 58 & 60 & 50 & 54 & 61 & 59 & 63 & 67 & 69
\end{array}$
Find the multiple regression equation that expresses the job satisfaction scores in terms of the productivity and dexterity scores.
A) $\hat { S } = 28.28 + 0.0860 P + 0.517 D$
B) $\hat { S } = 28.28 + 0.011 P + 0.437 D$
C) $\hat { S } = 28.28 + 0.237 P + 0.728 D$
D) $\hat { S } = 28.28 + 0.517 P + 0.0860 D$

Quizplus · Accepted Answer

The correct choice is A because in multiple regression analysis, coefficients are determined through statistical methods to best fit the data. The given equation $\hat { S } = 28.28 + 0.0860 P + 0.517 D$ suggests a model where job satisfaction ($S$) is predicted by both productivity ($P$) and dexterity ($D$), with the coefficients (0.0860 for $P$ and 0.517 for $D$) representing the amount of change in $S$ for a one-unit change in $P$ and $D$, respectively. This choice is consistent with the principles of multiple regression, where each predictor variable's coefficient reflects its individual contribution to the outcome variable, assuming the coefficients are statistically derived from the given data.

Below Are the Productivity, Dexterity, and Job Satisfaction Ratings of Ten