The concessions manager at a beachside park recorded the high temperature, the number of people at the park, and the number of bottles of water sold for each of 12 consecutive Saturdays. The data are shown below. $$\begin{array} { c c c }
\hline \text { Bottles Sold } & \text { Temperature } \left( { } ^ { \circ } \mathrm { F } \right) &\text { People } \
\hline 341 & 73 & 1625 \
425 & 79 & 2100 \
457 & 80 & 2125 \
485 & 80 & 2800 \
469 & 81 & 2550 \
395 & 82 & 1975 \
511 & 83 & 2675 \
549 & 83 & 2800 \
543 & 85 & 2850 \
537 & 88 & 2775 \
621 & 89 & 2800 \
897 & 91 & 3100 \
\hline
\end{array}$$ a. Fit the model $E ( y ) = \beta _ { 0 } + \beta _ { 1 } x _ { 1 } + \beta _ { 2 } x _ { 2 }$ to the data, letting $y$ represent the number of bottles of water sold, $x _ { 1 }$ the temperature, and $x _ { 2 }$ the number of people at the park.
b. Find the $95 \%$ confidence interval for the mean number of bottles of water sold when the temperature is $84 ^ { \circ } \mathrm { F }$ and there are 2700 people at the park.
c. Find the $95 \%$ prediction interval for the number of bottles of water sold when the temperature is $84 ^ { \circ } \mathrm { F }$ and there are 2700 people at the park. 12.5 Interaction Models 1 Write Interaction Model

Question

The concessions manager at a beachside park recorded the high temperature, the number of people at the park, and the number of bottles of water sold for each of 12 consecutive Saturdays. The data are shown below. $$\begin{array} { c c c } 
\hline \text { Bottles Sold } & \text { Temperature } \left( { } ^ { \circ } \mathrm { F } \right) &\text { People } \
\hline 341 & 73 & 1625 \
425 & 79 & 2100 \
457 & 80 & 2125 \
485 & 80 & 2800 \
469 & 81 & 2550 \
395 & 82 & 1975 \
511 & 83 & 2675 \
549 & 83 & 2800 \
543 & 85 & 2850 \
537 & 88 & 2775 \
621 & 89 & 2800 \
897 & 91 & 3100 \
\hline
\end{array}$$ a. Fit the model $E ( y ) = \beta _ { 0 } + \beta _ { 1 } x _ { 1 } + \beta _ { 2 } x _ { 2 }$ to the data, letting $y$ represent the number of bottles of water sold, $x _ { 1 }$ the temperature, and $x _ { 2 }$ the number of people at the park.
b. Find the $95 \%$ confidence interval for the mean number of bottles of water sold when the temperature is $84 ^ { \circ } \mathrm { F }$ and there are 2700 people at the park.
c. Find the $95 \%$ prediction interval for the number of bottles of water sold when the temperature is $84 ^ { \circ } \mathrm { F }$ and there are 2700 people at the park. 12.5 Interaction Models 1 Write Interaction Model

Quizplus · Accepted Answer

The Answer of The concessions manager at a beachside park recorded the high temperature, the number of people at the park, and the number of bottles of water sold for each of 12 consecutive Saturdays. The data are shown below. $$\begin{array} { c c c } 
\hline \text { Bottles Sold } & \text { Temperature } \left( { } ^ { \circ } \mathrm { F } \right) &\text { People } \
\hline 341 & 73 & 1625 \
425 & 79 & 2100 \
457 & 80 & 2125 \
485 & 80 & 2800 \
469 & 81 & 2550 \
395 & 82 & 1975 \
511 & 83 & 2675 \
549 & 83 & 2800 \
543 & 85 & 2850 \
537 & 88 & 2775 \
621 & 89 & 2800 \
897 & 91 & 3100 \
\hline
\end{array}$$ a. Fit the model $E ( y ) = \beta _ { 0 } + \beta _ { 1 } x _ { 1 } + \beta _ { 2 } x _ { 2 }$ to the data, letting $y$ represent the number of bottles of water sold, $x _ { 1 }$ the temperature, and $x _ { 2 }$ the number of people at the park.
b. Find the $95 \%$ confidence interval for the mean number of bottles of water sold when the temperature is $84 ^ { \circ } \mathrm { F }$ and there are 2700 people at the park.
c. Find the $95 \%$ prediction interval for the number of bottles of water sold when the temperature is $84 ^ { \circ } \mathrm { F }$ and there are 2700 people at the park. 12.5 Interaction Models 1 Write Interaction Model

The Concessions Manager at a Beachside Park Recorded the High