Southwestern University $($SWU$),$ a large state college in Stephenville, Texas, enrolls close to $20,000$ students. The school is a dominant force in the small city, with more students during fall and spring than permanent residents.

Always a football powerhouse, SWU is usually in the top $20$ in college football rankings. Since the legendary Phil Flamm was hired as its head coach in $2015($in hopes of reaching the elusive number$-$one ranking$),$ attendance at the five Saturday home games each year increased. Prior to Flamm's arrival,

attendance generally averaged $25,000$ to $29,000$ per game. Season ticket sales bumped up by $10,000$ just with the announcement of the new coach's arrival. Stephenville and SWU were ready to move to the big time!

The immediate issue facing SWU, however, was not NCAA ranking. It was capacity. The existing SWU stadium, built in $1953,$ has seating for $54,000$ fans. The table indicates attendance at each game for the past $6$ years.

$201620172018201920202021$

Game Attendees Opponent Attendees Opponent Attendees Opponent Attendees Opponent Attendees Opponent Attendees Opponent

$134,200$ Rice $36,100$ Miami $35,900$ USC $41,900$ Arkansas $42,500$ Indiana $46,900$ LSU

$2$a $39,800$ Texas $40,200$ Nebraska $46,500$ Texas Tech $46,100$ Missouri $48,200$ North Texas $50,100$ Texas

$338,200$ Duke $39,100$ Ohio State $43,100$ Alaska $43,900$ Florida $44,200$ Texas A&M $45,900$ South FL

$4$b $26,900$ Arkansas $25,300$ Nevada $27,900$ Arizona $30,100$ Central FL $33,900$ Southern $36,300$ Montana

$535,100$ TCU $36,200$ Boise State $39,200$ Baylor $40,500$ LSU $47,800$ Oklahoma $49,900$ Arizona State

a Homecoming games.

b During the fourth week of each season, Stephenville hosted a hugely popular southwestern crafts festival. This event brought tens of thousands of tourists to the town, especially on weekends, and had an obvious negative impact on game attendance.

One of Flamm's demands upon joining SWU had been a stadium expansion, or possibly even a new stadium. With attendance increasing, SWU administrators began to face the issue head$-$on$.$ Flamm had wanted dormitories solely for his athletes in the stadium as an additional feature of any expansion.

SWU's president, Dr$.$ Joel Wisner, decided it was time for his vice president of development to forecast when the existing stadium would "max out." The expansion was, in his mind, a given. But Wisner needed to know how long he could wait. He also sought a revenue projection, assuming an average ticket price of $$50$ in $2022$ and a $5\%$ increase each year in future prices.

Answer the following questions here and show your detailed work $($solution$)$ below for each part starting next page. If you worked on a spreadsheet, copy it under each part of your solution. Once finished, create a pdf file, and upload it on Blackboard.

Part $1$: Produce a separate trend$-$projection least$-$squares model for each of the five game numbers $($weeks$).$ With those models, what is the total expected attendance for the $5$ games in $2022?$

$[$Your answer here$]$

Part $2$: Produce a separate trend$-$projection least$-$squares model for each of the five game numbers $($weeks$).$ With those models, what is the total expected attendance for the $5$ games in $2023$

Part $3$: Produce a separate trend$-$projection least$-$squares model for each of the five game numbers $($weeks$).$ With those models, what is the total expected revenue for the $5$ games in $2023?$

Part $4$: Produce a separate trend$-$projection least$-$squares model for each of the five game numbers $($weeks$).$ With those models, what is your recommendation and why?