The Concessions Manager at a Beachside Park Recorded the High $E ( y ) = \beta _ { 0 } + \beta _ { 1 } x _ { 1 } + \beta _ { 2 } x _ { 2 }$

Essay

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.


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.