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

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.

Understand the definitions and differentiators of key types of data: nominal, ordinal, and interval.

Identify examples of nominal, ordinal, and interval variables in practical contexts.

Distinguish between variables that can be ordered and those that cannot.

Understand the appropriate graphical representations and calculations for different types of data.

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Definitions:

H Zone

The region within a striated muscle fiber's sarcomere that contains only thick filaments and diminishes during muscle contraction.

Myosin Myofilaments

Filamentous proteins in muscle cells responsible for contraction by interacting with actin.

Actin Myofilaments

Protein filaments that, along with myosin, play a key role in the contraction of muscle cells by forming the thin filaments in the structure of muscle fibers.

Smooth Muscle

A type of muscle found in the walls of internal organs like the stomach and intestines, responsible for involuntary movements.