The Concessions Manager at a Beachside Park Recorded the High

question 105

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 $E ( y ) = \beta _ { 0 } + \beta _ { 1 } x _ { 1 } + \beta _ { 2 } x _ { 2 }$ 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. Find the $95 \%$ confidence interval for the mean number of bottles of water sold when the temperature is $84 ^ { \circ } \mathrm { F }$ and there are 2700 people at the park.
c. Find the $95 \%$ prediction interval for the number of bottles of water sold when the temperature is $84 ^ { \circ } \mathrm { F }$ and there are 2700 people at the park. 12.5 Interaction Models 1 Write Interaction Model

---

Definitions:

Taxpayer Contribution Amount

The sum of money contributed by a taxpayer towards taxes, retirement accounts, or other eligible investments, potentially affecting tax calculations.

AGI

Adjusted Gross Income is gross income minus adjustments to income, serving as a key figure in determining taxable income and eligibility for certain tax benefits.

Qualifying Child

A dependent child who meets specific IRS criteria concerning age, relationship, residency, and support, allowing the taxpayer to claim certain tax benefits.

EIC

The Earned Income Credit is a refundable tax credit designed for individuals and families with low to moderate income who work, especially those with children.