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The Concessions Manager at a Beachside Park Recorded the High

question 49

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.  Bottles Sold  Temperature (F) People 341731625425792100457802125485802800469812550395821975511832675549832800543852850537882775621892800897913100\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)=β0+β1x1+β2x2+β3x1x2E ( y ) = \beta _ { 0 } + \beta _ { 1 } x _ { 1 } + \beta _ { 2 } x _ { 2 } + \beta _ { 3 } x _ { 1 } x _ { 2 } to the data, letting yy represent the number of bottles of water sold, x1x _ { 1 } the temperature, and x2x _ { 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 103F103 ^ { \circ } \mathrm { F } and there are 3500 people at the park.

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