The Concessions Manager at a Beachside Park Recorded the High

question 11

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 consecutiveSaturdays. The data are shown below.

$\begin{array}{ccc}\hline \text { Bottles Sold Temperature }\left({ }^{\circ} \mathrm{F}\right) & \text { People } \\\hline 341 & 73 & 1625 \\425 & 79 & 2100 \\457 & 80 & 2125 \\485 & 80 & 2800 \\469 & 81 & 2550 \\395 & 82 & 1975 \\511 & 83 & 2675 \\549 & 83 & 2800 \\543 & 85 & 2850 \\537 & 88 & 2775 \\621 & 89 & 2800 \\897 & 91 & 3100 \\\hline\end{array}$

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.

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Definitions:

Debt-Equity Ratio

A financial ratio that measures the relative proportion of shareholders' equity and debt used to finance a company's assets.

Financial Risk

The chance of incurring a loss in capital in an investment or business operation.

Business Risk

The potential for losses or less-than-expected profits within the operations of a company, not related to financial debt but to the business's environment and operations.

Levered Firms

Companies that have incurred debt. Leveraging amplifies both the potential returns and risks of investments.