Great news! XYZ Advertising has called you in for an interview to join its advertising team. During the interview process, you are expected to solve a linear regression problem. Consider the following data in the table below that show the cost for a Super Bowl ad from the years 1990-2006 and the average number of homes and viewers of the game.
Based on the data in the attached document, please supply the following:
1) Provide graphs of Cost versus Year, Average Number of Homes versus Year, and Average Number of Viewers versus Year.
2) Which pair from the first part has the best linear graph for predicting? Explain.
3) Create prediction equations for all three graphs, and explain what these equations mean.
4) Complete a 5-year prediction for advertising costs. Next, complete a 20-year prediction. Explain the validity in these predictions.
5) In what year would you expect the average number of viewers to reach 100 million? In what year would you expect the average number of homes to reach 50 million? Explain the validity of these predictions.
Objective: Use the Cartesian coordinate system to find the distance between two points; illustrate linear functions and their relationship to business, economics, social science, etc., and find the intersection of two lines.
|
Year
|
Cost
|
Avg.
Number
Home
|
Avg.
Number
Viewers
|
|
1990
|
700,000
|
35,920,000
|
73,852,000
|
|
1991
|
800,000
|
39,010,000
|
79,510,000
|
|
1992
|
800,000
|
37,120,000
|
79,590,000
|
|
1993
|
850,000
|
41,990,000
|
90,990,000
|
|
1994
|
900,000
|
42,860,000
|
90,000,000
|
|
1995
|
1,000,000
|
39,400,000
|
83,420,000
|
|
1996
|
1,100,000
|
44,145,000
|
94,080,000
|
|
1997
|
1,200,000
|
42,000,000
|
87,870,000
|
|
1998
|
1,300,000
|
43,630,000
|
90,000,000
|
|
1999
|
1,600,000
|
39,992,000
|
83,720,000
|
|
2000
|
2,100,000
|
43,618,000
|
88,465,000
|
|
2001
|
2,050,000
|
41,270,000
|
84,335,000
|
|
2002
|
1,900,000
|
42,664,000
|
86,801,000
|
|
2003
|
2,100,000
|
43,433,000
|
88,637,000
|
|
2004
|
2,250,000
|
44,908,000
|
89,795,000
|
|
2005
|
2,400,000
|
45,081,000
|
86,072,000
|
|
2006
|
2,500,000
|
45,867,000
|
90,745,000
|
Reference
"Super Bowl 2007, Advertising History: 40 Years of Prices and Audience." (2008 September 14). Adveristing Age. Retrived September 27, 2008. From http://adage.com/SuperBowlBuyers/superbowlhistory07.html