Chapter 3.5, Problem 18E

Broadway The ordered pairs below give the starting year and gross ticket sales $S$ (in millions of dollars) for each Broadway season in New York City from 1997 through 2014.

$\left(1997,558\right)$ $\left(2003,771\right)$ $\left(2009,1020\right)$

$\left(1998,588\right)$ $\left(2004,769\right)$ $\left(2010,1081\right)$

$\left(1999,603\right)$ $\left(2005,862\right)$ $\left(2011,1139\right)$

$\left(2000,666\right)$ $\left(2006,939\right)$ $\left(2012,1139\right)$

$\left(2001,643\right)$ $\left(2007,938\right)$ $\left(2013,1269\right)$

$\left(2002,721\right)$ $\left(2008,943\right)$ $\left(2014,1365\right)$

(a) Use a graphing utility to create a scatter plot of the data. Let $t=7$ represent 1997.

(b) Use the $regression$ feature of the graphing utility to find the equation of the least squares regression line that fits the data.

(c) Use the graphing utility to graph the scatter plot you created in part (a) and the model you found in part (b) in the same viewing window. How closely does the model represent the data?

(d) Use the model to predict the gross ticket sales during the season starting in 2021.

(e) Interpret the meaning of the slope of the linear model in the context of the problem.