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}{ccc}\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 } + \beta _ { 3 } x _ { 1 } 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. Identify at least two indicators of multicollinearity in the model.
c. Comment on the usefulness of the model to predict the number of bottles of water sold on a Saturday when the high temperature is

103 ^ { \circ } \mathrm { F }

and there are 3500 people at the park.

The Model E(y)=β0+β1xE ( y ) = \beta _ { 0 } + \beta _ { 1 } xE(y)=β0​+β1​x

Essay

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The Model $E ( y ) = \beta _ { 0 } + \beta _ { 1 } x$

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