A fitness rating was obtained for 9 randomly selected adult women. Each person was also asked her age, weight, and the number of hours she spent exercising each week. The results are shown below. $\begin{array}{c|rrrrrrrrr}
\text { Age } & 39 & 27 & 41 & 48 & 56 & 59 & 22 & 64 & 35 \
\hline \text { Weight } & 140 & 129 & 137 & 125 & 162 & 152 & 118 & 142 & 126 \
\hline \text { Hours of exercise } & & & & & & & & & \
\text { per week } & 2 & 6 & 4 & 9 & 0 & 3 & 11 & 3 & 4 \
\hline \text { Fitness rating } & 72 & 88 & 63 & 84 & 47 & 52 & 90 & 31 & 64
\end{array}$
Identify the multiple regression equation that expresses fitness in terms of age and hours of exercise per week.
A) $\hat { \mathrm { F } } = 93.20 - 0.869 \mathrm {~A} + 2.19 \mathrm { E }$
B) $\hat { \mathrm { F } } = 12.98 + 0.871 \mathrm {~A} + 3.71 \mathrm { E }$
C) $\hat { F } = 104.0 - 1.27 \mathrm {~A} + 4.08 \mathrm { E }$
D) $\hat { \mathrm { F } } = 67.12 - 0.451 \mathrm {~A} + 7.29 \mathrm { E }$

Question

Quizplus · Accepted Answer

The correct multiple regression equation is chosen based on the relationship between the fitness rating and the independent variables (age and hours of exercise per week). Option A is the correct choice because it correctly represents the relationship with a negative coefficient for age (indicating that fitness rating decreases as age increases) and a positive coefficient for hours of exercise (indicating that fitness rating increases as the number of hours of exercise per week increases). This aligns with general expectations about the impact of age and exercise on fitness.

A Fitness Rating Was Obtained for 9 Randomly Selected Adult