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 Bo Pitterno was hired as its head coach in 2007 (in hopes of reaching the elusive number 1 ranking), attendance at the five Saturday home games each year increased. Prior to Pitterno's arrival, attendance generally averaged 25,000 to 30,000 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 1975, has seating for 54,000 fans. The following table indicates attendance at each game for the past 6 years.
One of Pitterno'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. Pitterno 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 $30 in 2013 and a 5% increase each year in future prices.
Please note, I need to use the Regression analysis method to calculate the project attendence through 2015.( Please show the step by step work so I can learn. not just the answer) Thanks in advance
\(\sum_{t=n}^{t=1}\)
(dt-Ft)^2
where dt= actual demand value foe period t
Ft= forecasted demand from the regression equation for period t
b= Sum of td-nt*d/ sum of t^2-nt^2
a= dt-bt
Where t= of all t values
dt= of all dt values
n= number of data point