The Concessions Manager at a Beachside Park Recorded the High

question 70

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. $$\begin{array} { c c c } \hline \text { Bottles Sold } & \text { Temperature } \left( { } ^ { \circ } \mathrm { F } \right) &\text { People } \\\hline 341 & 73 & 1625 \\425 & 79 & 2100 \\457 & 80 & 2125 \\485 & 80 & 2800 \\469 & 81 & 2550 \\395 & 82 & 1975 \\511 & 83 & 2675 \\549 & 83 & 2800 \\543 & 85 & 2850 \\537 & 88 & 2775 \\621 & 89 & 2800 \\897 & 91 & 3100 \\\hline\end{array}$$ a. Fit the model $$E ( y ) = \beta _ { 0 } + \beta _ { 1 } x _ { 1 } + \beta _ { 2 } x _ { 2 } + \beta _ { 3 } x _ { 1 } x _ { 2 }$$ to the data, letting y represent the number of bottles of water sold, x1 the temperature, and x2 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°F and there are 3500 people at the park.

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Definitions:

Brodsky v. United States

A specific legal case; without more context, it's likely a federal court decision but without details on its significance or outcome.

Nuisance

A person’s use of her property in a manner that unreasonably interferes with another’s use and enjoyment of his land.

Clean Air Act

United States federal law designed to control air pollution on a national level.

Civil Penalties

Financial sanctions imposed by a government agency as punishment for violations of statutes or regulations.